diff options
| -rw-r--r-- | src/ChangeLog | 6 | ||||
| -rw-r--r-- | src/algebra/Makefile.am | 16 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 16 | ||||
| -rw-r--r-- | src/algebra/exposed.lsp.pamphlet | 1 | ||||
| -rw-r--r-- | src/algebra/vector.spad.pamphlet | 33 | ||||
| -rw-r--r-- | src/hyper/pages/releaseNotes.ht | 1 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 2522 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 3971 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 35 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 7863 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 18808 |
11 files changed, 16612 insertions, 16660 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 0456e495..d63e76e7 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,11 @@ 2013-05-12 Gabriel Dos Reis <gdr@integrable-solutions.net> + * algebra/vector.spad.pamphlet (IndexedVector): Remove. + (Vector): Use OneDimensionalArray as base domain for implementation. + * algebra/Makefile.am: Update. + +2013-05-12 Gabriel Dos Reis <gdr@integrable-solutions.net> + * algebra/carten.spad.pamphlet (CartesianTensor): Use PrimitiveArray in lieu of 0-based IndexedVector. diff --git a/src/algebra/Makefile.am b/src/algebra/Makefile.am index 979b4314..2505b85a 100644 --- a/src/algebra/Makefile.am +++ b/src/algebra/Makefile.am @@ -744,10 +744,8 @@ strap-1/LIST.$(FASLEXT): strap-1/KOERCE.$(FASLEXT) \ strap-1/SETCAT.$(FASLEXT) strap-1/KONVERT.$(FASLEXT) \ strap-1/LSAGG.$(FASLEXT) -strap-1/VECTOR.$(FASLEXT): strap-1/IVECTOR.$(FASLEXT) - -strap-1/IVECTOR.$(FASLEXT): strap-1/VECTCAT.$(FASLEXT) \ - strap-1/IARRAY1.$(FASLEXT) strap-0/MATRIX.$(FASLEXT) +strap-1/VECTOR.$(FASLEXT): strap-1/VECTCAT.$(FASLEXT) \ + strap-1/ARRAY1.$(FASLEXT) strap-1/IARRAY1.$(FASLEXT): strap-1/A1AGG.$(FASLEXT) \ strap-0/PRIMARR.$(FASLEXT) @@ -1060,10 +1058,8 @@ strap-2/IDPAG.$(FASLEXT): strap-2/ABELGRP.$(FASLEXT) \ strap-2/IDPAM.$(FASLEXT): strap-2/ABELMON.$(FASLEXT) \ strap-2/IDPC.$(FASLEXT) strap-2/IDPO.$(FASLEXT) -strap-2/VECTOR.$(FASLEXT): strap-2/IVECTOR.$(FASLEXT) - -strap-2/IVECTOR.$(FASLEXT): strap-2/VECTCAT.$(FASLEXT) \ - strap-2/IARRAY1.$(FASLEXT) +strap-2/VECTOR.$(FASLEXT): strap-2/VECTCAT.$(FASLEXT) \ + strap-2/ARRAY1.$(FASLEXT) strap-2/IARRAY1.$(FASLEXT): strap-2/A1AGG.$(FASLEXT) \ strap-2/PRIMARR.$(FASLEXT) @@ -1742,7 +1738,7 @@ $(OUT)/SQMATRIX.$(FASLEXT): $(OUT)/SMATCAT.$(FASLEXT) \ $(OUT)/SMATCAT.$(FASLEXT): $(OUT)/RMATCAT.$(FASLEXT) $(OUT)/RMATCAT.$(FASLEXT): $(OUT)/DIRPROD.$(FASLEXT) $(OUT)/DIRPROD.$(FASLEXT): $(OUT)/DIRPCAT.$(FASLEXT) -$(OUT)/DIRPCAT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/IVECTOR.$(FASLEXT) +$(OUT)/DIRPCAT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/MATRIX.$(FASLEXT): $(OUT)/MATCAT.$(FASLEXT) $(OUT)/BTAGG.$(FASLEXT): $(OUT)/BOOLE.$(FASLEXT) $(OUT)/PATLRES.$(FASLEXT): $(OUT)/PATRES.$(FASLEXT) @@ -1776,7 +1772,7 @@ oa_algebra_layer_10 = \ VSPACE- XPOLYC XPR BTAGG BTAGG- \ FUNDESC XPBWPOLY SMATCAT SMATCAT- \ RMATRIX RMATCAT RMATCAT- DIRPROD \ - DIRPCAT DIRPCAT- IVECTOR MATRIX \ + DIRPCAT DIRPCAT- MATRIX \ MATCAT MATCAT- IARRAY2 FFIELDC FFIELDC- diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index 3594cecf..efab0a51 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -916,7 +916,7 @@ oa_algebra_layer_10 = \ VSPACE- XPOLYC XPR BTAGG BTAGG- \ FUNDESC XPBWPOLY SMATCAT SMATCAT- \ RMATRIX RMATCAT RMATCAT- DIRPROD \ - DIRPCAT DIRPCAT- IVECTOR MATRIX \ + DIRPCAT DIRPCAT- MATRIX \ MATCAT MATCAT- IARRAY2 FFIELDC FFIELDC- oa_algebra_layer_10_nrlibs = \ @@ -2234,10 +2234,8 @@ strap-1/LIST.$(FASLEXT): strap-1/KOERCE.$(FASLEXT) \ strap-1/SETCAT.$(FASLEXT) strap-1/KONVERT.$(FASLEXT) \ strap-1/LSAGG.$(FASLEXT) -strap-1/VECTOR.$(FASLEXT): strap-1/IVECTOR.$(FASLEXT) - -strap-1/IVECTOR.$(FASLEXT): strap-1/VECTCAT.$(FASLEXT) \ - strap-1/IARRAY1.$(FASLEXT) strap-0/MATRIX.$(FASLEXT) +strap-1/VECTOR.$(FASLEXT): strap-1/VECTCAT.$(FASLEXT) \ + strap-1/ARRAY1.$(FASLEXT) strap-1/IARRAY1.$(FASLEXT): strap-1/A1AGG.$(FASLEXT) \ strap-0/PRIMARR.$(FASLEXT) @@ -2547,10 +2545,8 @@ strap-2/IDPAG.$(FASLEXT): strap-2/ABELGRP.$(FASLEXT) \ strap-2/IDPAM.$(FASLEXT): strap-2/ABELMON.$(FASLEXT) \ strap-2/IDPC.$(FASLEXT) strap-2/IDPO.$(FASLEXT) -strap-2/VECTOR.$(FASLEXT): strap-2/IVECTOR.$(FASLEXT) - -strap-2/IVECTOR.$(FASLEXT): strap-2/VECTCAT.$(FASLEXT) \ - strap-2/IARRAY1.$(FASLEXT) +strap-2/VECTOR.$(FASLEXT): strap-2/VECTCAT.$(FASLEXT) \ + strap-2/ARRAY1.$(FASLEXT) strap-2/IARRAY1.$(FASLEXT): strap-2/A1AGG.$(FASLEXT) \ strap-2/PRIMARR.$(FASLEXT) @@ -2908,7 +2904,7 @@ $(OUT)/SQMATRIX.$(FASLEXT): $(OUT)/SMATCAT.$(FASLEXT) \ $(OUT)/SMATCAT.$(FASLEXT): $(OUT)/RMATCAT.$(FASLEXT) $(OUT)/RMATCAT.$(FASLEXT): $(OUT)/DIRPROD.$(FASLEXT) $(OUT)/DIRPROD.$(FASLEXT): $(OUT)/DIRPCAT.$(FASLEXT) -$(OUT)/DIRPCAT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/IVECTOR.$(FASLEXT) +$(OUT)/DIRPCAT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/MATRIX.$(FASLEXT): $(OUT)/MATCAT.$(FASLEXT) $(OUT)/BTAGG.$(FASLEXT): $(OUT)/BOOLE.$(FASLEXT) $(OUT)/PATLRES.$(FASLEXT): $(OUT)/PATRES.$(FASLEXT) diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet index e124fd63..45b55a9f 100644 --- a/src/algebra/exposed.lsp.pamphlet +++ b/src/algebra/exposed.lsp.pamphlet @@ -823,7 +823,6 @@ (|IndexedExponents| . INDE) (|IndexedFlexibleArray| . IFARRAY) (|IndexedOneDimensionalArray| . IARRAY1) - (|IndexedVector| . IVECTOR) (|InnerAlgFactor| . IALGFACT) (|InnerAlgebraicNumber| . IAN) (|InnerCommonDenominator| . ICDEN) diff --git a/src/algebra/vector.spad.pamphlet b/src/algebra/vector.spad.pamphlet index caca4c30..4bd83302 100644 --- a/src/algebra/vector.spad.pamphlet +++ b/src/algebra/vector.spad.pamphlet @@ -16,7 +16,7 @@ ++ Date Created: ++ Date Last Updated: ++ Basic Functions: -++ Related Constructors: DirectProductCategory, Vector, IndexedVector +++ Related Constructors: DirectProductCategory, Vector ++ Also See: ++ AMS Classifications: ++ Keywords: @@ -103,26 +103,7 @@ VectorCategory(R:Type): Category == OneDimensionalArrayAggregate R with sqrt(dot(p,p)) @ -\section{domain IVECTOR IndexedVector} -<<domain IVECTOR IndexedVector>>= -)abbrev domain IVECTOR IndexedVector -++ Author: -++ Date Created: -++ Date Last Updated: -++ Basic Functions: -++ Related Constructors: Vector, DirectProduct -++ Also See: -++ AMS Classifications: -++ Keywords: -++ References: -++ Description: -++ This type represents vector like objects with varying lengths -++ and a user-specified initial index. - -IndexedVector(R:Type, mn:Integer): - VectorCategory R == IndexedOneDimensionalArray(R, mn) - -@ + \section{domain VECTOR Vector} <<domain VECTOR Vector>>= )abbrev domain VECTOR Vector @@ -130,7 +111,7 @@ IndexedVector(R:Type, mn:Integer): ++ Date Created: ++ Date Last Updated: ++ Basic Functions: -++ Related Constructors: IndexedVector, DirectProduct +++ Related Constructors: DirectProduct ++ Also See: ++ AMS Classifications: ++ Keywords: @@ -140,11 +121,10 @@ IndexedVector(R:Type, mn:Integer): ++ and indexed by a finite segment of integers starting at 1. Vector(R:Type): Exports == Implementation where - Exports ==> VectorCategory R with + Exports == VectorCategory R with vector: List R -> % ++ vector(l) converts the list l to a vector. - Implementation ==> - IndexedVector(R, 1) add + Implementation == OneDimensionalArray R add vector l == construct l -- We want maxIndex to be inlined. Ideally, the definition should -- read @@ -306,7 +286,7 @@ DirectProductCategory(dim:NonNegativeInteger, R:Type): Category == ++ Date Created: ++ Date Last Updated: ++ Basic Functions: -++ Related Constructors: Vector, IndexedVector +++ Related Constructors: Vector ++ Also See: OrderedDirectProduct ++ AMS Classifications: ++ Keywords: @@ -619,7 +599,6 @@ LinearForm(K,B): Public == Private where <<license>> <<category VECTCAT VectorCategory>> -<<domain IVECTOR IndexedVector>> <<domain VECTOR Vector>> <<package VECTOR2 VectorFunctions2>> <<category DIRPCAT DirectProductCategory>> diff --git a/src/hyper/pages/releaseNotes.ht b/src/hyper/pages/releaseNotes.ht index 6e485e95..0c93b843 100644 --- a/src/hyper/pages/releaseNotes.ht +++ b/src/hyper/pages/releaseNotes.ht @@ -38,6 +38,7 @@ contains additions of new features and domains including: 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. + The domain IndexedVector was removed. \endscroll \autobuttons diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 111cb2bf..88eeb6be 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(1961899 . 3577395494) +(1960708 . 3577398026) (-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."))) -((-3995 . T) (-3994 . T)) +((-3994 . T) (-3993 . 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}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-3991 . T) (-3989 . T) (-3988 . T) ((-3996 "*") . T) (-3987 . T) (-3992 . T) (-3986 . T)) +((-3990 . T) (-3988 . T) (-3987 . T) ((-3995 "*") . T) (-3986 . T) (-3991 . T) (-3985 . T)) NIL (-30) ((|refine| (($ $ (|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 -3092) +(-32 R -3091) ((|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 (-950 (-483))))) +((|HasCategory| |#1| (QUOTE (-949 (-483))))) (-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 -3994))) +((|HasAttribute| |#1| (QUOTE -3993))) (-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}."))) -((-3994 . T) (-3995 . T)) +((-3993 . T) (-3994 . 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"))) -((-3988 . T) (-3989 . T) (-3991 . T)) +((-3987 . T) (-3988 . T) (-3990 . 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 -3092 UP UPUP -2614) +(-40 -3091 UP UPUP -2613) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-3987 |has| (-348 |#2|) (-312)) (-3992 |has| (-348 |#2|) (-312)) (-3986 |has| (-348 |#2|) (-312)) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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 (-809 (-1089))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-299))) (|HasCategory| (-348 |#2|) (QUOTE (-809 (-1089)))))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-809 (-1089))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1089)))))) (|HasCategory| (-348 |#2|) (QUOTE (-580 (-483)))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-950 (-348 (-483)))))) (|HasCategory| (-348 |#2|) (QUOTE (-950 (-348 (-483))))) (|HasCategory| (-348 |#2|) (QUOTE (-950 (-483)))) (|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 (-811 (-1089))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-809 (-1089)))))) -(-41 R -3092) +((-3986 |has| (-348 |#2|) (-312)) (-3991 |has| (-348 |#2|) (-312)) (-3985 |has| (-348 |#2|) (-312)) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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 (-808 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-299))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088)))))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1088)))))) (|HasCategory| (-348 |#2|) (QUOTE (-579 (-483)))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-348 (-483)))))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-483)))) (|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 (-810 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088)))))) +(-41 R -3091) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -362) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -362) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-258)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-3991 |has| |#1| (-494)) (-3989 . T) (-3988 . T)) +((-3990 |has| |#1| (-494)) (-3988 . T) (-3987 . T)) ((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-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."))) -((-3994 . T) (-3995 . T)) -((OR (-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-756)))) (-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))) +((-3993 . T) (-3994 . T)) +((OR (-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-755)))) (-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-755))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-755))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-755))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-483))))) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| $ (QUOTE (-960))) (|HasCategory| $ (QUOTE (-949 (-483))))) (-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}."))) -((-3991 . T)) +((-3990 . 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 -3092) +(-54 |Base| R -3091) ((|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"))) -((-3994 . T) (-3995 . T)) +((-3993 . T) (-3994 . 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}"))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((-3994 . T) (-3993 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|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."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|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}."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|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."))) -((-3994 . T) ((-3996 "*") . T) (-3995 . T) (-3991 . T) (-3989 . T) (-3988 . T) (-3987 . T) (-3992 . T) (-3986 . T) (-3985 . T) (-3984 . T) (-3983 . T) (-3982 . T) (-3990 . T) (-3993 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3981 . T)) +((-3993 . T) ((-3995 "*") . T) (-3994 . T) (-3990 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3991 . T) (-3985 . T) (-3984 . T) (-3983 . T) (-3982 . T) (-3981 . T) (-3989 . T) (-3992 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3980 . 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}."))) -((-3991 . T)) +((-3990 . 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}."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|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 (-3996 "*")))) +((|HasAttribute| |#1| (QUOTE (-3995 "*")))) (-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."))) -((-3995 . T)) +((-3994 . 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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1089)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1065))) (|HasCategory| (-483) (QUOTE (-796 (-328)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1089)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1089)))) (|HasCategory| (-483) (QUOTE (-454 (-1089) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| (-483) (QUOTE (-820))) (|HasCategory| (-483) (QUOTE (-949 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-552 (-472)))) (|HasCategory| (-483) (QUOTE (-932))) (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755))) (OR (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755)))) (|HasCategory| (-483) (QUOTE (-949 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-795 (-328)))) (|HasCategory| (-483) (QUOTE (-795 (-483)))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-810 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-808 (-1088)))) (|HasCategory| (-483) (QUOTE (-454 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-579 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (|HasCategory| (-483) (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}"))) -((-3995 . T) (-3994 . T)) -((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1013)))) (|HasCategory| (-85) (QUOTE (-553 (-472)))) (|HasCategory| (-85) (QUOTE (-756))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| (-85) (QUOTE (-1013))) (|HasCategory| (-85) (QUOTE (-552 (-772)))) (|HasCategory| (-85) (QUOTE (-72)))) +((-3994 . T) (-3993 . T)) +((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1012)))) (|HasCategory| (-85) (QUOTE (-552 (-472)))) (|HasCategory| (-85) (QUOTE (-755))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| (-85) (QUOTE (-1012))) (|HasCategory| (-85) (QUOTE (-551 (-771)))) (|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}"))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . 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 -3092 UP) +(-88 -3091 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}."))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| (-89 |#1|) (QUOTE (-821))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-1089)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-472)))) (|HasCategory| (-89 |#1|) (QUOTE (-933))) (|HasCategory| (-89 |#1|) (QUOTE (-740))) (|HasCategory| (-89 |#1|) (QUOTE (-756))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-740))) (|HasCategory| (-89 |#1|) (QUOTE (-756)))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-1065))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-328)))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-89 |#1|) (QUOTE (-580 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-811 (-1089)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-809 (-1089)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -454) (QUOTE (-1089)) (|%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 (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| (-89 |#1|) (QUOTE (-820))) (|HasCategory| (-89 |#1|) (QUOTE (-949 (-1088)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-552 (-472)))) (|HasCategory| (-89 |#1|) (QUOTE (-932))) (|HasCategory| (-89 |#1|) (QUOTE (-739))) (|HasCategory| (-89 |#1|) (QUOTE (-755))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-739))) (|HasCategory| (-89 |#1|) (QUOTE (-755)))) (|HasCategory| (-89 |#1|) (QUOTE (-949 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-1064))) (|HasCategory| (-89 |#1|) (QUOTE (-795 (-328)))) (|HasCategory| (-89 |#1|) (QUOTE (-795 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-89 |#1|) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-89 |#1|) (QUOTE (-579 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-810 (-1088)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-808 (-1088)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -454) (QUOTE (-1088)) (|%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 (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-820)))) (|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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -3995))) +((|HasAttribute| |#1| (QUOTE -3994))) (-92 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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"))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) (-95 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-96) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-3995 . T) (-3994 . T)) +((-3994 . T) (-3993 . T)) NIL (-97 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#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| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-3994 . T) (-3995 . T)) +((-3993 . T) (-3994 . T)) NIL (-99 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|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."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|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."))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-756)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1013))))) (|HasCategory| (-101) (QUOTE (-552 (-772)))) (|HasCategory| (-101) (QUOTE (-553 (-472)))) (OR (|HasCategory| (-101) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1013)))) (|HasCategory| (-101) (QUOTE (-756))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1013))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1013))))) +((-3994 . T) (-3993 . T)) +((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-755)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1012))))) (|HasCategory| (-101) (QUOTE (-551 (-771)))) (|HasCategory| (-101) (QUOTE (-552 (-472)))) (OR (|HasCategory| (-101) (QUOTE (-755))) (|HasCategory| (-101) (QUOTE (-1012)))) (|HasCategory| (-101) (QUOTE (-755))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-755))) (|HasCategory| (-101) (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| (-101) (QUOTE (-1012))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1012))))) (-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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-3996 "*") . T)) +(((-3995 "*") . T)) NIL -(-108 |minix| -2621 R) +(-108 |minix| -2620 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree."))) NIL NIL -(-109 |minix| -2621 S T$) +(-109 |minix| -2620 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}."))) -((-3994 . T) (-3984 . T) (-3995 . T)) -((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-318)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (|HasCategory| (-117) (QUOTE (-553 (-472)))) (|HasCategory| (-117) (QUOTE (-318))) (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013))) (|HasCategory| (-117) (QUOTE (-552 (-772)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) +((-3993 . T) (-3983 . T) (-3994 . T)) +((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-318)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) (|HasCategory| (-117) (QUOTE (-552 (-472)))) (|HasCategory| (-117) (QUOTE (-318))) (|HasCategory| (-117) (QUOTE (-755))) (|HasCategory| (-117) (QUOTE (-1012))) (|HasCategory| (-117) (QUOTE (-551 (-771)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) (-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."))) -((-3991 . T)) +((-3990 . 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."))) -((-3991 . T)) +((-3990 . T)) NIL -(-121 -3092 UP UPUP) +(-121 -3091 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 (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasAttribute| |#1| (QUOTE -3994))) +((|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasAttribute| |#1| (QUOTE -3993))) (-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."))) -((-3989 . T) (-3988 . T) (-3991 . T)) +((-3988 . T) (-3987 . T) (-3990 . 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 -3092) +(-131 R -3091) ((|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 (-821))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-1114))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3990)) (|HasAttribute| |#2| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-494)))) +((|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-914))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3989)) (|HasAttribute| |#2| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-494)))) (-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})"))) -((-3987 OR (|has| |#1| (-494)) (-12 (|has| |#1| (-258)) (|has| |#1| (-821)))) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3990 |has| |#1| (-6 -3990)) (-3993 |has| |#1| (-6 -3993)) (-1375 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 OR (|has| |#1| (-494)) (-12 (|has| |#1| (-258)) (|has| |#1| (-820)))) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3989 |has| |#1| (-6 -3989)) (-3992 |has| |#1| (-6 -3992)) (-1374 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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}."))) -((-3987 OR (|has| |#1| (-494)) (-12 (|has| |#1| (-258)) (|has| |#1| (-821)))) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3990 |has| |#1| (-6 -3990)) (-3993 |has| |#1| (-6 -3993)) (-1375 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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 (-494))) (|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 (-809 (-1089)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1089))))) (|HasCategory| |#1| (QUOTE (-811 (-1089))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-821))))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-1114)))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#1| (QUOTE (-796 (-328)))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1114)))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasAttribute| |#1| (QUOTE -3990)) (|HasAttribute| |#1| (QUOTE -3993)) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1089))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +((-3986 OR (|has| |#1| (-494)) (-12 (|has| |#1| (-258)) (|has| |#1| (-820)))) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3989 |has| |#1| (-6 -3989)) (-3992 |has| |#1| (-6 -3992)) (-1374 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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 (-494))) (|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 (-808 (-1088)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-808 (-1088))))) (|HasCategory| |#1| (QUOTE (-810 (-1088))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-820)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-820)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-820)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-820))))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-914))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1088)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-972))) (-12 (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-820))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-190))) (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasAttribute| |#1| (QUOTE -3989)) (|HasAttribute| |#1| (QUOTE -3992)) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-808 (-1088))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-820))) (|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."))) -(((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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}."))) -(((-3996 "*") . T) (-3987 . T) (-3992 . T) (-3986 . T) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") . T) (-3986 . T) (-3991 . T) (-3985 . T) (-3987 . T) (-3988 . T) (-3990 . 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|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -539,7 +539,7 @@ NIL (-152 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-857 |#2|) (|%list| (QUOTE -796) (|devaluate| |#1|)))) +((|HasCategory| (-856 |#2|) (|%list| (QUOTE -795) (|devaluate| |#1|)))) (-153 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) NIL @@ -576,7 +576,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`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 -3092) +(-162 R -3091) ((|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 -3092 UP UPUP R) +(-169 -3091 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 -3092 FP) +(-170 -3091 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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1089)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1065))) (|HasCategory| (-483) (QUOTE (-796 (-328)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1089)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1089)))) (|HasCategory| (-483) (QUOTE (-454 (-1089) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| (-483) (QUOTE (-820))) (|HasCategory| (-483) (QUOTE (-949 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-552 (-472)))) (|HasCategory| (-483) (QUOTE (-932))) (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755))) (OR (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755)))) (|HasCategory| (-483) (QUOTE (-949 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-795 (-328)))) (|HasCategory| (-483) (QUOTE (-795 (-483)))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-810 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-808 (-1088)))) (|HasCategory| (-483) (QUOTE (-454 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-579 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (|HasCategory| (-483) (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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-173 R -3092) +(-173 R -3091) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -634,19 +634,19 @@ NIL NIL (-176 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|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}."))) -((-3991 . T)) +((-3990 . T)) NIL -(-178 R -3092) +(-178 R -3091) ((|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}."))) -((-3769 . T) (-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3768 . T) (-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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}"))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-494))) (|HasAttribute| |#1| (QUOTE (-3996 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-494))) (|HasAttribute| |#1| (QUOTE (-3995 "*"))) (|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."))) -((-3995 . T)) +((-3994 . 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 \\%."))) -((-3991 . T)) +((-3990 . 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| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -678,7 +678,7 @@ NIL NIL (-187 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . T)) NIL (-188 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|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"))) -((-3991 . T)) +((-3990 . 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 -3994))) +((|HasAttribute| |#1| (QUOTE -3993))) (-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}."))) -((-3995 . T)) +((-3994 . 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 -2621 R) +(-195 S -2620 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-756))) (|HasAttribute| |#3| (QUOTE -3991)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-1013)))) -(-196 -2621 R) +((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-716))) (|HasCategory| |#3| (QUOTE (-755))) (|HasAttribute| |#3| (QUOTE -3990)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-662))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-960))) (|HasCategory| |#3| (QUOTE (-1012)))) +(-196 -2620 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"))) -((-3988 |has| |#2| (-961)) (-3989 |has| |#2| (-961)) (-3991 |has| |#2| (-6 -3991)) (-3994 . T)) +((-3987 |has| |#2| (-960)) (-3988 |has| |#2| (-960)) (-3990 |has| |#2| (-6 -3990)) (-3993 . T)) NIL -(-197 -2621 R) +(-197 -2620 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. 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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}."))) -((-3987 . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) (-3987 . T) (-3988 . T) (-3990 . 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}"))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((-3994 . T) (-3993 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-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"))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . T)) 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"))) -(((-3996 "*") |has| |#2| (-146)) (-3987 |has| |#2| (-494)) (-3992 |has| |#2| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . 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T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#2| (QUOTE (-820))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-820)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-328)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-483)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-472))))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3991)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) (-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|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 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((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . 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}."))) -((-3994 . T) (-3995 . T)) +((-3993 . T) (-3994 . 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 (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-189)))) +((|HasCategory| |#2| (QUOTE (-810 (-1088)))) (|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"))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-328)))) (|HasCategory| |#3| (QUOTE (-796 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#3| (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#3| (QUOTE (-553 (-800 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#3| (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#3| (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-820))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| |#3| (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#3| (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#3| (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#3| (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#3| (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|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 -3092) +(-230 R -3091) ((|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 -3092) +(-231 R -3091) ((|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 (-756))) (|HasCategory| |#2| (QUOTE (-1013)))) +((|HasCategory| |#2| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012)))) (-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}."))) -((-3995 . T)) +((-3994 . 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 -3995))) +((|HasAttribute| |#1| (QUOTE -3994))) (-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| -2037 -3517 |exactQuo|) +(-244 S R |Mod| -2036 -3516 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL (-245 S) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) @@ -914,7 +914,7 @@ NIL NIL (-246) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-3987 . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL (-247) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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."))) -((-3991 OR (|has| |#1| (-961)) (|has| |#1| (-411))) (-3988 |has| |#1| (-961)) (-3989 |has| |#1| (-961))) -((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (OR (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-663)))) (|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 (-663))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1089)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-411)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-663)))) +((-3990 OR (|has| |#1| (-960)) (|has| |#1| (-411))) (-3987 |has| |#1| (-960)) (-3988 |has| |#1| (-960))) +((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (OR (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-662)))) (|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 (-662))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1012)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-662))) (|HasCategory| |#1| (QUOTE (-1024)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1088)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-411)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-662)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-662)))) (-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."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#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 (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-961)))) +((|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-960)))) (-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 -3092 S) +(-255 -3091 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 -3092) +(-256 E -3091) ((|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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL (-259 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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 -3092) +(-261 -3091) ((|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))}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-472)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-933))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-756))) (OR (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-756)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-483)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-1065))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-328)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-483)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-580 (-483)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-811 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-809 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -454) (QUOTE (-1089)) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-949 (-1088)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-552 (-472)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-932))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-739))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-755))) (OR (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-739))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-755)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-949 (-483)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-1064))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-795 (-328)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-795 (-483)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-579 (-483)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-810 (-1088)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-808 (-1088)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -454) (QUOTE (-1088)) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-820)))) (|HasCategory| (-1164 |#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."))) -((-3991 OR (-12 (|has| |#1| (-494)) (OR (|has| |#1| (-961)) (|has| |#1| (-411)))) (|has| |#1| (-961)) (|has| |#1| (-411))) (-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) ((-3996 "*") |has| |#1| (-494)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-494)) (-3986 |has| |#1| (-494))) -((OR (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE 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(|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1024)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-949 (-483)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| $ (QUOTE (-960))) (|HasCategory| $ (QUOTE (-949 (-483))))) (-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 -3092) +(-268 R -3091) ((|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."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|))))))) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|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."))) -((-3989 . T) (-3988 . T)) -((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| (-483) (QUOTE (-716)))) +((-3988 . T) (-3987 . T)) +((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| (-483) (QUOTE (-715)))) (-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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL @@ -1031,26 +1031,26 @@ NIL (-275 S) ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) NIL -((|HasCategory| (-694) (QUOTE (-716)))) +((|HasCategory| (-693) (QUOTE (-715)))) (-276 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL ((|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146)))) (-277 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . 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."))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-279 S -3092) +((-3994 . T) (-3993 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-279 S -3091) ((|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 -3092) +(-280 -3091) ((|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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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 -3092 UP UPUP R) +(-283 -3091 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 -3092 UP UPUP R) +(-285 S -3091 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 -3092 UP UPUP R) +(-286 -3091 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|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1089)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1088)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) (-288 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|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}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-318)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-318))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) -(-290 S -3092 UP UPUP) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((OR (|HasCategory| (-816 |#1|) (QUOTE (-118))) (|HasCategory| (-816 |#1|) (QUOTE (-318)))) (|HasCategory| (-816 |#1|) (QUOTE (-120))) (|HasCategory| (-816 |#1|) (QUOTE (-318))) (|HasCategory| (-816 |#1|) (QUOTE (-118)))) +(-290 S -3091 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 -3092 UP UPUP) +(-291 -3091 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."))) -((-3987 |has| (-348 |#2|) (-312)) (-3992 |has| (-348 |#2|) (-312)) (-3986 |has| (-348 |#2|) (-312)) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 |has| (-348 |#2|) (-312)) (-3991 |has| (-348 |#2|) (-312)) (-3985 |has| (-348 |#2|) (-312)) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-318)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-318))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((OR (|HasCategory| (-816 |#1|) (QUOTE (-118))) (|HasCategory| (-816 |#1|) (QUOTE (-318)))) (|HasCategory| (-816 |#1|) (QUOTE (-120))) (|HasCategory| (-816 |#1|) (QUOTE (-318))) (|HasCategory| (-816 |#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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-300 R UP -3092) +(-300 R UP -3091) ((|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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-318)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-318))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((OR (|HasCategory| (-816 |#1|) (QUOTE (-118))) (|HasCategory| (-816 |#1|) (QUOTE (-318)))) (|HasCategory| (-816 |#1|) (QUOTE (-120))) (|HasCategory| (-816 |#1|) (QUOTE (-318))) (|HasCategory| (-816 |#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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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 -3092 GF) +(-306 -3091 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 -3092 FP FPP) +(-307 -3091 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}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-3991 . T)) +((-3990 . T)) NIL (-311 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1178,7 +1178,7 @@ NIL NIL (-312) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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."))) @@ -1194,7 +1194,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-494)))) (-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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-3991 |has| |#1| (-494)) (-3989 . T) (-3988 . T)) +((-3990 |has| |#1| (-494)) (-3988 . T) (-3987 . T)) NIL (-317 S) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-3988 . T) (-3989 . T) (-3991 . T)) +((-3987 . T) (-3988 . T) (-3990 . T)) NIL (-321 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013)))) +((|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012)))) (-322 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-3994 . T)) +((-3993 . T)) NIL (-323 S A R B) ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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) (-3989 . T) (-3988 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3988 . T) (-3987 . 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 (-580 (-483))))) +((|HasCategory| |#2| (QUOTE (-579 (-483))))) (-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}."))) -((-3977 . T) (-3985 . T) (-3769 . T) (-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3976 . T) (-3984 . T) (-3768 . T) (-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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."))) -((-3989 . T) (-3988 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) +((-3988 . T) (-3987 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) (-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}"))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . 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}."))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1271,7 +1271,7 @@ NIL (-335 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) NIL -((|HasCategory| |#1| (QUOTE (-756)))) +((|HasCategory| |#1| (QUOTE (-755)))) (-336) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) NIL @@ -1282,13 +1282,13 @@ NIL NIL (-338 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . T)) NIL -(-339 -3092 UP UPUP R) +(-339 -3091 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL -(-340 -3092 UP) +(-340 -3091 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL (-344 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -3977)) (|HasAttribute| |#1| (QUOTE -3985))) +((|HasAttribute| |#1| (QUOTE -3976)) (|HasAttribute| |#1| (QUOTE -3984))) (-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\"."))) -((-3769 . T) (-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3768 . T) (-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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."))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-454 (-1089) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-1133))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1089)) (|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 (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-390)))) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-454 (-1088) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-1132))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1088)) (|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 (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-482))) (|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."))) -((-3981 -12 (|has| |#1| (-6 -3992)) (|has| |#1| (-390)) (|has| |#1| (-6 -3981))) (-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-950 (-1089)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-796 (-328)))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1089)) (|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 (-482))) (-12 (|HasAttribute| |#1| (QUOTE -3981)) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-390)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +((-3980 -12 (|has| |#1| (-6 -3991)) (|has| |#1| (-390)) (|has| |#1| (-6 -3980))) (-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-949 (-1088)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1088)) (|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 (-482))) (-12 (|HasAttribute| |#1| (QUOTE -3980)) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390)))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-3988 . T) (-3989 . T) (-3991 . T)) +((-3987 . T) (-3988 . T) (-3990 . T)) NIL (-352 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483))))) +((|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483))))) (-353 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-354 R -3092 UP A) +(-354 R -3091 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-3991 . T)) +((-3990 . 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 -3092 UP A |ibasis|) +(-356 R -3091 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (|%list| (QUOTE -950) (|devaluate| |#2|)))) +((|HasCategory| |#4| (|%list| (QUOTE -949) (|devaluate| |#2|)))) (-357 AR R AS S) ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1366,7 +1366,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-312)))) (-359 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) -((-3991 |has| |#1| (-494)) (-3989 . T) (-3988 . T)) +((-3990 |has| |#1| (-494)) (-3988 . T) (-3987 . 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 (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-553 (-472))))) +((|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-1024))) (|HasCategory| |#2| (QUOTE (-552 (-472))))) (-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}."))) -((-3991 OR (|has| |#1| (-961)) (|has| |#1| (-411))) (-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) ((-3996 "*") |has| |#1| (-494)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-494)) (-3986 |has| |#1| (-494))) +((-3990 OR (|has| |#1| (-960)) (|has| |#1| (-411))) (-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) ((-3995 "*") |has| |#1| (-494)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-494)) (-3985 |has| |#1| (-494))) 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 (-756))) (|HasCategory| |#2| (QUOTE (-318)))) +((|HasCategory| |#2| (QUOTE (-755))) (|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-3994 . T) (-3984 . T) (-3995 . T)) +((-3993 . T) (-3983 . T) (-3994 . T)) NIL (-368 S A R B) ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -3092) +(-369 R -3091) ((|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"))) -((-3981 -12 (|has| |#1| (-6 -3981)) (|has| |#2| (-6 -3981))) (-3988 . T) (-3989 . T) (-3991 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -3981)) (|HasAttribute| |#2| (QUOTE -3981)))) -(-371 R -3092) +((-3980 -12 (|has| |#1| (-6 -3980)) (|has| |#2| (-6 -3980))) (-3987 . T) (-3988 . T) (-3990 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -3980)) (|HasAttribute| |#2| (QUOTE -3980)))) +(-371 R -3091) ((|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 -3092) +(-372 R -3091) ((|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 -3092) +(-373 R -3091) ((|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 -3092) +(-374 R -3091) ((|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 -3092 UP) +(-376 R -3091 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 (-950 (-48))))) +((|HasCategory| |#2| (QUOTE (-949 (-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 -3092) +(-381 R UP -3091) ((|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}."))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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"))) -((-3991 |has| (-348 (-857 |#1|)) (-494)) (-3989 . T) (-3988 . T)) -((|HasCategory| (-348 (-857 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-348 (-857 |#1|)) (QUOTE (-494)))) +((-3990 |has| (-348 (-856 |#1|)) (-494)) (-3988 . T) (-3987 . T)) +((|HasCategory| (-348 (-856 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-348 (-856 |#1|)) (QUOTE (-494)))) (-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"))) -(((-3996 "*") |has| |#2| (-146)) (-3987 |has| |#2| (-494)) (-3992 |has| |#2| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-328)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-472))))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#2| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(((-3995 "*") |has| |#2| (-146)) (-3986 |has| |#2| (-494)) (-3991 |has| |#2| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#2| (QUOTE (-820))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-820)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-328)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-483)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-472))))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3991)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-820))) (|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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . T)) NIL (-400 E V R P Q) ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1534,8 +1534,8 @@ NIL NIL (-401 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) -((-3995 . T) (-3994 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) +((-3994 . T) (-3993 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#4| (QUOTE (-551 (-771)))) (|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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-409 |lv| -3092 R) +(-409 |lv| -3091 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1574,23 +1574,23 @@ NIL NIL (-411) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-3991 . T)) +((-3990 . T)) NIL (-412 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|))))))) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|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."))) -((-3995 . T)) -((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) +((-3994 . T)) +((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (-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)}"))) -((-3995 . T) (-3994 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) +((-3994 . T) (-3993 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-551 (-771)))) (|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}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#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"))) -(((-3996 "*") |has| |#2| (-146)) (-3987 |has| |#2| (-494)) (-3992 |has| |#2| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . 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|#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-1012)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-662))) (|HasCategory| |#2| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-960))))) (|HasCategory| (-483) (QUOTE (-755))) (-12 (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-960)))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-960)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1088)))) (|HasCategory| |#2| (QUOTE (-960)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-1012)))) (|HasCategory| |#2| (QUOTE (-960)))) (-12 (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-1012)))) (-12 (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-1012)))) (|HasAttribute| |#2| (QUOTE -3990)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-960)))) (-12 (|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (QUOTE (-960)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|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}."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-423 -3092 UP UPUP R) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-423 -3091 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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1089)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1065))) (|HasCategory| (-483) (QUOTE (-796 (-328)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1089)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1089)))) (|HasCategory| (-483) (QUOTE (-454 (-1089) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| (-483) (QUOTE (-820))) (|HasCategory| (-483) (QUOTE (-949 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-552 (-472)))) (|HasCategory| (-483) (QUOTE (-932))) (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755))) (OR (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755)))) (|HasCategory| (-483) (QUOTE (-949 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-795 (-328)))) (|HasCategory| (-483) (QUOTE (-795 (-483)))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-810 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-808 (-1088)))) (|HasCategory| (-483) (QUOTE (-454 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-579 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (|HasCategory| (-483) (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 -3994)) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) +((|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (-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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1656,34 +1656,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-432 -3092 UP |AlExt| |AlPol|) +(-432 -3091 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-433) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-483))))) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| $ (QUOTE (-960))) (|HasCategory| $ (QUOTE (-949 (-483))))) (-434 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((-3994 . T) (-3993 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-435 R |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."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|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 -3092) +(-437 R UP -3091) ((|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."))) -((-3995 . T) (-3994 . T)) -((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1013)))) (|HasCategory| (-85) (QUOTE (-553 (-472)))) (|HasCategory| (-85) (QUOTE (-756))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| (-85) (QUOTE (-1013))) (|HasCategory| (-85) (QUOTE (-552 (-772)))) (|HasCategory| (-85) (QUOTE (-72)))) +((-3994 . T) (-3993 . T)) +((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1012)))) (|HasCategory| (-85) (QUOTE (-552 (-472)))) (|HasCategory| (-85) (QUOTE (-755))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| (-85) (QUOTE (-1012))) (|HasCategory| (-85) (QUOTE (-551 (-771)))) (|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 -3092 |Expon| |VarSet| |DPoly|) +(-442 -3091 |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 (-553 (-1089))))) +((|HasCategory| |#3| (QUOTE (-552 (-1088))))) (-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|)) (-3056 (|f| |x| |x|) |x|))) . T)) +(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3055 (|f| |x| |x|) |x|))) . T)) NIL (-445) ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) (-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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) (-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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) (-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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) (-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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) (-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 @@ -1751,27 +1751,27 @@ NIL (-455 S E |un|) ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) NIL -((|HasCategory| |#2| (QUOTE (-716)))) +((|HasCategory| |#2| (QUOTE (-715)))) (-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}"))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((-3994 . T) (-3993 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|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}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) ((OR (|HasCategory| (-516 |#1|) (QUOTE (-118))) (|HasCategory| (-516 |#1|) (QUOTE (-318)))) (|HasCategory| (-516 |#1|) (QUOTE (-120))) (|HasCategory| (-516 |#1|) (QUOTE (-318))) (|HasCategory| (-516 |#1|) (QUOTE (-118)))) (-459 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 -3995))) +((|HasAttribute| |#3| (QUOTE -3994))) (-460 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 -3995))) +((|HasAttribute| |#7| (QUOTE -3994))) (-461) ((|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 @@ -1803,8 +1803,8 @@ NIL (-468 |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 (-1013))) (|HasCategory| (-694) (QUOTE (-1013))))) -(-469 K -3092 |Par|) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-693) (QUOTE (-1012))))) +(-469 K -3091 |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 @@ -1828,7 +1828,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-475 K -3092 |Par|) +(-475 K -3091 |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 @@ -1858,11 +1858,11 @@ NIL NIL (-482) ((|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."))) -((-3992 . T) (-3993 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3991 . T) (-3992 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL (-483) ((|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."))) -((-3982 . T) (-3986 . T) (-3981 . T) (-3992 . T) (-3993 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3981 . T) (-3985 . T) (-3980 . T) (-3991 . T) (-3992 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL (-484) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -1882,13 +1882,13 @@ NIL NIL (-488 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) -(-489 R -3092) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) +(-489 R -3091) ((|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 -(-490 R0 -3092 UP UPUP R) +(-490 R0 -3091 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 @@ -1898,7 +1898,7 @@ NIL NIL (-492 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."))) -((-3769 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3768 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL (-493 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."))) @@ -1906,9 +1906,9 @@ NIL NIL (-494) ((|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."))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-495 R -3092) +(-495 R -3091) ((|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 @@ -1916,31 +1916,31 @@ NIL ((|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 -(-497 R -3092 L) +(-497 R -3091 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 -600) (|devaluate| |#2|)))) +((|HasCategory| |#3| (|%list| (QUOTE -599) (|devaluate| |#2|)))) (-498) ((|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 -(-499 -3092 UP UPUP R) +(-499 -3091 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 -(-500 -3092 UP) +(-500 -3091 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 -(-501 R -3092 L) +(-501 R -3091 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 -600) (|devaluate| |#2|)))) -(-502 R -3092) +((|HasCategory| |#3| (|%list| (QUOTE -599) (|devaluate| |#2|)))) +(-502 R -3091) ((|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 (-553 (-800 (-483))))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-1052)))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-569))))) -(-503 -3092 UP) +((-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-1051)))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-568))))) +(-503 -3091 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 @@ -1948,27 +1948,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-505 -3092) +(-505 -3091) ((|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 (-506 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."))) -((-3769 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3768 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL (-507) ((|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 -(-508 R -3092) +(-508 R -3091) ((|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 (-553 (-800 (-483))))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-950 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-494)))) -(-509 -3092 UP) +((-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-949 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-494)))) +(-509 -3091 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 -(-510 R -3092) +(-510 R -3091) ((|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 @@ -1990,25 +1990,25 @@ NIL NIL (-515 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL (-516 |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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-318)))) (-517) ((|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 -(-518 -3092) +(-518 -3091) ((|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}."))) -((-3989 . T) (-3988 . T)) -((|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-950 (-1089))))) -(-519 E -3092) +((-3988 . T) (-3987 . T)) +((|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-949 (-1088))))) +(-519 E -3091) ((|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 -(-520 R -3092) +(-520 R -3091) ((|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 @@ -2046,11 +2046,11 @@ NIL NIL (-529 |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}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|)))) (|HasCategory| (-483) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-483)))))) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|)))) (|HasCategory| (-483) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-483)))))) (-530 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-3996 "*") |has| |#1| (-494)) (-3987 |has| |#1| (-494)) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-494)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) ((|HasCategory| |#1| (QUOTE (-494)))) (-531) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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"))) @@ -2064,7 +2064,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-534 R -3092 FG) +(-534 R -3091 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 @@ -2072,2697 +2072,2693 @@ NIL ((|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 -(-536 R |mn|) -((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-537 S |Index| |Entry|) +(-536 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 -3995)) (|HasCategory| |#2| (QUOTE (-756))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#3| (QUOTE (-1013)))) -(-538 |Index| |Entry|) +((|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-755))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#3| (QUOTE (-1012)))) +(-537 |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 -(-539) +(-538) ((|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 -(-540 R A) +(-539 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-3991 OR (-2562 (|has| |#2| (-316 |#1|)) (|has| |#1| (-494))) (-12 (|has| |#2| (-359 |#1|)) (|has| |#1| (-494)))) (-3989 . T) (-3988 . T)) +((-3990 OR (-2561 (|has| |#2| (-316 |#1|)) (|has| |#1| (-494))) (-12 (|has| |#2| (-359 |#1|)) (|has| |#1| (-494)))) (-3988 . T) (-3987 . 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 (-494))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) -(-541) +(-540) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL NIL -(-542) +(-541) ((|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| (($) "The class was declared public,{} therefore may be accessed from outside its package"))) NIL NIL -(-543) +(-542) ((|constructor| (NIL "JVM class file constant pool tags.")) (|jvmNameAndTypeConstantTag| (($) "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 -(-544) +(-543) ((|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| (($) "The field was declared public; therefore mey accessed from outside its package."))) NIL NIL -(-545) +(-544) ((|constructor| (NIL "JVM class method access bitmask and values.")) (|jvmStrict| (($) "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 -(-546) +(-545) ((|constructor| (NIL "This is the datatype for the JVM opcodes."))) NIL NIL -(-547 |Entry|) +(-546 |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."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3859 (-1072))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-1072) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72)))) -(-548 S |Key| |Entry|) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3858 (-1071))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-1071) (QUOTE (-755))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72)))) +(-547 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 -(-549 |Key| |Entry|) +(-548 |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}."))) -((-3995 . T)) +((-3994 . T)) NIL -(-550 S) +(-549 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 (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-483)))))) -(-551 R S) +((|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#1| (QUOTE (-552 (-799 (-483)))))) +(-550 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 -(-552 S) +(-551 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 -(-553 S) +(-552 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-554 -3092 UP) +(-553 -3091 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 -(-555 S) +(-554 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 -(-556) +(-555) ((|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| (($) "the indefinite `unknown'"))) NIL NIL -(-557 S) +(-556 S) ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'."))) NIL NIL -(-558 A R S) +(-557 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}."))) -((-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-755)))) -(-559 S R) +((-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-754)))) +(-558 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 -(-560 R) +(-559 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."))) -((-3991 . T)) +((-3990 . T)) NIL -(-561 R -3092) +(-560 R -3091) ((|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 -(-562 R UP) +(-561 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"))) -((-3989 . T) (-3988 . T) ((-3996 "*") . T) (-3987 . T) (-3991 . T)) -((|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) -(-563 R E V P TS ST) +((-3988 . T) (-3987 . T) ((-3995 "*") . T) (-3986 . T) (-3990 . T)) +((|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (QUOTE (-810 (-1088)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483))))) +(-562 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 -(-564 OV E Z P) +(-563 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 -(-565) +(-564) ((|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 -(-566 |VarSet| R |Order|) +(-565 |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}}."))) -((-3991 . T)) +((-3990 . T)) NIL -(-567 R |ls|) +(-566 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 -(-568 R -3092) +(-567 R -3091) ((|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 -(-569) +(-568) ((|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 -(-570 |lv| -3092) +(-569 |lv| -3091) ((|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 -(-571) +(-570) ((|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."))) -((-3995 . T)) -((-12 (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3859 (-1072)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-552 (-772)))) (|HasCategory| (-51) (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-553 (-472)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1013)))) (|HasCategory| (-1072) (QUOTE (-756))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) -(-572 R A) +((-3994 . T)) +((-12 (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3858 (-1071)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| (-51))) (QUOTE (-1012)))) (OR (|HasCategory| (-51) (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| (-51))) (QUOTE (-1012)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| (-51))) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| (-51))) (QUOTE (-551 (-771)))) (|HasCategory| (-51) (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| (-51))) (QUOTE (-552 (-472)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1012)))) (|HasCategory| (-1071) (QUOTE (-755))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1012))) (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| (-51))) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| (-51))) (QUOTE (-1012)))) +(-571 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)."))) -((-3991 OR (-2562 (|has| |#2| (-316 |#1|)) (|has| |#1| (-494))) (-12 (|has| |#2| (-359 |#1|)) (|has| |#1| (-494)))) (-3989 . T) (-3988 . T)) +((-3990 OR (-2561 (|has| |#2| (-316 |#1|)) (|has| |#1| (-494))) (-12 (|has| |#2| (-359 |#1|)) (|has| |#1| (-494)))) (-3988 . T) (-3987 . 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 (-494))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) -(-573 S R) +(-572 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-312)))) -(-574 R) +(-573 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#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) (-3989 . T) (-3988 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3988 . T) (-3987 . T)) NIL -(-575 R FE) +(-574 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 -(-576 R) +(-575 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 -(-577 |vars|) +(-576 |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 -(-578 S R) +(-577 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 -((-2560 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) -(-579 K B) +((-2559 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) +(-578 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}."))) -((-3989 . T) (-3988 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-577 |#2|) (QUOTE (-1013))))) -(-580 R) +((-3988 . T) (-3987 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-576 |#2|) (QUOTE (-1012))))) +(-579 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 -(-581 K B) +(-580 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}."))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . T)) NIL -(-582 S) +(-581 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 -(-583 S) +(-582 S) ((|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."))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-584 A B) +((-3994 . T) (-3993 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-583 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 -(-585 A B) +(-584 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 -(-586 A B C) +(-585 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 -(-587 T$) +(-586 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL -(-588 S) +(-587 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-589 S) +(-588 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-590 R) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-589 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL NIL -(-591 S E |un|) +(-590 S E |un|) ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|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 -(-592 A S) +(-591 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -3995))) -(-593 S) +((|HasAttribute| |#1| (QUOTE -3994))) +(-592 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 -(-594 M R S) +(-593 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}."))) -((-3989 . T) (-3988 . T)) -((|HasCategory| |#1| (QUOTE (-714)))) -(-595 R -3092 L) +((-3988 . T) (-3987 . T)) +((|HasCategory| |#1| (QUOTE (-713)))) +(-594 R -3091 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 -(-596 A -2492) +(-595 A -2491) ((|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}}"))) -((-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) -(-597 A) +((-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) +(-596 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}}"))) -((-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) -(-598 A M) +((-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) +(-597 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) -(-599 S A) +((-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) +(-598 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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)))) -(-600 A) +(-599 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}."))) -((-3988 . T) (-3989 . T) (-3991 . T)) +((-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-601 -3092 UP) +(-600 -3091 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)))) -(-602 A L) +(-601 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 -(-603 S) +(-602 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-604) +(-603) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-605 R) +(-604 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) NIL NIL -(-606 |VarSet| R) +(-605 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|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) (-3989 . T) (-3988 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3988 . T) (-3987 . T)) ((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-146)))) -(-607 A S) +(-606 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 -(-608 S) +(-607 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}."))) -((-3995 . T) (-3994 . T)) +((-3994 . T) (-3993 . T)) NIL -(-609 -3092 |Row| |Col| M) +(-608 -3091 |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 -(-610 -3092) +(-609 -3091) ((|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 -(-611 R E OV P) +(-610 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 -(-612 |n| R) +(-611 |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."))) -((-3991 . T) (-3994 . T) (-3988 . T) (-3989 . T)) -((|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3996 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-494))) (OR (|HasAttribute| |#2| (QUOTE (-3996 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1089))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) -(-613) +((-3990 . T) (-3993 . T) (-3987 . T) (-3988 . T)) +((|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (QUOTE (-810 (-1088)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3995 #1="*"))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-494))) (OR (|HasAttribute| |#2| (QUOTE (-3995 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-808 (-1088))))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) +(-612) ((|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 -(-614 |VarSet|) +(-613 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL NIL -(-615 A S) +(-614 A S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) NIL NIL -(-616 S) +(-615 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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 -(-617) +(-616) ((|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 -(-618 |VarSet|) +(-617 |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 -(-619 A) +(-618 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 -(-620 A C) +(-619 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 -(-621 A B C) +(-620 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 -(-622) +(-621) ((|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 -(-623 A) +(-622 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 -(-624 A C) +(-623 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 -(-625 A B C) +(-624 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 -(-626 S R |Row| |Col|) +(-625 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 (-3996 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-494)))) -(-627 R |Row| |Col|) +((|HasAttribute| |#2| (QUOTE (-3995 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-494)))) +(-626 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"))) -((-3994 . T) (-3995 . T)) +((-3993 . T) (-3994 . T)) NIL -(-628 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +(-627 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 -(-629 R |Row| |Col| M) +(-628 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 (-494)))) -(-630 R) +(-629 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."))) -((-3994 . T) (-3995 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-494))) (|HasAttribute| |#1| (QUOTE (-3996 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-631 R) +((-3993 . T) (-3994 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-494))) (|HasAttribute| |#1| (QUOTE (-3995 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-630 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 -(-632 T$) +(-631 T$) ((|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 -(-633 R Q) +(-632 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 -(-634 S) +(-633 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}."))) -((-3995 . T)) +((-3994 . T)) NIL -(-635 U) +(-634 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 -(-636) +(-635) ((|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 -(-637 OV E -3092 PG) +(-636 OV E -3091 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 -(-638 R) +(-637 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 -(-639 S D1 D2 I) +(-638 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 -(-640 S) +(-639 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 -(-641 S) +(-640 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 -(-642 S T$) +(-641 S T$) ((|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 -(-643 S -2669 I) +(-642 S -2668 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 -(-644 E OV R P) +(-643 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 -(-645 R) +(-644 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)}.}"))) -((-3988 . T) (-3989 . T) (-3991 . T)) +((-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-646 R1 UP1 UPUP1 R2 UP2 UPUP2) +(-645 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 -(-647) +(-646) ((|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 -(-648 R |Mod| -2037 -3517 |exactQuo|) +(-647 R |Mod| -2036 -3516 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-649 R P) +(-648 R P) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3990 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . 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T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| (-993) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| (-993) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-993) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-993) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-993) (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-649 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL -(-651 R M) +(-650 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) (-3991 . T)) +((-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) (-3990 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) -(-652 R |Mod| -2037 -3517 |exactQuo|) +(-651 R |Mod| -2036 -3516 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-3991 . T)) +((-3990 . T)) NIL -(-653 S R) +(-652 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) NIL NIL -(-654 R) +(-653 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . T)) NIL -(-655 -3092) +(-654 -3091) ((|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]]}."))) -((-3991 . T)) +((-3990 . T)) NIL -(-656 S) +(-655 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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-657) +(-656) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|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 -(-658 S) +(-657 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 -(-659) +(-658) ((|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 -(-660 S R UP) +(-659 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)))) -(-661 R UP) +(-660 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."))) -((-3987 |has| |#1| (-312)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 |has| |#1| (-312)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-662 S) +(-661 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 -(-663) +(-662) ((|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| (($) "1 is the multiplicative identity."))) NIL NIL -(-664 T$) +(-663 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 (-3056 (|f| |x| (-2412 |f|)) |x|) (|exit| 1 (-3056 (|f| (-2412 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3055 (|f| |x| (-2411 |f|)) |x|) (|exit| 1 (-3055 (|f| (-2411 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-665 T$) +(-664 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 (-3056 (|f| |x| (-2412 |f|)) |x|) (|exit| 1 (-3056 (|f| (-2412 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3055 (|f| |x| (-2411 |f|)) |x|) (|exit| 1 (-3055 (|f| (-2411 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-666 -3092 UP) +(-665 -3091 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 -(-667 |VarSet| E1 E2 R S PR PS) +(-666 |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 -(-668 |Vars1| |Vars2| E1 E2 R PR1 PR2) +(-667 |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 -(-669 E OV R PPR) +(-668 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 -(-670 |vl| R) +(-669 |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."))) -(((-3996 "*") |has| |#2| (-146)) (-3987 |has| |#2| (-494)) (-3992 |has| |#2| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-328)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-472))))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#2| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-671 E OV R PRF) +(((-3995 "*") |has| |#2| (-146)) (-3986 |has| |#2| (-494)) (-3991 |has| |#2| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#2| (QUOTE (-820))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-820)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-328)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-483)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-472))))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3991)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-670 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 -(-672 E OV R P) +(-671 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 -(-673 R S M) +(-672 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 -(-674 R M) +(-673 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}."))) -((-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) (-3991 . 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 (-756)))) -(-675 S) +((-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) (-3990 . 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 (-755)))) +(-674 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}."))) -((-3994 . T) (-3984 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-676 S) +((-3993 . T) (-3983 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-675 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-3984 . T) (-3995 . T)) +((-3983 . T) (-3994 . T)) NIL -(-677) +(-676) ((|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 -(-678 S) +(-677 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 -(-679 |Coef| |Var|) +(-678 |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}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3989 . T) (-3988 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3988 . T) (-3987 . T) (-3990 . T)) NIL -(-680 OV E R P) +(-679 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 -(-681 E OV R P) +(-680 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 -(-682 S R) +(-681 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 -(-683 R) +(-682 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}."))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . T)) NIL -(-684 S) +(-683 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| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-685) +(-684) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-686 S) +(-685 S) ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|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 -(-687) +(-686) ((|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 -(-688 |Par|) +(-687 |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 -(-689 -3092) +(-688 -3091) ((|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 -(-690 P -3092) +(-689 P -3091) ((|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 -(-691 T$) +(-690 T$) NIL NIL NIL -(-692 UP -3092) +(-691 UP -3091) ((|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 -(-693 R) +(-692 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 -(-694) +(-693) ((|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."))) -(((-3996 "*") . T)) +(((-3995 "*") . T)) NIL -(-695 R -3092) +(-694 R -3091) ((|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 -(-696) +(-695) ((|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 -(-697 S) +(-696 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 -(-698 R |PolR| E |PolE|) +(-697 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 -(-699 R E V P TS) +(-698 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 -(-700 -3092 |ExtF| |SUEx| |ExtP| |n|) +(-699 -3091 |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 -(-701 BP E OV R P) +(-700 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 -(-702 |Par|) +(-701 |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 -(-703 R |VarSet|) +(-702 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."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . 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(|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)}"))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3990 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-328)))) (|HasCategory| (-994) (QUOTE (-796 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| (-994) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| (-994) (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-705 R S) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3989 |has| |#1| (-312)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| (-993) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| (-993) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-993) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-993) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-993) (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-704 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 -(-706 R) +(-705 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 (-483)))))) -(-707 R E V P) +(-706 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.}"))) -((-3995 . T) (-3994 . T)) +((-3994 . T) (-3993 . T)) NIL -(-708 S) +(-707 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 (-494))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-146)))) -(-709) +((-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-146)))) +(-708) ((|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 -(-710) +(-709) ((|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 -(-711) +(-710) ((|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 -(-712 |Curve|) +(-711 |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 -(-713 S) +(-712 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|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) NIL NIL -(-714) +(-713) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\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 -(-715 S) +(-714 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 -(-716) +(-715) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) NIL NIL -(-717) +(-716) ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) NIL NIL -(-718) +(-717) ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) NIL NIL -(-719 S R) +(-718 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-318)))) -(-720 R) +((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-318)))) +(-719 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-3988 . T) (-3989 . T) (-3991 . T)) +((-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-721) +(-720) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-722 R) +(-721 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-348 (-483)))))) (OR (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-348 (-483))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) -(-723 OR R OS S) +((-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1088)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-908 |#1|) (QUOTE (-949 (-348 (-483)))))) (OR (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| (-908 |#1|) (QUOTE (-949 (-483))))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-908 |#1|) (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-908 |#1|) (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483))))) +(-722 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 -(-724 R -3092 L) +(-723 R -3091 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 -(-725 R -3092) +(-724 R -3091) ((|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 -(-726 R -3092) +(-725 R -3091) ((|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 -(-727 -3092 UP UPUP R) +(-726 -3091 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 -(-728 -3092 UP L LQ) +(-727 -3091 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 -(-729 -3092 UP L LQ) +(-728 -3091 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 -(-730 -3092 UP) +(-729 -3091 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 -(-731 -3092 L UP A LO) +(-730 -3091 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 -(-732 -3092 UP) +(-731 -3091 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)))) -(-733 -3092 LO) +(-732 -3091 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 -(-734 -3092 LODO) +(-733 -3091 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 -(-735 -2621 S |f|) +(-734 -2620 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}."))) -((-3988 |has| |#2| (-961)) (-3989 |has| |#2| (-961)) (-3991 |has| |#2| (-6 -3991)) (-3994 . 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(-189))) (|HasCategory| |#2| (QUOTE (-960)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1088)))) (|HasCategory| |#2| (QUOTE (-960)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-1012)))) (|HasCategory| |#2| (QUOTE (-960)))) (-12 (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-1012)))) (-12 (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-1012)))) (|HasAttribute| |#2| (QUOTE -3990)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-960)))) (-12 (|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (QUOTE (-960)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) +(-735 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"))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-328)))) (|HasCategory| (-738 (-1089)) (QUOTE (-796 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| (-738 (-1089)) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-738 (-1089)) (QUOTE (-553 (-800 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-738 (-1089)) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| (-738 (-1089)) (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-737 |Kernels| R |var|) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-820))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| (-737 (-1088)) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| (-737 (-1088)) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-737 (-1088)) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-737 (-1088)) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-737 (-1088)) (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-736 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-3996 "*") |has| |#2| (-312)) (-3987 |has| |#2| (-312)) (-3992 |has| |#2| (-312)) (-3986 |has| |#2| (-312)) (-3991 . T) (-3989 . T) (-3988 . T)) +(((-3995 "*") |has| |#2| (-312)) (-3986 |has| |#2| (-312)) (-3991 |has| |#2| (-312)) (-3985 |has| |#2| (-312)) (-3990 . T) (-3988 . T) (-3987 . T)) ((|HasCategory| |#2| (QUOTE (-312)))) -(-738 S) +(-737 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 -(-739 S) +(-738 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| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) NIL -((|HasCategory| |#1| (QUOTE (-756)))) -(-740) +((|HasCategory| |#1| (QUOTE (-755)))) +(-739) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-741 P R) +(-740 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) -((-3988 . T) (-3989 . T) (-3991 . T)) +((-3987 . T) (-3988 . T) (-3990 . T)) ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190)))) -(-742 S) +(-741 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-3994 . T) (-3984 . T) (-3995 . T)) +((-3993 . T) (-3983 . T) (-3994 . T)) NIL -(-743 R) +(-742 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."))) -((-3991 |has| |#1| (-755))) -((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-482)))) -(-744 R S) +((-3990 |has| |#1| (-754))) +((|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-754)))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-949 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-482)))) +(-743 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 -(-745 R) +(-744 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) (-3991 . T)) +((-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) (-3990 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) -(-746 A S) +(-745 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 -(-747 S) +(-746 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| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL NIL -(-748) +(-747) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) NIL NIL -(-749) +(-748) ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|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 -(-750 R) +(-749 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-3991 |has| |#1| (-755))) -((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-482)))) -(-751 R S) +((-3990 |has| |#1| (-754))) +((|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-754)))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-949 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-482)))) +(-750 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL -(-752) +(-751) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-753 -2621 S) +(-752 -2620 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL -(-754) +(-753) ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) NIL NIL -(-755) +(-754) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) -((-3991 . T)) +((-3990 . T)) NIL -(-756) +(-755) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) NIL NIL -(-757 T$ |f|) +(-756 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 (-552 (-772))))) -(-758 S) +((|HasCategory| |#1| (QUOTE (-551 (-771))))) +(-757 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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-759) +(-758) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-760 S R) +(-759 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) NIL ((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146)))) -(-761 R) +(-760 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-3988 . T) (-3989 . T) (-3991 . T)) +((-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-762 R C) +(-761 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 (-494)))) -(-763 R |sigma| -3244) +(-762 R |sigma| -3243) ((|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."))) -((-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) -(-764 |x| R |sigma| -3244) +((-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) +(-763 |x| R |sigma| -3243) ((|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}."))) -((-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-312)))) -(-765 R) +((-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-312)))) +(-764 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 (-483)))))) -(-766) +(-765) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL NIL -(-767) +(-766) ((|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 -(-768) +(-767) ((|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 -(-769 S) +(-768 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 -(-770) +(-769) ((|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 -(-771) +(-770) ((|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 -(-772) +(-771) ((|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 -(-773 |VariableList|) +(-772 |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 -(-774) +(-773) ((|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 -(-775 R |vl| |wl| |wtlevel|) +(-774 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)"))) -((-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) (-3991 . T)) +((-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) (-3990 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) -(-776 R PS UP) +(-775 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 -(-777 R |x| |pt|) +(-776 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 -(-778 |p|) +(-777 |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)."))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-779 |p|) +(-778 |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}."))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-780 |p|) +(-779 |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)."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| (-778 |#1|) (QUOTE (-821))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-1089)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-120))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-472)))) (|HasCategory| (-778 |#1|) (QUOTE (-933))) (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756))) (OR (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756)))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-1065))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-328)))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-778 |#1|) (QUOTE (-580 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-189))) (|HasCategory| (-778 |#1|) (QUOTE (-811 (-1089)))) (|HasCategory| (-778 |#1|) (QUOTE (-190))) (|HasCategory| (-778 |#1|) (QUOTE (-809 (-1089)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -454) (QUOTE (-1089)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -778) (|devaluate| |#1|)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (QUOTE (-258))) (|HasCategory| (-778 |#1|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))))) -(-781 |p| PADIC) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| (-777 |#1|) (QUOTE (-820))) (|HasCategory| (-777 |#1|) (QUOTE (-949 (-1088)))) (|HasCategory| (-777 |#1|) (QUOTE (-118))) (|HasCategory| (-777 |#1|) (QUOTE (-120))) (|HasCategory| (-777 |#1|) (QUOTE (-552 (-472)))) (|HasCategory| (-777 |#1|) (QUOTE (-932))) (|HasCategory| (-777 |#1|) (QUOTE (-739))) (|HasCategory| (-777 |#1|) (QUOTE (-755))) (OR (|HasCategory| (-777 |#1|) (QUOTE (-739))) (|HasCategory| (-777 |#1|) (QUOTE (-755)))) (|HasCategory| (-777 |#1|) (QUOTE (-949 (-483)))) (|HasCategory| (-777 |#1|) (QUOTE (-1064))) (|HasCategory| (-777 |#1|) (QUOTE (-795 (-328)))) (|HasCategory| (-777 |#1|) (QUOTE (-795 (-483)))) (|HasCategory| (-777 |#1|) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-777 |#1|) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-777 |#1|) (QUOTE (-579 (-483)))) (|HasCategory| (-777 |#1|) (QUOTE (-189))) (|HasCategory| (-777 |#1|) (QUOTE (-810 (-1088)))) (|HasCategory| (-777 |#1|) (QUOTE (-190))) (|HasCategory| (-777 |#1|) (QUOTE (-808 (-1088)))) (|HasCategory| (-777 |#1|) (|%list| (QUOTE -454) (QUOTE (-1088)) (|%list| (QUOTE -777) (|devaluate| |#1|)))) (|HasCategory| (-777 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -777) (|devaluate| |#1|)))) (|HasCategory| (-777 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -777) (|devaluate| |#1|)) (|%list| (QUOTE -777) (|devaluate| |#1|)))) (|HasCategory| (-777 |#1|) (QUOTE (-258))) (|HasCategory| (-777 |#1|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-777 |#1|) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-777 |#1|) (QUOTE (-820)))) (|HasCategory| (-777 |#1|) (QUOTE (-118))))) +(-780 |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)}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-950 (-1089)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756)))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (QUOTE (-796 (-328)))) (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1089)) (|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 (-482))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-782 S T$) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-949 (-1088)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-739))) (|HasCategory| |#2| (QUOTE (-755))) (OR (|HasCategory| |#2| (QUOTE (-739))) (|HasCategory| |#2| (QUOTE (-755)))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (QUOTE (-795 (-328)))) (|HasCategory| |#2| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-810 (-1088)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1088)) (|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 (-482))) (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-781 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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))))) -(-783) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) (-12 (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771)))))) +(-782) ((|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 -(-784) +(-783) ((|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 -(-785) +(-784) ((|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 -(-786 CF1 CF2) +(-785 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-787 |ComponentFunction|) +(-786 |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 -(-788 CF1 CF2) +(-787 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-789 |ComponentFunction|) +(-788 |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 -(-790) +(-789) ((|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 -(-791 CF1 CF2) +(-790 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-792 |ComponentFunction|) +(-791 |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 -(-793) +(-792) ((|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 -(-794 R) +(-793 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 -(-795 R S L) +(-794 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 -(-796 S) +(-795 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 -(-797 |Base| |Subject| |Pat|) +(-796 |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 (-2560 (|HasCategory| |#2| (QUOTE (-950 (-1089))))) (-2560 (|HasCategory| |#2| (QUOTE (-961))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (-2560 (|HasCategory| |#2| (QUOTE (-950 (-1089)))))) (|HasCategory| |#2| (QUOTE (-950 (-1089))))) -(-798 R S) +((-12 (-2559 (|HasCategory| |#2| (QUOTE (-949 (-1088))))) (-2559 (|HasCategory| |#2| (QUOTE (-960))))) (-12 (|HasCategory| |#2| (QUOTE (-960))) (-2559 (|HasCategory| |#2| (QUOTE (-949 (-1088)))))) (|HasCategory| |#2| (QUOTE (-949 (-1088))))) +(-797 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 -(-799 R A B) +(-798 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 -(-800 R) +(-799 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 -(-801 R -2669) +(-800 R -2668) ((|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 -(-802 R S) +(-801 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 -(-803 |VarSet|) +(-802 |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 -(-804 UP R) +(-803 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) NIL NIL -(-805 A T$ S) +(-804 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 -(-806 T$ S) +(-805 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 -(-807 UP -3092) +(-806 UP -3091) ((|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 -(-808 R S) +(-807 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . T)) NIL -(-809 S) +(-808 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-3991 . T)) +((-3990 . T)) NIL -(-810 A S) +(-809 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 -(-811 S) +(-810 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 -(-812 S) +(-811 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 (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-813 S) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-812 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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-3991 . T)) -((OR (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-756)))) -(-814 |n| R) +((-3990 . T)) +((OR (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-755)))) +(-813 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 -(-815 S) +(-814 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."))) -((-3991 . T)) +((-3990 . T)) NIL -(-816 S) +(-815 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 -(-817 |p|) +(-816 |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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-318)))) -(-818 R E |VarSet| S) +(-817 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 -(-819 R S) +(-818 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 -(-820 S) +(-819 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)))) -(-821) +(-820) ((|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}."))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-822 R0 -3092 UP UPUP R) +(-821 R0 -3091 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 -(-823 UP UPUP R) +(-822 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 -(-824 UP UPUP) +(-823 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 -(-825 R) +(-824 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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-826 R) +(-825 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 -(-827 E OV R P) +(-826 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 -(-828) +(-827) ((|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 -(-829 -3092) +(-828 -3091) ((|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 -(-830) +(-829) ((|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}."))) -(((-3996 "*") . T)) +(((-3995 "*") . T)) NIL -(-831 R) +(-830 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 -(-832) +(-831) ((|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)}"))) -((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-833 |xx| -3092) +(-832 |xx| -3091) ((|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 -(-834 -3092 P) +(-833 -3091 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-835 R |Var| |Expon| GR) +(-834 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 -(-836) +(-835) ((|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 -(-837 S) +(-836 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 -(-838) +(-837) ((|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 -(-839) +(-838) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-840) +(-839) ((|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 -(-841 R -3092) +(-840 R -3091) ((|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 -(-842 S A B) +(-841 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 -(-843 S R -3092) +(-842 S R -3091) ((|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 -(-844 I) +(-843 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 -(-845 S E) +(-844 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 -(-846 S R L) +(-845 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 -(-847 S E V R P) +(-846 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 -796) (|devaluate| |#1|)))) -(-848 -2669) +((|HasCategory| |#3| (|%list| (QUOTE -795) (|devaluate| |#1|)))) +(-847 -2668) ((|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 -(-849 R -3092 -2669) +(-848 R -3091 -2668) ((|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 -(-850 S R Q) +(-849 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 -(-851 S) +(-850 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 -(-852 S R P) +(-851 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 -(-853) +(-852) ((|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 -(-854 R) +(-853 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-855 |lv| R) +((-3994 . T) (-3993 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-662))) (|HasCategory| |#1| (QUOTE (-960))) (-12 (|HasCategory| |#1| (QUOTE (-914))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-854 |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 -(-856 |TheField| |ThePols|) +(-855 |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 (-755)))) -(-857 R) +((|HasCategory| |#1| (QUOTE (-754)))) +(-856 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}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-328)))) (|HasCategory| (-1089) (QUOTE (-796 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| (-1089) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-1089) (QUOTE (-553 (-800 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-1089) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| (-1089) (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-858 R S) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-820))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| (-1088) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| (-1088) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-1088) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-1088) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-1088) (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-857 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 -(-859 |x| R) +(-858 |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 -(-860 S R E |VarSet|) +(-859 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 (-821))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-796 (-328)))) (|HasCategory| |#2| (QUOTE (-796 (-328)))) (|HasCategory| |#4| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| |#4| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#4| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-553 (-472))))) -(-861 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-820))) (|HasAttribute| |#2| (QUOTE -3991)) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-795 (-328)))) (|HasCategory| |#2| (QUOTE (-795 (-328)))) (|HasCategory| |#4| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-795 (-483)))) (|HasCategory| |#4| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#4| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-552 (-472))))) +(-860 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}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) NIL -(-862 E V R P -3092) +(-861 E V R P -3091) ((|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 -(-863 E |Vars| R P S) +(-862 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 -(-864 E V R P -3092) +(-863 E V R P -3091) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-390)))) -(-865) +(-864) ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) NIL NIL -(-866) +(-865) ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-867 R E) +(-866 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-6 -3992)) (-3988 . T) (-3989 . T) (-3991 . 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T)) +((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3991))) +(-867 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 -(-869 S) +(-868 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"))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-870 A B) +((-3994 . T) (-3993 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-869 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 -(-871) +(-870) ((|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 -(-872 -3092) +(-871 -3091) ((|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 -(-873 I) +(-872 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 -(-874) +(-873) ((|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 -(-875 A B) +(-874 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"))) -((-3991 -12 (|has| |#2| (-411)) (|has| |#1| (-411)))) -((OR (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-756))))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-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 (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-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 (-663))) (|HasCategory| |#2| (QUOTE (-663))))) (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-318)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-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 (-663))) (|HasCategory| |#2| (QUOTE (-663))))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-756))))) -(-876) +((-3990 -12 (|has| |#2| (-411)) (|has| |#1| (-411)))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-755))))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-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 (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-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 (-662))) (|HasCategory| |#2| (QUOTE (-662))))) (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-318)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-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 (-662))) (|HasCategory| |#2| (QUOTE (-662))))) (-12 (|HasCategory| |#1| (QUOTE (-662))) (|HasCategory| |#2| (QUOTE (-662)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-755))))) +(-875) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-877 T$) +(-876 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|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-878 T$) +(-877 T$) ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) NIL NIL -(-879 S T$) +(-878 S T$) ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) NIL NIL -(-880) +(-879) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-881 S) +(-880 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-3994 . T) (-3995 . T)) +((-3993 . T) (-3994 . T)) NIL -(-882 R |polR|) +(-881 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)))) -(-883) +(-882) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-884) +(-883) ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\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 -(-885 S |Coef| |Expon| |Var|) +(-884 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 -(-886 |Coef| |Expon| |Var|) +(-885 |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}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-887) +(-886) ((|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 -(-888 S R E |VarSet| P) +(-887 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 (-494)))) -(-889 R E |VarSet| P) +(-888 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."))) -((-3994 . T)) +((-3993 . T)) NIL -(-890 R E V P) +(-889 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)))) -(-891 K) +(-890 K) ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) NIL NIL -(-892 |VarSet| E RC P) +(-891 |VarSet| E RC P) ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary gcd domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) NIL NIL -(-893 R) +(-892 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}."))) -((-3995 . T) (-3994 . T)) +((-3994 . T) (-3993 . T)) NIL -(-894 R1 R2) +(-893 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-895 R) +(-894 R) ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) NIL NIL -(-896 K) +(-895 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 -(-897 R E OV PPR) +(-896 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 -(-898 K R UP -3092) +(-897 K R UP -3091) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-899 R |Var| |Expon| |Dpoly|) +(-898 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))))) -(-900 |vl| |nv|) +(-899 |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 -(-901 R E V P TS) +(-900 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 -(-902) +(-901) ((|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 -(-903 A S) +(-902 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 (-821))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-950 (-1089)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-1065)))) -(-904 S) +((|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-949 (-1088)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-739))) (|HasCategory| |#2| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-1064)))) +(-903 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}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-905 A B R S) +(-904 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 -(-906 |n| K) +(-905 |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 -(-907) +(-906) ((|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 -(-908 S) +(-907 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."))) -((-3994 . T) (-3995 . T)) +((-3993 . T) (-3994 . T)) NIL -(-909 R) +(-908 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.}"))) -((-3987 |has| |#1| (-246)) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1089)) (|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 (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-482)))) -(-910 S R) +((-3986 |has| |#1| (-246)) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1088)) (|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 (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-482)))) +(-909 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 (-482))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-246)))) -(-911 R) +((|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-246)))) +(-910 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-3987 |has| |#1| (-246)) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3986 |has| |#1| (-246)) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-912 QR R QS S) +(-911 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL -(-913 S) +(-912 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-914 S) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-913 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-915) +(-914) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-916 -3092 UP UPUP |radicnd| |n|) +(-915 -3091 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-3987 |has| (-348 |#2|) (-312)) (-3992 |has| (-348 |#2|) (-312)) (-3986 |has| (-348 |#2|) (-312)) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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T) (-3987 . T) (-3988 . T) (-3990 . 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 (-808 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-299))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088)))))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1088)))))) (|HasCategory| (-348 |#2|) (QUOTE (-579 (-483)))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-348 (-483)))))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-483)))) (|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 (-810 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088)))))) +(-916 |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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1089)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1065))) (|HasCategory| (-483) (QUOTE (-796 (-328)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1089)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1089)))) (|HasCategory| (-483) (QUOTE (-454 (-1089) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) -(-918) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| (-483) (QUOTE (-820))) (|HasCategory| (-483) (QUOTE (-949 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-552 (-472)))) (|HasCategory| (-483) (QUOTE (-932))) (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755))) (OR (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755)))) (|HasCategory| (-483) (QUOTE (-949 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-795 (-328)))) (|HasCategory| (-483) (QUOTE (-795 (-483)))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-810 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-808 (-1088)))) (|HasCategory| (-483) (QUOTE (-454 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-579 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (|HasCategory| (-483) (QUOTE (-118))))) +(-917) ((|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 -(-919) +(-918) ((|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 -(-920 RP) +(-919 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 -(-921 S) +(-920 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 -(-922 A S) +(-921 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 -3995)) (|HasCategory| |#2| (QUOTE (-1013)))) -(-923 S) +((|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-1012)))) +(-922 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 -(-924 S) +(-923 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 -(-925) +(-924) ((|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}}"))) -((-3987 . T) (-3992 . T) (-3986 . T) (-3989 . T) (-3988 . T) ((-3996 "*") . T) (-3991 . T)) +((-3986 . T) (-3991 . T) (-3985 . T) (-3988 . T) (-3987 . T) ((-3995 "*") . T) (-3990 . T)) NIL -(-926 R -3092) +(-925 R -3091) ((|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 -(-927 R -3092) +(-926 R -3091) ((|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 -(-928 -3092 UP) +(-927 -3091 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 -(-929 -3092 UP) +(-928 -3091 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 -(-930 S) +(-929 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 -(-931 F1 UP UPUP R F2) +(-930 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 -(-932) +(-931) ((|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 -(-933) +(-932) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-934 |Pol|) +(-933 |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 -(-935 |Pol|) +(-934 |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 -(-936) +(-935) ((|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 -(-937 |TheField|) +(-936 |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"))) -((-3987 . T) (-3992 . T) (-3986 . T) (-3989 . T) (-3988 . T) ((-3996 "*") . T) (-3991 . T)) -((OR (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| (-348 (-483)) (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| (-348 (-483)) (QUOTE (-950 (-348 (-483))))) (|HasCategory| (-348 (-483)) (QUOTE (-950 (-483))))) -(-938 -3092 L) +((-3986 . T) (-3991 . T) (-3985 . T) (-3988 . T) (-3987 . T) ((-3995 "*") . T) (-3990 . T)) +((OR (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| (-348 (-483)) (QUOTE (-949 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| (-348 (-483)) (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-348 (-483)) (QUOTE (-949 (-483))))) +(-937 -3091 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 -(-939 S) +(-938 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 -(-940 R E V P) +(-939 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."))) -((-3995 . T) (-3994 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) -(-941) +((-3994 . T) (-3993 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-551 (-771)))) (|HasCategory| |#4| (QUOTE (-72)))) +(-940) ((|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 -(-942 R) +(-941 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 (-3996 "*")))) -(-943 R) +((|HasAttribute| |#1| (QUOTE (-3995 "*")))) +(-942 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)))) -(-944 S) +(-943 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.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-945 S) +(-944 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL NIL -(-946 S) +(-945 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 -(-947 -3092 |Expon| |VarSet| |FPol| |LFPol|) +(-946 -3091 |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"))) -(((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-948) +(-947) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-949 A S) +(-948 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 -(-950 S) +(-949 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 -(-951 Q R) +(-950 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 -(-952 R) +(-951 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 -(-953) +(-952) ((|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 -(-954 UP) +(-953 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 -(-955 R) +(-954 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 -(-956 T$) +(-955 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| $) "\\spad{red(c)} returns the `red' component of `c'."))) NIL NIL -(-957 T$) +(-956 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 -(-958 R |ls|) +(-957 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}."))) -((-3995 . T) (-3994 . T)) -((-12 (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-1013))) (|HasCategory| (-703 |#1| (-773 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -703) (|devaluate| |#1|) (|%list| (QUOTE -773) (|devaluate| |#2|)))))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-553 (-472)))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-773 |#2|) (QUOTE (-318))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-72)))) -(-959) +((-3994 . T) (-3993 . T)) +((-12 (|HasCategory| (-702 |#1| (-772 |#2|)) (QUOTE (-1012))) (|HasCategory| (-702 |#1| (-772 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -702) (|devaluate| |#1|) (|%list| (QUOTE -772) (|devaluate| |#2|)))))) (|HasCategory| (-702 |#1| (-772 |#2|)) (QUOTE (-552 (-472)))) (|HasCategory| (-702 |#1| (-772 |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-772 |#2|) (QUOTE (-318))) (|HasCategory| (-702 |#1| (-772 |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-702 |#1| (-772 |#2|)) (QUOTE (-72)))) +(-958) ((|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 -(-960 S) +(-959 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 -(-961) +(-960) ((|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."))) -((-3991 . T)) +((-3990 . T)) NIL -(-962 |xx| -3092) +(-961 |xx| -3091) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-963 S) +(-962 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 -(-964 S |m| |n| R |Row| |Col|) +(-963 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 (-494))) (|HasCategory| |#4| (QUOTE (-146)))) -(-965 |m| |n| R |Row| |Col|) +(-964 |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"))) -((-3994 . T) (-3989 . T) (-3988 . T)) +((-3993 . T) (-3988 . T) (-3987 . T)) NIL -(-966 |m| |n| R) +(-965 |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}."))) -((-3994 . T) (-3989 . T) (-3988 . 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 (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-494))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-552 (-772))))) -(-967 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-3993 . T) (-3988 . T) (-3987 . 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 (-1012))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-1012))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-494))) (-12 (|HasCategory| |#3| (QUOTE (-1012))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-551 (-771))))) +(-966 |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 -(-968 R) +(-967 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 -(-969 S) +(-968 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 -(-970) +(-969) ((|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|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) NIL NIL -(-971 S T$) +(-970 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 (-1013)))) -(-972 S) +((|HasCategory| |#1| (QUOTE (-1012)))) +(-971 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-973) +(-972) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-974 |TheField| |ThePolDom|) +(-973 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-975) +(-974) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-3982 . T) (-3986 . T) (-3981 . T) (-3992 . T) (-3993 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3981 . T) (-3985 . T) (-3980 . T) (-3991 . T) (-3992 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-976 S R E V) +(-975 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-38 (-483)))) (|HasCategory| |#2| (QUOTE (-904 (-483)))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#4| (QUOTE (-553 (-1089))))) -(-977 R E V) +((|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-38 (-483)))) (|HasCategory| |#2| (QUOTE (-903 (-483)))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#4| (QUOTE (-552 (-1088))))) +(-976 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) NIL -(-978) +(-977) ((|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 -(-979 S |TheField| |ThePols|) +(-978 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 -(-980 |TheField| |ThePols|) +(-979 |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 -(-981 R E V P TS) +(-980 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 -(-982 S R E V P) +(-981 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 -(-983 R E V P) +(-982 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}."))) -((-3995 . T) (-3994 . T)) +((-3994 . T) (-3993 . T)) NIL -(-984 R E V P TS) +(-983 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 -(-985) +(-984) ((|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 -(-986) +(-985) ((|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 -(-987 |Base| R -3092) +(-986 |Base| R -3091) ((|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 -(-988 |f|) +(-987 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-989 |Base| R -3092) +(-988 |Base| R -3091) ((|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 -(-990 R |ls|) +(-989 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 -(-991 R UP M) +(-990 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."))) -((-3987 |has| |#1| (-312)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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 (-809 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1089))))) (-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 (-809 (-1089)))))) -(-992 UP SAE UPA) +((-3986 |has| |#1| (-312)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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 (-808 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-808 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1088))))) (-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 (-808 (-1088)))))) +(-991 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 -(-993 UP SAE UPA) +(-992 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 -(-994) +(-993) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-995) +(-994) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-996 S) +(-995 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 -(-997) +(-996) ((|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 -(-998 R) +(-997 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 -(-999 R) +(-998 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"))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-328)))) (|HasCategory| (-1000 (-1089)) (QUOTE (-796 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| (-1000 (-1089)) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-1000 (-1089)) (QUOTE (-553 (-800 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-1000 (-1089)) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| (-1000 (-1089)) (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-1000 S) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-820))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| (-999 (-1088)) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| (-999 (-1088)) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-999 (-1088)) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-999 (-1088)) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-999 (-1088)) (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-999 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 -(-1001 S) +(-1000 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1013)))) -(-1002 R S) +((|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-1012)))) +(-1001 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 (-755)))) -(-1003) +((|HasCategory| |#1| (QUOTE (-754)))) +(-1002) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1004 S) +(-1003 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1001 |#1|) (QUOTE (-1013)))) -(-1005 R S) +((|HasCategory| (-1000 |#1|) (QUOTE (-1012)))) +(-1004 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1006 S) +(-1005 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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 -(-1007 S L) +(-1006 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 -(-1008) +(-1007) ((|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 -(-1009 S) +(-1008 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)}}"))) -((-3994 . T) (-3984 . T) (-3995 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-1010 A S) +((-3993 . T) (-3983 . T) (-3994 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-1009 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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1011 S) +(-1010 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-3984 . T)) +((-3983 . T)) NIL -(-1012 S) +(-1011 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 -(-1013) +(-1012) ((|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 -(-1014 |m| |n|) +(-1013 |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 -(-1015) +(-1014) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1016 |Str| |Sym| |Int| |Flt| |Expr|) +(-1015 |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 -(-1017 |Str| |Sym| |Int| |Flt| |Expr|) +(-1016 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1018 R E V P TS) +(-1017 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 -(-1019 R E V P TS) +(-1018 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 -(-1020 R E V P) +(-1019 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.}"))) -((-3995 . T) (-3994 . T)) +((-3994 . T) (-3993 . T)) NIL -(-1021) +(-1020) ((|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 -(-1022 T$) +(-1021 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|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-1023 T$) +(-1022 T$) ((|constructor| (NIL "This is the category of all domains that implement semigroup operations"))) -(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-1024 S) +(-1023 S) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1025) +(-1024) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 -(-1026 |dimtot| |dim1| S) +(-1025 |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}."))) -((-3988 |has| |#3| (-961)) (-3989 |has| |#3| (-961)) (-3991 |has| |#3| (-6 -3991)) (-3994 . 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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)))) -(-1028) +(-1027) ((|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 -(-1029) +(-1028) ((|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 -(-1030 R -3092) +(-1029 R -3091) ((|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 -(-1031 R) +(-1030 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 -(-1032) +(-1031) ((|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 -(-1033) +(-1032) ((|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."))) -((-3982 . T) (-3986 . T) (-3981 . T) (-3992 . T) (-3993 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3981 . T) (-3985 . T) (-3980 . T) (-3991 . T) (-3992 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-1034 S) +(-1033 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-3994 . T) (-3995 . T)) +((-3993 . T) (-3994 . T)) NIL -(-1035 S |ndim| R |Row| |Col|) +(-1034 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-3996 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) -(-1036 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3995 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) +(-1035 |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."))) -((-3994 . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3993 . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-1037 R |Row| |Col| M) +(-1036 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 -(-1038 R |VarSet|) +(-1037 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."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-328)))) (|HasCategory| |#2| (QUOTE (-796 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-1039 |Coef| |Var| SMP) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-820))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| |#2| (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-1038 |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}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3989 . T) (-3988 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3988 . T) (-3987 . T) (-3990 . T)) ((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-312)))) -(-1040 R E V P) +(-1039 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}"))) -((-3995 . T) (-3994 . T)) +((-3994 . T) (-3993 . T)) NIL -(-1041 UP -3092) +(-1040 UP -3091) ((|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 -(-1042 R) +(-1041 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 -(-1043 R) +(-1042 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 -(-1044 R) +(-1043 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 -(-1045 S A) +(-1044 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 (-756)))) -(-1046 R) +((|HasCategory| |#1| (QUOTE (-755)))) +(-1045 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 -(-1047 R) +(-1046 R) ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1048) +(-1047) ((|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 -(-1049) +(-1048) ((|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 -(-1050) +(-1049) ((|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 -(-1051) +(-1050) ((|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 -(-1052) +(-1051) ((|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 -(-1053 V C) +(-1052 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 -(-1054 V C) +(-1053 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| (-1053 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1053) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013))) (OR (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-552 (-772)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-72)))) -(-1055 |ndim| R) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| (-1052 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1052) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1012)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1012))) (OR (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1012)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-551 (-771)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-72)))) +(-1054 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-3991 . T) (-3983 |has| |#2| (-6 (-3996 "*"))) (-3994 . T) (-3988 . T) (-3989 . T)) -((|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3996 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3996 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1089))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) -(-1056 S) +((-3990 . T) (-3982 |has| |#2| (-6 (-3995 "*"))) (-3993 . T) (-3987 . T) (-3988 . T)) +((|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (QUOTE (-810 (-1088)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3995 #1="*"))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3995 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-808 (-1088))))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) +(-1055 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1057) +(-1056) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-3995 . T) (-3994 . T)) +((-3994 . T) (-3993 . T)) NIL -(-1058 R E V P TS) +(-1057 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 -(-1059 R E V P) +(-1058 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."))) -((-3995 . T) (-3994 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) -(-1060) +((-3994 . T) (-3993 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-551 (-771)))) (|HasCategory| |#4| (QUOTE (-72)))) +(-1059) ((|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 -(-1061 S) +(-1060 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}."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-1062 A S) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-1061 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 -(-1063 S) +(-1062 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 -(-1064 |Key| |Ent| |dent|) +(-1063 |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."))) -((-3995 . T)) -((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) -(-1065) +((-3994 . T)) +((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) +(-1064) ((|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 -(-1066) +(-1065) ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL NIL -(-1067 |Coef|) +(-1066 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-1068 S) +(-1067 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) -((-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72)))) -(-1069 S) +((-3994 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-72)))) +(-1068 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 -(-1070 A B) +(-1069 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 -(-1071 A B C) +(-1070 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 -(-1072) +(-1071) ((|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"))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-756)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (|HasCategory| (-117) (QUOTE (-552 (-772)))) (|HasCategory| (-117) (QUOTE (-553 (-472)))) (OR (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| (-117) (QUOTE (-756))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) -(-1073 |Entry|) +((-3994 . T) (-3993 . T)) +((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-755)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) (|HasCategory| (-117) (QUOTE (-551 (-771)))) (|HasCategory| (-117) (QUOTE (-552 (-472)))) (OR (|HasCategory| (-117) (QUOTE (-755))) (|HasCategory| (-117) (QUOTE (-1012)))) (|HasCategory| (-117) (QUOTE (-755))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-755))) (|HasCategory| (-117) (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| (-117) (QUOTE (-1012))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) +(-1072 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3859 (-1072))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013))) (|HasCategory| (-1072) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72)))) -(-1074 A) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3858 (-1071))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (OR (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012))) (|HasCategory| (-1071) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72)))) +(-1073 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 (-483)))))) -(-1075 |Coef|) +(-1074 |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 -(-1076 |Coef|) +(-1075 |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 -(-1077 R UP) +(-1076 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)))) -(-1078 |n| R) +(-1077 |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| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL -(-1083 R) +(-1082 R) ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) NIL NIL -(-1084 R) +(-1083 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|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."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3990 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-328)))) (|HasCategory| (-994) (QUOTE (-796 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| (-994) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-328))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| (-994) (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-1085 R S) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3989 |has| |#1| (-312)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| (-993) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| (-993) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-993) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-993) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-993) (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-1084 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 -(-1086 E OV R P) +(-1085 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 -(-1087 |Coef| |var| |cen|) +(-1086 |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."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|))))))) -(-1088 |Coef| |var| |cen|) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#1|))))))) +(-1087 |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}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|)))) (|HasCategory| (-694) (QUOTE (-1025))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|))))))) -(-1089) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-693)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-693)) (|devaluate| |#1|)))) (|HasCategory| (-693) (QUOTE (-1024))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-693))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-693))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#1|))))))) +(-1088) ((|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 -(-1090 R) +(-1089 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 -(-1091 R) +(-1090 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-6 -3992)) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-884) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3992))) -(-1092) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-883) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3991))) +(-1091) ((|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 -(-1093) +(-1092) ((|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 -(-1094) +(-1093) ((|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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1095 N) +(-1094 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1096 N) +(-1095 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 -(-1097) +(-1096) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1098 R) +(-1097 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 -(-1099) +(-1098) ((|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 -(-1100 S) +(-1099 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 -(-1101 |Key| |Entry|) +(-1100 |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}"))) -((-3994 . T) (-3995 . T)) -((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) -(-1102 S) +((-3993 . T) (-3994 . T)) +((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) +(-1101 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 -(-1103 S) +(-1102 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 -(-1104 R) +(-1103 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 -(-1105 S |Key| |Entry|) +(-1104 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 -(-1106 |Key| |Entry|) +(-1105 |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})}."))) -((-3995 . T)) +((-3994 . T)) NIL -(-1107 |Key| |Entry|) +(-1106 |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 -(-1108) +(-1107) ((|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 -(-1109 S) +(-1108 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 -(-1110) +(-1109) ((|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 -(-1111 R) +(-1110 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 -(-1112) +(-1111) ((|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 -(-1113 S) +(-1112 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1114) +(-1113) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1115 S) +(-1114 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-3995 . T) (-3994 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-1116 S) +((-3994 . T) (-3993 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-1115 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1117) +(-1116) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1118 R -3092) +(-1117 R -3091) ((|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 -(-1119 R |Row| |Col| M) +(-1118 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 -(-1120 R -3092) +(-1119 R -3091) ((|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 -553) (|%list| (QUOTE -800) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -796) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -553) (|%list| (QUOTE -800) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -796) (|devaluate| |#1|))))) -(-1121 |Coef|) +((-12 (|HasCategory| |#1| (|%list| (QUOTE -552) (|%list| (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -795) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -552) (|%list| (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -795) (|devaluate| |#1|))))) +(-1120 |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}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3989 . T) (-3988 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3988 . T) (-3987 . T) (-3990 . T)) ((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-312)))) -(-1122 S R E V P) +(-1121 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)))) -(-1123 R E V P) +(-1122 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-3995 . T) (-3994 . T)) +((-3994 . T) (-3993 . T)) NIL -(-1124 |Curve|) +(-1123 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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 -(-1125) +(-1124) ((|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 -(-1126 S) +(-1125 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 (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) -(-1127 -3092) +((|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-551 (-771))))) +(-1126 -3091) ((|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 -(-1128) +(-1127) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1129) +(-1128) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1130 S) +(-1129 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])}.")) 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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}."))) 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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)))) -(-1142 |Coef| UTS) +(-1141 |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)}.")) 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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 -(-1145 S) +(-1144 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 (-755))) (|HasCategory| |#1| (QUOTE (-1013)))) -(-1146 R S) +((|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-1012)))) +(-1145 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.") 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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 -(-1149 R Q UP) +(-1148 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 -(-1150 R UP) +(-1149 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 -(-1151 R UP) +(-1150 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 -(-1152 R U) +(-1151 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 -(-1153 S R) +(-1152 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 (-483))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1065)))) -(-1154 R) +((|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1064)))) +(-1153 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}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3990 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3989 |has| |#1| (-312)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) NIL -(-1155 R PR S PS) +(-1154 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 -(-1156 S |Coef| |Expon|) +(-1155 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 (-809 (-1089)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1025))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#2|) (QUOTE (-1089)))))) -(-1157 |Coef| |Expon|) +((|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1024))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#2|) (QUOTE (-1088)))))) +(-1156 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-1158 RC P) +(-1157 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1159 |Coef| |var| |cen|) +(-1158 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|))))))) -(-1160 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#1|))))))) +(-1159 |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 -(-1161 |Coef|) +(-1160 |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."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-1162 S |Coef| ULS) +(-1161 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 -(-1163 |Coef| ULS) +(-1162 |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)}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-1164 |Coef| ULS) +(-1163 |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)}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483)))))) -(-1165 R FE |var| |cen|) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483)))))) +(-1164 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))}."))) -(((-3996 "*") |has| (-1159 |#2| |#3| |#4|) (-146)) (-3987 |has| (-1159 |#2| |#3| |#4|) (-494)) (-3988 . T) (-3989 . T) (-3991 . T)) -((|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-483))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-483))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-950 (-348 (-483)))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-950 (-348 (-483))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-950 (-483)))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-390))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-494)))) -(-1166 A S) +(((-3995 "*") |has| (-1158 |#2| |#3| |#4|) (-146)) (-3986 |has| (-1158 |#2| |#3| |#4|) (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-483))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-483))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-949 (-348 (-483)))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-949 (-483)))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-390))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-494)))) +(-1165 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -3995))) -(-1167 S) +((|HasAttribute| |#1| (QUOTE -3994))) +(-1166 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1168 |Coef| |var| |cen|) +(-1167 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3988 . 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T)) -((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|)))) (|HasCategory| (-694) (QUOTE (-1025))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|))))))) -(-1169 |Coef1| |Coef2| UTS1 UTS2) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-693)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-693)) (|devaluate| |#1|)))) (|HasCategory| (-693) (QUOTE (-1024))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-693))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-693))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#1|))))))) +(-1168 |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 -(-1170 S |Coef|) +(-1169 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 (-483)))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1114))) (|HasSignature| |#2| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1089))))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312)))) -(-1171 |Coef|) +((|HasCategory| |#2| (QUOTE (-29 (-483)))) (|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasSignature| |#2| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1088))))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312)))) +(-1170 |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."))) -(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-494)) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-1172 |Coef| UTS) +(-1171 |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 -(-1173 -3092 UP L UTS) +(-1172 -3091 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 (-494)))) -(-1174) +(-1173) ((|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 -(-1175 |sym|) +(-1174 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1176 S R) +(-1175 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 (-915))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1177 R) +((|HasCategory| |#2| (QUOTE (-914))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-662))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1176 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-3995 . T) (-3994 . T)) +((-3994 . T) (-3993 . T)) NIL -(-1178 R) +(-1177 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-3995 . T) (-3994 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-1179 A B) +((-3994 . T) (-3993 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-662))) (|HasCategory| |#1| (QUOTE (-960))) (-12 (|HasCategory| |#1| (QUOTE (-914))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-1178 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 -(-1180) +(-1179) ((|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 -(-1181) +(-1180) ((|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 -(-1182) +(-1181) ((|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 -(-1183) +(-1182) ((|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 -(-1184) +(-1183) ((|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| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1185 A S) +(-1184 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1186 S) +(-1185 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}."))) -((-3989 . T) (-3988 . T)) +((-3988 . T) (-3987 . T)) NIL -(-1187 R) +(-1186 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 -(-1188 K R UP -3092) +(-1187 K R UP -3091) ((|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 -(-1189) +(-1188) ((|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 -(-1190) +(-1189) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1191 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1190 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)"))) -((-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) (-3991 . T)) +((-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) (-3990 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) -(-1192 R E V P) +(-1191 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}."))) -((-3995 . T) (-3994 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) -(-1193 R) +((-3994 . T) (-3993 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-551 (-771)))) (|HasCategory| |#4| (QUOTE (-72)))) +(-1192 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)"))) -((-3988 . T) (-3989 . T) (-3991 . T)) +((-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-1194 |vl| R) +(-1193 |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."))) -((-3991 . T) (-3987 |has| |#2| (-6 -3987)) (-3989 . T) (-3988 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3987))) -(-1195 R |VarSet| XPOLY) +((-3990 . T) (-3986 |has| |#2| (-6 -3986)) (-3988 . T) (-3987 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3986))) +(-1194 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 -(-1196 S -3092) +(-1195 S -3091) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) -(-1197 -3092) +(-1196 -3091) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) -((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL -(-1198 |vl| R) +(-1197 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-3987 |has| |#2| (-6 -3987)) (-3989 . T) (-3988 . T) (-3991 . T)) +((-3986 |has| |#2| (-6 -3986)) (-3988 . T) (-3987 . T) (-3990 . T)) NIL -(-1199 |VarSet| R) +(-1198 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|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}}."))) -((-3987 |has| |#2| (-6 -3987)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-654 (-348 (-483))))) (|HasAttribute| |#2| (QUOTE -3987))) -(-1200 R) +((-3986 |has| |#2| (-6 -3986)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-653 (-348 (-483))))) (|HasAttribute| |#2| (QUOTE -3986))) +(-1199 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."))) -((-3987 |has| |#1| (-6 -3987)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3987))) -(-1201 |vl| R) +((-3986 |has| |#1| (-6 -3986)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3986))) +(-1200 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-3987 |has| |#2| (-6 -3987)) (-3989 . T) (-3988 . T) (-3991 . T)) +((-3986 |has| |#2| (-6 -3986)) (-3988 . T) (-3987 . T) (-3990 . T)) NIL -(-1202 R E) +(-1201 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-3991 . T) (-3992 |has| |#1| (-6 -3992)) (-3987 |has| |#1| (-6 -3987)) (-3989 . T) (-3988 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasAttribute| |#1| (QUOTE -3992)) (|HasAttribute| |#1| (QUOTE -3987))) -(-1203 |VarSet| R) +((-3990 . T) (-3991 |has| |#1| (-6 -3991)) (-3986 |has| |#1| (-6 -3986)) (-3988 . T) (-3987 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3990)) (|HasAttribute| |#1| (QUOTE -3991)) (|HasAttribute| |#1| (QUOTE -3986))) +(-1202 |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."))) -((-3987 |has| |#2| (-6 -3987)) (-3989 . T) (-3988 . T) (-3991 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3987))) -(-1204) +((-3986 |has| |#2| (-6 -3986)) (-3988 . T) (-3987 . T) (-3990 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3986))) +(-1203) ((|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 -(-1205 A) +(-1204 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 -(-1206 R |ls| |ls2|) +(-1205 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 -(-1207 R) +(-1206 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 -(-1208 |p|) +(-1207 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) +(((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) NIL NIL NIL @@ -4780,4 +4776,4 @@ NIL NIL NIL NIL -((-3 NIL 1961879 1961884 1961889 1961894) (-2 NIL 1961859 1961864 1961869 1961874) (-1 NIL 1961839 1961844 1961849 1961854) (0 NIL 1961819 1961824 1961829 1961834) (-1208 "ZMOD.spad" 1961628 1961641 1961757 1961814) (-1207 "ZLINDEP.spad" 1960726 1960737 1961618 1961623) (-1206 "ZDSOLVE.spad" 1950687 1950709 1960716 1960721) (-1205 "YSTREAM.spad" 1950182 1950193 1950677 1950682) (-1204 "YDIAGRAM.spad" 1949816 1949825 1950172 1950177) (-1203 "XRPOLY.spad" 1949036 1949056 1949672 1949741) (-1202 "XPR.spad" 1946831 1946844 1948754 1948853) (-1201 "XPOLYC.spad" 1946150 1946166 1946757 1946826) (-1200 "XPOLY.spad" 1945705 1945716 1946006 1946075) (-1199 "XPBWPOLY.spad" 1944176 1944196 1945511 1945580) (-1198 "XFALG.spad" 1941224 1941240 1944102 1944171) (-1197 "XF.spad" 1939687 1939702 1941126 1941219) (-1196 "XF.spad" 1938130 1938147 1939571 1939576) (-1195 "XEXPPKG.spad" 1937389 1937415 1938120 1938125) (-1194 "XDPOLY.spad" 1937003 1937019 1937245 1937314) (-1193 "XALG.spad" 1936671 1936682 1936959 1936998) (-1192 "WUTSET.spad" 1932674 1932691 1936305 1936332) (-1191 "WP.spad" 1931881 1931925 1932532 1932599) (-1190 "WHILEAST.spad" 1931679 1931688 1931871 1931876) (-1189 "WHEREAST.spad" 1931350 1931359 1931669 1931674) (-1188 "WFFINTBS.spad" 1929013 1929035 1931340 1931345) (-1187 "WEIER.spad" 1927235 1927246 1929003 1929008) (-1186 "VSPACE.spad" 1926908 1926919 1927203 1927230) (-1185 "VSPACE.spad" 1926601 1926614 1926898 1926903) (-1184 "VOID.spad" 1926278 1926287 1926591 1926596) (-1183 "VIEWDEF.spad" 1921479 1921488 1926268 1926273) (-1182 "VIEW3D.spad" 1905440 1905449 1921469 1921474) (-1181 "VIEW2D.spad" 1893339 1893348 1905430 1905435) (-1180 "VIEW.spad" 1891059 1891068 1893329 1893334) (-1179 "VECTOR2.spad" 1889698 1889711 1891049 1891054) (-1178 "VECTOR.spad" 1888417 1888428 1888668 1888695) (-1177 "VECTCAT.spad" 1886329 1886340 1888385 1888412) (-1176 "VECTCAT.spad" 1884050 1884063 1886108 1886113) (-1175 "VARIABLE.spad" 1883830 1883845 1884040 1884045) (-1174 "UTYPE.spad" 1883474 1883483 1883820 1883825) (-1173 "UTSODETL.spad" 1882769 1882793 1883430 1883435) (-1172 "UTSODE.spad" 1880985 1881005 1882759 1882764) (-1171 "UTSCAT.spad" 1878464 1878480 1880883 1880980) (-1170 "UTSCAT.spad" 1875611 1875629 1878032 1878037) (-1169 "UTS2.spad" 1875206 1875241 1875601 1875606) (-1168 "UTS.spad" 1870218 1870246 1873738 1873835) (-1167 "URAGG.spad" 1864939 1864950 1870208 1870213) (-1166 "URAGG.spad" 1859624 1859637 1864895 1864900) (-1165 "UPXSSING.spad" 1857392 1857418 1858828 1858961) (-1164 "UPXSCONS.spad" 1855210 1855230 1855583 1855732) (-1163 "UPXSCCA.spad" 1853781 1853801 1855056 1855205) (-1162 "UPXSCCA.spad" 1852494 1852516 1853771 1853776) (-1161 "UPXSCAT.spad" 1851083 1851099 1852340 1852489) (-1160 "UPXS2.spad" 1850626 1850679 1851073 1851078) (-1159 "UPXS.spad" 1847981 1848009 1848817 1848966) (-1158 "UPSQFREE.spad" 1846396 1846410 1847971 1847976) (-1157 "UPSCAT.spad" 1844191 1844215 1846294 1846391) (-1156 "UPSCAT.spad" 1841687 1841713 1843792 1843797) (-1155 "UPOLYC2.spad" 1841158 1841177 1841677 1841682) (-1154 "UPOLYC.spad" 1836238 1836249 1841000 1841153) (-1153 "UPOLYC.spad" 1831236 1831249 1836000 1836005) (-1152 "UPMP.spad" 1830168 1830181 1831226 1831231) (-1151 "UPDIVP.spad" 1829733 1829747 1830158 1830163) (-1150 "UPDECOMP.spad" 1827994 1828008 1829723 1829728) (-1149 "UPCDEN.spad" 1827211 1827227 1827984 1827989) (-1148 "UP2.spad" 1826575 1826596 1827201 1827206) (-1147 "UP.spad" 1824045 1824060 1824432 1824585) (-1146 "UNISEG2.spad" 1823542 1823555 1824001 1824006) (-1145 "UNISEG.spad" 1822895 1822906 1823461 1823466) (-1144 "UNIFACT.spad" 1821998 1822010 1822885 1822890) (-1143 "ULSCONS.spad" 1815844 1815864 1816214 1816363) (-1142 "ULSCCAT.spad" 1813581 1813601 1815690 1815839) (-1141 "ULSCCAT.spad" 1811426 1811448 1813537 1813542) (-1140 "ULSCAT.spad" 1809666 1809682 1811272 1811421) (-1139 "ULS2.spad" 1809180 1809233 1809656 1809661) (-1138 "ULS.spad" 1801213 1801241 1802158 1802581) (-1137 "UINT8.spad" 1801090 1801099 1801203 1801208) (-1136 "UINT64.spad" 1800966 1800975 1801080 1801085) (-1135 "UINT32.spad" 1800842 1800851 1800956 1800961) (-1134 "UINT16.spad" 1800718 1800727 1800832 1800837) (-1133 "UFD.spad" 1799783 1799792 1800644 1800713) (-1132 "UFD.spad" 1798910 1798921 1799773 1799778) (-1131 "UDVO.spad" 1797791 1797800 1798900 1798905) (-1130 "UDPO.spad" 1795372 1795383 1797747 1797752) (-1129 "TYPEAST.spad" 1795291 1795300 1795362 1795367) (-1128 "TYPE.spad" 1795223 1795232 1795281 1795286) (-1127 "TWOFACT.spad" 1793875 1793890 1795213 1795218) (-1126 "TUPLE.spad" 1793382 1793393 1793787 1793792) (-1125 "TUBETOOL.spad" 1790249 1790258 1793372 1793377) (-1124 "TUBE.spad" 1788896 1788913 1790239 1790244) (-1123 "TSETCAT.spad" 1776967 1776984 1788864 1788891) (-1122 "TSETCAT.spad" 1765024 1765043 1776923 1776928) (-1121 "TS.spad" 1763652 1763668 1764618 1764715) (-1120 "TRMANIP.spad" 1758016 1758033 1763340 1763345) (-1119 "TRIMAT.spad" 1756979 1757004 1758006 1758011) (-1118 "TRIGMNIP.spad" 1755506 1755523 1756969 1756974) (-1117 "TRIGCAT.spad" 1755018 1755027 1755496 1755501) (-1116 "TRIGCAT.spad" 1754528 1754539 1755008 1755013) (-1115 "TREE.spad" 1753168 1753179 1754200 1754227) (-1114 "TRANFUN.spad" 1753007 1753016 1753158 1753163) (-1113 "TRANFUN.spad" 1752844 1752855 1752997 1753002) (-1112 "TOPSP.spad" 1752518 1752527 1752834 1752839) (-1111 "TOOLSIGN.spad" 1752181 1752192 1752508 1752513) (-1110 "TEXTFILE.spad" 1750742 1750751 1752171 1752176) (-1109 "TEX1.spad" 1750298 1750309 1750732 1750737) (-1108 "TEX.spad" 1747492 1747501 1750288 1750293) (-1107 "TBCMPPK.spad" 1745593 1745616 1747482 1747487) (-1106 "TBAGG.spad" 1744651 1744674 1745573 1745588) (-1105 "TBAGG.spad" 1743717 1743742 1744641 1744646) (-1104 "TANEXP.spad" 1743125 1743136 1743707 1743712) (-1103 "TALGOP.spad" 1742849 1742860 1743115 1743120) (-1102 "TABLEAU.spad" 1742330 1742341 1742839 1742844) (-1101 "TABLE.spad" 1740605 1740628 1740875 1740902) (-1100 "TABLBUMP.spad" 1737384 1737395 1740595 1740600) (-1099 "SYSTEM.spad" 1736612 1736621 1737374 1737379) (-1098 "SYSSOLP.spad" 1734095 1734106 1736602 1736607) (-1097 "SYSPTR.spad" 1733994 1734003 1734085 1734090) (-1096 "SYSNNI.spad" 1733217 1733228 1733984 1733989) (-1095 "SYSINT.spad" 1732621 1732632 1733207 1733212) (-1094 "SYNTAX.spad" 1728955 1728964 1732611 1732616) (-1093 "SYMTAB.spad" 1727023 1727032 1728945 1728950) (-1092 "SYMS.spad" 1723052 1723061 1727013 1727018) (-1091 "SYMPOLY.spad" 1722185 1722196 1722267 1722394) (-1090 "SYMFUNC.spad" 1721686 1721697 1722175 1722180) (-1089 "SYMBOL.spad" 1719181 1719190 1721676 1721681) (-1088 "SUTS.spad" 1716294 1716322 1717713 1717810) (-1087 "SUPXS.spad" 1713636 1713664 1714485 1714634) (-1086 "SUPFRACF.spad" 1712741 1712759 1713626 1713631) (-1085 "SUP2.spad" 1712133 1712146 1712731 1712736) (-1084 "SUP.spad" 1709217 1709228 1709990 1710143) (-1083 "SUMRF.spad" 1708191 1708202 1709207 1709212) (-1082 "SUMFS.spad" 1707820 1707837 1708181 1708186) (-1081 "SULS.spad" 1699840 1699868 1700798 1701221) (-1080 "syntax.spad" 1699609 1699618 1699830 1699835) (-1079 "SUCH.spad" 1699299 1699314 1699599 1699604) (-1078 "SUBSPACE.spad" 1691430 1691445 1699289 1699294) (-1077 "SUBRESP.spad" 1690600 1690614 1691386 1691391) (-1076 "STTFNC.spad" 1687068 1687084 1690590 1690595) (-1075 "STTF.spad" 1683167 1683183 1687058 1687063) (-1074 "STTAYLOR.spad" 1675844 1675855 1683074 1683079) (-1073 "STRTBL.spad" 1674231 1674248 1674380 1674407) (-1072 "STRING.spad" 1673099 1673108 1673484 1673511) (-1071 "STREAM3.spad" 1672672 1672687 1673089 1673094) (-1070 "STREAM2.spad" 1671800 1671813 1672662 1672667) (-1069 "STREAM1.spad" 1671506 1671517 1671790 1671795) (-1068 "STREAM.spad" 1668502 1668513 1671109 1671124) (-1067 "STINPROD.spad" 1667438 1667454 1668492 1668497) (-1066 "STEPAST.spad" 1666672 1666681 1667428 1667433) (-1065 "STEP.spad" 1665989 1665998 1666662 1666667) (-1064 "STBL.spad" 1664379 1664407 1664546 1664561) (-1063 "STAGG.spad" 1663078 1663089 1664369 1664374) (-1062 "STAGG.spad" 1661775 1661788 1663068 1663073) (-1061 "STACK.spad" 1661197 1661208 1661447 1661474) (-1060 "SRING.spad" 1660957 1660966 1661187 1661192) (-1059 "SREGSET.spad" 1658689 1658706 1660591 1660618) (-1058 "SRDCMPK.spad" 1657266 1657286 1658679 1658684) (-1057 "SRAGG.spad" 1652449 1652458 1657234 1657261) (-1056 "SRAGG.spad" 1647652 1647663 1652439 1652444) (-1055 "SQMATRIX.spad" 1645329 1645347 1646245 1646332) (-1054 "SPLTREE.spad" 1640071 1640084 1644867 1644894) (-1053 "SPLNODE.spad" 1636691 1636704 1640061 1640066) (-1052 "SPFCAT.spad" 1635500 1635509 1636681 1636686) (-1051 "SPECOUT.spad" 1634052 1634061 1635490 1635495) (-1050 "SPADXPT.spad" 1626143 1626152 1634042 1634047) (-1049 "spad-parser.spad" 1625608 1625617 1626133 1626138) (-1048 "SPADAST.spad" 1625309 1625318 1625598 1625603) (-1047 "SPACEC.spad" 1609524 1609535 1625299 1625304) (-1046 "SPACE3.spad" 1609300 1609311 1609514 1609519) (-1045 "SORTPAK.spad" 1608849 1608862 1609256 1609261) (-1044 "SOLVETRA.spad" 1606612 1606623 1608839 1608844) (-1043 "SOLVESER.spad" 1605068 1605079 1606602 1606607) (-1042 "SOLVERAD.spad" 1601094 1601105 1605058 1605063) (-1041 "SOLVEFOR.spad" 1599556 1599574 1601084 1601089) (-1040 "SNTSCAT.spad" 1599156 1599173 1599524 1599551) (-1039 "SMTS.spad" 1597473 1597499 1598750 1598847) (-1038 "SMP.spad" 1595281 1595301 1595671 1595798) (-1037 "SMITH.spad" 1594126 1594151 1595271 1595276) (-1036 "SMATCAT.spad" 1592244 1592274 1594070 1594121) (-1035 "SMATCAT.spad" 1590294 1590326 1592122 1592127) (-1034 "SKAGG.spad" 1589263 1589274 1590262 1590289) (-1033 "SINT.spad" 1588562 1588571 1589129 1589258) (-1032 "SIMPAN.spad" 1588290 1588299 1588552 1588557) (-1031 "SIGNRF.spad" 1587415 1587426 1588280 1588285) (-1030 "SIGNEF.spad" 1586701 1586718 1587405 1587410) (-1029 "syntax.spad" 1586118 1586127 1586691 1586696) (-1028 "SIG.spad" 1585480 1585489 1586108 1586113) (-1027 "SHP.spad" 1583424 1583439 1585436 1585441) (-1026 "SHDP.spad" 1572917 1572944 1573434 1573531) (-1025 "SGROUP.spad" 1572525 1572534 1572907 1572912) (-1024 "SGROUP.spad" 1572131 1572142 1572515 1572520) (-1023 "catdef.spad" 1571841 1571853 1571952 1572126) (-1022 "catdef.spad" 1571397 1571409 1571662 1571836) (-1021 "SGCF.spad" 1564536 1564545 1571387 1571392) (-1020 "SFRTCAT.spad" 1563482 1563499 1564504 1564531) (-1019 "SFRGCD.spad" 1562545 1562565 1563472 1563477) (-1018 "SFQCMPK.spad" 1557358 1557378 1562535 1562540) (-1017 "SEXOF.spad" 1557201 1557241 1557348 1557353) (-1016 "SEXCAT.spad" 1555029 1555069 1557191 1557196) (-1015 "SEX.spad" 1554921 1554930 1555019 1555024) (-1014 "SETMN.spad" 1553381 1553398 1554911 1554916) (-1013 "SETCAT.spad" 1552866 1552875 1553371 1553376) (-1012 "SETCAT.spad" 1552349 1552360 1552856 1552861) (-1011 "SETAGG.spad" 1548898 1548909 1552329 1552344) (-1010 "SETAGG.spad" 1545455 1545468 1548888 1548893) (-1009 "SET.spad" 1543764 1543775 1544861 1544900) (-1008 "syntax.spad" 1543467 1543476 1543754 1543759) (-1007 "SEGXCAT.spad" 1542623 1542636 1543457 1543462) (-1006 "SEGCAT.spad" 1541548 1541559 1542613 1542618) (-1005 "SEGBIND2.spad" 1541246 1541259 1541538 1541543) (-1004 "SEGBIND.spad" 1541004 1541015 1541193 1541198) (-1003 "SEGAST.spad" 1540734 1540743 1540994 1540999) (-1002 "SEG2.spad" 1540169 1540182 1540690 1540695) (-1001 "SEG.spad" 1539982 1539993 1540088 1540093) (-1000 "SDVAR.spad" 1539258 1539269 1539972 1539977) (-999 "SDPOL.spad" 1536951 1536961 1537241 1537368) (-998 "SCPKG.spad" 1535041 1535051 1536941 1536946) (-997 "SCOPE.spad" 1534219 1534227 1535031 1535036) (-996 "SCACHE.spad" 1532916 1532926 1534209 1534214) (-995 "SASTCAT.spad" 1532826 1532834 1532906 1532911) (-994 "SAOS.spad" 1532699 1532707 1532816 1532821) (-993 "SAERFFC.spad" 1532413 1532432 1532689 1532694) (-992 "SAEFACT.spad" 1532115 1532134 1532403 1532408) (-991 "SAE.spad" 1529766 1529781 1530376 1530511) (-990 "RURPK.spad" 1527426 1527441 1529756 1529761) (-989 "RULESET.spad" 1526880 1526903 1527416 1527421) (-988 "RULECOLD.spad" 1526733 1526745 1526870 1526875) (-987 "RULE.spad" 1524982 1525005 1526723 1526728) (-986 "RTVALUE.spad" 1524718 1524726 1524972 1524977) (-985 "syntax.spad" 1524436 1524444 1524708 1524713) (-984 "RSETGCD.spad" 1520879 1520898 1524426 1524431) (-983 "RSETCAT.spad" 1510848 1510864 1520847 1520874) (-982 "RSETCAT.spad" 1500837 1500855 1510838 1510843) (-981 "RSDCMPK.spad" 1499338 1499357 1500827 1500832) (-980 "RRCC.spad" 1497723 1497752 1499328 1499333) (-979 "RRCC.spad" 1496106 1496137 1497713 1497718) (-978 "RPTAST.spad" 1495809 1495817 1496096 1496101) (-977 "RPOLCAT.spad" 1475314 1475328 1495677 1495804) (-976 "RPOLCAT.spad" 1454612 1454628 1474977 1474982) (-975 "ROMAN.spad" 1453941 1453949 1454478 1454607) (-974 "ROIRC.spad" 1453022 1453053 1453931 1453936) (-973 "RNS.spad" 1451999 1452007 1452924 1453017) (-972 "RNS.spad" 1451062 1451072 1451989 1451994) (-971 "RNGBIND.spad" 1450223 1450236 1451017 1451022) (-970 "RNG.spad" 1449832 1449840 1450213 1450218) (-969 "RNG.spad" 1449439 1449449 1449822 1449827) (-968 "RMODULE.spad" 1449221 1449231 1449429 1449434) (-967 "RMCAT2.spad" 1448642 1448698 1449211 1449216) (-966 "RMATRIX.spad" 1447452 1447470 1447794 1447833) (-965 "RMATCAT.spad" 1443032 1443062 1447408 1447447) (-964 "RMATCAT.spad" 1438502 1438534 1442880 1442885) (-963 "RLINSET.spad" 1438207 1438217 1438492 1438497) (-962 "RINTERP.spad" 1438096 1438115 1438197 1438202) (-961 "RING.spad" 1437567 1437575 1438076 1438091) (-960 "RING.spad" 1437046 1437056 1437557 1437562) (-959 "RIDIST.spad" 1436439 1436447 1437036 1437041) (-958 "RGCHAIN.spad" 1434994 1435009 1435887 1435914) (-957 "RGBCSPC.spad" 1434784 1434795 1434984 1434989) (-956 "RGBCMDL.spad" 1434347 1434358 1434774 1434779) (-955 "RFFACTOR.spad" 1433810 1433820 1434337 1434342) (-954 "RFFACT.spad" 1433546 1433557 1433800 1433805) (-953 "RFDIST.spad" 1432543 1432551 1433536 1433541) (-952 "RF.spad" 1430218 1430228 1432533 1432538) (-951 "RETSOL.spad" 1429638 1429650 1430208 1430213) (-950 "RETRACT.spad" 1429067 1429077 1429628 1429633) (-949 "RETRACT.spad" 1428494 1428506 1429057 1429062) (-948 "RETAST.spad" 1428307 1428315 1428484 1428489) (-947 "RESRING.spad" 1427655 1427701 1428245 1428302) (-946 "RESLATC.spad" 1426980 1426990 1427645 1427650) (-945 "REPSQ.spad" 1426712 1426722 1426970 1426975) (-944 "REPDB.spad" 1426420 1426430 1426702 1426707) (-943 "REP2.spad" 1416135 1416145 1426262 1426267) (-942 "REP1.spad" 1410356 1410366 1416085 1416090) (-941 "REP.spad" 1407911 1407919 1410346 1410351) (-940 "REGSET.spad" 1405737 1405753 1407545 1407572) (-939 "REF.spad" 1405256 1405266 1405727 1405732) (-938 "REDORDER.spad" 1404463 1404479 1405246 1405251) (-937 "RECLOS.spad" 1403360 1403379 1404063 1404156) (-936 "REALSOLV.spad" 1402501 1402509 1403350 1403355) (-935 "REAL0Q.spad" 1399800 1399814 1402491 1402496) (-934 "REAL0.spad" 1396645 1396659 1399790 1399795) (-933 "REAL.spad" 1396518 1396526 1396635 1396640) (-932 "RDUCEAST.spad" 1396240 1396248 1396508 1396513) (-931 "RDIV.spad" 1395896 1395920 1396230 1396235) (-930 "RDIST.spad" 1395464 1395474 1395886 1395891) (-929 "RDETRS.spad" 1394329 1394346 1395454 1395459) (-928 "RDETR.spad" 1392469 1392486 1394319 1394324) (-927 "RDEEFS.spad" 1391569 1391585 1392459 1392464) (-926 "RDEEF.spad" 1390580 1390596 1391559 1391564) (-925 "RCFIELD.spad" 1387799 1387807 1390482 1390575) (-924 "RCFIELD.spad" 1385104 1385114 1387789 1387794) (-923 "RCAGG.spad" 1383041 1383051 1385094 1385099) (-922 "RCAGG.spad" 1380905 1380917 1382960 1382965) (-921 "RATRET.spad" 1380266 1380276 1380895 1380900) (-920 "RATFACT.spad" 1379959 1379970 1380256 1380261) (-919 "RANDSRC.spad" 1379279 1379287 1379949 1379954) (-918 "RADUTIL.spad" 1379036 1379044 1379269 1379274) (-917 "RADIX.spad" 1376081 1376094 1377626 1377719) (-916 "RADFF.spad" 1373998 1374034 1374116 1374272) (-915 "RADCAT.spad" 1373594 1373602 1373988 1373993) (-914 "RADCAT.spad" 1373188 1373198 1373584 1373589) (-913 "QUEUE.spad" 1372602 1372612 1372860 1372887) (-912 "QUATCT2.spad" 1372223 1372241 1372592 1372597) (-911 "QUATCAT.spad" 1370394 1370404 1372153 1372218) (-910 "QUATCAT.spad" 1368330 1368342 1370091 1370096) (-909 "QUAT.spad" 1366937 1366947 1367279 1367344) (-908 "QUAGG.spad" 1365771 1365781 1366905 1366932) (-907 "QQUTAST.spad" 1365540 1365548 1365761 1365766) (-906 "QFORM.spad" 1365159 1365173 1365530 1365535) (-905 "QFCAT2.spad" 1364852 1364868 1365149 1365154) (-904 "QFCAT.spad" 1363555 1363565 1364754 1364847) (-903 "QFCAT.spad" 1361891 1361903 1363092 1363097) (-902 "QEQUAT.spad" 1361450 1361458 1361881 1361886) (-901 "QCMPACK.spad" 1356365 1356384 1361440 1361445) (-900 "QALGSET2.spad" 1354361 1354379 1356355 1356360) (-899 "QALGSET.spad" 1350466 1350498 1354275 1354280) (-898 "PWFFINTB.spad" 1347882 1347903 1350456 1350461) (-897 "PUSHVAR.spad" 1347221 1347240 1347872 1347877) (-896 "PTRANFN.spad" 1343357 1343367 1347211 1347216) (-895 "PTPACK.spad" 1340445 1340455 1343347 1343352) (-894 "PTFUNC2.spad" 1340268 1340282 1340435 1340440) (-893 "PTCAT.spad" 1339523 1339533 1340236 1340263) (-892 "PSQFR.spad" 1338838 1338862 1339513 1339518) (-891 "PSEUDLIN.spad" 1337724 1337734 1338828 1338833) (-890 "PSETPK.spad" 1324429 1324445 1337602 1337607) (-889 "PSETCAT.spad" 1318829 1318852 1324409 1324424) (-888 "PSETCAT.spad" 1313203 1313228 1318785 1318790) (-887 "PSCURVE.spad" 1312202 1312210 1313193 1313198) (-886 "PSCAT.spad" 1310985 1311014 1312100 1312197) (-885 "PSCAT.spad" 1309858 1309889 1310975 1310980) (-884 "PRTITION.spad" 1308556 1308564 1309848 1309853) (-883 "PRTDAST.spad" 1308275 1308283 1308546 1308551) (-882 "PRS.spad" 1297893 1297910 1308231 1308236) (-881 "PRQAGG.spad" 1297328 1297338 1297861 1297888) (-880 "PROPLOG.spad" 1296932 1296940 1297318 1297323) (-879 "PROPFUN2.spad" 1296555 1296568 1296922 1296927) (-878 "PROPFUN1.spad" 1295961 1295972 1296545 1296550) (-877 "PROPFRML.spad" 1294529 1294540 1295951 1295956) (-876 "PROPERTY.spad" 1294025 1294033 1294519 1294524) (-875 "PRODUCT.spad" 1291722 1291734 1292006 1292061) (-874 "PRINT.spad" 1291474 1291482 1291712 1291717) (-873 "PRIMES.spad" 1289735 1289745 1291464 1291469) (-872 "PRIMELT.spad" 1287856 1287870 1289725 1289730) (-871 "PRIMCAT.spad" 1287499 1287507 1287846 1287851) (-870 "PRIMARR2.spad" 1286266 1286278 1287489 1287494) (-869 "PRIMARR.spad" 1285321 1285331 1285491 1285518) (-868 "PREASSOC.spad" 1284703 1284715 1285311 1285316) (-867 "PR.spad" 1283221 1283233 1283920 1284047) (-866 "PPCURVE.spad" 1282358 1282366 1283211 1283216) (-865 "PORTNUM.spad" 1282149 1282157 1282348 1282353) (-864 "POLYROOT.spad" 1280998 1281020 1282105 1282110) (-863 "POLYLIFT.spad" 1280263 1280286 1280988 1280993) (-862 "POLYCATQ.spad" 1278389 1278411 1280253 1280258) (-861 "POLYCAT.spad" 1271891 1271912 1278257 1278384) (-860 "POLYCAT.spad" 1264913 1264936 1271281 1271286) (-859 "POLY2UP.spad" 1264365 1264379 1264903 1264908) (-858 "POLY2.spad" 1263962 1263974 1264355 1264360) (-857 "POLY.spad" 1261630 1261640 1262145 1262272) (-856 "POLUTIL.spad" 1260595 1260624 1261586 1261591) (-855 "POLTOPOL.spad" 1259343 1259358 1260585 1260590) (-854 "POINT.spad" 1258226 1258236 1258313 1258340) (-853 "PNTHEORY.spad" 1254928 1254936 1258216 1258221) (-852 "PMTOOLS.spad" 1253703 1253717 1254918 1254923) (-851 "PMSYM.spad" 1253252 1253262 1253693 1253698) (-850 "PMQFCAT.spad" 1252843 1252857 1253242 1253247) (-849 "PMPREDFS.spad" 1252305 1252327 1252833 1252838) (-848 "PMPRED.spad" 1251792 1251806 1252295 1252300) (-847 "PMPLCAT.spad" 1250869 1250887 1251721 1251726) (-846 "PMLSAGG.spad" 1250454 1250468 1250859 1250864) (-845 "PMKERNEL.spad" 1250033 1250045 1250444 1250449) (-844 "PMINS.spad" 1249613 1249623 1250023 1250028) (-843 "PMFS.spad" 1249190 1249208 1249603 1249608) (-842 "PMDOWN.spad" 1248480 1248494 1249180 1249185) (-841 "PMASSFS.spad" 1247455 1247471 1248470 1248475) (-840 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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 290994 290999) (-220 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227907 228301 228306) (-199 "DISPLAY.spad" 226087 226095 227887 227892) (-198 "DIRPROD2.spad" 224905 224923 226077 226082) (-197 "DIRPROD.spad" 214275 214291 214915 215012) (-196 "DIRPCAT.spad" 213470 213486 214173 214270) (-195 "DIRPCAT.spad" 212291 212309 212996 213001) (-194 "DIOSP.spad" 211116 211124 212281 212286) (-193 "DIOPS.spad" 210112 210122 211096 211111) (-192 "DIOPS.spad" 209082 209094 210068 210073) (-191 "catdef.spad" 208940 208948 209072 209077) (-190 "DIFRING.spad" 208778 208786 208920 208935) (-189 "DIFFSPC.spad" 208357 208365 208768 208773) (-188 "DIFFSPC.spad" 207934 207944 208347 208352) (-187 "DIFFMOD.spad" 207423 207433 207902 207929) (-186 "DIFFDOM.spad" 206588 206599 207413 207418) (-185 "DIFFDOM.spad" 205751 205764 206578 206583) (-184 "DIFEXT.spad" 205570 205580 205731 205746) (-183 "DIAGG.spad" 205200 205210 205550 205565) (-182 "DIAGG.spad" 204838 204850 205190 205195) (-181 "DHMATRIX.spad" 203215 203225 204360 204387) (-180 "DFSFUN.spad" 196855 196863 203205 203210) (-179 "DFLOAT.spad" 193462 193470 196745 196850) (-178 "DFINTTLS.spad" 191693 191709 193452 193457) (-177 "DERHAM.spad" 189607 189639 191673 191688) (-176 "DEQUEUE.spad" 188996 189006 189279 189306) (-175 "DEGRED.spad" 188613 188627 188986 188991) (-174 "DEFINTRF.spad" 186195 186205 188603 188608) (-173 "DEFINTEF.spad" 184733 184749 186185 186190) (-172 "DEFAST.spad" 184117 184125 184723 184728) (-171 "DECIMAL.spad" 182346 182354 182707 182800) (-170 "DDFACT.spad" 180167 180184 182336 182341) (-169 "DBLRESP.spad" 179767 179791 180157 180162) (-168 "DBASIS.spad" 179393 179408 179757 179762) (-167 "DBASE.spad" 178057 178067 179383 179388) (-166 "DATAARY.spad" 177543 177556 178047 178052) (-165 "CYCLOTOM.spad" 177049 177057 177533 177538) (-164 "CYCLES.spad" 173841 173849 177039 177044) (-163 "CVMP.spad" 173258 173268 173831 173836) (-162 "CTRIGMNP.spad" 171758 171774 173248 173253) (-161 "CTORKIND.spad" 171361 171369 171748 171753) (-160 "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 1960688 1960693 1960698 1960703) (-2 NIL 1960668 1960673 1960678 1960683) (-1 NIL 1960648 1960653 1960658 1960663) (0 NIL 1960628 1960633 1960638 1960643) (-1207 "ZMOD.spad" 1960437 1960450 1960566 1960623) (-1206 "ZLINDEP.spad" 1959535 1959546 1960427 1960432) (-1205 "ZDSOLVE.spad" 1949496 1949518 1959525 1959530) (-1204 "YSTREAM.spad" 1948991 1949002 1949486 1949491) (-1203 "YDIAGRAM.spad" 1948625 1948634 1948981 1948986) (-1202 "XRPOLY.spad" 1947845 1947865 1948481 1948550) (-1201 "XPR.spad" 1945640 1945653 1947563 1947662) (-1200 "XPOLYC.spad" 1944959 1944975 1945566 1945635) (-1199 "XPOLY.spad" 1944514 1944525 1944815 1944884) (-1198 "XPBWPOLY.spad" 1942985 1943005 1944320 1944389) (-1197 "XFALG.spad" 1940033 1940049 1942911 1942980) (-1196 "XF.spad" 1938496 1938511 1939935 1940028) (-1195 "XF.spad" 1936939 1936956 1938380 1938385) (-1194 "XEXPPKG.spad" 1936198 1936224 1936929 1936934) (-1193 "XDPOLY.spad" 1935812 1935828 1936054 1936123) (-1192 "XALG.spad" 1935480 1935491 1935768 1935807) (-1191 "WUTSET.spad" 1931483 1931500 1935114 1935141) (-1190 "WP.spad" 1930690 1930734 1931341 1931408) (-1189 "WHILEAST.spad" 1930488 1930497 1930680 1930685) (-1188 "WHEREAST.spad" 1930159 1930168 1930478 1930483) (-1187 "WFFINTBS.spad" 1927822 1927844 1930149 1930154) (-1186 "WEIER.spad" 1926044 1926055 1927812 1927817) (-1185 "VSPACE.spad" 1925717 1925728 1926012 1926039) (-1184 "VSPACE.spad" 1925410 1925423 1925707 1925712) (-1183 "VOID.spad" 1925087 1925096 1925400 1925405) (-1182 "VIEWDEF.spad" 1920288 1920297 1925077 1925082) (-1181 "VIEW3D.spad" 1904249 1904258 1920278 1920283) (-1180 "VIEW2D.spad" 1892148 1892157 1904239 1904244) (-1179 "VIEW.spad" 1889868 1889877 1892138 1892143) (-1178 "VECTOR2.spad" 1888507 1888520 1889858 1889863) (-1177 "VECTOR.spad" 1887226 1887237 1887477 1887504) (-1176 "VECTCAT.spad" 1885138 1885149 1887194 1887221) (-1175 "VECTCAT.spad" 1882859 1882872 1884917 1884922) (-1174 "VARIABLE.spad" 1882639 1882654 1882849 1882854) (-1173 "UTYPE.spad" 1882283 1882292 1882629 1882634) (-1172 "UTSODETL.spad" 1881578 1881602 1882239 1882244) (-1171 "UTSODE.spad" 1879794 1879814 1881568 1881573) (-1170 "UTSCAT.spad" 1877273 1877289 1879692 1879789) (-1169 "UTSCAT.spad" 1874420 1874438 1876841 1876846) (-1168 "UTS2.spad" 1874015 1874050 1874410 1874415) (-1167 "UTS.spad" 1869027 1869055 1872547 1872644) (-1166 "URAGG.spad" 1863748 1863759 1869017 1869022) (-1165 "URAGG.spad" 1858433 1858446 1863704 1863709) (-1164 "UPXSSING.spad" 1856201 1856227 1857637 1857770) (-1163 "UPXSCONS.spad" 1854019 1854039 1854392 1854541) (-1162 "UPXSCCA.spad" 1852590 1852610 1853865 1854014) (-1161 "UPXSCCA.spad" 1851303 1851325 1852580 1852585) (-1160 "UPXSCAT.spad" 1849892 1849908 1851149 1851298) (-1159 "UPXS2.spad" 1849435 1849488 1849882 1849887) (-1158 "UPXS.spad" 1846790 1846818 1847626 1847775) (-1157 "UPSQFREE.spad" 1845205 1845219 1846780 1846785) (-1156 "UPSCAT.spad" 1843000 1843024 1845103 1845200) (-1155 "UPSCAT.spad" 1840496 1840522 1842601 1842606) (-1154 "UPOLYC2.spad" 1839967 1839986 1840486 1840491) (-1153 "UPOLYC.spad" 1835047 1835058 1839809 1839962) (-1152 "UPOLYC.spad" 1830045 1830058 1834809 1834814) (-1151 "UPMP.spad" 1828977 1828990 1830035 1830040) (-1150 "UPDIVP.spad" 1828542 1828556 1828967 1828972) (-1149 "UPDECOMP.spad" 1826803 1826817 1828532 1828537) (-1148 "UPCDEN.spad" 1826020 1826036 1826793 1826798) (-1147 "UP2.spad" 1825384 1825405 1826010 1826015) (-1146 "UP.spad" 1822854 1822869 1823241 1823394) (-1145 "UNISEG2.spad" 1822351 1822364 1822810 1822815) (-1144 "UNISEG.spad" 1821704 1821715 1822270 1822275) (-1143 "UNIFACT.spad" 1820807 1820819 1821694 1821699) (-1142 "ULSCONS.spad" 1814653 1814673 1815023 1815172) (-1141 "ULSCCAT.spad" 1812390 1812410 1814499 1814648) (-1140 "ULSCCAT.spad" 1810235 1810257 1812346 1812351) (-1139 "ULSCAT.spad" 1808475 1808491 1810081 1810230) (-1138 "ULS2.spad" 1807989 1808042 1808465 1808470) (-1137 "ULS.spad" 1800022 1800050 1800967 1801390) (-1136 "UINT8.spad" 1799899 1799908 1800012 1800017) (-1135 "UINT64.spad" 1799775 1799784 1799889 1799894) (-1134 "UINT32.spad" 1799651 1799660 1799765 1799770) (-1133 "UINT16.spad" 1799527 1799536 1799641 1799646) (-1132 "UFD.spad" 1798592 1798601 1799453 1799522) (-1131 "UFD.spad" 1797719 1797730 1798582 1798587) (-1130 "UDVO.spad" 1796600 1796609 1797709 1797714) (-1129 "UDPO.spad" 1794181 1794192 1796556 1796561) (-1128 "TYPEAST.spad" 1794100 1794109 1794171 1794176) (-1127 "TYPE.spad" 1794032 1794041 1794090 1794095) (-1126 "TWOFACT.spad" 1792684 1792699 1794022 1794027) (-1125 "TUPLE.spad" 1792191 1792202 1792596 1792601) (-1124 "TUBETOOL.spad" 1789058 1789067 1792181 1792186) (-1123 "TUBE.spad" 1787705 1787722 1789048 1789053) (-1122 "TSETCAT.spad" 1775776 1775793 1787673 1787700) (-1121 "TSETCAT.spad" 1763833 1763852 1775732 1775737) (-1120 "TS.spad" 1762461 1762477 1763427 1763524) (-1119 "TRMANIP.spad" 1756825 1756842 1762149 1762154) (-1118 "TRIMAT.spad" 1755788 1755813 1756815 1756820) (-1117 "TRIGMNIP.spad" 1754315 1754332 1755778 1755783) (-1116 "TRIGCAT.spad" 1753827 1753836 1754305 1754310) (-1115 "TRIGCAT.spad" 1753337 1753348 1753817 1753822) (-1114 "TREE.spad" 1751977 1751988 1753009 1753036) (-1113 "TRANFUN.spad" 1751816 1751825 1751967 1751972) (-1112 "TRANFUN.spad" 1751653 1751664 1751806 1751811) (-1111 "TOPSP.spad" 1751327 1751336 1751643 1751648) (-1110 "TOOLSIGN.spad" 1750990 1751001 1751317 1751322) (-1109 "TEXTFILE.spad" 1749551 1749560 1750980 1750985) (-1108 "TEX1.spad" 1749107 1749118 1749541 1749546) (-1107 "TEX.spad" 1746301 1746310 1749097 1749102) (-1106 "TBCMPPK.spad" 1744402 1744425 1746291 1746296) (-1105 "TBAGG.spad" 1743460 1743483 1744382 1744397) (-1104 "TBAGG.spad" 1742526 1742551 1743450 1743455) (-1103 "TANEXP.spad" 1741934 1741945 1742516 1742521) (-1102 "TALGOP.spad" 1741658 1741669 1741924 1741929) (-1101 "TABLEAU.spad" 1741139 1741150 1741648 1741653) (-1100 "TABLE.spad" 1739414 1739437 1739684 1739711) (-1099 "TABLBUMP.spad" 1736193 1736204 1739404 1739409) (-1098 "SYSTEM.spad" 1735421 1735430 1736183 1736188) (-1097 "SYSSOLP.spad" 1732904 1732915 1735411 1735416) (-1096 "SYSPTR.spad" 1732803 1732812 1732894 1732899) (-1095 "SYSNNI.spad" 1732026 1732037 1732793 1732798) (-1094 "SYSINT.spad" 1731430 1731441 1732016 1732021) (-1093 "SYNTAX.spad" 1727764 1727773 1731420 1731425) (-1092 "SYMTAB.spad" 1725832 1725841 1727754 1727759) (-1091 "SYMS.spad" 1721861 1721870 1725822 1725827) (-1090 "SYMPOLY.spad" 1720994 1721005 1721076 1721203) (-1089 "SYMFUNC.spad" 1720495 1720506 1720984 1720989) (-1088 "SYMBOL.spad" 1717990 1717999 1720485 1720490) (-1087 "SUTS.spad" 1715103 1715131 1716522 1716619) (-1086 "SUPXS.spad" 1712445 1712473 1713294 1713443) (-1085 "SUPFRACF.spad" 1711550 1711568 1712435 1712440) (-1084 "SUP2.spad" 1710942 1710955 1711540 1711545) (-1083 "SUP.spad" 1708026 1708037 1708799 1708952) (-1082 "SUMRF.spad" 1707000 1707011 1708016 1708021) (-1081 "SUMFS.spad" 1706629 1706646 1706990 1706995) (-1080 "SULS.spad" 1698649 1698677 1699607 1700030) (-1079 "syntax.spad" 1698418 1698427 1698639 1698644) (-1078 "SUCH.spad" 1698108 1698123 1698408 1698413) (-1077 "SUBSPACE.spad" 1690239 1690254 1698098 1698103) (-1076 "SUBRESP.spad" 1689409 1689423 1690195 1690200) (-1075 "STTFNC.spad" 1685877 1685893 1689399 1689404) (-1074 "STTF.spad" 1681976 1681992 1685867 1685872) (-1073 "STTAYLOR.spad" 1674653 1674664 1681883 1681888) (-1072 "STRTBL.spad" 1673040 1673057 1673189 1673216) (-1071 "STRING.spad" 1671908 1671917 1672293 1672320) (-1070 "STREAM3.spad" 1671481 1671496 1671898 1671903) (-1069 "STREAM2.spad" 1670609 1670622 1671471 1671476) (-1068 "STREAM1.spad" 1670315 1670326 1670599 1670604) (-1067 "STREAM.spad" 1667311 1667322 1669918 1669933) (-1066 "STINPROD.spad" 1666247 1666263 1667301 1667306) (-1065 "STEPAST.spad" 1665481 1665490 1666237 1666242) (-1064 "STEP.spad" 1664798 1664807 1665471 1665476) (-1063 "STBL.spad" 1663188 1663216 1663355 1663370) (-1062 "STAGG.spad" 1661887 1661898 1663178 1663183) (-1061 "STAGG.spad" 1660584 1660597 1661877 1661882) (-1060 "STACK.spad" 1660006 1660017 1660256 1660283) (-1059 "SRING.spad" 1659766 1659775 1659996 1660001) (-1058 "SREGSET.spad" 1657498 1657515 1659400 1659427) (-1057 "SRDCMPK.spad" 1656075 1656095 1657488 1657493) (-1056 "SRAGG.spad" 1651258 1651267 1656043 1656070) (-1055 "SRAGG.spad" 1646461 1646472 1651248 1651253) (-1054 "SQMATRIX.spad" 1644138 1644156 1645054 1645141) (-1053 "SPLTREE.spad" 1638880 1638893 1643676 1643703) (-1052 "SPLNODE.spad" 1635500 1635513 1638870 1638875) (-1051 "SPFCAT.spad" 1634309 1634318 1635490 1635495) (-1050 "SPECOUT.spad" 1632861 1632870 1634299 1634304) (-1049 "SPADXPT.spad" 1624952 1624961 1632851 1632856) (-1048 "spad-parser.spad" 1624417 1624426 1624942 1624947) (-1047 "SPADAST.spad" 1624118 1624127 1624407 1624412) (-1046 "SPACEC.spad" 1608333 1608344 1624108 1624113) (-1045 "SPACE3.spad" 1608109 1608120 1608323 1608328) (-1044 "SORTPAK.spad" 1607658 1607671 1608065 1608070) (-1043 "SOLVETRA.spad" 1605421 1605432 1607648 1607653) (-1042 "SOLVESER.spad" 1603877 1603888 1605411 1605416) (-1041 "SOLVERAD.spad" 1599903 1599914 1603867 1603872) (-1040 "SOLVEFOR.spad" 1598365 1598383 1599893 1599898) (-1039 "SNTSCAT.spad" 1597965 1597982 1598333 1598360) (-1038 "SMTS.spad" 1596282 1596308 1597559 1597656) (-1037 "SMP.spad" 1594090 1594110 1594480 1594607) (-1036 "SMITH.spad" 1592935 1592960 1594080 1594085) (-1035 "SMATCAT.spad" 1591053 1591083 1592879 1592930) (-1034 "SMATCAT.spad" 1589103 1589135 1590931 1590936) (-1033 "SKAGG.spad" 1588072 1588083 1589071 1589098) (-1032 "SINT.spad" 1587371 1587380 1587938 1588067) (-1031 "SIMPAN.spad" 1587099 1587108 1587361 1587366) (-1030 "SIGNRF.spad" 1586224 1586235 1587089 1587094) (-1029 "SIGNEF.spad" 1585510 1585527 1586214 1586219) (-1028 "syntax.spad" 1584927 1584936 1585500 1585505) (-1027 "SIG.spad" 1584289 1584298 1584917 1584922) (-1026 "SHP.spad" 1582233 1582248 1584245 1584250) (-1025 "SHDP.spad" 1571726 1571753 1572243 1572340) (-1024 "SGROUP.spad" 1571334 1571343 1571716 1571721) (-1023 "SGROUP.spad" 1570940 1570951 1571324 1571329) (-1022 "catdef.spad" 1570650 1570662 1570761 1570935) (-1021 "catdef.spad" 1570206 1570218 1570471 1570645) (-1020 "SGCF.spad" 1563345 1563354 1570196 1570201) (-1019 "SFRTCAT.spad" 1562291 1562308 1563313 1563340) (-1018 "SFRGCD.spad" 1561354 1561374 1562281 1562286) (-1017 "SFQCMPK.spad" 1556167 1556187 1561344 1561349) (-1016 "SEXOF.spad" 1556010 1556050 1556157 1556162) (-1015 "SEXCAT.spad" 1553838 1553878 1556000 1556005) (-1014 "SEX.spad" 1553730 1553739 1553828 1553833) (-1013 "SETMN.spad" 1552190 1552207 1553720 1553725) (-1012 "SETCAT.spad" 1551675 1551684 1552180 1552185) (-1011 "SETCAT.spad" 1551158 1551169 1551665 1551670) (-1010 "SETAGG.spad" 1547707 1547718 1551138 1551153) (-1009 "SETAGG.spad" 1544264 1544277 1547697 1547702) (-1008 "SET.spad" 1542573 1542584 1543670 1543709) (-1007 "syntax.spad" 1542276 1542285 1542563 1542568) (-1006 "SEGXCAT.spad" 1541432 1541445 1542266 1542271) (-1005 "SEGCAT.spad" 1540357 1540368 1541422 1541427) (-1004 "SEGBIND2.spad" 1540055 1540068 1540347 1540352) (-1003 "SEGBIND.spad" 1539813 1539824 1540002 1540007) (-1002 "SEGAST.spad" 1539543 1539552 1539803 1539808) (-1001 "SEG2.spad" 1538978 1538991 1539499 1539504) (-1000 "SEG.spad" 1538791 1538802 1538897 1538902) (-999 "SDVAR.spad" 1538068 1538078 1538781 1538786) (-998 "SDPOL.spad" 1535766 1535776 1536056 1536183) (-997 "SCPKG.spad" 1533856 1533866 1535756 1535761) (-996 "SCOPE.spad" 1533034 1533042 1533846 1533851) (-995 "SCACHE.spad" 1531731 1531741 1533024 1533029) (-994 "SASTCAT.spad" 1531641 1531649 1531721 1531726) (-993 "SAOS.spad" 1531514 1531522 1531631 1531636) (-992 "SAERFFC.spad" 1531228 1531247 1531504 1531509) (-991 "SAEFACT.spad" 1530930 1530949 1531218 1531223) (-990 "SAE.spad" 1528581 1528596 1529191 1529326) (-989 "RURPK.spad" 1526241 1526256 1528571 1528576) (-988 "RULESET.spad" 1525695 1525718 1526231 1526236) (-987 "RULECOLD.spad" 1525548 1525560 1525685 1525690) (-986 "RULE.spad" 1523797 1523820 1525538 1525543) (-985 "RTVALUE.spad" 1523533 1523541 1523787 1523792) (-984 "syntax.spad" 1523251 1523259 1523523 1523528) (-983 "RSETGCD.spad" 1519694 1519713 1523241 1523246) (-982 "RSETCAT.spad" 1509663 1509679 1519662 1519689) (-981 "RSETCAT.spad" 1499652 1499670 1509653 1509658) (-980 "RSDCMPK.spad" 1498153 1498172 1499642 1499647) (-979 "RRCC.spad" 1496538 1496567 1498143 1498148) (-978 "RRCC.spad" 1494921 1494952 1496528 1496533) (-977 "RPTAST.spad" 1494624 1494632 1494911 1494916) (-976 "RPOLCAT.spad" 1474129 1474143 1494492 1494619) (-975 "RPOLCAT.spad" 1453427 1453443 1473792 1473797) (-974 "ROMAN.spad" 1452756 1452764 1453293 1453422) (-973 "ROIRC.spad" 1451837 1451868 1452746 1452751) (-972 "RNS.spad" 1450814 1450822 1451739 1451832) (-971 "RNS.spad" 1449877 1449887 1450804 1450809) (-970 "RNGBIND.spad" 1449038 1449051 1449832 1449837) (-969 "RNG.spad" 1448647 1448655 1449028 1449033) (-968 "RNG.spad" 1448254 1448264 1448637 1448642) (-967 "RMODULE.spad" 1448036 1448046 1448244 1448249) (-966 "RMCAT2.spad" 1447457 1447513 1448026 1448031) (-965 "RMATRIX.spad" 1446267 1446285 1446609 1446648) (-964 "RMATCAT.spad" 1441847 1441877 1446223 1446262) (-963 "RMATCAT.spad" 1437317 1437349 1441695 1441700) (-962 "RLINSET.spad" 1437022 1437032 1437307 1437312) (-961 "RINTERP.spad" 1436911 1436930 1437012 1437017) (-960 "RING.spad" 1436382 1436390 1436891 1436906) (-959 "RING.spad" 1435861 1435871 1436372 1436377) (-958 "RIDIST.spad" 1435254 1435262 1435851 1435856) (-957 "RGCHAIN.spad" 1433809 1433824 1434702 1434729) (-956 "RGBCSPC.spad" 1433599 1433610 1433799 1433804) (-955 "RGBCMDL.spad" 1433162 1433173 1433589 1433594) (-954 "RFFACTOR.spad" 1432625 1432635 1433152 1433157) (-953 "RFFACT.spad" 1432361 1432372 1432615 1432620) (-952 "RFDIST.spad" 1431358 1431366 1432351 1432356) (-951 "RF.spad" 1429033 1429043 1431348 1431353) (-950 "RETSOL.spad" 1428453 1428465 1429023 1429028) (-949 "RETRACT.spad" 1427882 1427892 1428443 1428448) (-948 "RETRACT.spad" 1427309 1427321 1427872 1427877) (-947 "RETAST.spad" 1427122 1427130 1427299 1427304) (-946 "RESRING.spad" 1426470 1426516 1427060 1427117) (-945 "RESLATC.spad" 1425795 1425805 1426460 1426465) (-944 "REPSQ.spad" 1425527 1425537 1425785 1425790) (-943 "REPDB.spad" 1425235 1425245 1425517 1425522) (-942 "REP2.spad" 1414950 1414960 1425077 1425082) (-941 "REP1.spad" 1409171 1409181 1414900 1414905) (-940 "REP.spad" 1406726 1406734 1409161 1409166) (-939 "REGSET.spad" 1404552 1404568 1406360 1406387) (-938 "REF.spad" 1404071 1404081 1404542 1404547) (-937 "REDORDER.spad" 1403278 1403294 1404061 1404066) (-936 "RECLOS.spad" 1402175 1402194 1402878 1402971) (-935 "REALSOLV.spad" 1401316 1401324 1402165 1402170) (-934 "REAL0Q.spad" 1398615 1398629 1401306 1401311) (-933 "REAL0.spad" 1395460 1395474 1398605 1398610) (-932 "REAL.spad" 1395333 1395341 1395450 1395455) (-931 "RDUCEAST.spad" 1395055 1395063 1395323 1395328) (-930 "RDIV.spad" 1394711 1394735 1395045 1395050) (-929 "RDIST.spad" 1394279 1394289 1394701 1394706) (-928 "RDETRS.spad" 1393144 1393161 1394269 1394274) (-927 "RDETR.spad" 1391284 1391301 1393134 1393139) (-926 "RDEEFS.spad" 1390384 1390400 1391274 1391279) (-925 "RDEEF.spad" 1389395 1389411 1390374 1390379) (-924 "RCFIELD.spad" 1386614 1386622 1389297 1389390) (-923 "RCFIELD.spad" 1383919 1383929 1386604 1386609) (-922 "RCAGG.spad" 1381856 1381866 1383909 1383914) (-921 "RCAGG.spad" 1379720 1379732 1381775 1381780) (-920 "RATRET.spad" 1379081 1379091 1379710 1379715) (-919 "RATFACT.spad" 1378774 1378785 1379071 1379076) (-918 "RANDSRC.spad" 1378094 1378102 1378764 1378769) (-917 "RADUTIL.spad" 1377851 1377859 1378084 1378089) (-916 "RADIX.spad" 1374896 1374909 1376441 1376534) (-915 "RADFF.spad" 1372813 1372849 1372931 1373087) (-914 "RADCAT.spad" 1372409 1372417 1372803 1372808) (-913 "RADCAT.spad" 1372003 1372013 1372399 1372404) (-912 "QUEUE.spad" 1371417 1371427 1371675 1371702) (-911 "QUATCT2.spad" 1371038 1371056 1371407 1371412) (-910 "QUATCAT.spad" 1369209 1369219 1370968 1371033) (-909 "QUATCAT.spad" 1367145 1367157 1368906 1368911) (-908 "QUAT.spad" 1365752 1365762 1366094 1366159) (-907 "QUAGG.spad" 1364586 1364596 1365720 1365747) (-906 "QQUTAST.spad" 1364355 1364363 1364576 1364581) (-905 "QFORM.spad" 1363974 1363988 1364345 1364350) (-904 "QFCAT2.spad" 1363667 1363683 1363964 1363969) (-903 "QFCAT.spad" 1362370 1362380 1363569 1363662) (-902 "QFCAT.spad" 1360706 1360718 1361907 1361912) (-901 "QEQUAT.spad" 1360265 1360273 1360696 1360701) (-900 "QCMPACK.spad" 1355180 1355199 1360255 1360260) (-899 "QALGSET2.spad" 1353176 1353194 1355170 1355175) (-898 "QALGSET.spad" 1349281 1349313 1353090 1353095) (-897 "PWFFINTB.spad" 1346697 1346718 1349271 1349276) (-896 "PUSHVAR.spad" 1346036 1346055 1346687 1346692) (-895 "PTRANFN.spad" 1342172 1342182 1346026 1346031) (-894 "PTPACK.spad" 1339260 1339270 1342162 1342167) (-893 "PTFUNC2.spad" 1339083 1339097 1339250 1339255) (-892 "PTCAT.spad" 1338338 1338348 1339051 1339078) (-891 "PSQFR.spad" 1337653 1337677 1338328 1338333) (-890 "PSEUDLIN.spad" 1336539 1336549 1337643 1337648) (-889 "PSETPK.spad" 1323244 1323260 1336417 1336422) (-888 "PSETCAT.spad" 1317644 1317667 1323224 1323239) (-887 "PSETCAT.spad" 1312018 1312043 1317600 1317605) (-886 "PSCURVE.spad" 1311017 1311025 1312008 1312013) (-885 "PSCAT.spad" 1309800 1309829 1310915 1311012) (-884 "PSCAT.spad" 1308673 1308704 1309790 1309795) (-883 "PRTITION.spad" 1307371 1307379 1308663 1308668) (-882 "PRTDAST.spad" 1307090 1307098 1307361 1307366) (-881 "PRS.spad" 1296708 1296725 1307046 1307051) (-880 "PRQAGG.spad" 1296143 1296153 1296676 1296703) (-879 "PROPLOG.spad" 1295747 1295755 1296133 1296138) (-878 "PROPFUN2.spad" 1295370 1295383 1295737 1295742) (-877 "PROPFUN1.spad" 1294776 1294787 1295360 1295365) (-876 "PROPFRML.spad" 1293344 1293355 1294766 1294771) (-875 "PROPERTY.spad" 1292840 1292848 1293334 1293339) (-874 "PRODUCT.spad" 1290537 1290549 1290821 1290876) (-873 "PRINT.spad" 1290289 1290297 1290527 1290532) (-872 "PRIMES.spad" 1288550 1288560 1290279 1290284) (-871 "PRIMELT.spad" 1286671 1286685 1288540 1288545) (-870 "PRIMCAT.spad" 1286314 1286322 1286661 1286666) (-869 "PRIMARR2.spad" 1285081 1285093 1286304 1286309) (-868 "PRIMARR.spad" 1284136 1284146 1284306 1284333) (-867 "PREASSOC.spad" 1283518 1283530 1284126 1284131) (-866 "PR.spad" 1282036 1282048 1282735 1282862) (-865 "PPCURVE.spad" 1281173 1281181 1282026 1282031) (-864 "PORTNUM.spad" 1280964 1280972 1281163 1281168) (-863 "POLYROOT.spad" 1279813 1279835 1280920 1280925) (-862 "POLYLIFT.spad" 1279078 1279101 1279803 1279808) (-861 "POLYCATQ.spad" 1277204 1277226 1279068 1279073) (-860 "POLYCAT.spad" 1270706 1270727 1277072 1277199) (-859 "POLYCAT.spad" 1263728 1263751 1270096 1270101) (-858 "POLY2UP.spad" 1263180 1263194 1263718 1263723) (-857 "POLY2.spad" 1262777 1262789 1263170 1263175) (-856 "POLY.spad" 1260445 1260455 1260960 1261087) (-855 "POLUTIL.spad" 1259410 1259439 1260401 1260406) (-854 "POLTOPOL.spad" 1258158 1258173 1259400 1259405) (-853 "POINT.spad" 1257041 1257051 1257128 1257155) (-852 "PNTHEORY.spad" 1253743 1253751 1257031 1257036) (-851 "PMTOOLS.spad" 1252518 1252532 1253733 1253738) (-850 "PMSYM.spad" 1252067 1252077 1252508 1252513) (-849 "PMQFCAT.spad" 1251658 1251672 1252057 1252062) (-848 "PMPREDFS.spad" 1251120 1251142 1251648 1251653) (-847 "PMPRED.spad" 1250607 1250621 1251110 1251115) (-846 "PMPLCAT.spad" 1249684 1249702 1250536 1250541) (-845 "PMLSAGG.spad" 1249269 1249283 1249674 1249679) (-844 "PMKERNEL.spad" 1248848 1248860 1249259 1249264) (-843 "PMINS.spad" 1248428 1248438 1248838 1248843) (-842 "PMFS.spad" 1248005 1248023 1248418 1248423) (-841 "PMDOWN.spad" 1247295 1247309 1247995 1248000) (-840 "PMASSFS.spad" 1246270 1246286 1247285 1247290) (-839 "PMASS.spad" 1245288 1245296 1246260 1246265) (-838 "PLOTTOOL.spad" 1245068 1245076 1245278 1245283) (-837 "PLOT3D.spad" 1241532 1241540 1245058 1245063) (-836 "PLOT1.spad" 1240705 1240715 1241522 1241527) (-835 "PLOT.spad" 1235628 1235636 1240695 1240700) (-834 "PLEQN.spad" 1223030 1223057 1235618 1235623) (-833 "PINTERPA.spad" 1222814 1222830 1223020 1223025) (-832 "PINTERP.spad" 1222436 1222455 1222804 1222809) (-831 "PID.spad" 1221410 1221418 1222362 1222431) (-830 "PICOERCE.spad" 1221067 1221077 1221400 1221405) (-829 "PI.spad" 1220684 1220692 1221041 1221062) (-828 "PGROEB.spad" 1219293 1219307 1220674 1220679) (-827 "PGE.spad" 1210966 1210974 1219283 1219288) (-826 "PGCD.spad" 1209920 1209937 1210956 1210961) (-825 "PFRPAC.spad" 1209069 1209079 1209910 1209915) (-824 "PFR.spad" 1205772 1205782 1208971 1209064) (-823 "PFOTOOLS.spad" 1205030 1205046 1205762 1205767) (-822 "PFOQ.spad" 1204400 1204418 1205020 1205025) (-821 "PFO.spad" 1203819 1203846 1204390 1204395) (-820 "PFECAT.spad" 1201529 1201537 1203745 1203814) (-819 "PFECAT.spad" 1199267 1199277 1201485 1201490) (-818 "PFBRU.spad" 1197155 1197167 1199257 1199262) (-817 "PFBR.spad" 1194715 1194738 1197145 1197150) (-816 "PF.spad" 1194289 1194301 1194520 1194613) (-815 "PERMGRP.spad" 1189059 1189069 1194279 1194284) (-814 "PERMCAT.spad" 1187720 1187730 1189039 1189054) (-813 "PERMAN.spad" 1186276 1186290 1187710 1187715) (-812 "PERM.spad" 1182086 1182096 1186109 1186124) (-811 "PENDTREE.spad" 1181500 1181510 1181780 1181785) (-810 "PDSPC.spad" 1180313 1180323 1181490 1181495) (-809 "PDSPC.spad" 1179124 1179136 1180303 1180308) (-808 "PDRING.spad" 1178966 1178976 1179104 1179119) (-807 "PDMOD.spad" 1178782 1178794 1178934 1178961) (-806 "PDECOMP.spad" 1178252 1178269 1178772 1178777) (-805 "PDDOM.spad" 1177690 1177703 1178242 1178247) (-804 "PDDOM.spad" 1177126 1177141 1177680 1177685) (-803 "PCOMP.spad" 1176979 1176992 1177116 1177121) (-802 "PBWLB.spad" 1175577 1175594 1176969 1176974) (-801 "PATTERN2.spad" 1175315 1175327 1175567 1175572) (-800 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1154956 1155824 1155829) (-781 "PAIR.spad" 1154022 1154035 1154591 1154596) (-780 "PADICRC.spad" 1151427 1151445 1152590 1152683) (-779 "PADICRAT.spad" 1149487 1149499 1149700 1149793) (-778 "PADICCT.spad" 1148036 1148048 1149413 1149482) (-777 "PADIC.spad" 1147739 1147751 1147962 1148031) (-776 "PADEPAC.spad" 1146428 1146447 1147729 1147734) (-775 "PADE.spad" 1145180 1145196 1146418 1146423) (-774 "OWP.spad" 1144428 1144458 1145038 1145105) (-773 "OVERSET.spad" 1144001 1144009 1144418 1144423) (-772 "OVAR.spad" 1143782 1143805 1143991 1143996) (-771 "OUTFORM.spad" 1133190 1133198 1143772 1143777) (-770 "OUTBFILE.spad" 1132624 1132632 1133180 1133185) (-769 "OUTBCON.spad" 1131694 1131702 1132614 1132619) (-768 "OUTBCON.spad" 1130762 1130772 1131684 1131689) (-767 "OUT.spad" 1129880 1129888 1130752 1130757) (-766 "OSI.spad" 1129355 1129363 1129870 1129875) (-765 "OSGROUP.spad" 1129273 1129281 1129345 1129350) (-764 "ORTHPOL.spad" 1127784 1127794 1129216 1129221) (-763 "OREUP.spad" 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T) (((-348 (-483))) . T)) ((((-483)) . T)) -((((-772)) . T)) -((((-772)) . T)) +((((-771)) . T)) +((((-771)) . T)) (((|#1| |#1| |#1|) . T)) (((|#1|) . T)) ((((-85)) . T)) ((((-85)) . T)) ((((-483) (-85)) . T)) ((((-483) (-85)) . T)) -((((-483) (-85)) . T) (((-1145 (-483)) $) . T)) +((((-483) (-85)) . T) (((-1144 (-483)) $) . T)) ((((-472)) . T)) ((((-85)) . T)) -((((-772)) . T)) +((((-771)) . T)) ((((-85)) . T)) ((((-85)) . T)) ((((-472)) . T)) -((((-772)) . T)) -((((-1089)) . T)) -((((-772)) . T)) +((((-771)) . T)) +((((-1088)) . T)) +((((-771)) . T)) ((($) . T)) -((((-772)) . T)) +((((-771)) . T)) ((($) . T) (((-483)) . T)) ((($) . T)) ((($ $) . T)) @@ -193,7 +193,7 @@ ((($) . T)) ((((-483)) . T) (($) . T)) (((|#1|) . T)) -((((-772)) . T)) +((((-771)) . T)) ((((-89 |#1|)) . T)) ((((-89 |#1|)) . T)) ((((-89 |#1|)) . T) (($) . T) (((-348 (-483))) . T)) @@ -204,7 +204,7 @@ ((((-89 |#1|)) . T) (((-348 (-483))) . T) (($) . T)) ((((-89 |#1|) (-89 |#1|)) . T) (((-348 (-483)) (-348 (-483))) . T) (($ $) . T)) ((((-89 |#1|)) . T)) -((((-1089) (-89 |#1|)) |has| (-89 |#1|) (-454 (-1089) (-89 |#1|))) (((-89 |#1|) (-89 |#1|)) |has| (-89 |#1|) (-260 (-89 |#1|)))) +((((-1088) (-89 |#1|)) |has| (-89 |#1|) (-454 (-1088) (-89 |#1|))) (((-89 |#1|) (-89 |#1|)) |has| (-89 |#1|) (-260 (-89 |#1|)))) ((((-89 |#1|)) |has| (-89 |#1|) (-260 (-89 |#1|)))) ((((-89 |#1|) $) |has| (-89 |#1|) (-241 (-89 |#1|) (-89 |#1|)))) ((((-89 |#1|)) . T)) @@ -217,63 +217,63 @@ ((((-89 |#1|)) . T)) (((|#1|) . T)) (((|#1|) . 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T)) -((((-772)) . T)) +((((-157)) . T) (((-771)) . T)) +((((-771)) . T)) ((((-117)) . T)) ((((-117)) . T)) ((((-117)) . T)) @@ -281,9 +281,9 @@ ((((-117)) . T)) ((((-117)) . T)) ((((-117)) . T)) -((((-583 (-117))) . T) (((-1072)) . T)) -((((-772)) . T)) -((((-772)) . T)) +((((-582 (-117))) . T) (((-1071)) . T)) +((((-771)) . T)) +((((-771)) . T)) (((|#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -293,26 +293,26 @@ (((|#2|) . T)) (((|#2|) . T) (((-483)) . T)) (((|#2|) . T) (($) . T)) -((((-772)) . T)) +((((-771)) . T)) (((|#2|) . T) (($) . T) (((-483)) . T)) -((((-1094)) . T)) -((((-772)) . T) (((-1094)) . T)) -((((-1094)) . T)) -((((-1094)) . T)) -((((-772)) . T) (((-1094)) . T)) -((((-1094)) . T)) -((((-772)) . T)) -((((-772)) . T)) -((((-1094)) . T)) -((((-772)) . T) (((-1094)) . T)) -((((-1094)) . T)) +((((-1093)) . T)) +((((-771)) . T) (((-1093)) . T)) +((((-1093)) . T)) +((((-1093)) . T)) +((((-771)) . T) (((-1093)) . T)) +((((-1093)) . T)) +((((-771)) . T)) +((((-771)) . 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T) ((|#1|) . T)) -((((-772)) . T)) -((((-1094)) . T)) -((((-772)) . T) (((-1094)) . T)) -((((-1094)) . T)) +((((-771)) . T)) +((((-1093)) . T)) +((((-771)) . T) (((-1093)) . T)) +((((-1093)) . T)) ((((-445)) . T)) -((((-772)) . T)) -((((-772)) . T)) -((((-772)) . T)) -((((-772)) . T)) -((((-583 |#1|)) . T)) -((((-772)) . T)) -((((-772)) . T)) -((((-917 10)) . T) (((-348 (-483))) . T) (((-772)) . T)) +((((-771)) . T)) +((((-771)) . T)) +((((-771)) . T)) +((((-771)) . T)) +((((-582 |#1|)) . T)) +((((-771)) . T)) +((((-771)) . T)) +((((-916 10)) . T) (((-348 (-483))) . T) (((-771)) . T)) ((((-483)) . T)) ((((-483)) . T)) ((($) . T)) @@ -403,25 +403,25 @@ ((((-483)) . T)) ((((-483)) . T)) ((((-483)) . T)) -((((-472)) . T) (((-800 (-483))) . T) (((-328)) . T) (((-179)) . T)) +((((-472)) . T) (((-799 (-483))) . T) (((-328)) . T) (((-179)) . T)) ((((-348 (-483))) . T) (((-483)) . T)) ((((-483)) . T) (($) . T) (((-348 (-483))) . T)) ((((-483)) . T)) -((((-1094)) . T)) -((((-772)) . 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T) (($) . T)) (((|#1|) . T) (((-348 (-483))) . T) (($) . T) (((-483)) . T)) @@ -959,7 +959,7 @@ ((((-348 (-483))) . T) (($) . T)) (((|#1|) . T) (((-348 (-483))) . T) (($) . T)) (((|#1|) . T) (((-348 (-483))) . T) (($) . T)) -((((-772)) . T)) +((((-771)) . T)) (((|#1|) . T) (((-348 (-483))) . T) (((-483)) . T) (($) . T)) (((|#1|) . T) (((-348 (-483))) . T) (($) . T)) (((|#1|) . T) (((-348 (-483))) . T) (($) . T) (((-483)) . T)) @@ -971,22 +971,22 @@ ((($) |has| |#1| (-318))) (|has| |#1| (-318)) (((|#1|) . T)) -((((-817 |#1|)) . T)) -((((-817 |#1|)) . T)) -((((-817 |#1|)) . T)) -((((-817 |#1|)) . T) (($) . T) (((-348 (-483))) . T)) -((((-817 |#1|)) . T) (($) . T) (((-348 (-483))) . T)) -((((-817 |#1|) (-817 |#1|)) . T) (($ $) . T) (((-348 (-483)) (-348 (-483))) . T)) +((((-816 |#1|)) . T)) +((((-816 |#1|)) . T)) +((((-816 |#1|)) . T)) +((((-816 |#1|)) . T) (($) . T) (((-348 (-483))) . T)) +((((-816 |#1|)) . T) (($) . T) (((-348 (-483))) . T)) +((((-816 |#1|) (-816 |#1|)) . T) (($ $) . 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T) (((-348 (-483))) |has| (-1158 |#2| |#3| |#4|) (-38 (-348 (-483)))) (((-483)) . T)) +((($) . T) (((-1158 |#2| |#3| |#4|)) |has| (-1158 |#2| |#3| |#4|) (-146)) (((-348 (-483))) |has| (-1158 |#2| |#3| |#4|) (-38 (-348 (-483))))) +((((-1158 |#2| |#3| |#4|)) . T)) +((((-1158 |#2| |#3| |#4|)) . T)) +((((-1158 |#2| |#3| |#4|) (-270 |#2| |#3| |#4|)) . T)) (|has| |#1| (-38 (-348 (-483)))) (|has| |#1| (-38 (-348 (-483)))) (|has| |#1| (-38 (-348 (-483)))) @@ -3883,8 +3866,8 @@ (|has| |#1| (-38 (-348 (-483)))) (|has| |#1| (-38 (-348 (-483)))) (|has| |#1| (-38 (-348 (-483)))) -(((|#1| (-694)) . T)) -(((|#1| (-694)) . T)) +(((|#1| (-693)) . T)) +(((|#1| (-693)) . T)) (|has| |#1| (-494)) (|has| |#1| (-494)) (OR (|has| |#1| (-146)) (|has| |#1| (-494))) @@ -3896,46 +3879,46 @@ ((($) OR (|has| |#1| (-146)) (|has| |#1| (-494))) ((|#1|) . T) (((-348 (-483))) |has| |#1| (-38 (-348 (-483))))) ((($ $) OR (|has| |#1| (-146)) (|has| |#1| (-494))) ((|#1| |#1|) . T) (((-348 (-483)) (-348 (-483))) |has| |#1| (-38 (-348 (-483))))) ((($) |has| |#1| (-494)) ((|#1|) |has| |#1| (-146)) (((-348 (-483))) |has| |#1| (-38 (-348 (-483))))) -(((|#1| (-694) (-994)) . T)) -((((-1089)) -12 (|has| |#1| (-809 (-1089))) (|has| |#1| (-15 * (|#1| (-694) |#1|))))) -((($ (-1175 |#2|)) . T) (($ (-1089)) -12 (|has| |#1| (-809 (-1089))) (|has| |#1| (-15 * (|#1| (-694) |#1|))))) -((((-1089)) -12 (|has| |#1| (-809 (-1089))) (|has| |#1| (-15 * (|#1| (-694) |#1|))))) -((((-694) |#1|) . T) (($ $) . T)) -(|has| |#1| (-15 * (|#1| (-694) |#1|))) -((($) |has| |#1| (-15 * (|#1| (-694) |#1|)))) -((((-772)) . T)) +(((|#1| (-693) (-993)) . T)) +((((-1088)) -12 (|has| |#1| (-808 (-1088))) (|has| |#1| (-15 * (|#1| (-693) |#1|))))) +((($ (-1174 |#2|)) . T) (($ (-1088)) -12 (|has| |#1| (-808 (-1088))) (|has| |#1| (-15 * (|#1| (-693) |#1|))))) +((((-1088)) -12 (|has| |#1| (-808 (-1088))) (|has| |#1| (-15 * (|#1| (-693) |#1|))))) +((((-693) |#1|) . T) (($ $) . T)) +(|has| |#1| (-15 * (|#1| (-693) |#1|))) +((($) |has| |#1| (-15 * (|#1| (-693) |#1|)))) +((((-771)) . T)) (((|#1|) . T) (((-348 (-483))) |has| |#1| (-38 (-348 (-483)))) (((-483)) . T) (($) . T)) (((|#1|) . T) (((-348 (-483))) |has| |#1| (-38 (-348 (-483)))) (($) . T)) ((($) |has| |#1| (-494)) ((|#1|) |has| |#1| (-146)) (((-348 (-483))) |has| |#1| (-38 (-348 (-483)))) (((-483)) . T)) -(|has| |#1| (-15 * (|#1| (-694) |#1|))) +(|has| |#1| (-15 * (|#1| (-693) |#1|))) (((|#1|) . T)) -((((-1089)) . T) (((-772)) . T)) +((((-1088)) . T) (((-771)) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-483) |#1|) . T)) ((((-483) |#1|) . T)) -((((-483) |#1|) . T) (((-1145 (-483)) $) . T)) -((((-472)) |has| |#1| (-553 (-472)))) -(((|#1|) . T)) -(OR (|has| |#1| (-756)) (|has| |#1| (-1013))) -(((|#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013)))) -(((|#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013)))) -((((-772)) OR (|has| |#1| (-552 (-772))) (|has| |#1| (-756)) (|has| |#1| (-1013)))) -(OR (|has| |#1| (-72)) (|has| |#1| (-756)) (|has| |#1| (-1013))) -(((|#1|) . T)) -(|has| |#1| (-756)) -(|has| |#1| (-756)) -(((|#1|) . T)) -(((|#1|) . T)) -((((-772)) . T)) -((((-772)) . T)) -((((-772)) . T)) -((((-1094)) . T)) -((((-772)) . T) (((-1094)) . T)) -((((-1094)) . T)) -((((-1094)) . T)) -((((-772)) . T) (((-1094)) . T)) -((((-1094)) . T)) +((((-483) |#1|) . T) (((-1144 (-483)) $) . T)) +((((-472)) |has| |#1| (-552 (-472)))) +(((|#1|) . T)) +(OR (|has| |#1| (-755)) (|has| |#1| (-1012))) +(((|#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1012)))) +(((|#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1012)))) +((((-771)) OR (|has| |#1| (-551 (-771))) (|has| |#1| (-755)) (|has| |#1| (-1012)))) +(OR (|has| |#1| (-72)) (|has| |#1| (-755)) (|has| |#1| (-1012))) +(((|#1|) . T)) +(|has| |#1| (-755)) +(|has| |#1| (-755)) +(((|#1|) . T)) +(((|#1|) . T)) +((((-771)) . T)) +((((-771)) . T)) +((((-771)) . T)) +((((-1093)) . T)) +((((-771)) . T) (((-1093)) . T)) +((((-1093)) . T)) +((((-1093)) . T)) +((((-771)) . T) (((-1093)) . T)) +((((-1093)) . T)) (((|#1|) |has| |#1| (-146))) (((|#1|) |has| |#1| (-146))) (((|#1|) |has| |#1| (-146))) @@ -3945,15 +3928,15 @@ (((|#4|) . T)) (((|#1|) |has| |#1| (-146)) ((|#4|) . T) (((-483)) . T)) (((|#1|) |has| |#1| (-146)) (($) . T)) -(((|#4|) . T) (((-772)) . T)) +(((|#4|) . T) (((-771)) . T)) (((|#1|) |has| |#1| (-146)) (($) . T) (((-483)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-472)) |has| |#4| (-553 (-472)))) +((((-472)) |has| |#4| (-552 (-472)))) (((|#4|) . T)) -(((|#4| |#4|) -12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1013)))) -(((|#4|) -12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1013)))) +(((|#4| |#4|) -12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1012)))) +(((|#4|) -12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1012)))) (((|#4|) . T)) -((((-772)) . T) (((-583 |#4|)) . T)) +((((-771)) . T) (((-582 |#4|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) (((|#2|) |has| |#2| (-146))) @@ -3962,15 +3945,15 @@ (((|#2| |#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) -((((-772)) . T)) +((((-771)) . T)) ((($) . T) (((-483)) . T) ((|#2|) . T)) ((($) . T) ((|#2|) . T)) (((|#2|) |has| |#2| (-146))) (((|#2|) |has| |#2| (-146))) -((((-739 |#1|)) . T)) -(((|#2|) . T) (((-483)) . T) (((-739 |#1|)) . T)) -(((|#2| (-739 |#1|)) . T)) -(((|#2| (-803 |#1|)) . T)) +((((-738 |#1|)) . T)) +(((|#2|) . T) (((-483)) . T) (((-738 |#1|)) . T)) +(((|#2| (-738 |#1|)) . T)) +(((|#2| (-802 |#1|)) . T)) (((|#1| |#2|) . T)) (((|#2|) |has| |#2| (-146))) (((|#2| |#2|) . T)) @@ -3980,12 +3963,12 @@ (((|#2|) |has| |#2| (-146))) (((|#2|) . T)) (((|#2|) . T) (($) . T)) -((((-772)) . T)) +((((-771)) . T)) (((|#2|) . T) (($) . T) (((-483)) . T)) -((((-803 |#1|)) . T) ((|#2|) . T) (((-483)) . T) (((-739 |#1|)) . T)) -((((-803 |#1|)) . T) (((-739 |#1|)) . T)) +((((-802 |#1|)) . T) ((|#2|) . T) (((-483)) . T) (((-738 |#1|)) . T)) +((((-802 |#1|)) . T) (((-738 |#1|)) . T)) (((|#1| |#2|) . T)) -((((-1089) |#1|) . T)) +((((-1088) |#1|) . T)) (((|#1|) |has| |#1| (-146))) (((|#1| |#1|) . T)) (((|#1|) . T)) @@ -3994,11 +3977,11 @@ (((|#1|) |has| |#1| (-146))) (((|#1|) . T)) (((|#1|) . T) (($) . T)) -((((-772)) . T)) +((((-771)) . T)) (((|#1|) . T) (($) . T) (((-483)) . T)) -(((|#1|) . T) (((-483)) . T) (((-739 (-1089))) . T)) -((((-739 (-1089))) . T)) -((((-1089) |#1|) . T)) +(((|#1|) . T) (((-483)) . T) (((-738 (-1088))) . T)) +((((-738 (-1088))) . T)) +((((-1088) |#1|) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-146))) @@ -4010,7 +3993,7 @@ (((|#1|) . T)) (((|#2|) . T) ((|#1|) . T) (((-483)) . T)) (((|#1|) . T) (($) . T)) -((((-772)) . T)) +((((-771)) . T)) (((|#1|) . T) (($) . T) (((-483)) . T)) (((|#1| |#2|) . T)) (((|#2|) |has| |#2| (-146))) @@ -4021,20 +4004,20 @@ (((|#2|) |has| |#2| (-146))) (((|#2|) . T)) (((|#2|) . T) (($) . T)) -((((-772)) . T)) +((((-771)) . T)) (((|#2|) . T) (($) . T) (((-483)) . T)) -(((|#2|) . T) (((-483)) . T) (((-739 |#1|)) . T)) -((((-739 |#1|)) . T)) +(((|#2|) . T) (((-483)) . T) (((-738 |#1|)) . T)) +((((-738 |#1|)) . T)) (((|#1| |#2|) . T)) -((((-884)) . T)) -((((-884)) . T)) -((((-884)) . T) (((-772)) . T)) +((((-883)) . T)) +((((-883)) . T)) +((((-883)) . T) (((-771)) . T)) ((((-483)) . T)) ((($ $) . T)) ((($) . T)) ((($) . T)) -((((-772)) . T)) +((((-771)) . T)) ((((-483)) . T) (($) . T)) ((($) . T)) ((((-483)) . 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198028) ((-1200 . -23) T) ((-1200 . -1013) T) ((-1200 . -552) 198010) ((-1200 . -1128) T) ((-1200 . -13) T) ((-1200 . -72) T) ((-1200 . -25) T) ((-1200 . -104) T) ((-1200 . -590) 197984) ((-1200 . -1193) 197968) ((-1200 . -654) 197938) ((-1200 . -582) 197908) ((-1200 . -968) 197892) ((-1200 . -963) 197876) ((-1200 . -82) 197855) ((-1200 . -38) 197825) ((-1200 . -1198) 197801) ((-1199 . -1201) 197780) ((-1199 . -950) 197737) ((-1199 . -555) 197666) ((-1199 . -961) T) ((-1199 . -663) T) ((-1199 . -1060) T) ((-1199 . -1025) T) ((-1199 . -970) T) ((-1199 . -21) T) ((-1199 . -588) 197625) ((-1199 . -23) T) ((-1199 . -1013) T) ((-1199 . -552) 197607) ((-1199 . -1128) T) ((-1199 . -13) T) ((-1199 . -72) T) ((-1199 . -25) T) ((-1199 . -104) T) ((-1199 . -590) 197581) ((-1199 . -1193) 197565) ((-1199 . -654) 197535) ((-1199 . -582) 197505) ((-1199 . -968) 197489) ((-1199 . -963) 197473) ((-1199 . -82) 197452) ((-1199 . -38) 197422) ((-1199 . -1198) 197401) ((-1199 . -333) 197373) ((-1194 . 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-1177) 196086) ((-1178 . -322) 196070) ((-1178 . -759) 196049) ((-1178 . -756) 196028) ((-1178 . -124) 196012) ((-1178 . -34) T) ((-1178 . -13) T) ((-1178 . -1128) T) ((-1178 . -72) 195946) ((-1178 . -552) 195861) ((-1178 . -260) 195799) ((-1178 . -454) 195732) ((-1178 . -1013) 195685) ((-1178 . -427) 195669) ((-1178 . -553) 195630) ((-1178 . -241) 195582) ((-1178 . -538) 195559) ((-1178 . -243) 195536) ((-1178 . -593) 195520) ((-1178 . -19) 195504) ((-1175 . -1013) T) ((-1175 . -552) 195470) ((-1175 . -1128) T) ((-1175 . -13) T) ((-1175 . -72) T) ((-1168 . -1171) 195454) ((-1168 . -190) 195413) ((-1168 . -555) 195295) ((-1168 . -590) 195220) ((-1168 . -588) 195130) ((-1168 . -104) T) ((-1168 . -25) T) ((-1168 . -72) T) ((-1168 . -552) 195112) ((-1168 . -1013) T) ((-1168 . -23) T) ((-1168 . -21) T) ((-1168 . -970) T) ((-1168 . -1025) T) ((-1168 . -1060) T) ((-1168 . -663) T) ((-1168 . -961) T) ((-1168 . -186) 195065) ((-1168 . -13) T) ((-1168 . -1128) T) ((-1168 . -189) 195024) ((-1168 . -241) 194989) ((-1168 . -809) 194902) ((-1168 . -806) 194790) ((-1168 . -811) 194703) ((-1168 . -886) 194673) ((-1168 . -38) 194570) ((-1168 . -82) 194435) ((-1168 . -963) 194321) ((-1168 . -968) 194207) ((-1168 . -582) 194104) ((-1168 . -654) 194001) ((-1168 . -118) 193980) ((-1168 . -120) 193959) ((-1168 . -146) 193913) ((-1168 . -494) 193892) ((-1168 . -246) 193871) ((-1168 . -47) 193848) ((-1168 . -1157) 193825) ((-1168 . -35) 193791) ((-1168 . -66) 193757) ((-1168 . -239) 193723) ((-1168 . -431) 193689) ((-1168 . -1117) 193655) ((-1168 . -1114) 193621) ((-1168 . -915) 193587) ((-1165 . -277) 193531) ((-1165 . -950) 193497) ((-1165 . -353) 193463) ((-1165 . -38) 193320) ((-1165 . -555) 193194) ((-1165 . -590) 193083) ((-1165 . -588) 192957) ((-1165 . -970) T) ((-1165 . -1025) T) ((-1165 . -1060) T) ((-1165 . -663) T) ((-1165 . -961) T) ((-1165 . -82) 192807) ((-1165 . -963) 192696) ((-1165 . -968) 192585) ((-1165 . -21) T) ((-1165 . -23) T) ((-1165 . -1013) T) ((-1165 . -552) 192567) ((-1165 . -1128) T) ((-1165 . -13) T) ((-1165 . -72) T) ((-1165 . -25) T) ((-1165 . -104) T) ((-1165 . -582) 192424) ((-1165 . -654) 192281) ((-1165 . -118) 192242) ((-1165 . -120) 192203) ((-1165 . -146) T) ((-1165 . -494) T) ((-1165 . -246) T) ((-1165 . -47) 192147) ((-1164 . -1163) 192126) ((-1164 . -312) 192105) ((-1164 . -1133) 192084) ((-1164 . -832) 192063) ((-1164 . -494) 192017) ((-1164 . -146) 191951) ((-1164 . -555) 191770) ((-1164 . -654) 191617) ((-1164 . -582) 191464) ((-1164 . -38) 191311) ((-1164 . -390) 191290) ((-1164 . -258) 191269) ((-1164 . -590) 191169) ((-1164 . -588) 191054) ((-1164 . -970) T) ((-1164 . -1025) T) ((-1164 . -1060) T) ((-1164 . -663) T) ((-1164 . -961) T) ((-1164 . -82) 190874) ((-1164 . -963) 190715) ((-1164 . -968) 190556) ((-1164 . -21) T) ((-1164 . -23) T) ((-1164 . -1013) T) ((-1164 . -552) 190538) ((-1164 . -1128) T) ((-1164 . -13) T) ((-1164 . -72) T) ((-1164 . -25) T) ((-1164 . -104) T) ((-1164 . -246) 190492) ((-1164 . -201) 190471) ((-1164 . -915) 190437) ((-1164 . -1114) 190403) ((-1164 . -1117) 190369) ((-1164 . -431) 190335) ((-1164 . -239) 190301) ((-1164 . -66) 190267) ((-1164 . -35) 190233) ((-1164 . -1157) 190203) ((-1164 . -47) 190173) ((-1164 . -120) 190152) ((-1164 . -118) 190131) ((-1164 . -886) 190094) ((-1164 . -811) 190000) ((-1164 . -806) 189904) ((-1164 . -809) 189810) ((-1164 . -241) 189768) ((-1164 . -189) 189720) ((-1164 . -186) 189666) ((-1164 . -190) 189618) ((-1164 . -1161) 189602) ((-1164 . -950) 189586) ((-1159 . -1163) 189547) ((-1159 . -312) 189526) ((-1159 . -1133) 189505) ((-1159 . -832) 189484) ((-1159 . -494) 189438) ((-1159 . -146) 189372) ((-1159 . -555) 189121) ((-1159 . -654) 188968) ((-1159 . -582) 188815) ((-1159 . -38) 188662) ((-1159 . -390) 188641) ((-1159 . -258) 188620) ((-1159 . -590) 188520) ((-1159 . -588) 188405) ((-1159 . -970) T) ((-1159 . -1025) T) ((-1159 . -1060) T) ((-1159 . -663) T) ((-1159 . -961) T) ((-1159 . -82) 188225) ((-1159 . -963) 188066) ((-1159 . -968) 187907) ((-1159 . -21) T) ((-1159 . -23) T) ((-1159 . -1013) T) ((-1159 . -552) 187889) ((-1159 . -1128) T) ((-1159 . -13) T) ((-1159 . -72) T) ((-1159 . -25) T) ((-1159 . -104) T) ((-1159 . -246) 187843) ((-1159 . -201) 187822) ((-1159 . -915) 187788) ((-1159 . -1114) 187754) ((-1159 . -1117) 187720) ((-1159 . -431) 187686) ((-1159 . -239) 187652) ((-1159 . -66) 187618) ((-1159 . -35) 187584) ((-1159 . -1157) 187554) ((-1159 . -47) 187524) ((-1159 . -120) 187503) ((-1159 . -118) 187482) ((-1159 . -886) 187445) ((-1159 . -811) 187351) ((-1159 . -806) 187232) ((-1159 . -809) 187138) ((-1159 . -241) 187096) ((-1159 . -189) 187048) ((-1159 . -186) 186994) ((-1159 . -190) 186946) ((-1159 . -1161) 186930) ((-1159 . -950) 186865) ((-1147 . -1154) 186849) ((-1147 . -1065) 186827) ((-1147 . -553) NIL) ((-1147 . -260) 186814) ((-1147 . -454) 186762) ((-1147 . -277) 186739) ((-1147 . -950) 186622) ((-1147 . -353) 186606) ((-1147 . -38) 186438) ((-1147 . -82) 186243) ((-1147 . -963) 186069) ((-1147 . -968) 185895) ((-1147 . -588) 185805) ((-1147 . -590) 185694) ((-1147 . -582) 185526) ((-1147 . -654) 185358) ((-1147 . -555) 185114) ((-1147 . -118) 185093) ((-1147 . -120) 185072) ((-1147 . -47) 185049) ((-1147 . -327) 185033) ((-1147 . -580) 184981) ((-1147 . -809) 184925) ((-1147 . -806) 184832) ((-1147 . -811) 184743) ((-1147 . -796) NIL) ((-1147 . -821) 184722) ((-1147 . -1133) 184701) ((-1147 . -861) 184671) ((-1147 . -832) 184650) ((-1147 . -494) 184564) ((-1147 . -246) 184478) ((-1147 . -146) 184372) ((-1147 . -390) 184306) ((-1147 . -258) 184285) ((-1147 . -241) 184212) ((-1147 . -190) T) ((-1147 . -104) T) ((-1147 . -25) T) ((-1147 . -72) T) ((-1147 . -552) 184194) ((-1147 . -1013) T) ((-1147 . -23) T) ((-1147 . -21) T) ((-1147 . -970) T) ((-1147 . -1025) T) ((-1147 . -1060) T) ((-1147 . -663) T) ((-1147 . -961) T) ((-1147 . -186) 184181) ((-1147 . -13) T) ((-1147 . -1128) T) ((-1147 . -189) T) ((-1147 . -225) 184165) ((-1147 . -184) 184149) ((-1145 . -1006) 184133) ((-1145 . -557) 184117) ((-1145 . -1013) 184095) ((-1145 . -552) 184062) ((-1145 . -1128) 184040) ((-1145 . -13) 184018) ((-1145 . -72) 183996) ((-1145 . -1007) 183953) ((-1143 . -1142) 183932) ((-1143 . -915) 183898) ((-1143 . -1114) 183864) ((-1143 . -1117) 183830) ((-1143 . -431) 183796) ((-1143 . -239) 183762) ((-1143 . -66) 183728) ((-1143 . -35) 183694) ((-1143 . -1157) 183671) ((-1143 . -47) 183648) ((-1143 . -555) 183403) ((-1143 . -654) 183223) ((-1143 . -582) 183043) ((-1143 . -590) 182854) ((-1143 . -588) 182712) ((-1143 . -968) 182526) ((-1143 . -963) 182340) ((-1143 . -82) 182128) ((-1143 . -38) 181948) ((-1143 . -886) 181918) ((-1143 . -241) 181818) ((-1143 . -1140) 181802) ((-1143 . -970) T) ((-1143 . -1025) T) ((-1143 . -1060) T) ((-1143 . -663) T) ((-1143 . -961) T) ((-1143 . -21) T) ((-1143 . -23) T) ((-1143 . -1013) T) ((-1143 . -552) 181784) ((-1143 . -1128) T) ((-1143 . -13) T) ((-1143 . -72) T) ((-1143 . -25) T) ((-1143 . -104) T) ((-1143 . -118) 181712) ((-1143 . -120) 181594) ((-1143 . -553) 181267) ((-1143 . -184) 181237) ((-1143 . -809) 181091) ((-1143 . -811) 180891) ((-1143 . -806) 180689) ((-1143 . -225) 180659) ((-1143 . -189) 180521) ((-1143 . -186) 180377) ((-1143 . -190) 180285) ((-1143 . -312) 180264) ((-1143 . -1133) 180243) ((-1143 . -832) 180222) ((-1143 . -494) 180176) ((-1143 . -146) 180110) ((-1143 . -390) 180089) ((-1143 . -258) 180068) ((-1143 . -246) 180022) ((-1143 . -201) 180001) ((-1143 . -288) 179971) ((-1143 . -454) 179831) ((-1143 . -260) 179770) ((-1143 . -327) 179740) ((-1143 . -580) 179648) ((-1143 . -341) 179618) ((-1143 . -796) 179491) ((-1143 . -740) 179444) ((-1143 . -714) 179397) ((-1143 . -716) 179350) ((-1143 . -756) 179252) ((-1143 . -759) 179154) ((-1143 . -718) 179107) ((-1143 . -721) 179060) ((-1143 . -755) 179013) ((-1143 . -794) 178983) ((-1143 . -821) 178936) ((-1143 . -933) 178889) ((-1143 . -950) 178678) ((-1143 . -1065) 178630) ((-1143 . -904) 178600) ((-1138 . -1142) 178561) ((-1138 . -915) 178527) ((-1138 . -1114) 178493) ((-1138 . -1117) 178459) ((-1138 . -431) 178425) ((-1138 . -239) 178391) ((-1138 . -66) 178357) ((-1138 . -35) 178323) ((-1138 . -1157) 178300) ((-1138 . -47) 178277) ((-1138 . -555) 178078) ((-1138 . -654) 177880) ((-1138 . -582) 177682) ((-1138 . -590) 177537) ((-1138 . -588) 177377) ((-1138 . -968) 177173) ((-1138 . -963) 176969) ((-1138 . -82) 176721) ((-1138 . -38) 176523) ((-1138 . -886) 176493) ((-1138 . -241) 176321) ((-1138 . -1140) 176305) ((-1138 . -970) T) ((-1138 . -1025) T) ((-1138 . -1060) T) ((-1138 . -663) T) ((-1138 . -961) T) ((-1138 . -21) T) ((-1138 . -23) T) ((-1138 . -1013) T) ((-1138 . -552) 176287) ((-1138 . -1128) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -25) T) ((-1138 . -104) T) ((-1138 . -118) 176197) ((-1138 . -120) 176107) ((-1138 . -553) NIL) ((-1138 . -184) 176059) ((-1138 . -809) 175895) ((-1138 . -811) 175659) ((-1138 . -806) 175398) ((-1138 . -225) 175350) ((-1138 . -189) 175176) ((-1138 . -186) 174996) ((-1138 . -190) 174886) ((-1138 . -312) 174865) ((-1138 . -1133) 174844) ((-1138 . -832) 174823) ((-1138 . -494) 174777) ((-1138 . -146) 174711) ((-1138 . -390) 174690) ((-1138 . -258) 174669) ((-1138 . -246) 174623) ((-1138 . -201) 174602) ((-1138 . -288) 174554) ((-1138 . -454) 174288) ((-1138 . -260) 174173) ((-1138 . -327) 174125) ((-1138 . -580) 174077) ((-1138 . -341) 174029) ((-1138 . -796) NIL) ((-1138 . -740) NIL) ((-1138 . -714) NIL) ((-1138 . -716) NIL) ((-1138 . -756) NIL) ((-1138 . -759) NIL) ((-1138 . -718) NIL) ((-1138 . -721) NIL) ((-1138 . -755) NIL) ((-1138 . -794) 173981) ((-1138 . -821) NIL) ((-1138 . -933) NIL) ((-1138 . -950) 173947) ((-1138 . -1065) NIL) ((-1138 . -904) 173899) ((-1137 . -752) T) ((-1137 . -759) T) ((-1137 . -756) T) ((-1137 . -1013) T) ((-1137 . -552) 173881) ((-1137 . -1128) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -318) T) ((-1137 . -604) T) ((-1136 . -752) T) ((-1136 . -759) T) ((-1136 . -756) T) ((-1136 . -1013) T) ((-1136 . -552) 173863) ((-1136 . -1128) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -318) T) ((-1136 . -604) T) ((-1135 . -752) T) ((-1135 . -759) T) ((-1135 . -756) T) ((-1135 . -1013) T) ((-1135 . -552) 173845) ((-1135 . -1128) T) ((-1135 . -13) T) ((-1135 . -72) T) ((-1135 . -318) T) ((-1135 . -604) T) ((-1134 . -752) T) ((-1134 . -759) T) ((-1134 . -756) T) ((-1134 . -1013) T) ((-1134 . -552) 173827) ((-1134 . -1128) T) ((-1134 . -13) T) ((-1134 . -72) T) ((-1134 . -318) T) ((-1134 . -604) T) ((-1129 . -995) T) ((-1129 . -428) 173808) ((-1129 . -552) 173774) ((-1129 . -555) 173755) ((-1129 . -1013) T) ((-1129 . -1128) T) ((-1129 . -13) T) ((-1129 . -72) T) ((-1129 . -64) T) ((-1126 . -428) 173732) ((-1126 . -552) 173673) ((-1126 . -555) 173650) ((-1126 . -1013) 173628) ((-1126 . -1128) 173606) ((-1126 . -13) 173584) ((-1126 . -72) 173562) ((-1121 . -679) 173538) ((-1121 . -35) 173504) ((-1121 . -66) 173470) ((-1121 . -239) 173436) ((-1121 . -431) 173402) ((-1121 . -1117) 173368) ((-1121 . -1114) 173334) ((-1121 . -915) 173300) ((-1121 . -47) 173269) ((-1121 . -38) 173166) ((-1121 . -582) 173063) ((-1121 . -654) 172960) ((-1121 . -555) 172842) ((-1121 . -246) 172821) ((-1121 . -494) 172800) ((-1121 . -82) 172665) ((-1121 . -963) 172551) ((-1121 . -968) 172437) ((-1121 . -146) 172391) ((-1121 . -120) 172370) ((-1121 . -118) 172349) ((-1121 . -590) 172274) ((-1121 . -588) 172184) ((-1121 . -886) 172145) ((-1121 . -811) 172126) ((-1121 . -1128) T) ((-1121 . -13) T) ((-1121 . -806) 172105) ((-1121 . -961) T) ((-1121 . -663) T) ((-1121 . -1060) T) ((-1121 . -1025) T) ((-1121 . -970) T) ((-1121 . -21) T) ((-1121 . -23) T) ((-1121 . -1013) T) ((-1121 . -552) 172087) ((-1121 . -72) T) ((-1121 . -25) T) ((-1121 . -104) T) ((-1121 . -809) 172068) ((-1121 . -454) 172035) ((-1121 . -260) 172022) ((-1115 . -923) 172006) ((-1115 . -34) T) ((-1115 . -13) T) ((-1115 . -1128) T) ((-1115 . -72) 171960) ((-1115 . -552) 171895) ((-1115 . -260) 171833) ((-1115 . -454) 171766) ((-1115 . -1013) 171744) ((-1115 . -427) 171728) ((-1110 . -314) 171702) ((-1110 . -72) T) ((-1110 . -13) T) ((-1110 . -1128) T) ((-1110 . -552) 171684) ((-1110 . -1013) T) ((-1108 . -1013) T) ((-1108 . -552) 171666) ((-1108 . -1128) T) ((-1108 . -13) T) ((-1108 . -72) T) ((-1108 . -555) 171648) ((-1103 . -747) 171632) ((-1103 . -72) T) ((-1103 . -13) T) ((-1103 . -1128) T) ((-1103 . -552) 171614) ((-1103 . -1013) T) ((-1101 . -1106) 171593) ((-1101 . -183) 171541) ((-1101 . -76) 171489) ((-1101 . -260) 171287) ((-1101 . -454) 171039) ((-1101 . -427) 170974) ((-1101 . -124) 170922) ((-1101 . -553) NIL) ((-1101 . -193) 170870) ((-1101 . -549) 170849) ((-1101 . -243) 170828) ((-1101 . -1128) T) ((-1101 . -13) T) ((-1101 . -241) 170807) ((-1101 . -1013) T) ((-1101 . -552) 170789) ((-1101 . -72) T) ((-1101 . -34) T) ((-1101 . -538) 170768) ((-1097 . -1013) T) ((-1097 . -552) 170750) ((-1097 . -1128) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1096 . -752) T) ((-1096 . -759) T) ((-1096 . -756) T) ((-1096 . -1013) T) ((-1096 . -552) 170732) ((-1096 . -1128) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -318) T) ((-1096 . -604) T) ((-1095 . -752) T) ((-1095 . -759) T) ((-1095 . -756) T) ((-1095 . -1013) T) ((-1095 . -552) 170714) ((-1095 . -1128) T) ((-1095 . -13) T) ((-1095 . -72) T) ((-1095 . -318) T) ((-1094 . -1174) T) ((-1094 . -1013) T) ((-1094 . -552) 170681) ((-1094 . -1128) T) ((-1094 . -13) T) ((-1094 . -72) T) ((-1094 . -950) 170617) ((-1094 . -555) 170553) ((-1093 . -552) 170535) ((-1092 . -552) 170517) ((-1091 . -277) 170494) ((-1091 . -950) 170392) ((-1091 . -353) 170376) ((-1091 . -38) 170273) ((-1091 . -555) 170130) ((-1091 . -590) 170055) ((-1091 . -588) 169965) ((-1091 . -970) T) ((-1091 . -1025) T) ((-1091 . -1060) T) ((-1091 . -663) T) ((-1091 . -961) T) ((-1091 . -82) 169830) ((-1091 . -963) 169716) ((-1091 . -968) 169602) ((-1091 . -21) T) ((-1091 . -23) T) ((-1091 . -1013) T) ((-1091 . -552) 169584) ((-1091 . -1128) T) ((-1091 . -13) T) ((-1091 . -72) T) ((-1091 . -25) T) ((-1091 . -104) T) ((-1091 . -582) 169481) ((-1091 . -654) 169378) ((-1091 . -118) 169357) ((-1091 . -120) 169336) ((-1091 . -146) 169290) ((-1091 . -494) 169269) ((-1091 . -246) 169248) ((-1091 . -47) 169225) ((-1089 . -756) T) ((-1089 . -552) 169207) ((-1089 . -1013) T) ((-1089 . -72) T) ((-1089 . -13) T) ((-1089 . -1128) T) ((-1089 . -759) T) ((-1089 . -553) 169129) ((-1089 . -555) 169095) ((-1089 . -950) 169077) ((-1089 . -796) 169044) ((-1088 . -1171) 169028) ((-1088 . -190) 168987) ((-1088 . -555) 168869) ((-1088 . -590) 168794) ((-1088 . -588) 168704) ((-1088 . -104) T) ((-1088 . -25) T) ((-1088 . -72) T) ((-1088 . -552) 168686) ((-1088 . -1013) T) ((-1088 . -23) T) ((-1088 . -21) T) ((-1088 . -970) T) ((-1088 . -1025) T) ((-1088 . -1060) T) ((-1088 . -663) T) ((-1088 . -961) T) ((-1088 . -186) 168639) ((-1088 . -13) T) ((-1088 . -1128) T) ((-1088 . -189) 168598) ((-1088 . -241) 168563) ((-1088 . -809) 168476) ((-1088 . -806) 168364) ((-1088 . -811) 168277) ((-1088 . -886) 168247) ((-1088 . -38) 168144) ((-1088 . -82) 168009) ((-1088 . -963) 167895) ((-1088 . -968) 167781) ((-1088 . -582) 167678) ((-1088 . -654) 167575) ((-1088 . -118) 167554) ((-1088 . -120) 167533) ((-1088 . -146) 167487) ((-1088 . -494) 167466) ((-1088 . -246) 167445) ((-1088 . -47) 167422) ((-1088 . -1157) 167399) ((-1088 . -35) 167365) ((-1088 . -66) 167331) ((-1088 . -239) 167297) ((-1088 . -431) 167263) ((-1088 . -1117) 167229) ((-1088 . -1114) 167195) ((-1088 . -915) 167161) ((-1087 . -1163) 167122) ((-1087 . -312) 167101) ((-1087 . -1133) 167080) ((-1087 . -832) 167059) ((-1087 . -494) 167013) ((-1087 . -146) 166947) ((-1087 . -555) 166696) ((-1087 . -654) 166543) ((-1087 . -582) 166390) ((-1087 . -38) 166237) ((-1087 . -390) 166216) ((-1087 . -258) 166195) ((-1087 . -590) 166095) ((-1087 . -588) 165980) ((-1087 . -970) T) ((-1087 . -1025) T) ((-1087 . -1060) T) ((-1087 . -663) T) ((-1087 . -961) T) ((-1087 . -82) 165800) ((-1087 . -963) 165641) ((-1087 . -968) 165482) ((-1087 . -21) T) ((-1087 . -23) T) ((-1087 . -1013) T) ((-1087 . -552) 165464) ((-1087 . -1128) T) ((-1087 . -13) T) ((-1087 . -72) T) ((-1087 . -25) T) ((-1087 . -104) T) ((-1087 . -246) 165418) ((-1087 . -201) 165397) ((-1087 . -915) 165363) ((-1087 . -1114) 165329) ((-1087 . -1117) 165295) ((-1087 . -431) 165261) ((-1087 . -239) 165227) ((-1087 . -66) 165193) ((-1087 . -35) 165159) ((-1087 . -1157) 165129) ((-1087 . -47) 165099) ((-1087 . -120) 165078) ((-1087 . -118) 165057) ((-1087 . -886) 165020) ((-1087 . -811) 164926) ((-1087 . -806) 164807) ((-1087 . -809) 164713) ((-1087 . -241) 164671) ((-1087 . -189) 164623) ((-1087 . -186) 164569) ((-1087 . -190) 164521) ((-1087 . -1161) 164505) ((-1087 . -950) 164440) ((-1084 . -1154) 164424) ((-1084 . -1065) 164402) ((-1084 . -553) NIL) ((-1084 . -260) 164389) ((-1084 . -454) 164337) ((-1084 . -277) 164314) ((-1084 . -950) 164197) ((-1084 . -353) 164181) ((-1084 . -38) 164013) ((-1084 . -82) 163818) ((-1084 . -963) 163644) ((-1084 . -968) 163470) ((-1084 . -588) 163380) ((-1084 . -590) 163269) ((-1084 . -582) 163101) ((-1084 . -654) 162933) ((-1084 . -555) 162710) ((-1084 . -118) 162689) ((-1084 . -120) 162668) ((-1084 . -47) 162645) ((-1084 . -327) 162629) ((-1084 . -580) 162577) ((-1084 . -809) 162521) ((-1084 . -806) 162428) ((-1084 . -811) 162339) ((-1084 . -796) NIL) ((-1084 . -821) 162318) ((-1084 . -1133) 162297) ((-1084 . -861) 162267) ((-1084 . -832) 162246) ((-1084 . -494) 162160) ((-1084 . -246) 162074) ((-1084 . -146) 161968) ((-1084 . -390) 161902) ((-1084 . -258) 161881) ((-1084 . -241) 161808) ((-1084 . -190) T) ((-1084 . -104) T) ((-1084 . -25) T) ((-1084 . -72) T) ((-1084 . -552) 161790) ((-1084 . -1013) T) ((-1084 . -23) T) ((-1084 . -21) T) ((-1084 . -970) T) ((-1084 . -1025) T) ((-1084 . -1060) T) ((-1084 . -663) T) ((-1084 . -961) T) ((-1084 . -186) 161777) ((-1084 . -13) T) ((-1084 . -1128) T) ((-1084 . -189) T) ((-1084 . -225) 161761) ((-1084 . -184) 161745) ((-1081 . -1142) 161706) ((-1081 . -915) 161672) ((-1081 . -1114) 161638) ((-1081 . -1117) 161604) ((-1081 . -431) 161570) ((-1081 . -239) 161536) ((-1081 . -66) 161502) ((-1081 . -35) 161468) ((-1081 . -1157) 161445) ((-1081 . -47) 161422) ((-1081 . -555) 161223) ((-1081 . -654) 161025) ((-1081 . -582) 160827) ((-1081 . -590) 160682) ((-1081 . -588) 160522) ((-1081 . -968) 160318) ((-1081 . -963) 160114) ((-1081 . -82) 159866) ((-1081 . -38) 159668) ((-1081 . -886) 159638) ((-1081 . -241) 159466) ((-1081 . -1140) 159450) ((-1081 . -970) T) ((-1081 . -1025) T) ((-1081 . -1060) T) ((-1081 . -663) T) ((-1081 . -961) T) ((-1081 . -21) T) ((-1081 . -23) T) ((-1081 . -1013) T) ((-1081 . -552) 159432) ((-1081 . -1128) T) ((-1081 . -13) T) ((-1081 . -72) T) ((-1081 . -25) T) ((-1081 . -104) T) ((-1081 . -118) 159342) ((-1081 . -120) 159252) ((-1081 . -553) NIL) ((-1081 . -184) 159204) ((-1081 . -809) 159040) ((-1081 . -811) 158804) ((-1081 . -806) 158543) ((-1081 . -225) 158495) ((-1081 . -189) 158321) ((-1081 . -186) 158141) ((-1081 . -190) 158031) ((-1081 . -312) 158010) ((-1081 . -1133) 157989) ((-1081 . -832) 157968) ((-1081 . -494) 157922) ((-1081 . -146) 157856) ((-1081 . -390) 157835) ((-1081 . -258) 157814) ((-1081 . -246) 157768) ((-1081 . -201) 157747) ((-1081 . -288) 157699) ((-1081 . -454) 157433) ((-1081 . -260) 157318) ((-1081 . -327) 157270) ((-1081 . -580) 157222) ((-1081 . -341) 157174) ((-1081 . -796) NIL) ((-1081 . -740) NIL) ((-1081 . -714) NIL) ((-1081 . -716) NIL) ((-1081 . -756) NIL) ((-1081 . -759) NIL) ((-1081 . -718) NIL) ((-1081 . -721) NIL) ((-1081 . -755) NIL) ((-1081 . -794) 157126) ((-1081 . -821) NIL) ((-1081 . -933) NIL) ((-1081 . -950) 157092) ((-1081 . -1065) NIL) ((-1081 . -904) 157044) ((-1080 . -995) T) ((-1080 . -428) 157025) ((-1080 . -552) 156991) ((-1080 . -555) 156972) ((-1080 . -1013) T) ((-1080 . -1128) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1080 . -64) T) ((-1079 . -1013) T) ((-1079 . -552) 156954) ((-1079 . -1128) T) ((-1079 . -13) T) ((-1079 . -72) T) ((-1078 . -1013) T) ((-1078 . -552) 156936) ((-1078 . -1128) T) ((-1078 . -13) T) ((-1078 . -72) T) ((-1073 . -1106) 156912) ((-1073 . -183) 156857) ((-1073 . -76) 156802) ((-1073 . -260) 156591) ((-1073 . -454) 156331) ((-1073 . -427) 156263) ((-1073 . -124) 156208) ((-1073 . -553) NIL) ((-1073 . -193) 156153) ((-1073 . -549) 156129) ((-1073 . -243) 156105) ((-1073 . -1128) T) ((-1073 . -13) T) ((-1073 . -241) 156081) ((-1073 . -1013) T) ((-1073 . -552) 156063) ((-1073 . -72) T) ((-1073 . -34) T) ((-1073 . -538) 156039) ((-1072 . -1057) T) ((-1072 . -322) 156021) ((-1072 . -759) T) ((-1072 . -756) T) ((-1072 . -124) 156003) ((-1072 . -34) T) ((-1072 . -13) T) ((-1072 . -1128) T) ((-1072 . -72) T) ((-1072 . -552) 155985) ((-1072 . -260) NIL) ((-1072 . -454) NIL) ((-1072 . -1013) T) ((-1072 . -427) 155967) ((-1072 . -553) NIL) ((-1072 . -241) 155917) ((-1072 . -538) 155892) ((-1072 . -243) 155867) ((-1072 . -593) 155849) ((-1072 . -19) 155831) ((-1068 . -616) 155815) ((-1068 . -593) 155799) ((-1068 . -243) 155776) ((-1068 . -241) 155728) ((-1068 . -538) 155705) ((-1068 . -553) 155666) ((-1068 . -427) 155650) ((-1068 . -1013) 155628) ((-1068 . -454) 155561) ((-1068 . -260) 155499) ((-1068 . -552) 155434) ((-1068 . -72) 155388) ((-1068 . -1128) T) ((-1068 . -13) T) ((-1068 . -34) T) ((-1068 . -124) 155372) ((-1068 . -1167) 155356) ((-1068 . -923) 155340) ((-1068 . -1063) 155324) ((-1068 . -555) 155301) ((-1066 . -995) T) ((-1066 . -428) 155282) ((-1066 . -552) 155248) ((-1066 . -555) 155229) ((-1066 . -1013) T) ((-1066 . -1128) T) ((-1066 . -13) T) ((-1066 . -72) T) ((-1066 . -64) T) ((-1064 . -1106) 155208) ((-1064 . -183) 155156) ((-1064 . -76) 155104) ((-1064 . -260) 154902) ((-1064 . -454) 154654) ((-1064 . -427) 154589) ((-1064 . -124) 154537) ((-1064 . -553) NIL) ((-1064 . -193) 154485) ((-1064 . -549) 154464) ((-1064 . -243) 154443) ((-1064 . -1128) T) ((-1064 . -13) T) ((-1064 . -241) 154422) ((-1064 . -1013) T) ((-1064 . -552) 154404) ((-1064 . -72) T) ((-1064 . -34) T) ((-1064 . -538) 154383) ((-1061 . -1034) 154367) ((-1061 . -427) 154351) ((-1061 . -1013) 154329) ((-1061 . -454) 154262) ((-1061 . -260) 154200) ((-1061 . -552) 154135) ((-1061 . -72) 154089) ((-1061 . -1128) T) ((-1061 . -13) T) ((-1061 . -34) T) ((-1061 . -76) 154073) ((-1059 . -1020) 154042) ((-1059 . -1123) 154011) ((-1059 . -552) 153973) ((-1059 . -124) 153957) ((-1059 . -34) T) ((-1059 . -13) T) ((-1059 . -1128) T) ((-1059 . -72) T) ((-1059 . -260) 153895) ((-1059 . -454) 153828) ((-1059 . -1013) T) ((-1059 . -427) 153812) ((-1059 . -553) 153773) ((-1059 . -889) 153742) ((-1059 . -983) 153711) ((-1055 . -1036) 153656) ((-1055 . -427) 153640) ((-1055 . -454) 153573) ((-1055 . -260) 153511) ((-1055 . -34) T) ((-1055 . -965) 153451) ((-1055 . -950) 153349) ((-1055 . -555) 153268) ((-1055 . -353) 153252) ((-1055 . -580) 153200) ((-1055 . -590) 153138) ((-1055 . -327) 153122) ((-1055 . -190) 153101) ((-1055 . -186) 153049) ((-1055 . -189) 153003) ((-1055 . -225) 152987) ((-1055 . -806) 152911) ((-1055 . -811) 152837) ((-1055 . -809) 152796) ((-1055 . -184) 152780) ((-1055 . -654) 152715) ((-1055 . -582) 152650) ((-1055 . -588) 152609) ((-1055 . -104) T) ((-1055 . -25) T) ((-1055 . -72) T) ((-1055 . -13) T) ((-1055 . -1128) T) ((-1055 . -552) 152571) ((-1055 . -1013) T) ((-1055 . -23) T) ((-1055 . -21) T) ((-1055 . -968) 152555) ((-1055 . -963) 152539) ((-1055 . -82) 152518) ((-1055 . -961) T) ((-1055 . -663) T) ((-1055 . -1060) T) ((-1055 . -1025) T) ((-1055 . -970) T) ((-1055 . -38) 152478) ((-1055 . -553) 152439) ((-1054 . -923) 152410) ((-1054 . -34) T) ((-1054 . -13) T) ((-1054 . -1128) T) ((-1054 . -72) T) ((-1054 . -552) 152392) ((-1054 . -260) 152318) ((-1054 . -454) 152226) ((-1054 . -1013) T) ((-1054 . -427) 152197) ((-1053 . -1013) T) ((-1053 . -552) 152179) ((-1053 . -1128) T) ((-1053 . -13) T) ((-1053 . -72) T) ((-1048 . -1050) T) ((-1048 . -1174) T) ((-1048 . -64) T) ((-1048 . -72) T) ((-1048 . -13) T) ((-1048 . -1128) T) ((-1048 . -552) 152145) ((-1048 . -1013) T) ((-1048 . -555) 152126) ((-1048 . -428) 152107) ((-1048 . -995) T) ((-1046 . -1047) 152091) ((-1046 . -72) T) ((-1046 . -13) T) ((-1046 . -1128) T) ((-1046 . -552) 152073) ((-1046 . -1013) T) ((-1039 . -679) 152052) ((-1039 . -35) 152018) ((-1039 . -66) 151984) ((-1039 . -239) 151950) ((-1039 . -431) 151916) ((-1039 . -1117) 151882) ((-1039 . -1114) 151848) ((-1039 . -915) 151814) ((-1039 . -47) 151786) ((-1039 . -38) 151683) ((-1039 . -582) 151580) ((-1039 . -654) 151477) ((-1039 . -555) 151359) ((-1039 . -246) 151338) ((-1039 . -494) 151317) ((-1039 . -82) 151182) ((-1039 . -963) 151068) ((-1039 . -968) 150954) ((-1039 . -146) 150908) ((-1039 . -120) 150887) ((-1039 . -118) 150866) ((-1039 . -590) 150791) ((-1039 . -588) 150701) ((-1039 . -886) 150668) ((-1039 . -811) 150652) ((-1039 . -1128) T) ((-1039 . -13) T) ((-1039 . -806) 150634) ((-1039 . -961) T) ((-1039 . -663) T) ((-1039 . -1060) T) ((-1039 . -1025) T) ((-1039 . -970) T) ((-1039 . -21) T) ((-1039 . -23) T) ((-1039 . -1013) T) ((-1039 . -552) 150616) ((-1039 . -72) T) ((-1039 . -25) T) ((-1039 . -104) T) ((-1039 . -809) 150600) ((-1039 . -454) 150570) ((-1039 . -260) 150557) ((-1038 . -861) 150524) ((-1038 . -555) 150323) ((-1038 . -950) 150208) ((-1038 . -1133) 150187) ((-1038 . -821) 150166) ((-1038 . -796) 150025) ((-1038 . -811) 150009) ((-1038 . -806) 149991) ((-1038 . -809) 149975) ((-1038 . -454) 149927) ((-1038 . -390) 149881) ((-1038 . -580) 149829) ((-1038 . -590) 149718) ((-1038 . -327) 149702) ((-1038 . -47) 149674) ((-1038 . -38) 149526) ((-1038 . -582) 149378) ((-1038 . -654) 149230) ((-1038 . -246) 149164) ((-1038 . -494) 149098) ((-1038 . -82) 148923) ((-1038 . -963) 148769) ((-1038 . -968) 148615) ((-1038 . -146) 148529) ((-1038 . -120) 148508) ((-1038 . -118) 148487) ((-1038 . -588) 148397) ((-1038 . -104) T) ((-1038 . -25) T) ((-1038 . -72) T) ((-1038 . -13) T) ((-1038 . -1128) T) ((-1038 . -552) 148379) ((-1038 . -1013) T) ((-1038 . -23) T) ((-1038 . -21) T) ((-1038 . -961) T) ((-1038 . -663) T) ((-1038 . -1060) T) ((-1038 . -1025) T) ((-1038 . -970) T) ((-1038 . -353) 148363) ((-1038 . -277) 148335) ((-1038 . -260) 148322) ((-1038 . -553) 148070) ((-1033 . -482) T) ((-1033 . -1133) T) ((-1033 . -1065) T) ((-1033 . -950) 148052) ((-1033 . -553) 147967) ((-1033 . -933) T) ((-1033 . -796) 147949) ((-1033 . -755) T) ((-1033 . -721) T) ((-1033 . -718) T) ((-1033 . -759) T) ((-1033 . -756) T) ((-1033 . -716) T) ((-1033 . -714) T) ((-1033 . -740) T) ((-1033 . -590) 147921) ((-1033 . -580) 147903) ((-1033 . -832) T) ((-1033 . -494) T) ((-1033 . -246) T) ((-1033 . -146) T) ((-1033 . -555) 147875) ((-1033 . -654) 147862) ((-1033 . -582) 147849) ((-1033 . -968) 147836) ((-1033 . -963) 147823) ((-1033 . -82) 147808) ((-1033 . -38) 147795) ((-1033 . -390) T) ((-1033 . -258) T) ((-1033 . -189) T) ((-1033 . -186) 147782) ((-1033 . -190) T) ((-1033 . -116) T) ((-1033 . -961) T) ((-1033 . -663) T) ((-1033 . 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T) ((-1026 . -538) 147075) ((-1026 . -950) 146904) ((-1026 . -555) 146708) ((-1026 . -353) 146677) ((-1026 . -580) 146585) ((-1026 . -590) 146424) ((-1026 . -327) 146394) ((-1026 . -318) 146373) ((-1026 . -190) 146326) ((-1026 . -588) 146114) ((-1026 . -970) 146093) ((-1026 . -1025) 146072) ((-1026 . -1060) 146051) ((-1026 . -663) 146030) ((-1026 . -961) 146009) ((-1026 . -186) 145905) ((-1026 . -189) 145807) ((-1026 . -225) 145777) ((-1026 . -806) 145649) ((-1026 . -811) 145523) ((-1026 . -809) 145456) ((-1026 . -184) 145426) ((-1026 . -552) 145123) ((-1026 . -968) 145048) ((-1026 . -963) 144953) ((-1026 . -82) 144873) ((-1026 . -104) 144748) ((-1026 . -25) 144585) ((-1026 . -72) 144322) ((-1026 . -13) T) ((-1026 . -1128) T) ((-1026 . -1013) 144078) ((-1026 . -23) 143934) ((-1026 . -21) 143849) ((-1022 . -1023) 143833) ((-1022 . |MappingCategory|) 143807) ((-1022 . -1128) T) ((-1022 . -80) 143791) ((-1022 . -1013) T) ((-1022 . -552) 143773) ((-1022 . -13) T) ((-1022 . -72) T) ((-1017 . -1016) 143737) ((-1017 . -72) T) ((-1017 . -552) 143719) ((-1017 . -1013) T) ((-1017 . -241) 143675) ((-1017 . -1128) T) ((-1017 . -13) T) ((-1017 . -557) 143590) ((-1015 . -1016) 143542) ((-1015 . -72) T) ((-1015 . -552) 143524) ((-1015 . -1013) T) ((-1015 . -241) 143480) ((-1015 . -1128) T) ((-1015 . -13) T) ((-1015 . -557) 143383) ((-1014 . -318) T) ((-1014 . -72) T) ((-1014 . -13) T) ((-1014 . -1128) T) ((-1014 . -552) 143365) ((-1014 . -1013) T) ((-1009 . -367) 143349) ((-1009 . -1011) 143333) ((-1009 . -318) 143312) ((-1009 . -193) 143296) ((-1009 . -553) 143257) ((-1009 . -124) 143241) ((-1009 . -427) 143225) ((-1009 . -1013) T) ((-1009 . -454) 143158) ((-1009 . -260) 143096) ((-1009 . -552) 143078) ((-1009 . -72) T) ((-1009 . -1128) T) ((-1009 . -13) T) ((-1009 . -34) T) ((-1009 . -76) 143062) ((-1009 . -183) 143046) ((-1008 . -995) T) ((-1008 . -428) 143027) ((-1008 . -552) 142993) ((-1008 . -555) 142974) ((-1008 . -1013) T) ((-1008 . -1128) T) ((-1008 . -13) T) ((-1008 . -72) T) ((-1008 . -64) T) ((-1004 . -1128) T) ((-1004 . -13) T) ((-1004 . -1013) 142944) ((-1004 . -552) 142903) ((-1004 . -72) 142873) ((-1003 . -995) T) ((-1003 . -428) 142854) ((-1003 . -552) 142820) ((-1003 . -555) 142801) ((-1003 . -1013) T) ((-1003 . -1128) T) ((-1003 . -13) T) ((-1003 . -72) T) ((-1003 . -64) T) ((-1001 . -1006) 142785) ((-1001 . -557) 142769) ((-1001 . -1013) 142747) ((-1001 . -552) 142714) ((-1001 . -1128) 142692) ((-1001 . -13) 142670) ((-1001 . -72) 142648) ((-1001 . -1007) 142606) ((-1000 . -228) 142590) ((-1000 . -555) 142574) ((-1000 . -950) 142558) ((-1000 . -759) T) ((-1000 . -72) T) ((-1000 . -1013) T) ((-1000 . -552) 142540) ((-1000 . -756) T) ((-1000 . -186) 142527) ((-1000 . -13) T) ((-1000 . -1128) T) ((-1000 . -189) T) ((-999 . -213) 142464) ((-999 . -555) 142207) ((-999 . -950) 142036) ((-999 . -553) NIL) ((-999 . -277) 141997) ((-999 . -353) 141981) ((-999 . -38) 141833) ((-999 . -82) 141658) ((-999 . -963) 141504) ((-999 . -968) 141350) ((-999 . -588) 141260) ((-999 . -590) 141149) ((-999 . -582) 141001) ((-999 . -654) 140853) ((-999 . -118) 140832) ((-999 . -120) 140811) ((-999 . -146) 140725) ((-999 . -494) 140659) ((-999 . -246) 140593) ((-999 . -47) 140554) ((-999 . -327) 140538) ((-999 . -580) 140486) ((-999 . -390) 140440) ((-999 . -454) 140303) ((-999 . -809) 140238) ((-999 . -806) 140136) ((-999 . -811) 140038) ((-999 . -796) NIL) ((-999 . -821) 140017) ((-999 . -1133) 139996) ((-999 . -861) 139941) ((-999 . -260) 139928) ((-999 . -190) 139907) ((-999 . -104) T) ((-999 . -25) T) ((-999 . -72) T) ((-999 . -552) 139889) ((-999 . -1013) T) ((-999 . -23) T) ((-999 . -21) T) ((-999 . -970) T) ((-999 . -1025) T) ((-999 . -1060) T) ((-999 . -663) T) ((-999 . -961) T) ((-999 . -186) 139837) ((-999 . -13) T) ((-999 . -1128) T) ((-999 . -189) 139791) ((-999 . -225) 139775) ((-999 . -184) 139759) ((-997 . -552) 139741) ((-994 . -756) T) ((-994 . -552) 139723) ((-994 . -1013) T) ((-994 . -72) T) ((-994 . -13) T) ((-994 . -1128) T) ((-994 . -759) T) ((-994 . -553) 139704) ((-991 . -661) 139683) ((-991 . -950) 139581) ((-991 . -353) 139565) ((-991 . -580) 139513) ((-991 . -590) 139390) ((-991 . -327) 139374) ((-991 . -320) 139353) ((-991 . -120) 139332) ((-991 . -555) 139157) ((-991 . -654) 139031) ((-991 . -582) 138905) ((-991 . -588) 138803) ((-991 . -968) 138716) ((-991 . -963) 138629) ((-991 . -82) 138521) ((-991 . -38) 138395) ((-991 . -351) 138374) ((-991 . -343) 138353) ((-991 . -118) 138307) ((-991 . -1065) 138286) ((-991 . -299) 138265) ((-991 . -318) 138219) ((-991 . -201) 138173) ((-991 . -246) 138127) ((-991 . -258) 138081) ((-991 . -390) 138035) ((-991 . -494) 137989) ((-991 . -832) 137943) ((-991 . -1133) 137897) ((-991 . -312) 137851) ((-991 . -190) 137779) ((-991 . -186) 137655) ((-991 . -189) 137537) ((-991 . -225) 137507) ((-991 . -806) 137379) ((-991 . -811) 137253) ((-991 . -809) 137186) ((-991 . -184) 137156) ((-991 . -553) 137140) ((-991 . -21) T) ((-991 . -23) T) ((-991 . -1013) T) ((-991 . -552) 137122) ((-991 . -1128) T) ((-991 . -13) T) ((-991 . -72) T) ((-991 . -25) T) ((-991 . -104) T) ((-991 . -961) T) ((-991 . -663) T) ((-991 . -1060) T) ((-991 . -1025) T) ((-991 . -970) T) ((-991 . -146) T) ((-989 . -1013) T) ((-989 . -552) 137104) ((-989 . -1128) T) ((-989 . -13) T) ((-989 . -72) T) ((-989 . -241) 137083) ((-988 . -1013) T) ((-988 . -552) 137065) ((-988 . -1128) T) ((-988 . -13) T) ((-988 . -72) T) ((-987 . -1013) T) ((-987 . -552) 137047) ((-987 . -1128) T) ((-987 . -13) T) ((-987 . -72) T) ((-987 . -241) 137026) ((-987 . -950) 137003) ((-987 . -555) 136980) ((-986 . -1128) T) ((-986 . -13) T) ((-985 . -995) T) ((-985 . -428) 136961) ((-985 . -552) 136927) ((-985 . -555) 136908) ((-985 . -1013) T) ((-985 . -1128) T) ((-985 . -13) T) ((-985 . -72) T) ((-985 . -64) T) ((-978 . -995) T) ((-978 . -428) 136889) ((-978 . -552) 136855) ((-978 . -555) 136836) ((-978 . -1013) T) ((-978 . -1128) T) ((-978 . -13) T) ((-978 . -72) T) ((-978 . -64) T) ((-975 . -482) T) 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136462) ((-974 . -72) T) ((-974 . -13) T) ((-974 . -1128) T) ((-974 . -552) 136444) ((-974 . -1013) T) ((-971 . -1128) T) ((-971 . -13) T) ((-971 . -1013) 136422) ((-971 . -552) 136389) ((-971 . -72) 136367) ((-966 . -965) 136307) ((-966 . -582) 136252) ((-966 . -654) 136197) ((-966 . -34) T) ((-966 . -260) 136135) ((-966 . -454) 136068) ((-966 . -427) 136052) ((-966 . -590) 136036) ((-966 . -588) 136005) ((-966 . -104) T) ((-966 . -25) T) ((-966 . -72) T) ((-966 . -13) T) ((-966 . -1128) T) ((-966 . -552) 135967) ((-966 . -1013) T) ((-966 . -23) T) ((-966 . -21) T) ((-966 . -968) 135951) ((-966 . -963) 135935) ((-966 . -82) 135914) ((-966 . -1186) 135884) ((-966 . -553) 135845) ((-958 . -983) 135774) ((-958 . -889) 135703) ((-958 . -553) 135645) ((-958 . -427) 135610) ((-958 . -1013) T) ((-958 . -454) 135494) ((-958 . -260) 135402) ((-958 . -552) 135345) ((-958 . -72) T) ((-958 . -1128) T) ((-958 . -13) T) ((-958 . -34) T) ((-958 . -124) 135310) ((-958 . -1123) 135239) ((-948 . -995) T) ((-948 . -428) 135220) ((-948 . -552) 135186) ((-948 . -555) 135167) ((-948 . -1013) T) ((-948 . -1128) T) ((-948 . -13) T) ((-948 . -72) T) ((-948 . -64) T) ((-947 . -146) T) ((-947 . -555) 135136) ((-947 . -970) T) ((-947 . -1025) T) ((-947 . -1060) T) ((-947 . -663) T) ((-947 . -961) T) ((-947 . -590) 135110) ((-947 . -588) 135069) ((-947 . -104) T) ((-947 . -25) T) ((-947 . -72) T) ((-947 . -13) T) ((-947 . -1128) T) ((-947 . -552) 135051) ((-947 . -1013) T) ((-947 . -23) T) ((-947 . -21) T) ((-947 . -968) 135025) ((-947 . -963) 134999) ((-947 . -82) 134966) ((-947 . -38) 134950) ((-947 . -582) 134934) ((-947 . -654) 134918) ((-940 . -983) 134887) ((-940 . -889) 134856) ((-940 . -553) 134817) ((-940 . -427) 134801) ((-940 . -1013) T) ((-940 . -454) 134734) ((-940 . -260) 134672) ((-940 . -552) 134634) ((-940 . -72) T) ((-940 . -1128) T) ((-940 . -13) T) ((-940 . -34) T) ((-940 . -124) 134618) ((-940 . -1123) 134587) ((-939 . -1013) T) ((-939 . -552) 134569) ((-939 . -1128) T) 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-1128) T) ((-932 . -13) T) ((-932 . -72) T) ((-932 . -64) T) ((-917 . -904) 133713) ((-917 . -1065) T) ((-917 . -555) 133663) ((-917 . -950) 133623) ((-917 . -553) 133553) ((-917 . -933) T) ((-917 . -821) NIL) ((-917 . -794) 133535) ((-917 . -755) T) ((-917 . -721) T) ((-917 . -718) T) ((-917 . -759) T) ((-917 . -756) T) ((-917 . -716) T) ((-917 . -714) T) ((-917 . -740) T) ((-917 . -796) 133517) ((-917 . -341) 133499) ((-917 . -580) 133481) ((-917 . -327) 133463) ((-917 . -241) NIL) ((-917 . -260) NIL) ((-917 . -454) NIL) ((-917 . -288) 133445) ((-917 . -201) T) ((-917 . -82) 133372) ((-917 . -963) 133322) ((-917 . -968) 133272) ((-917 . -246) T) ((-917 . -654) 133222) ((-917 . -582) 133172) ((-917 . -590) 133122) ((-917 . -588) 133072) ((-917 . -38) 133022) ((-917 . -258) T) ((-917 . -390) T) ((-917 . -146) T) ((-917 . -494) T) ((-917 . -832) T) ((-917 . -1133) T) ((-917 . -312) T) ((-917 . -190) T) ((-917 . -186) 133009) ((-917 . -189) T) ((-917 . -225) 132991) ((-917 . -806) NIL) ((-917 . -811) NIL) ((-917 . -809) NIL) ((-917 . -184) 132973) ((-917 . -120) T) ((-917 . -118) NIL) ((-917 . -104) T) ((-917 . -25) T) ((-917 . -72) T) ((-917 . -13) T) ((-917 . -1128) T) ((-917 . -552) 132933) ((-917 . -1013) T) ((-917 . -23) T) ((-917 . -21) T) ((-917 . -961) T) ((-917 . -663) T) ((-917 . -1060) T) ((-917 . -1025) T) ((-917 . -970) T) ((-916 . -291) 132907) ((-916 . -146) T) ((-916 . -555) 132837) ((-916 . -970) T) ((-916 . -1025) T) ((-916 . -1060) T) ((-916 . -663) T) ((-916 . -961) T) ((-916 . -590) 132739) ((-916 . -588) 132669) ((-916 . -104) T) ((-916 . -25) T) ((-916 . -72) T) ((-916 . -13) T) ((-916 . -1128) T) ((-916 . -552) 132651) ((-916 . -1013) T) ((-916 . -23) T) ((-916 . -21) T) ((-916 . -968) 132596) ((-916 . -963) 132541) ((-916 . -82) 132458) ((-916 . -553) 132442) ((-916 . -184) 132419) ((-916 . -809) 132371) ((-916 . -811) 132283) ((-916 . -806) 132193) ((-916 . -225) 132170) ((-916 . -189) 132110) ((-916 . -186) 132044) ((-916 . -190) 132016) 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T) ((-906 . -552) 129364) ((-906 . -1128) T) ((-906 . -13) T) ((-906 . -72) T) ((-906 . -25) T) ((-906 . -104) T) ((-906 . -241) 129331) ((-902 . -552) 129313) ((-899 . -1013) T) ((-899 . -552) 129295) ((-899 . -1128) T) ((-899 . -13) T) ((-899 . -72) T) ((-884 . -721) T) ((-884 . -718) T) ((-884 . -759) T) ((-884 . -756) T) ((-884 . -716) T) ((-884 . -23) T) ((-884 . -1013) T) ((-884 . -552) 129255) ((-884 . -1128) T) ((-884 . -13) T) ((-884 . -72) T) ((-884 . -25) T) ((-884 . -104) T) ((-883 . -995) T) ((-883 . -428) 129236) ((-883 . -552) 129202) ((-883 . -555) 129183) ((-883 . -1013) T) ((-883 . -1128) T) ((-883 . -13) T) ((-883 . -72) T) ((-883 . -64) T) ((-877 . -880) T) ((-877 . -72) T) ((-877 . -552) 129165) ((-877 . -1013) T) ((-877 . -604) T) ((-877 . -13) T) ((-877 . -1128) T) ((-877 . -84) T) ((-877 . -555) 129149) ((-876 . -552) 129131) ((-875 . -1013) T) ((-875 . -552) 129113) ((-875 . -1128) T) ((-875 . -13) T) ((-875 . -72) T) ((-875 . -318) 129066) ((-875 . -663) 128968) ((-875 . -1025) 128870) ((-875 . -23) 128684) ((-875 . -25) 128498) ((-875 . -104) 128356) ((-875 . -411) 128309) ((-875 . -21) 128264) ((-875 . -588) 128208) ((-875 . -717) 128161) ((-875 . -716) 128114) ((-875 . -756) 128016) ((-875 . -759) 127918) ((-875 . -718) 127871) ((-875 . -721) 127824) ((-869 . -19) 127808) ((-869 . -593) 127792) ((-869 . -243) 127769) ((-869 . -241) 127721) ((-869 . -538) 127698) ((-869 . -553) 127659) ((-869 . -427) 127643) ((-869 . -1013) 127596) ((-869 . -454) 127529) ((-869 . -260) 127467) ((-869 . -552) 127382) ((-869 . -72) 127316) ((-869 . -1128) T) ((-869 . -13) T) ((-869 . -34) T) ((-869 . -124) 127300) ((-869 . -756) 127279) ((-869 . -759) 127258) ((-869 . -322) 127242) ((-867 . -277) 127221) ((-867 . -950) 127119) ((-867 . -353) 127103) ((-867 . -38) 127000) ((-867 . -555) 126857) ((-867 . -590) 126782) ((-867 . -588) 126692) ((-867 . -970) T) ((-867 . -1025) T) ((-867 . -1060) T) ((-867 . -663) T) ((-867 . -961) T) ((-867 . -82) 126557) ((-867 . -963) 126443) ((-867 . -968) 126329) ((-867 . -21) T) ((-867 . -23) T) ((-867 . -1013) T) ((-867 . -552) 126311) ((-867 . -1128) T) ((-867 . -13) T) ((-867 . -72) T) ((-867 . -25) T) ((-867 . -104) T) ((-867 . -582) 126208) ((-867 . -654) 126105) ((-867 . -118) 126084) ((-867 . -120) 126063) ((-867 . -146) 126017) ((-867 . -494) 125996) ((-867 . -246) 125975) ((-867 . -47) 125954) ((-865 . -1013) T) ((-865 . -552) 125920) ((-865 . -1128) T) ((-865 . -13) T) ((-865 . -72) T) ((-857 . -861) 125881) ((-857 . -555) 125677) ((-857 . -950) 125559) ((-857 . -1133) 125538) ((-857 . -821) 125517) ((-857 . -796) 125442) ((-857 . -811) 125423) ((-857 . -806) 125402) ((-857 . -809) 125383) ((-857 . -454) 125329) ((-857 . -390) 125283) ((-857 . -580) 125231) ((-857 . -590) 125120) ((-857 . -327) 125104) ((-857 . -47) 125073) ((-857 . -38) 124925) ((-857 . -582) 124777) ((-857 . -654) 124629) ((-857 . -246) 124563) ((-857 . -494) 124497) ((-857 . -82) 124322) ((-857 . -963) 124168) ((-857 . 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T) ((-836 . -552) 122906) ((-830 . -718) T) ((-830 . -759) T) ((-830 . -756) T) ((-830 . -1013) T) ((-830 . -552) 122888) ((-830 . -1128) T) ((-830 . -13) T) ((-830 . -72) T) ((-830 . -25) T) ((-830 . -663) T) ((-830 . -1025) T) ((-825 . -312) T) ((-825 . -1133) T) ((-825 . -832) T) ((-825 . -494) T) ((-825 . -146) T) ((-825 . -555) 122825) ((-825 . -654) 122777) ((-825 . -582) 122729) ((-825 . -38) 122681) ((-825 . -390) T) ((-825 . -258) T) ((-825 . -590) 122633) ((-825 . -588) 122570) ((-825 . -970) T) ((-825 . -1025) T) ((-825 . -1060) T) ((-825 . -663) T) ((-825 . -961) T) ((-825 . -82) 122501) ((-825 . -963) 122453) ((-825 . -968) 122405) ((-825 . -21) T) ((-825 . -23) T) ((-825 . -1013) T) ((-825 . -552) 122387) ((-825 . -1128) T) ((-825 . -13) T) ((-825 . -72) T) ((-825 . -25) T) ((-825 . -104) T) ((-825 . -246) T) ((-825 . -201) T) ((-817 . -299) T) ((-817 . -1065) T) ((-817 . -318) T) ((-817 . -118) T) ((-817 . -312) T) ((-817 . -1133) T) ((-817 . -832) T) ((-817 . -494) T) 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-72) T) ((-813 . -1025) T) ((-813 . -411) T) ((-813 . -1128) T) ((-813 . -13) T) ((-813 . -241) 121742) ((-812 . -92) 121726) ((-812 . -427) 121710) ((-812 . -1013) 121688) ((-812 . -454) 121621) ((-812 . -260) 121559) ((-812 . -552) 121473) ((-812 . -72) 121427) ((-812 . -1128) T) ((-812 . -13) T) ((-812 . -34) T) ((-812 . -923) 121411) ((-803 . -756) T) ((-803 . -552) 121393) ((-803 . -1013) T) ((-803 . -72) T) ((-803 . -13) T) ((-803 . -1128) T) ((-803 . -759) T) ((-803 . -950) 121370) ((-803 . -555) 121347) ((-800 . -1013) T) ((-800 . -552) 121329) ((-800 . -1128) T) ((-800 . -13) T) ((-800 . -72) T) ((-800 . -950) 121297) ((-800 . -555) 121265) ((-798 . -1013) T) ((-798 . -552) 121247) ((-798 . -1128) T) ((-798 . -13) T) ((-798 . -72) T) ((-795 . -1013) T) ((-795 . -552) 121229) ((-795 . -1128) T) ((-795 . -13) T) ((-795 . -72) T) ((-785 . -995) T) ((-785 . -428) 121210) ((-785 . -552) 121176) ((-785 . -555) 121157) ((-785 . -1013) T) ((-785 . -1128) T) ((-785 . -13) T) ((-785 . -72) T) ((-785 . -64) T) ((-785 . -1174) T) ((-783 . -1013) T) ((-783 . -552) 121139) ((-783 . -1128) T) ((-783 . -13) T) ((-783 . -72) T) ((-783 . -555) 121121) ((-782 . -1128) T) ((-782 . -13) T) ((-782 . -552) 120996) ((-782 . -1013) 120947) ((-782 . -72) 120898) ((-781 . -904) 120882) ((-781 . -1065) 120860) ((-781 . -950) 120727) ((-781 . -555) 120626) ((-781 . -553) 120429) ((-781 . -933) 120408) ((-781 . -821) 120387) ((-781 . -794) 120371) ((-781 . -755) 120350) ((-781 . -721) 120329) ((-781 . -718) 120308) ((-781 . -759) 120262) ((-781 . -756) 120216) ((-781 . -716) 120195) ((-781 . -714) 120174) ((-781 . -740) 120153) ((-781 . -796) 120078) ((-781 . -341) 120062) ((-781 . -580) 120010) ((-781 . -590) 119926) ((-781 . -327) 119910) ((-781 . -241) 119868) ((-781 . -260) 119833) ((-781 . -454) 119745) ((-781 . -288) 119729) ((-781 . -201) T) ((-781 . -82) 119660) ((-781 . -963) 119612) ((-781 . -968) 119564) ((-781 . -246) T) ((-781 . -654) 119516) ((-781 . -582) 119468) ((-781 . -588) 119405) ((-781 . -38) 119357) ((-781 . -258) T) ((-781 . -390) T) ((-781 . -146) T) ((-781 . -494) T) ((-781 . -832) T) ((-781 . -1133) T) ((-781 . -312) T) ((-781 . -190) 119336) ((-781 . -186) 119284) ((-781 . -189) 119238) ((-781 . -225) 119222) ((-781 . -806) 119146) ((-781 . -811) 119072) ((-781 . -809) 119031) ((-781 . -184) 119015) ((-781 . -120) 118969) ((-781 . -118) 118948) ((-781 . -104) T) ((-781 . -25) T) ((-781 . -72) T) ((-781 . -13) T) ((-781 . -1128) T) ((-781 . -552) 118930) ((-781 . -1013) T) ((-781 . -23) T) ((-781 . -21) T) ((-781 . -961) T) ((-781 . -663) T) ((-781 . -1060) T) ((-781 . -1025) T) ((-781 . -970) T) ((-780 . -904) 118907) ((-780 . -1065) NIL) ((-780 . -950) 118884) ((-780 . -555) 118814) ((-780 . -553) NIL) ((-780 . -933) NIL) ((-780 . -821) NIL) ((-780 . -794) 118791) ((-780 . -755) NIL) ((-780 . -721) NIL) ((-780 . -718) NIL) ((-780 . -759) NIL) ((-780 . -756) NIL) ((-780 . -716) NIL) ((-780 . -714) NIL) ((-780 . -740) NIL) ((-780 . -796) NIL) ((-780 . -341) 118768) ((-780 . -580) 118745) ((-780 . -590) 118690) ((-780 . -327) 118667) ((-780 . -241) 118597) ((-780 . -260) 118541) ((-780 . -454) 118404) ((-780 . -288) 118381) ((-780 . -201) T) ((-780 . -82) 118298) ((-780 . -963) 118243) ((-780 . -968) 118188) ((-780 . -246) T) ((-780 . -654) 118133) ((-780 . -582) 118078) ((-780 . -588) 118008) ((-780 . -38) 117953) ((-780 . -258) T) ((-780 . -390) T) ((-780 . -146) T) ((-780 . -494) T) ((-780 . -832) T) ((-780 . -1133) T) ((-780 . -312) T) ((-780 . -190) NIL) ((-780 . -186) NIL) ((-780 . -189) NIL) ((-780 . -225) 117930) ((-780 . -806) NIL) ((-780 . -811) NIL) ((-780 . -809) NIL) ((-780 . -184) 117907) ((-780 . -120) T) ((-780 . -118) NIL) ((-780 . -104) T) ((-780 . -25) T) ((-780 . -72) T) ((-780 . -13) T) ((-780 . -1128) T) ((-780 . -552) 117889) ((-780 . -1013) T) ((-780 . -23) T) ((-780 . -21) T) ((-780 . -961) T) ((-780 . -663) T) ((-780 . -1060) T) ((-780 . -1025) T) ((-780 . -970) T) ((-778 . -779) 117873) ((-778 . -832) T) ((-778 . -494) T) ((-778 . -246) T) ((-778 . -146) T) ((-778 . -555) 117845) ((-778 . -654) 117832) ((-778 . -582) 117819) ((-778 . -968) 117806) ((-778 . -963) 117793) ((-778 . -82) 117778) ((-778 . -38) 117765) ((-778 . -390) T) ((-778 . -258) T) ((-778 . -961) T) ((-778 . -663) T) ((-778 . -1060) T) ((-778 . -1025) T) ((-778 . -970) T) ((-778 . -21) T) ((-778 . -588) 117737) ((-778 . -23) T) ((-778 . -1013) T) ((-778 . -552) 117719) ((-778 . -1128) T) ((-778 . -13) T) ((-778 . -72) T) ((-778 . -25) T) ((-778 . -104) T) ((-778 . -590) 117706) ((-778 . -120) T) ((-775 . -961) T) ((-775 . -663) T) ((-775 . -1060) T) ((-775 . -1025) T) ((-775 . -970) T) ((-775 . -21) T) ((-775 . -588) 117651) ((-775 . -23) T) ((-775 . -1013) T) ((-775 . -552) 117613) ((-775 . -1128) T) ((-775 . -13) T) ((-775 . -72) T) ((-775 . -25) T) ((-775 . -104) T) ((-775 . -590) 117573) ((-775 . -555) 117508) ((-775 . -428) 117485) ((-775 . -38) 117455) ((-775 . -82) 117420) ((-775 . -963) 117390) 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-968) 116735) ((-764 . -963) 116719) ((-764 . -82) 116698) ((-764 . -961) T) ((-764 . -663) T) ((-764 . -1060) T) ((-764 . -1025) T) ((-764 . -970) T) ((-764 . -38) 116668) ((-763 . -761) 116652) ((-763 . -950) 116550) ((-763 . -555) 116469) ((-763 . -353) 116453) ((-763 . -654) 116423) ((-763 . -582) 116393) ((-763 . -590) 116367) ((-763 . -588) 116326) ((-763 . -104) T) ((-763 . -25) T) ((-763 . -72) T) ((-763 . -13) T) ((-763 . -1128) T) ((-763 . -552) 116308) ((-763 . -1013) T) ((-763 . -23) T) ((-763 . -21) T) ((-763 . -968) 116292) ((-763 . -963) 116276) ((-763 . -82) 116255) ((-763 . -961) T) ((-763 . -663) T) ((-763 . -1060) T) ((-763 . -1025) T) ((-763 . -970) T) ((-763 . -38) 116225) ((-757 . -759) T) ((-757 . -1128) T) ((-757 . -13) T) ((-757 . -72) T) ((-757 . -428) 116209) ((-757 . -552) 116157) ((-757 . -555) 116141) ((-750 . -1013) T) ((-750 . -552) 116123) ((-750 . -1128) T) ((-750 . -13) T) ((-750 . -72) T) ((-750 . -353) 116107) ((-750 . -555) 115980) ((-750 . -950) 115878) ((-750 . -21) 115833) ((-750 . -588) 115753) ((-750 . -23) 115708) ((-750 . -25) 115663) ((-750 . -104) 115618) ((-750 . -755) 115597) ((-750 . -721) 115576) ((-750 . -718) 115555) ((-750 . -759) 115534) ((-750 . -756) 115513) ((-750 . -716) 115492) ((-750 . -714) 115471) ((-750 . -961) 115450) ((-750 . -663) 115429) ((-750 . -1060) 115408) ((-750 . -1025) 115387) ((-750 . -970) 115366) ((-750 . -590) 115339) ((-750 . -120) 115318) ((-749 . -747) 115300) ((-749 . -72) T) ((-749 . -13) T) ((-749 . -1128) T) ((-749 . -552) 115282) ((-749 . -1013) T) ((-745 . -961) T) ((-745 . -663) T) ((-745 . -1060) T) ((-745 . -1025) T) ((-745 . -970) T) ((-745 . -21) T) ((-745 . -588) 115227) ((-745 . -23) T) ((-745 . -1013) T) ((-745 . -552) 115209) ((-745 . -1128) T) ((-745 . -13) T) ((-745 . -72) T) ((-745 . -25) T) ((-745 . -104) T) ((-745 . -590) 115169) ((-745 . -555) 115124) ((-745 . -950) 115094) ((-745 . -241) 115073) ((-745 . -120) 115052) ((-745 . -118) 115031) ((-745 . -38) 115001) 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T) ((-737 . -25) T) ((-737 . -104) T) ((-737 . -590) 113213) ((-737 . -190) T) ((-737 . -555) 113122) ((-737 . -970) T) ((-737 . -1025) T) ((-737 . -1060) T) ((-737 . -663) T) ((-737 . -961) T) ((-737 . -186) 113109) ((-737 . -189) T) ((-737 . -428) 113093) ((-737 . -312) 113072) ((-737 . -1133) 113051) ((-737 . -832) 113030) ((-737 . -494) 113009) ((-737 . -146) 112988) ((-737 . -654) 112925) ((-737 . -582) 112862) ((-737 . -38) 112799) ((-737 . -390) 112778) ((-737 . -258) 112757) ((-737 . -246) 112736) ((-737 . -201) 112715) ((-736 . -213) 112654) ((-736 . -555) 112398) ((-736 . -950) 112228) ((-736 . -553) NIL) ((-736 . -277) 112190) ((-736 . -353) 112174) ((-736 . -38) 112026) ((-736 . -82) 111851) ((-736 . -963) 111697) ((-736 . -968) 111543) ((-736 . -588) 111453) ((-736 . -590) 111342) ((-736 . -582) 111194) ((-736 . -654) 111046) ((-736 . -118) 111025) ((-736 . -120) 111004) ((-736 . -146) 110918) ((-736 . -494) 110852) ((-736 . -246) 110786) ((-736 . -47) 110748) ((-736 . -327) 110732) ((-736 . -580) 110680) ((-736 . -390) 110634) ((-736 . -454) 110499) ((-736 . -809) 110435) ((-736 . -806) 110334) ((-736 . -811) 110237) ((-736 . -796) NIL) ((-736 . -821) 110216) ((-736 . -1133) 110195) ((-736 . -861) 110142) ((-736 . -260) 110129) ((-736 . -190) 110108) ((-736 . -104) T) ((-736 . -25) T) ((-736 . -72) T) ((-736 . -552) 110090) ((-736 . -1013) T) ((-736 . -23) T) ((-736 . -21) T) ((-736 . -970) T) ((-736 . -1025) T) ((-736 . -1060) T) ((-736 . -663) T) ((-736 . -961) T) ((-736 . -186) 110038) ((-736 . -13) T) ((-736 . -1128) T) ((-736 . -189) 109992) ((-736 . -225) 109976) ((-736 . -184) 109960) ((-735 . -196) 109939) ((-735 . -1186) 109909) ((-735 . -721) 109888) ((-735 . -718) 109867) ((-735 . -759) 109821) ((-735 . -756) 109775) ((-735 . -716) 109754) ((-735 . -717) 109733) ((-735 . -654) 109678) ((-735 . -582) 109603) ((-735 . -243) 109580) ((-735 . -241) 109557) ((-735 . -427) 109541) ((-735 . -454) 109474) ((-735 . -260) 109412) ((-735 . -34) T) 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103393) ((-704 . -580) 103341) ((-704 . -809) 103285) ((-704 . -806) 103192) ((-704 . -811) 103103) ((-704 . -796) NIL) ((-704 . -821) 103082) ((-704 . -1133) 103061) ((-704 . -861) 103031) ((-704 . -832) 103010) ((-704 . -494) 102924) ((-704 . -246) 102838) ((-704 . -146) 102732) ((-704 . -390) 102666) ((-704 . -258) 102645) ((-704 . -241) 102572) ((-704 . -190) T) ((-704 . -104) T) ((-704 . -25) T) ((-704 . -72) T) ((-704 . -552) 102533) ((-704 . -1013) T) ((-704 . -23) T) ((-704 . -21) T) ((-704 . -970) T) ((-704 . -1025) T) ((-704 . -1060) T) ((-704 . -663) T) ((-704 . -961) T) ((-704 . -186) 102520) ((-704 . -13) T) ((-704 . -1128) T) ((-704 . -189) T) ((-704 . -225) 102504) ((-704 . -184) 102488) ((-703 . -977) 102455) ((-703 . -553) 102090) ((-703 . -260) 102077) ((-703 . -454) 102029) ((-703 . -277) 102001) ((-703 . -950) 101860) ((-703 . -353) 101844) ((-703 . -38) 101696) ((-703 . -555) 101469) ((-703 . -590) 101358) ((-703 . -588) 101268) ((-703 . -970) T) ((-703 . -1025) T) 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. -64) T) ((-614 . -756) T) ((-614 . -552) 92017) ((-614 . -1013) T) ((-614 . -72) T) ((-614 . -13) T) ((-614 . -1128) T) ((-614 . -759) T) ((-614 . -950) 92001) ((-614 . -555) 91985) ((-613 . -995) T) ((-613 . -428) 91966) ((-613 . -552) 91932) ((-613 . -555) 91913) ((-613 . -1013) T) ((-613 . -1128) T) ((-613 . -13) T) ((-613 . -72) T) ((-613 . -64) T) ((-612 . -1036) 91858) ((-612 . -427) 91842) ((-612 . -454) 91775) ((-612 . -260) 91713) ((-612 . -34) T) ((-612 . -965) 91653) ((-612 . -950) 91551) ((-612 . -555) 91470) ((-612 . -353) 91454) ((-612 . -580) 91402) ((-612 . -590) 91340) ((-612 . -327) 91324) ((-612 . -190) 91303) ((-612 . -186) 91251) ((-612 . -189) 91205) ((-612 . -225) 91189) ((-612 . -806) 91113) ((-612 . -811) 91039) ((-612 . -809) 90998) ((-612 . -184) 90982) ((-612 . -654) 90966) ((-612 . -582) 90950) ((-612 . -588) 90909) ((-612 . -104) T) ((-612 . -25) T) ((-612 . -72) T) ((-612 . -13) T) ((-612 . -1128) T) ((-612 . -552) 90871) ((-612 . -1013) T) ((-612 . 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88678) ((-591 . -555) 88662) ((-589 . -634) 88646) ((-589 . -76) 88630) ((-589 . -34) T) ((-589 . -13) T) ((-589 . -1128) T) ((-589 . -72) 88584) ((-589 . -552) 88519) ((-589 . -260) 88457) ((-589 . -454) 88390) ((-589 . -1013) 88368) ((-589 . -427) 88352) ((-589 . -124) 88336) ((-589 . -553) 88297) ((-589 . -193) 88281) ((-587 . -995) T) ((-587 . -428) 88262) ((-587 . -552) 88215) ((-587 . -555) 88196) ((-587 . -1013) T) ((-587 . -1128) T) ((-587 . -13) T) ((-587 . -72) T) ((-587 . -64) T) ((-583 . -608) 88180) ((-583 . -1167) 88164) ((-583 . -923) 88148) ((-583 . -1063) 88132) ((-583 . -756) 88111) ((-583 . -759) 88090) ((-583 . -322) 88074) ((-583 . -593) 88058) ((-583 . -243) 88035) ((-583 . -241) 87987) ((-583 . -538) 87964) ((-583 . -553) 87925) ((-583 . -427) 87909) ((-583 . -1013) 87862) ((-583 . -454) 87795) ((-583 . -260) 87733) ((-583 . -552) 87648) ((-583 . -72) 87582) ((-583 . -1128) T) ((-583 . -13) T) ((-583 . -34) T) ((-583 . -124) 87566) ((-583 . -237) 87550) ((-581 . -1186) 87534) ((-581 . -82) 87513) ((-581 . -963) 87497) ((-581 . -968) 87481) ((-581 . -21) T) ((-581 . -588) 87450) ((-581 . -23) T) ((-581 . -1013) T) ((-581 . -552) 87432) ((-581 . -1128) T) ((-581 . -13) T) ((-581 . -72) T) ((-581 . -25) T) ((-581 . -104) T) ((-581 . -590) 87416) ((-581 . -582) 87400) ((-581 . -654) 87384) ((-581 . -241) 87351) ((-579 . -1186) 87335) ((-579 . -82) 87314) ((-579 . -963) 87298) ((-579 . -968) 87282) ((-579 . -21) T) ((-579 . -588) 87251) ((-579 . -23) T) ((-579 . -1013) T) ((-579 . -552) 87233) ((-579 . -1128) T) ((-579 . -13) T) ((-579 . -72) T) ((-579 . -25) T) ((-579 . -104) T) ((-579 . -590) 87217) ((-579 . -582) 87201) ((-579 . -654) 87185) ((-579 . -555) 87162) ((-579 . -448) 87134) ((-579 . -557) 87092) ((-577 . -752) T) ((-577 . -759) T) ((-577 . -756) T) ((-577 . -1013) T) ((-577 . -552) 87074) ((-577 . -1128) T) ((-577 . -13) T) ((-577 . -72) T) ((-577 . -318) T) ((-577 . -555) 87051) ((-572 . -683) 87035) ((-572 . -657) T) ((-572 . -685) T) ((-572 . -82) 87014) ((-572 . -963) 86998) ((-572 . -968) 86982) ((-572 . -21) T) ((-572 . -588) 86951) ((-572 . -23) T) ((-572 . -1013) T) ((-572 . -552) 86920) ((-572 . -1128) T) ((-572 . -13) T) ((-572 . -72) T) ((-572 . -25) T) ((-572 . -104) T) ((-572 . -590) 86904) ((-572 . -582) 86888) ((-572 . -654) 86872) ((-572 . -359) 86837) ((-572 . -316) 86772) ((-572 . -241) 86730) ((-571 . -1106) 86705) ((-571 . -183) 86649) ((-571 . -76) 86593) ((-571 . -260) 86438) ((-571 . -454) 86238) ((-571 . -427) 86168) ((-571 . -124) 86112) ((-571 . -553) NIL) ((-571 . -193) 86056) ((-571 . -549) 86031) ((-571 . -243) 86006) ((-571 . -1128) T) ((-571 . -13) T) ((-571 . -241) 85959) ((-571 . -1013) T) ((-571 . -552) 85941) ((-571 . -72) T) ((-571 . -34) T) ((-571 . -538) 85916) ((-566 . -411) T) ((-566 . -1025) T) ((-566 . -72) T) ((-566 . -13) T) ((-566 . -1128) T) ((-566 . -552) 85898) ((-566 . -1013) T) ((-566 . -663) T) ((-565 . -995) T) ((-565 . -428) 85879) ((-565 . -552) 85845) ((-565 . 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. -759) T) ((-438 . -756) T) ((-438 . -124) 74977) ((-438 . -34) T) ((-438 . -72) T) ((-438 . -552) 74959) ((-438 . -260) NIL) ((-438 . -454) NIL) ((-438 . -1013) T) ((-438 . -427) 74942) ((-438 . -553) 74924) ((-438 . -241) 74875) ((-438 . -538) 74851) ((-438 . -243) 74827) ((-438 . -593) 74810) ((-438 . -19) 74793) ((-438 . -604) T) ((-438 . -13) T) ((-438 . -1128) T) ((-438 . -84) T) ((-435 . -57) 74767) ((-435 . -34) T) ((-435 . -13) T) ((-435 . -1128) T) ((-435 . -72) 74721) ((-435 . -552) 74656) ((-435 . -260) 74594) ((-435 . -454) 74527) ((-435 . -1013) 74505) ((-435 . -427) 74489) ((-434 . -19) 74473) ((-434 . -593) 74457) ((-434 . -243) 74434) ((-434 . -241) 74386) ((-434 . -538) 74363) ((-434 . -553) 74324) ((-434 . -427) 74308) ((-434 . -1013) 74261) ((-434 . -454) 74194) ((-434 . -260) 74132) ((-434 . -552) 74047) ((-434 . -72) 73981) ((-434 . -1128) T) ((-434 . -13) T) ((-434 . -34) T) ((-434 . -124) 73965) ((-434 . -756) 73944) ((-434 . -759) 73923) ((-434 . -322) 73907) 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. -889) 60648) ((-401 . -553) 60609) ((-401 . -427) 60593) ((-401 . -1013) T) ((-401 . -454) 60526) ((-401 . -260) 60464) ((-401 . -552) 60426) ((-401 . -72) T) ((-401 . -1128) T) ((-401 . -13) T) ((-401 . -34) T) ((-401 . -124) 60410) ((-399 . -654) 60381) ((-399 . -582) 60352) ((-399 . -590) 60323) ((-399 . -588) 60279) ((-399 . -104) T) ((-399 . -25) T) ((-399 . -72) T) ((-399 . -13) T) ((-399 . -1128) T) ((-399 . -552) 60261) ((-399 . -1013) T) ((-399 . -23) T) ((-399 . -21) T) ((-399 . -968) 60232) ((-399 . -963) 60203) ((-399 . -82) 60164) ((-392 . -861) 60131) ((-392 . -555) 59923) ((-392 . -950) 59801) ((-392 . -1133) 59780) ((-392 . -821) 59759) ((-392 . -796) NIL) ((-392 . -811) 59736) ((-392 . -806) 59711) ((-392 . -809) 59688) ((-392 . -454) 59626) ((-392 . -390) 59580) ((-392 . -580) 59528) ((-392 . -590) 59417) ((-392 . -327) 59401) ((-392 . -47) 59380) ((-392 . -38) 59232) ((-392 . -582) 59084) ((-392 . -654) 58936) ((-392 . -246) 58870) ((-392 . -494) 58804) ((-392 . 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55219) ((-348 . -120) 55173) ((-348 . -118) 55152) ((-348 . -104) T) ((-348 . -25) T) ((-348 . -72) T) ((-348 . -13) T) ((-348 . -1128) T) ((-348 . -552) 55134) ((-348 . -1013) T) ((-348 . -23) T) ((-348 . -21) T) ((-348 . -961) T) ((-348 . -663) T) ((-348 . -1060) T) ((-348 . -1025) T) ((-348 . -970) T) ((-346 . -494) T) ((-346 . -246) T) ((-346 . -146) T) ((-346 . -555) 55043) ((-346 . -654) 55017) ((-346 . -582) 54991) ((-346 . -590) 54965) ((-346 . -588) 54924) ((-346 . -104) T) ((-346 . -25) T) ((-346 . -72) T) ((-346 . -13) T) ((-346 . -1128) T) ((-346 . -552) 54906) ((-346 . -1013) T) ((-346 . -23) T) ((-346 . -21) T) ((-346 . -968) 54880) ((-346 . -963) 54854) ((-346 . -82) 54821) ((-346 . -961) T) ((-346 . -663) T) ((-346 . -1060) T) ((-346 . -1025) T) ((-346 . -970) T) ((-346 . -38) 54795) ((-346 . -184) 54779) ((-346 . -809) 54738) ((-346 . -811) 54664) ((-346 . -806) 54588) ((-346 . -225) 54572) ((-346 . -189) 54526) ((-346 . -186) 54474) ((-346 . -190) 54453) ((-346 . 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53459) ((-335 . -1025) T) ((-335 . -72) T) ((-335 . -13) T) ((-335 . -1128) T) ((-335 . -552) 53441) ((-335 . -1013) T) ((-335 . -663) T) ((-332 . -333) 53420) ((-332 . -555) 53404) ((-332 . -950) 53388) ((-332 . -582) 53358) ((-332 . -654) 53328) ((-332 . -590) 53312) ((-332 . -588) 53281) ((-332 . -104) T) ((-332 . -25) T) ((-332 . -72) T) ((-332 . -13) T) ((-332 . -1128) T) ((-332 . -552) 53263) ((-332 . -1013) T) ((-332 . -23) T) ((-332 . -21) T) ((-332 . -968) 53247) ((-332 . -963) 53231) ((-332 . -82) 53210) ((-331 . -82) 53189) ((-331 . -963) 53173) ((-331 . -968) 53157) ((-331 . -21) T) ((-331 . -588) 53126) ((-331 . -23) T) ((-331 . -1013) T) ((-331 . -552) 53108) ((-331 . -1128) T) ((-331 . -13) T) ((-331 . -72) T) ((-331 . -25) T) ((-331 . -104) T) ((-331 . -590) 53092) ((-331 . -448) 53071) ((-331 . -557) 53036) ((-331 . -654) 53006) ((-331 . -582) 52976) ((-328 . -345) T) ((-328 . -120) T) ((-328 . -555) 52926) ((-328 . -590) 52891) ((-328 . -588) 52841) ((-328 . -104) T) 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10123) ((-114 . -454) NIL) ((-114 . -260) NIL) ((-114 . -34) T) ((-114 . -76) 10105) ((-114 . -183) 10087) ((-113 . -552) 10069) ((-112 . -160) T) ((-112 . -1013) T) ((-112 . -552) 10036) ((-112 . -1128) T) ((-112 . -13) T) ((-112 . -72) T) ((-112 . -747) 10018) ((-111 . -995) T) ((-111 . -428) 9999) ((-111 . -552) 9965) ((-111 . -555) 9946) ((-111 . -1013) T) ((-111 . -1128) T) ((-111 . -13) T) ((-111 . -72) T) ((-111 . -64) T) ((-110 . -995) T) ((-110 . -428) 9927) ((-110 . -552) 9893) ((-110 . -555) 9874) ((-110 . -1013) T) ((-110 . -1128) T) ((-110 . -13) T) ((-110 . -72) T) ((-110 . -64) T) ((-108 . -403) 9851) ((-108 . -555) 9747) ((-108 . -950) 9731) ((-108 . -1013) T) ((-108 . -552) 9713) ((-108 . -1128) T) ((-108 . -13) T) ((-108 . -72) T) ((-108 . -408) 9668) ((-108 . -241) 9645) ((-107 . -756) T) ((-107 . -552) 9627) ((-107 . -1013) T) ((-107 . -72) T) ((-107 . -13) T) ((-107 . -1128) T) ((-107 . -759) T) ((-107 . -23) T) ((-107 . -25) T) ((-107 . -663) T) ((-107 . -1025) T) 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-72) T) ((-1177 . -1176) 195475) ((-1177 . -322) 195459) ((-1177 . -758) 195438) ((-1177 . -755) 195417) ((-1177 . -124) 195401) ((-1177 . -34) T) ((-1177 . -13) T) ((-1177 . -1127) T) ((-1177 . -72) 195335) ((-1177 . -551) 195250) ((-1177 . -260) 195188) ((-1177 . -454) 195121) ((-1177 . -1012) 195074) ((-1177 . -427) 195058) ((-1177 . -552) 195019) ((-1177 . -241) 194971) ((-1177 . -537) 194948) ((-1177 . -243) 194925) ((-1177 . -592) 194909) ((-1177 . -19) 194893) ((-1174 . -1012) T) ((-1174 . -551) 194859) ((-1174 . -1127) T) ((-1174 . -13) T) ((-1174 . -72) T) ((-1167 . -1170) 194843) ((-1167 . -190) 194802) ((-1167 . -554) 194684) ((-1167 . -589) 194609) ((-1167 . -587) 194519) ((-1167 . -104) T) ((-1167 . -25) T) ((-1167 . -72) T) ((-1167 . -551) 194501) ((-1167 . -1012) T) ((-1167 . -23) T) ((-1167 . -21) T) ((-1167 . -969) T) ((-1167 . -1024) T) ((-1167 . -1059) T) ((-1167 . -662) T) ((-1167 . -960) T) ((-1167 . -186) 194454) ((-1167 . -13) T) ((-1167 . -1127) T) ((-1167 . -189) 194413) ((-1167 . -241) 194378) ((-1167 . -808) 194291) ((-1167 . -805) 194179) ((-1167 . -810) 194092) ((-1167 . -885) 194062) ((-1167 . -38) 193959) ((-1167 . -82) 193824) ((-1167 . -962) 193710) ((-1167 . -967) 193596) ((-1167 . -581) 193493) ((-1167 . -653) 193390) ((-1167 . -118) 193369) ((-1167 . -120) 193348) ((-1167 . -146) 193302) ((-1167 . -494) 193281) ((-1167 . -246) 193260) ((-1167 . -47) 193237) ((-1167 . -1156) 193214) ((-1167 . -35) 193180) ((-1167 . -66) 193146) ((-1167 . -239) 193112) ((-1167 . -431) 193078) ((-1167 . -1116) 193044) ((-1167 . -1113) 193010) ((-1167 . -914) 192976) ((-1164 . -277) 192920) ((-1164 . -949) 192886) ((-1164 . -353) 192852) ((-1164 . -38) 192709) ((-1164 . -554) 192583) ((-1164 . -589) 192472) ((-1164 . -587) 192346) ((-1164 . -969) T) ((-1164 . -1024) T) ((-1164 . -1059) T) ((-1164 . -662) T) ((-1164 . -960) T) ((-1164 . -82) 192196) ((-1164 . -962) 192085) ((-1164 . -967) 191974) ((-1164 . -21) T) ((-1164 . -23) T) ((-1164 . -1012) T) ((-1164 . -551) 191956) ((-1164 . -1127) T) ((-1164 . -13) T) ((-1164 . -72) T) ((-1164 . -25) T) ((-1164 . -104) T) ((-1164 . -581) 191813) ((-1164 . -653) 191670) ((-1164 . -118) 191631) ((-1164 . -120) 191592) ((-1164 . -146) T) ((-1164 . -494) T) ((-1164 . -246) T) ((-1164 . -47) 191536) ((-1163 . -1162) 191515) ((-1163 . -312) 191494) ((-1163 . -1132) 191473) ((-1163 . -831) 191452) ((-1163 . -494) 191406) ((-1163 . -146) 191340) ((-1163 . -554) 191159) ((-1163 . -653) 191006) ((-1163 . -581) 190853) ((-1163 . -38) 190700) ((-1163 . -390) 190679) ((-1163 . -258) 190658) ((-1163 . -589) 190558) ((-1163 . -587) 190443) ((-1163 . -969) T) ((-1163 . -1024) T) ((-1163 . -1059) T) ((-1163 . -662) T) ((-1163 . -960) T) ((-1163 . -82) 190263) ((-1163 . -962) 190104) ((-1163 . -967) 189945) ((-1163 . -21) T) ((-1163 . -23) T) ((-1163 . -1012) T) ((-1163 . -551) 189927) ((-1163 . -1127) T) ((-1163 . -13) T) ((-1163 . -72) T) ((-1163 . -25) T) ((-1163 . -104) T) ((-1163 . -246) 189881) ((-1163 . -201) 189860) ((-1163 . -914) 189826) ((-1163 . -1113) 189792) ((-1163 . -1116) 189758) ((-1163 . -431) 189724) ((-1163 . -239) 189690) ((-1163 . -66) 189656) ((-1163 . -35) 189622) ((-1163 . -1156) 189592) ((-1163 . -47) 189562) ((-1163 . -120) 189541) ((-1163 . -118) 189520) ((-1163 . -885) 189483) ((-1163 . -810) 189389) ((-1163 . -805) 189293) ((-1163 . -808) 189199) ((-1163 . -241) 189157) ((-1163 . -189) 189109) ((-1163 . -186) 189055) ((-1163 . -190) 189007) ((-1163 . -1160) 188991) ((-1163 . -949) 188975) ((-1158 . -1162) 188936) ((-1158 . -312) 188915) ((-1158 . -1132) 188894) ((-1158 . -831) 188873) ((-1158 . -494) 188827) ((-1158 . -146) 188761) ((-1158 . -554) 188510) ((-1158 . -653) 188357) ((-1158 . -581) 188204) ((-1158 . -38) 188051) ((-1158 . -390) 188030) ((-1158 . -258) 188009) ((-1158 . -589) 187909) ((-1158 . -587) 187794) ((-1158 . -969) T) ((-1158 . -1024) T) ((-1158 . -1059) T) ((-1158 . -662) T) ((-1158 . -960) T) ((-1158 . -82) 187614) ((-1158 . -962) 187455) ((-1158 . -967) 187296) ((-1158 . -21) T) ((-1158 . -23) T) ((-1158 . -1012) T) ((-1158 . -551) 187278) ((-1158 . -1127) T) ((-1158 . -13) T) ((-1158 . -72) T) ((-1158 . -25) T) ((-1158 . -104) T) ((-1158 . -246) 187232) ((-1158 . -201) 187211) ((-1158 . -914) 187177) ((-1158 . -1113) 187143) ((-1158 . -1116) 187109) ((-1158 . -431) 187075) ((-1158 . -239) 187041) ((-1158 . -66) 187007) ((-1158 . -35) 186973) ((-1158 . -1156) 186943) ((-1158 . -47) 186913) ((-1158 . -120) 186892) ((-1158 . -118) 186871) ((-1158 . -885) 186834) ((-1158 . -810) 186740) ((-1158 . -805) 186621) ((-1158 . -808) 186527) ((-1158 . -241) 186485) ((-1158 . -189) 186437) ((-1158 . -186) 186383) ((-1158 . -190) 186335) ((-1158 . -1160) 186319) ((-1158 . -949) 186254) ((-1146 . -1153) 186238) ((-1146 . -1064) 186216) ((-1146 . -552) NIL) ((-1146 . -260) 186203) ((-1146 . -454) 186151) ((-1146 . -277) 186128) ((-1146 . -949) 186011) ((-1146 . -353) 185995) ((-1146 . -38) 185827) ((-1146 . -82) 185632) ((-1146 . -962) 185458) ((-1146 . -967) 185284) ((-1146 . -587) 185194) ((-1146 . -589) 185083) ((-1146 . -581) 184915) ((-1146 . -653) 184747) ((-1146 . -554) 184503) ((-1146 . -118) 184482) ((-1146 . -120) 184461) ((-1146 . -47) 184438) ((-1146 . -327) 184422) ((-1146 . -579) 184370) ((-1146 . -808) 184314) ((-1146 . -805) 184221) ((-1146 . -810) 184132) ((-1146 . -795) NIL) ((-1146 . -820) 184111) ((-1146 . -1132) 184090) ((-1146 . -860) 184060) ((-1146 . -831) 184039) ((-1146 . -494) 183953) ((-1146 . -246) 183867) ((-1146 . -146) 183761) ((-1146 . -390) 183695) ((-1146 . -258) 183674) ((-1146 . -241) 183601) ((-1146 . -190) T) ((-1146 . -104) T) ((-1146 . -25) T) ((-1146 . -72) T) ((-1146 . -551) 183583) ((-1146 . -1012) T) ((-1146 . -23) T) ((-1146 . -21) T) ((-1146 . -969) T) ((-1146 . -1024) T) ((-1146 . -1059) T) ((-1146 . -662) T) ((-1146 . -960) T) ((-1146 . -186) 183570) ((-1146 . -13) T) ((-1146 . -1127) T) ((-1146 . -189) T) ((-1146 . -225) 183554) ((-1146 . -184) 183538) ((-1144 . -1005) 183522) ((-1144 . -556) 183506) ((-1144 . -1012) 183484) ((-1144 . -551) 183451) ((-1144 . -1127) 183429) ((-1144 . -13) 183407) ((-1144 . -72) 183385) ((-1144 . -1006) 183342) ((-1142 . -1141) 183321) ((-1142 . -914) 183287) ((-1142 . -1113) 183253) ((-1142 . -1116) 183219) ((-1142 . -431) 183185) ((-1142 . -239) 183151) ((-1142 . -66) 183117) ((-1142 . -35) 183083) ((-1142 . -1156) 183060) ((-1142 . -47) 183037) ((-1142 . -554) 182792) ((-1142 . -653) 182612) ((-1142 . -581) 182432) ((-1142 . -589) 182243) ((-1142 . -587) 182101) ((-1142 . -967) 181915) ((-1142 . -962) 181729) ((-1142 . -82) 181517) ((-1142 . -38) 181337) ((-1142 . -885) 181307) ((-1142 . -241) 181207) ((-1142 . -1139) 181191) ((-1142 . -969) T) ((-1142 . -1024) T) ((-1142 . -1059) T) ((-1142 . -662) T) ((-1142 . -960) T) ((-1142 . -21) T) ((-1142 . -23) T) ((-1142 . -1012) T) ((-1142 . -551) 181173) ((-1142 . -1127) T) ((-1142 . -13) T) ((-1142 . -72) T) ((-1142 . -25) T) ((-1142 . -104) T) ((-1142 . -118) 181101) ((-1142 . -120) 180983) ((-1142 . -552) 180656) ((-1142 . -184) 180626) ((-1142 . -808) 180480) ((-1142 . -810) 180280) ((-1142 . -805) 180078) ((-1142 . -225) 180048) ((-1142 . -189) 179910) ((-1142 . -186) 179766) ((-1142 . -190) 179674) ((-1142 . -312) 179653) ((-1142 . -1132) 179632) ((-1142 . -831) 179611) ((-1142 . -494) 179565) ((-1142 . -146) 179499) ((-1142 . -390) 179478) ((-1142 . -258) 179457) ((-1142 . -246) 179411) ((-1142 . -201) 179390) ((-1142 . -288) 179360) ((-1142 . -454) 179220) ((-1142 . -260) 179159) ((-1142 . -327) 179129) ((-1142 . -579) 179037) ((-1142 . -341) 179007) ((-1142 . -795) 178880) ((-1142 . -739) 178833) ((-1142 . -713) 178786) ((-1142 . -715) 178739) ((-1142 . -755) 178641) ((-1142 . -758) 178543) ((-1142 . -717) 178496) ((-1142 . -720) 178449) ((-1142 . -754) 178402) ((-1142 . -793) 178372) ((-1142 . -820) 178325) ((-1142 . -932) 178278) ((-1142 . -949) 178067) ((-1142 . -1064) 178019) ((-1142 . -903) 177989) ((-1137 . -1141) 177950) ((-1137 . -914) 177916) ((-1137 . -1113) 177882) ((-1137 . -1116) 177848) ((-1137 . -431) 177814) ((-1137 . -239) 177780) ((-1137 . -66) 177746) ((-1137 . -35) 177712) ((-1137 . -1156) 177689) ((-1137 . -47) 177666) ((-1137 . -554) 177467) ((-1137 . -653) 177269) ((-1137 . -581) 177071) ((-1137 . -589) 176926) ((-1137 . -587) 176766) ((-1137 . -967) 176562) ((-1137 . -962) 176358) ((-1137 . -82) 176110) ((-1137 . -38) 175912) ((-1137 . -885) 175882) ((-1137 . -241) 175710) ((-1137 . -1139) 175694) ((-1137 . -969) T) ((-1137 . -1024) T) ((-1137 . -1059) T) ((-1137 . -662) T) ((-1137 . -960) T) ((-1137 . -21) T) ((-1137 . -23) T) ((-1137 . -1012) T) ((-1137 . -551) 175676) ((-1137 . -1127) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -25) T) ((-1137 . -104) T) ((-1137 . -118) 175586) ((-1137 . -120) 175496) ((-1137 . -552) NIL) ((-1137 . -184) 175448) ((-1137 . -808) 175284) ((-1137 . -810) 175048) ((-1137 . -805) 174787) ((-1137 . -225) 174739) ((-1137 . -189) 174565) ((-1137 . -186) 174385) ((-1137 . -190) 174275) ((-1137 . -312) 174254) ((-1137 . -1132) 174233) ((-1137 . -831) 174212) ((-1137 . -494) 174166) ((-1137 . -146) 174100) ((-1137 . -390) 174079) ((-1137 . -258) 174058) ((-1137 . -246) 174012) ((-1137 . -201) 173991) ((-1137 . -288) 173943) ((-1137 . -454) 173677) ((-1137 . -260) 173562) ((-1137 . -327) 173514) ((-1137 . -579) 173466) ((-1137 . -341) 173418) ((-1137 . -795) NIL) ((-1137 . -739) NIL) ((-1137 . -713) NIL) ((-1137 . -715) NIL) ((-1137 . -755) NIL) ((-1137 . -758) NIL) ((-1137 . -717) NIL) ((-1137 . -720) NIL) ((-1137 . -754) NIL) ((-1137 . -793) 173370) ((-1137 . -820) NIL) ((-1137 . -932) NIL) ((-1137 . -949) 173336) ((-1137 . -1064) NIL) ((-1137 . -903) 173288) ((-1136 . -751) T) ((-1136 . -758) T) ((-1136 . -755) T) ((-1136 . -1012) T) ((-1136 . -551) 173270) ((-1136 . -1127) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -318) T) ((-1136 . -603) T) ((-1135 . -751) T) ((-1135 . -758) T) ((-1135 . -755) T) ((-1135 . -1012) T) ((-1135 . -551) 173252) ((-1135 . -1127) T) ((-1135 . -13) T) ((-1135 . -72) T) ((-1135 . -318) T) ((-1135 . -603) T) ((-1134 . -751) T) ((-1134 . -758) T) ((-1134 . -755) T) ((-1134 . -1012) T) ((-1134 . -551) 173234) ((-1134 . -1127) T) ((-1134 . -13) T) ((-1134 . -72) T) ((-1134 . -318) T) ((-1134 . -603) T) ((-1133 . -751) T) ((-1133 . -758) T) ((-1133 . -755) T) ((-1133 . -1012) T) ((-1133 . -551) 173216) ((-1133 . -1127) T) ((-1133 . -13) T) ((-1133 . -72) T) ((-1133 . -318) T) ((-1133 . -603) T) ((-1128 . -994) T) ((-1128 . -428) 173197) ((-1128 . -551) 173163) ((-1128 . -554) 173144) ((-1128 . -1012) T) ((-1128 . -1127) T) ((-1128 . -13) T) ((-1128 . -72) T) ((-1128 . -64) T) ((-1125 . -428) 173121) ((-1125 . -551) 173062) ((-1125 . -554) 173039) ((-1125 . -1012) 173017) ((-1125 . -1127) 172995) ((-1125 . -13) 172973) ((-1125 . -72) 172951) ((-1120 . -678) 172927) ((-1120 . -35) 172893) ((-1120 . -66) 172859) ((-1120 . -239) 172825) ((-1120 . -431) 172791) ((-1120 . -1116) 172757) ((-1120 . -1113) 172723) ((-1120 . -914) 172689) ((-1120 . -47) 172658) ((-1120 . -38) 172555) ((-1120 . -581) 172452) ((-1120 . -653) 172349) ((-1120 . -554) 172231) ((-1120 . -246) 172210) ((-1120 . -494) 172189) ((-1120 . -82) 172054) ((-1120 . -962) 171940) ((-1120 . -967) 171826) ((-1120 . -146) 171780) ((-1120 . -120) 171759) ((-1120 . -118) 171738) ((-1120 . -589) 171663) ((-1120 . -587) 171573) ((-1120 . -885) 171534) ((-1120 . -810) 171515) ((-1120 . -1127) T) ((-1120 . -13) T) ((-1120 . -805) 171494) ((-1120 . -960) T) ((-1120 . -662) T) ((-1120 . -1059) T) ((-1120 . -1024) T) ((-1120 . -969) T) ((-1120 . -21) T) ((-1120 . -23) T) ((-1120 . -1012) T) ((-1120 . -551) 171476) ((-1120 . -72) T) ((-1120 . -25) T) ((-1120 . -104) T) ((-1120 . -808) 171457) ((-1120 . -454) 171424) ((-1120 . -260) 171411) ((-1114 . -922) 171395) ((-1114 . -34) T) ((-1114 . -13) T) ((-1114 . -1127) T) ((-1114 . -72) 171349) ((-1114 . -551) 171284) ((-1114 . -260) 171222) ((-1114 . -454) 171155) ((-1114 . -1012) 171133) ((-1114 . -427) 171117) ((-1109 . -314) 171091) ((-1109 . -72) T) ((-1109 . -13) T) ((-1109 . -1127) T) ((-1109 . -551) 171073) ((-1109 . -1012) T) ((-1107 . -1012) T) ((-1107 . -551) 171055) ((-1107 . -1127) T) ((-1107 . -13) T) ((-1107 . -72) T) ((-1107 . -554) 171037) ((-1102 . -746) 171021) ((-1102 . -72) T) ((-1102 . -13) T) ((-1102 . -1127) T) ((-1102 . -551) 171003) ((-1102 . -1012) T) ((-1100 . -1105) 170982) ((-1100 . -183) 170930) ((-1100 . -76) 170878) ((-1100 . -260) 170676) ((-1100 . -454) 170428) ((-1100 . -427) 170363) ((-1100 . -124) 170311) ((-1100 . -552) NIL) ((-1100 . -193) 170259) ((-1100 . -548) 170238) ((-1100 . -243) 170217) ((-1100 . -1127) T) ((-1100 . -13) T) ((-1100 . -241) 170196) ((-1100 . -1012) T) ((-1100 . -551) 170178) ((-1100 . -72) T) ((-1100 . -34) T) ((-1100 . -537) 170157) ((-1096 . -1012) T) ((-1096 . -551) 170139) ((-1096 . -1127) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1095 . -751) T) ((-1095 . -758) T) ((-1095 . -755) T) ((-1095 . -1012) T) ((-1095 . -551) 170121) ((-1095 . -1127) T) ((-1095 . -13) T) ((-1095 . -72) T) ((-1095 . -318) T) ((-1095 . -603) T) ((-1094 . -751) T) ((-1094 . -758) T) ((-1094 . -755) T) ((-1094 . -1012) T) ((-1094 . -551) 170103) ((-1094 . -1127) T) ((-1094 . -13) T) ((-1094 . -72) T) ((-1094 . -318) T) ((-1093 . -1173) T) ((-1093 . -1012) T) ((-1093 . -551) 170070) ((-1093 . -1127) T) ((-1093 . -13) T) ((-1093 . -72) T) ((-1093 . -949) 170006) ((-1093 . -554) 169942) ((-1092 . -551) 169924) ((-1091 . -551) 169906) ((-1090 . -277) 169883) ((-1090 . -949) 169781) ((-1090 . -353) 169765) ((-1090 . -38) 169662) ((-1090 . -554) 169519) ((-1090 . -589) 169444) ((-1090 . -587) 169354) ((-1090 . -969) T) ((-1090 . -1024) T) ((-1090 . -1059) T) ((-1090 . -662) T) ((-1090 . -960) T) ((-1090 . -82) 169219) ((-1090 . -962) 169105) ((-1090 . -967) 168991) ((-1090 . -21) T) ((-1090 . -23) T) ((-1090 . -1012) T) ((-1090 . -551) 168973) ((-1090 . -1127) T) ((-1090 . -13) T) ((-1090 . -72) T) ((-1090 . -25) T) ((-1090 . -104) T) ((-1090 . -581) 168870) ((-1090 . -653) 168767) ((-1090 . -118) 168746) ((-1090 . -120) 168725) ((-1090 . -146) 168679) ((-1090 . -494) 168658) ((-1090 . -246) 168637) ((-1090 . -47) 168614) ((-1088 . -755) T) ((-1088 . -551) 168596) ((-1088 . -1012) T) ((-1088 . -72) T) ((-1088 . -13) T) ((-1088 . -1127) T) ((-1088 . -758) T) ((-1088 . -552) 168518) ((-1088 . -554) 168484) ((-1088 . -949) 168466) ((-1088 . -795) 168433) ((-1087 . -1170) 168417) ((-1087 . -190) 168376) ((-1087 . -554) 168258) ((-1087 . -589) 168183) ((-1087 . -587) 168093) ((-1087 . -104) T) ((-1087 . -25) T) ((-1087 . -72) T) ((-1087 . -551) 168075) ((-1087 . -1012) T) ((-1087 . -23) T) ((-1087 . -21) T) ((-1087 . -969) T) ((-1087 . -1024) T) ((-1087 . -1059) T) ((-1087 . -662) T) ((-1087 . -960) T) ((-1087 . -186) 168028) ((-1087 . -13) T) ((-1087 . -1127) T) ((-1087 . -189) 167987) ((-1087 . -241) 167952) ((-1087 . -808) 167865) ((-1087 . -805) 167753) ((-1087 . -810) 167666) ((-1087 . -885) 167636) ((-1087 . -38) 167533) ((-1087 . -82) 167398) ((-1087 . -962) 167284) ((-1087 . -967) 167170) ((-1087 . -581) 167067) ((-1087 . -653) 166964) ((-1087 . -118) 166943) ((-1087 . -120) 166922) ((-1087 . -146) 166876) ((-1087 . -494) 166855) ((-1087 . -246) 166834) ((-1087 . -47) 166811) ((-1087 . -1156) 166788) ((-1087 . -35) 166754) ((-1087 . -66) 166720) ((-1087 . -239) 166686) ((-1087 . -431) 166652) ((-1087 . -1116) 166618) ((-1087 . -1113) 166584) ((-1087 . -914) 166550) ((-1086 . -1162) 166511) ((-1086 . -312) 166490) ((-1086 . -1132) 166469) ((-1086 . -831) 166448) ((-1086 . -494) 166402) ((-1086 . -146) 166336) ((-1086 . -554) 166085) ((-1086 . -653) 165932) ((-1086 . -581) 165779) ((-1086 . -38) 165626) ((-1086 . -390) 165605) ((-1086 . -258) 165584) ((-1086 . -589) 165484) ((-1086 . -587) 165369) ((-1086 . -969) T) ((-1086 . -1024) T) ((-1086 . -1059) T) ((-1086 . -662) T) ((-1086 . -960) T) ((-1086 . -82) 165189) ((-1086 . -962) 165030) ((-1086 . -967) 164871) ((-1086 . -21) T) ((-1086 . -23) T) ((-1086 . -1012) T) ((-1086 . -551) 164853) ((-1086 . -1127) T) ((-1086 . -13) T) ((-1086 . -72) T) ((-1086 . -25) T) ((-1086 . -104) T) ((-1086 . -246) 164807) ((-1086 . -201) 164786) ((-1086 . -914) 164752) ((-1086 . -1113) 164718) ((-1086 . -1116) 164684) ((-1086 . -431) 164650) ((-1086 . -239) 164616) ((-1086 . -66) 164582) ((-1086 . -35) 164548) ((-1086 . -1156) 164518) ((-1086 . -47) 164488) ((-1086 . -120) 164467) ((-1086 . -118) 164446) ((-1086 . -885) 164409) ((-1086 . -810) 164315) ((-1086 . -805) 164196) ((-1086 . -808) 164102) ((-1086 . -241) 164060) ((-1086 . -189) 164012) ((-1086 . -186) 163958) ((-1086 . -190) 163910) ((-1086 . -1160) 163894) ((-1086 . -949) 163829) ((-1083 . -1153) 163813) ((-1083 . -1064) 163791) ((-1083 . -552) NIL) ((-1083 . -260) 163778) ((-1083 . -454) 163726) ((-1083 . -277) 163703) ((-1083 . -949) 163586) ((-1083 . -353) 163570) ((-1083 . -38) 163402) ((-1083 . -82) 163207) ((-1083 . -962) 163033) ((-1083 . -967) 162859) ((-1083 . -587) 162769) ((-1083 . -589) 162658) ((-1083 . -581) 162490) ((-1083 . -653) 162322) ((-1083 . -554) 162099) ((-1083 . -118) 162078) ((-1083 . -120) 162057) ((-1083 . -47) 162034) ((-1083 . -327) 162018) ((-1083 . -579) 161966) ((-1083 . -808) 161910) ((-1083 . -805) 161817) ((-1083 . -810) 161728) ((-1083 . -795) NIL) ((-1083 . -820) 161707) ((-1083 . -1132) 161686) ((-1083 . -860) 161656) ((-1083 . -831) 161635) ((-1083 . -494) 161549) ((-1083 . -246) 161463) ((-1083 . -146) 161357) ((-1083 . -390) 161291) ((-1083 . -258) 161270) ((-1083 . -241) 161197) ((-1083 . -190) T) ((-1083 . -104) T) ((-1083 . -25) T) ((-1083 . -72) T) ((-1083 . -551) 161179) ((-1083 . -1012) T) ((-1083 . -23) T) ((-1083 . -21) T) ((-1083 . -969) T) ((-1083 . -1024) T) ((-1083 . -1059) T) ((-1083 . -662) T) ((-1083 . -960) T) ((-1083 . -186) 161166) ((-1083 . -13) T) ((-1083 . -1127) T) ((-1083 . -189) T) ((-1083 . -225) 161150) ((-1083 . -184) 161134) ((-1080 . -1141) 161095) ((-1080 . -914) 161061) ((-1080 . -1113) 161027) ((-1080 . -1116) 160993) ((-1080 . -431) 160959) ((-1080 . -239) 160925) ((-1080 . -66) 160891) ((-1080 . -35) 160857) ((-1080 . -1156) 160834) ((-1080 . -47) 160811) ((-1080 . -554) 160612) ((-1080 . -653) 160414) ((-1080 . -581) 160216) ((-1080 . -589) 160071) ((-1080 . -587) 159911) ((-1080 . -967) 159707) ((-1080 . -962) 159503) ((-1080 . -82) 159255) ((-1080 . -38) 159057) ((-1080 . -885) 159027) ((-1080 . -241) 158855) ((-1080 . -1139) 158839) ((-1080 . -969) T) ((-1080 . -1024) T) ((-1080 . -1059) T) ((-1080 . -662) T) ((-1080 . -960) T) ((-1080 . -21) T) ((-1080 . -23) T) ((-1080 . -1012) T) ((-1080 . -551) 158821) ((-1080 . -1127) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1080 . -25) T) ((-1080 . -104) T) ((-1080 . -118) 158731) ((-1080 . -120) 158641) ((-1080 . -552) NIL) ((-1080 . -184) 158593) ((-1080 . -808) 158429) ((-1080 . -810) 158193) ((-1080 . -805) 157932) ((-1080 . -225) 157884) ((-1080 . -189) 157710) ((-1080 . -186) 157530) ((-1080 . -190) 157420) ((-1080 . -312) 157399) ((-1080 . -1132) 157378) ((-1080 . -831) 157357) ((-1080 . -494) 157311) ((-1080 . -146) 157245) ((-1080 . -390) 157224) ((-1080 . -258) 157203) ((-1080 . -246) 157157) ((-1080 . -201) 157136) ((-1080 . -288) 157088) ((-1080 . -454) 156822) ((-1080 . -260) 156707) ((-1080 . -327) 156659) ((-1080 . -579) 156611) ((-1080 . -341) 156563) ((-1080 . -795) NIL) ((-1080 . -739) NIL) ((-1080 . -713) NIL) ((-1080 . -715) NIL) ((-1080 . -755) NIL) ((-1080 . -758) NIL) ((-1080 . -717) NIL) ((-1080 . -720) NIL) ((-1080 . -754) NIL) ((-1080 . -793) 156515) ((-1080 . -820) NIL) ((-1080 . -932) NIL) ((-1080 . -949) 156481) ((-1080 . -1064) NIL) ((-1080 . -903) 156433) ((-1079 . -994) T) ((-1079 . -428) 156414) ((-1079 . -551) 156380) ((-1079 . -554) 156361) ((-1079 . -1012) T) ((-1079 . -1127) T) ((-1079 . -13) T) ((-1079 . -72) T) ((-1079 . -64) T) ((-1078 . -1012) T) ((-1078 . -551) 156343) ((-1078 . -1127) T) 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. -615) 155204) ((-1067 . -592) 155188) ((-1067 . -243) 155165) ((-1067 . -241) 155117) ((-1067 . -537) 155094) ((-1067 . -552) 155055) ((-1067 . -427) 155039) ((-1067 . -1012) 155017) ((-1067 . -454) 154950) ((-1067 . -260) 154888) ((-1067 . -551) 154823) ((-1067 . -72) 154777) ((-1067 . -1127) T) ((-1067 . -13) T) ((-1067 . -34) T) ((-1067 . -124) 154761) ((-1067 . -1166) 154745) ((-1067 . -922) 154729) ((-1067 . -1062) 154713) ((-1067 . -554) 154690) ((-1065 . -994) T) ((-1065 . -428) 154671) ((-1065 . -551) 154637) ((-1065 . -554) 154618) ((-1065 . -1012) T) ((-1065 . -1127) T) ((-1065 . -13) T) ((-1065 . -72) T) ((-1065 . -64) T) ((-1063 . -1105) 154597) ((-1063 . -183) 154545) ((-1063 . -76) 154493) ((-1063 . -260) 154291) ((-1063 . -454) 154043) ((-1063 . -427) 153978) ((-1063 . -124) 153926) ((-1063 . -552) NIL) ((-1063 . -193) 153874) ((-1063 . -548) 153853) ((-1063 . -243) 153832) ((-1063 . -1127) T) ((-1063 . -13) T) ((-1063 . -241) 153811) ((-1063 . -1012) T) ((-1063 . 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T) ((-1025 . -537) 146464) ((-1025 . -949) 146293) ((-1025 . -554) 146097) ((-1025 . -353) 146066) ((-1025 . -579) 145974) ((-1025 . -589) 145813) ((-1025 . -327) 145783) ((-1025 . -318) 145762) ((-1025 . -190) 145715) ((-1025 . -587) 145503) ((-1025 . -969) 145482) ((-1025 . -1024) 145461) ((-1025 . -1059) 145440) ((-1025 . -662) 145419) ((-1025 . -960) 145398) ((-1025 . -186) 145294) ((-1025 . -189) 145196) ((-1025 . -225) 145166) ((-1025 . -805) 145038) ((-1025 . -810) 144912) ((-1025 . -808) 144845) ((-1025 . -184) 144815) ((-1025 . -551) 144512) ((-1025 . -967) 144437) ((-1025 . -962) 144342) ((-1025 . -82) 144262) ((-1025 . -104) 144137) ((-1025 . -25) 143974) ((-1025 . -72) 143711) ((-1025 . -13) T) ((-1025 . -1127) T) ((-1025 . -1012) 143467) ((-1025 . -23) 143323) ((-1025 . -21) 143238) ((-1021 . -1022) 143222) ((-1021 . |MappingCategory|) 143196) ((-1021 . -1127) T) ((-1021 . -80) 143180) ((-1021 . -1012) T) ((-1021 . -551) 143162) ((-1021 . -13) T) ((-1021 . -72) T) ((-1016 . -1015) 143126) ((-1016 . -72) T) ((-1016 . -551) 143108) ((-1016 . -1012) T) ((-1016 . -241) 143064) ((-1016 . -1127) T) ((-1016 . -13) T) ((-1016 . -556) 142979) ((-1014 . -1015) 142931) ((-1014 . -72) T) ((-1014 . -551) 142913) ((-1014 . -1012) T) ((-1014 . -241) 142869) ((-1014 . -1127) T) ((-1014 . -13) T) ((-1014 . -556) 142772) ((-1013 . -318) T) ((-1013 . -72) T) ((-1013 . -13) T) ((-1013 . -1127) T) ((-1013 . -551) 142754) ((-1013 . -1012) T) ((-1008 . -367) 142738) ((-1008 . -1010) 142722) ((-1008 . -318) 142701) ((-1008 . -193) 142685) ((-1008 . -552) 142646) ((-1008 . -124) 142630) ((-1008 . -427) 142614) ((-1008 . -1012) T) ((-1008 . -454) 142547) ((-1008 . -260) 142485) ((-1008 . -551) 142467) ((-1008 . -72) T) ((-1008 . -1127) T) ((-1008 . -13) T) ((-1008 . -34) T) ((-1008 . -76) 142451) ((-1008 . -183) 142435) ((-1007 . -994) T) ((-1007 . -428) 142416) ((-1007 . -551) 142382) ((-1007 . -554) 142363) ((-1007 . -1012) T) ((-1007 . -1127) T) ((-1007 . -13) T) ((-1007 . -72) T) ((-1007 . -64) T) ((-1003 . -1127) T) ((-1003 . -13) T) ((-1003 . -1012) 142333) ((-1003 . -551) 142292) ((-1003 . -72) 142262) ((-1002 . -994) T) ((-1002 . -428) 142243) ((-1002 . -551) 142209) ((-1002 . -554) 142190) ((-1002 . -1012) T) ((-1002 . -1127) T) ((-1002 . -13) T) ((-1002 . -72) T) ((-1002 . -64) T) ((-1000 . -1005) 142174) ((-1000 . -556) 142158) ((-1000 . -1012) 142136) ((-1000 . -551) 142103) ((-1000 . -1127) 142081) ((-1000 . -13) 142059) ((-1000 . -72) 142037) ((-1000 . -1006) 141995) ((-999 . -228) 141979) ((-999 . -554) 141963) ((-999 . -949) 141947) ((-999 . -758) T) ((-999 . -72) T) ((-999 . -1012) T) ((-999 . -551) 141929) ((-999 . -755) T) ((-999 . -186) 141916) ((-999 . -13) T) ((-999 . -1127) T) ((-999 . -189) T) ((-998 . -213) 141855) ((-998 . -554) 141599) ((-998 . -949) 141429) ((-998 . -552) NIL) ((-998 . -277) 141391) ((-998 . -353) 141375) ((-998 . -38) 141227) ((-998 . -82) 141052) ((-998 . -962) 140898) ((-998 . -967) 140744) ((-998 . -587) 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T) ((-835 . -551) 122308) ((-829 . -717) T) ((-829 . -758) T) ((-829 . -755) T) ((-829 . -1012) T) ((-829 . -551) 122290) ((-829 . -1127) T) ((-829 . -13) T) ((-829 . -72) T) ((-829 . -25) T) ((-829 . -662) T) ((-829 . -1024) T) ((-824 . -312) T) ((-824 . -1132) T) ((-824 . -831) T) ((-824 . -494) T) ((-824 . -146) T) ((-824 . -554) 122227) ((-824 . -653) 122179) ((-824 . -581) 122131) ((-824 . -38) 122083) ((-824 . -390) T) ((-824 . -258) T) ((-824 . -589) 122035) ((-824 . -587) 121972) ((-824 . -969) T) ((-824 . -1024) T) ((-824 . -1059) T) ((-824 . -662) T) ((-824 . -960) T) ((-824 . -82) 121903) ((-824 . -962) 121855) ((-824 . -967) 121807) ((-824 . -21) T) ((-824 . -23) T) ((-824 . -1012) T) ((-824 . -551) 121789) ((-824 . -1127) T) ((-824 . -13) T) ((-824 . -72) T) ((-824 . -25) T) ((-824 . -104) T) ((-824 . -246) T) ((-824 . -201) T) ((-816 . -299) T) ((-816 . -1064) T) ((-816 . -318) T) ((-816 . -118) T) ((-816 . -312) T) ((-816 . -1132) T) ((-816 . -831) T) ((-816 . -494) T) 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-72) T) ((-812 . -1024) T) ((-812 . -411) T) ((-812 . -1127) T) ((-812 . -13) T) ((-812 . -241) 121144) ((-811 . -92) 121128) ((-811 . -427) 121112) ((-811 . -1012) 121090) ((-811 . -454) 121023) ((-811 . -260) 120961) ((-811 . -551) 120875) ((-811 . -72) 120829) ((-811 . -1127) T) ((-811 . -13) T) ((-811 . -34) T) ((-811 . -922) 120813) ((-802 . -755) T) ((-802 . -551) 120795) ((-802 . -1012) T) ((-802 . -72) T) ((-802 . -13) T) ((-802 . -1127) T) ((-802 . -758) T) ((-802 . -949) 120772) ((-802 . -554) 120749) ((-799 . -1012) T) ((-799 . -551) 120731) ((-799 . -1127) T) ((-799 . -13) T) ((-799 . -72) T) ((-799 . -949) 120699) ((-799 . -554) 120667) ((-797 . -1012) T) ((-797 . -551) 120649) ((-797 . -1127) T) ((-797 . -13) T) ((-797 . -72) T) ((-794 . -1012) T) ((-794 . -551) 120631) ((-794 . -1127) T) ((-794 . -13) T) ((-794 . -72) T) ((-784 . -994) T) ((-784 . -428) 120612) ((-784 . -551) 120578) ((-784 . -554) 120559) ((-784 . -1012) T) ((-784 . -1127) T) ((-784 . -13) T) ((-784 . -72) T) ((-784 . -64) T) ((-784 . -1173) T) ((-782 . -1012) T) ((-782 . -551) 120541) ((-782 . -1127) T) ((-782 . -13) T) ((-782 . -72) T) ((-782 . -554) 120523) ((-781 . -1127) T) ((-781 . -13) T) ((-781 . -551) 120398) ((-781 . -1012) 120349) ((-781 . -72) 120300) ((-780 . -903) 120284) ((-780 . -1064) 120262) ((-780 . -949) 120129) ((-780 . -554) 120028) ((-780 . -552) 119831) ((-780 . -932) 119810) ((-780 . -820) 119789) ((-780 . -793) 119773) ((-780 . -754) 119752) ((-780 . -720) 119731) ((-780 . -717) 119710) ((-780 . -758) 119664) ((-780 . -755) 119618) ((-780 . -715) 119597) ((-780 . -713) 119576) ((-780 . -739) 119555) ((-780 . -795) 119480) ((-780 . -341) 119464) ((-780 . -579) 119412) ((-780 . -589) 119328) ((-780 . -327) 119312) ((-780 . -241) 119270) ((-780 . -260) 119235) ((-780 . -454) 119147) ((-780 . -288) 119131) ((-780 . -201) T) ((-780 . -82) 119062) ((-780 . -962) 119014) ((-780 . -967) 118966) ((-780 . -246) T) ((-780 . -653) 118918) ((-780 . -581) 118870) ((-780 . -587) 118807) ((-780 . -38) 118759) ((-780 . -258) T) ((-780 . -390) T) ((-780 . -146) T) ((-780 . -494) T) ((-780 . -831) T) ((-780 . -1132) T) ((-780 . -312) T) ((-780 . -190) 118738) ((-780 . -186) 118686) ((-780 . -189) 118640) ((-780 . -225) 118624) ((-780 . -805) 118548) ((-780 . -810) 118474) ((-780 . -808) 118433) ((-780 . -184) 118417) ((-780 . -120) 118371) ((-780 . -118) 118350) ((-780 . -104) T) ((-780 . -25) T) ((-780 . -72) T) ((-780 . -13) T) ((-780 . -1127) T) ((-780 . -551) 118332) ((-780 . -1012) T) ((-780 . -23) T) ((-780 . -21) T) ((-780 . -960) T) ((-780 . -662) T) ((-780 . -1059) T) ((-780 . -1024) T) ((-780 . -969) T) ((-779 . -903) 118309) ((-779 . -1064) NIL) ((-779 . -949) 118286) ((-779 . -554) 118216) ((-779 . -552) NIL) ((-779 . -932) NIL) ((-779 . -820) NIL) ((-779 . -793) 118193) ((-779 . -754) NIL) ((-779 . -720) NIL) ((-779 . -717) NIL) ((-779 . -758) NIL) ((-779 . -755) NIL) ((-779 . -715) NIL) ((-779 . -713) NIL) ((-779 . -739) NIL) ((-779 . -795) NIL) ((-779 . -341) 118170) ((-779 . -579) 118147) ((-779 . -589) 118092) ((-779 . -327) 118069) ((-779 . -241) 117999) ((-779 . -260) 117943) ((-779 . -454) 117806) ((-779 . -288) 117783) ((-779 . -201) T) ((-779 . -82) 117700) ((-779 . -962) 117645) ((-779 . -967) 117590) ((-779 . -246) T) ((-779 . -653) 117535) ((-779 . -581) 117480) ((-779 . -587) 117410) ((-779 . -38) 117355) ((-779 . -258) T) ((-779 . -390) T) ((-779 . -146) T) ((-779 . -494) T) ((-779 . -831) T) ((-779 . -1132) T) ((-779 . -312) T) ((-779 . -190) NIL) ((-779 . -186) NIL) ((-779 . -189) NIL) ((-779 . -225) 117332) ((-779 . -805) NIL) ((-779 . -810) NIL) ((-779 . -808) NIL) ((-779 . -184) 117309) ((-779 . -120) T) ((-779 . -118) NIL) ((-779 . -104) T) ((-779 . -25) T) ((-779 . -72) T) ((-779 . -13) T) ((-779 . -1127) T) ((-779 . -551) 117291) ((-779 . -1012) T) ((-779 . -23) T) ((-779 . -21) T) ((-779 . -960) T) ((-779 . -662) T) ((-779 . -1059) T) ((-779 . -1024) T) ((-779 . -969) T) ((-777 . -778) 117275) ((-777 . -831) T) ((-777 . -494) T) ((-777 . -246) T) ((-777 . -146) T) ((-777 . -554) 117247) ((-777 . -653) 117234) ((-777 . -581) 117221) ((-777 . -967) 117208) ((-777 . -962) 117195) ((-777 . -82) 117180) ((-777 . -38) 117167) ((-777 . -390) T) ((-777 . -258) T) ((-777 . -960) T) ((-777 . -662) T) ((-777 . -1059) T) ((-777 . -1024) T) ((-777 . -969) T) ((-777 . -21) T) ((-777 . -587) 117139) ((-777 . -23) T) ((-777 . -1012) T) ((-777 . -551) 117121) ((-777 . -1127) T) ((-777 . -13) T) ((-777 . -72) T) ((-777 . -25) T) ((-777 . -104) T) ((-777 . -589) 117108) ((-777 . -120) T) ((-774 . -960) T) ((-774 . -662) T) ((-774 . -1059) T) ((-774 . -1024) T) ((-774 . -969) T) ((-774 . -21) T) ((-774 . -587) 117053) ((-774 . -23) T) ((-774 . -1012) T) ((-774 . -551) 117015) ((-774 . -1127) T) ((-774 . -13) T) ((-774 . -72) T) ((-774 . -25) T) ((-774 . -104) T) ((-774 . -589) 116975) ((-774 . -554) 116910) ((-774 . -428) 116887) ((-774 . -38) 116857) ((-774 . -82) 116822) ((-774 . -962) 116792) 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-967) 116137) ((-763 . -962) 116121) ((-763 . -82) 116100) ((-763 . -960) T) ((-763 . -662) T) ((-763 . -1059) T) ((-763 . -1024) T) ((-763 . -969) T) ((-763 . -38) 116070) ((-762 . -760) 116054) ((-762 . -949) 115952) ((-762 . -554) 115871) ((-762 . -353) 115855) ((-762 . -653) 115825) ((-762 . -581) 115795) ((-762 . -589) 115769) ((-762 . -587) 115728) ((-762 . -104) T) ((-762 . -25) T) ((-762 . -72) T) ((-762 . -13) T) ((-762 . -1127) T) ((-762 . -551) 115710) ((-762 . -1012) T) ((-762 . -23) T) ((-762 . -21) T) ((-762 . -967) 115694) ((-762 . -962) 115678) ((-762 . -82) 115657) ((-762 . -960) T) ((-762 . -662) T) ((-762 . -1059) T) ((-762 . -1024) T) ((-762 . -969) T) ((-762 . -38) 115627) ((-756 . -758) T) ((-756 . -1127) T) ((-756 . -13) T) ((-756 . -72) T) ((-756 . -428) 115611) ((-756 . -551) 115559) ((-756 . -554) 115543) ((-749 . -1012) T) ((-749 . -551) 115525) ((-749 . -1127) T) ((-749 . -13) T) ((-749 . -72) T) ((-749 . -353) 115509) ((-749 . -554) 115382) ((-749 . -949) 115280) ((-749 . -21) 115235) ((-749 . -587) 115155) ((-749 . -23) 115110) ((-749 . -25) 115065) ((-749 . -104) 115020) ((-749 . -754) 114999) ((-749 . -720) 114978) ((-749 . -717) 114957) ((-749 . -758) 114936) ((-749 . -755) 114915) ((-749 . -715) 114894) ((-749 . -713) 114873) ((-749 . -960) 114852) ((-749 . -662) 114831) ((-749 . -1059) 114810) ((-749 . -1024) 114789) ((-749 . -969) 114768) ((-749 . -589) 114741) ((-749 . -120) 114720) ((-748 . -746) 114702) ((-748 . -72) T) ((-748 . -13) T) ((-748 . -1127) T) ((-748 . -551) 114684) ((-748 . -1012) T) ((-744 . -960) T) ((-744 . -662) T) ((-744 . -1059) T) ((-744 . -1024) T) ((-744 . -969) T) ((-744 . -21) T) ((-744 . -587) 114629) ((-744 . -23) T) ((-744 . -1012) T) ((-744 . -551) 114611) ((-744 . -1127) T) ((-744 . -13) T) ((-744 . -72) T) ((-744 . -25) T) ((-744 . -104) T) ((-744 . -589) 114571) ((-744 . -554) 114526) ((-744 . -949) 114496) ((-744 . -241) 114475) ((-744 . -120) 114454) ((-744 . -118) 114433) ((-744 . -38) 114403) ((-744 . -82) 114368) ((-744 . -962) 114338) ((-744 . -967) 114308) ((-744 . -581) 114278) ((-744 . -653) 114248) ((-742 . -1012) T) ((-742 . -551) 114230) ((-742 . -1127) T) ((-742 . -13) T) ((-742 . -72) T) ((-742 . -353) 114214) ((-742 . -554) 114087) ((-742 . -949) 113985) ((-742 . -21) 113940) ((-742 . -587) 113860) ((-742 . -23) 113815) ((-742 . -25) 113770) ((-742 . -104) 113725) ((-742 . -754) 113704) ((-742 . -720) 113683) ((-742 . -717) 113662) ((-742 . -758) 113641) ((-742 . -755) 113620) ((-742 . -715) 113599) ((-742 . -713) 113578) ((-742 . -960) 113557) ((-742 . -662) 113536) ((-742 . -1059) 113515) ((-742 . -1024) 113494) ((-742 . -969) 113473) ((-742 . -589) 113446) ((-742 . -120) 113425) ((-740 . -644) 113409) ((-740 . -554) 113364) ((-740 . -653) 113334) ((-740 . -581) 113304) ((-740 . -589) 113278) ((-740 . -587) 113237) ((-740 . -104) T) ((-740 . -25) T) ((-740 . -72) T) ((-740 . -13) T) ((-740 . -1127) T) ((-740 . -551) 113219) ((-740 . -1012) T) ((-740 . -23) T) ((-740 . -21) T) ((-740 . -967) 113203) ((-740 . -962) 113187) ((-740 . -82) 113166) ((-740 . -960) T) ((-740 . -662) T) ((-740 . -1059) T) ((-740 . -1024) T) ((-740 . -969) T) ((-740 . -38) 113136) ((-740 . -190) 113115) ((-740 . -186) 113088) ((-740 . -189) 113067) ((-738 . -334) 113051) ((-738 . -554) 113035) ((-738 . -949) 113019) ((-738 . -758) T) ((-738 . -755) T) ((-738 . -1024) T) ((-738 . -72) T) ((-738 . -13) T) ((-738 . -1127) T) ((-738 . -551) 113001) ((-738 . -1012) T) ((-738 . -662) T) ((-738 . -753) T) ((-738 . -765) T) ((-737 . -228) 112985) ((-737 . -554) 112969) ((-737 . -949) 112953) ((-737 . -758) T) ((-737 . -72) T) ((-737 . -1012) T) ((-737 . -551) 112935) ((-737 . -755) T) ((-737 . -186) 112922) ((-737 . -13) T) ((-737 . -1127) T) ((-737 . -189) T) ((-736 . -82) 112857) ((-736 . -962) 112808) ((-736 . -967) 112759) ((-736 . -21) T) ((-736 . -587) 112695) ((-736 . -23) T) ((-736 . -1012) T) ((-736 . -551) 112664) ((-736 . -1127) T) ((-736 . -13) T) ((-736 . -72) T) ((-736 . -25) T) ((-736 . -104) T) ((-736 . -589) 112615) ((-736 . -190) T) ((-736 . -554) 112524) ((-736 . -969) T) ((-736 . -1024) T) ((-736 . -1059) T) ((-736 . -662) T) ((-736 . -960) T) ((-736 . -186) 112511) ((-736 . -189) T) ((-736 . -428) 112495) ((-736 . -312) 112474) ((-736 . -1132) 112453) ((-736 . -831) 112432) ((-736 . -494) 112411) ((-736 . -146) 112390) ((-736 . -653) 112327) ((-736 . -581) 112264) ((-736 . -38) 112201) ((-736 . -390) 112180) ((-736 . -258) 112159) ((-736 . -246) 112138) ((-736 . -201) 112117) ((-735 . -213) 112056) ((-735 . -554) 111800) ((-735 . -949) 111630) ((-735 . -552) NIL) ((-735 . -277) 111592) ((-735 . -353) 111576) ((-735 . -38) 111428) ((-735 . -82) 111253) ((-735 . -962) 111099) ((-735 . -967) 110945) ((-735 . -587) 110855) ((-735 . -589) 110744) ((-735 . -581) 110596) ((-735 . -653) 110448) ((-735 . -118) 110427) ((-735 . -120) 110406) ((-735 . -146) 110320) ((-735 . -494) 110254) ((-735 . -246) 110188) ((-735 . -47) 110150) ((-735 . -327) 110134) ((-735 . -579) 110082) ((-735 . -390) 110036) ((-735 . -454) 109901) ((-735 . -808) 109837) ((-735 . -805) 109736) ((-735 . -810) 109639) ((-735 . -795) NIL) ((-735 . -820) 109618) ((-735 . -1132) 109597) ((-735 . -860) 109544) ((-735 . -260) 109531) ((-735 . -190) 109510) ((-735 . -104) T) ((-735 . -25) T) ((-735 . -72) T) ((-735 . -551) 109492) ((-735 . -1012) T) ((-735 . -23) T) ((-735 . -21) T) ((-735 . -969) T) ((-735 . -1024) T) ((-735 . -1059) T) ((-735 . -662) T) ((-735 . -960) T) ((-735 . -186) 109440) ((-735 . -13) T) ((-735 . -1127) T) ((-735 . -189) 109394) ((-735 . -225) 109378) ((-735 . -184) 109362) ((-734 . -196) 109341) ((-734 . -1185) 109311) ((-734 . -720) 109290) ((-734 . -717) 109269) ((-734 . -758) 109223) ((-734 . -755) 109177) ((-734 . -715) 109156) ((-734 . -716) 109135) ((-734 . -653) 109080) ((-734 . -581) 109005) ((-734 . -243) 108982) ((-734 . -241) 108959) ((-734 . -427) 108943) ((-734 . -454) 108876) ((-734 . -260) 108814) ((-734 . -34) T) ((-734 . -537) 108791) ((-734 . -949) 108620) ((-734 . -554) 108424) ((-734 . -353) 108393) ((-734 . -579) 108301) ((-734 . -589) 108140) ((-734 . -327) 108110) ((-734 . -318) 108089) ((-734 . -190) 108042) ((-734 . -587) 107830) ((-734 . -969) 107809) ((-734 . -1024) 107788) ((-734 . -1059) 107767) ((-734 . -662) 107746) ((-734 . -960) 107725) ((-734 . -186) 107621) ((-734 . -189) 107523) ((-734 . -225) 107493) ((-734 . -805) 107365) ((-734 . -810) 107239) ((-734 . -808) 107172) ((-734 . -184) 107142) ((-734 . -551) 106839) ((-734 . -967) 106764) ((-734 . -962) 106669) ((-734 . -82) 106589) ((-734 . -104) 106464) ((-734 . -25) 106301) ((-734 . -72) 106038) ((-734 . -13) T) ((-734 . -1127) T) ((-734 . -1012) 105794) ((-734 . -23) 105650) ((-734 . -21) 105565) ((-721 . -719) 105549) ((-721 . -758) 105528) ((-721 . -755) 105507) ((-721 . -949) 105300) ((-721 . -554) 105153) ((-721 . -353) 105117) ((-721 . -241) 105075) ((-721 . -260) 105040) ((-721 . -454) 104952) ((-721 . -288) 104936) ((-721 . -318) 104915) ((-721 . -552) 104876) ((-721 . -120) 104855) ((-721 . -118) 104834) ((-721 . -653) 104818) ((-721 . -581) 104802) ((-721 . -589) 104776) ((-721 . -587) 104735) ((-721 . -104) T) ((-721 . -25) T) ((-721 . -72) T) ((-721 . -13) T) ((-721 . -1127) T) ((-721 . -551) 104717) ((-721 . -1012) T) ((-721 . -23) T) ((-721 . -21) T) ((-721 . -967) 104701) ((-721 . -962) 104685) ((-721 . -82) 104664) ((-721 . -960) T) ((-721 . -662) T) ((-721 . -1059) T) ((-721 . -1024) T) ((-721 . -969) T) ((-721 . -38) 104648) ((-703 . -1153) 104632) ((-703 . -1064) 104610) ((-703 . -552) NIL) ((-703 . -260) 104597) ((-703 . -454) 104545) ((-703 . -277) 104522) ((-703 . -949) 104384) ((-703 . -353) 104368) ((-703 . -38) 104200) ((-703 . -82) 104005) ((-703 . -962) 103831) ((-703 . -967) 103657) ((-703 . -587) 103567) ((-703 . -589) 103456) ((-703 . -581) 103288) ((-703 . -653) 103120) ((-703 . -554) 102876) ((-703 . -118) 102855) ((-703 . -120) 102834) ((-703 . -47) 102811) ((-703 . -327) 102795) ((-703 . -579) 102743) ((-703 . -808) 102687) ((-703 . -805) 102594) ((-703 . -810) 102505) ((-703 . -795) NIL) ((-703 . -820) 102484) ((-703 . -1132) 102463) ((-703 . -860) 102433) ((-703 . -831) 102412) ((-703 . -494) 102326) ((-703 . -246) 102240) ((-703 . -146) 102134) ((-703 . -390) 102068) ((-703 . -258) 102047) ((-703 . -241) 101974) ((-703 . -190) T) ((-703 . -104) T) ((-703 . -25) T) ((-703 . -72) T) ((-703 . -551) 101935) ((-703 . -1012) T) ((-703 . -23) T) ((-703 . -21) T) ((-703 . -969) T) ((-703 . -1024) T) ((-703 . -1059) T) ((-703 . -662) T) ((-703 . -960) T) ((-703 . -186) 101922) ((-703 . -13) T) ((-703 . -1127) T) ((-703 . -189) T) ((-703 . -225) 101906) ((-703 . -184) 101890) ((-702 . -976) 101857) ((-702 . -552) 101492) ((-702 . -260) 101479) ((-702 . -454) 101431) ((-702 . -277) 101403) ((-702 . -949) 101262) ((-702 . -353) 101246) ((-702 . -38) 101098) ((-702 . -554) 100871) ((-702 . -589) 100760) ((-702 . -587) 100670) ((-702 . -969) T) ((-702 . -1024) T) 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. -994) T) ((-462 . -428) 77131) ((-462 . -551) 77097) ((-462 . -554) 77078) ((-462 . -1012) T) ((-462 . -1127) T) ((-462 . -13) T) ((-462 . -72) T) ((-462 . -64) T) ((-461 . -994) T) ((-461 . -428) 77059) ((-461 . -551) 77025) ((-461 . -554) 77006) ((-461 . -1012) T) ((-461 . -1127) T) ((-461 . -13) T) ((-461 . -72) T) ((-461 . -64) T) ((-458 . -280) 76983) ((-458 . -190) T) ((-458 . -186) 76970) ((-458 . -189) T) ((-458 . -318) T) ((-458 . -1064) T) ((-458 . -299) T) ((-458 . -120) 76952) ((-458 . -554) 76882) ((-458 . -589) 76827) ((-458 . -587) 76757) ((-458 . -104) T) ((-458 . -25) T) ((-458 . -72) T) ((-458 . -13) T) ((-458 . -1127) T) ((-458 . -551) 76739) ((-458 . -1012) T) ((-458 . -23) T) ((-458 . -21) T) ((-458 . -969) T) ((-458 . -1024) T) ((-458 . -1059) T) ((-458 . -662) T) ((-458 . -960) T) ((-458 . -312) T) ((-458 . -1132) T) ((-458 . -831) T) ((-458 . -494) T) ((-458 . -146) T) ((-458 . -653) 76684) ((-458 . -581) 76629) ((-458 . -38) 76594) ((-458 . -390) T) ((-458 . 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. -241) 56072) ((-348 . -260) 56037) ((-348 . -454) 55949) ((-348 . -288) 55933) ((-348 . -201) T) ((-348 . -82) 55864) ((-348 . -962) 55816) ((-348 . -967) 55768) ((-348 . -246) T) ((-348 . -653) 55720) ((-348 . -581) 55672) ((-348 . -587) 55609) ((-348 . -38) 55561) ((-348 . -258) T) ((-348 . -390) T) ((-348 . -146) T) ((-348 . -494) T) ((-348 . -831) T) ((-348 . -1132) T) ((-348 . -312) T) ((-348 . -190) 55540) ((-348 . -186) 55488) ((-348 . -189) 55442) ((-348 . -225) 55426) ((-348 . -805) 55350) ((-348 . -810) 55276) ((-348 . -808) 55235) ((-348 . -184) 55219) ((-348 . -120) 55173) ((-348 . -118) 55152) ((-348 . -104) T) ((-348 . -25) T) ((-348 . -72) T) ((-348 . -13) T) ((-348 . -1127) T) ((-348 . -551) 55134) ((-348 . -1012) T) ((-348 . -23) T) ((-348 . -21) T) ((-348 . -960) T) ((-348 . -662) T) ((-348 . -1059) T) ((-348 . -1024) T) ((-348 . -969) T) ((-346 . -494) T) ((-346 . -246) T) ((-346 . -146) T) ((-346 . -554) 55043) ((-346 . -653) 55017) ((-346 . -581) 54991) ((-346 . 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((-40 . -72) T) ((-40 . -13) T) ((-40 . -1127) T) ((-40 . -551) 1367) ((-40 . -1012) T) ((-40 . -23) T) ((-40 . -21) T) ((-40 . -967) 1312) ((-40 . -962) 1257) ((-40 . -82) 1174) ((-40 . -552) 1158) ((-40 . -184) 1135) ((-40 . -808) 1087) ((-40 . -810) 999) ((-40 . -805) 909) ((-40 . -225) 886) ((-40 . -189) 826) ((-40 . -186) 760) ((-40 . -190) 732) ((-40 . -312) T) ((-40 . -1132) T) ((-40 . -831) T) ((-40 . -494) T) ((-40 . -653) 677) ((-40 . -581) 622) ((-40 . -38) 567) ((-40 . -390) T) ((-40 . -258) T) ((-40 . -246) T) ((-40 . -201) T) ((-40 . -318) NIL) ((-40 . -299) NIL) ((-40 . -1064) NIL) ((-40 . -118) 539) ((-40 . -343) NIL) ((-40 . -351) 511) ((-40 . -120) 483) ((-40 . -320) 455) ((-40 . -327) 432) ((-40 . -579) 366) ((-40 . -353) 343) ((-40 . -949) 220) ((-40 . -660) 192) ((-31 . -994) T) ((-31 . -428) 173) ((-31 . -551) 139) ((-31 . -554) 120) ((-31 . -1012) T) ((-31 . -1127) T) ((-31 . -13) T) ((-31 . -72) T) ((-31 . -64) T) ((-30 . -865) T) ((-30 . -551) 102) ((0 . 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 8ad42fad..c11d83ef 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3577395493) -(3997 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3577398025) +(3996 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| @@ -173,22 +173,21 @@ |InternalRationalUnivariateRepresentationPackage| |IsAst| |InnerPolySum| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |InternalTypeForm| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| - |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedVector| - |IndexedAggregate&| |IndexedAggregate| |JoinAst| |AssociatedJordanAlgebra| - |JVMBytecode| |JVMClassFileAccess| |JVMConstantTag| |JVMFieldAccess| - |JVMMethodAccess| |JVMOpcode| |KeyedAccessFile| |KeyedDictionary&| - |KeyedDictionary| |Kernel| |KernelFunctions2| |CoercibleTo| |ConvertibleTo| - |Kovacic| |CoercibleFrom| |KleeneTrivalentLogic| |ConvertibleFrom| - |LocalAlgebra| |LeftAlgebra&| |LeftAlgebra| |LaplaceTransform| - |LaurentPolynomial| |LazardSetSolvingPackage| |LeadingCoefDetermination| - |LetAst| |LieExponentials| |LexTriangularPackage| |LiouvillianFunction| - |LiouvillianFunctionCategory| |LinGroebnerPackage| |Library| - |AssociatedLieAlgebra| |LieAlgebra&| |LieAlgebra| |PowerSeriesLimitPackage| - |RationalFunctionLimitPackage| |LinearBasis| |LinearDependence| - |LinearElement| |LinearlyExplicitRingOver| |LinearForm| |LinearSet| |List| - |ListFunctions2| |ListToMap| |ListFunctions3| |Literal| |LeftLinearSet| - |ListMultiDictionary| |LeftModule| |ListMonoidOps| |LinearAggregate&| - |LinearAggregate| |Localize| |ElementaryFunctionLODESolver| + |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedAggregate&| + |IndexedAggregate| |JoinAst| |AssociatedJordanAlgebra| |JVMBytecode| + |JVMClassFileAccess| |JVMConstantTag| |JVMFieldAccess| |JVMMethodAccess| + |JVMOpcode| |KeyedAccessFile| |KeyedDictionary&| |KeyedDictionary| |Kernel| + |KernelFunctions2| |CoercibleTo| |ConvertibleTo| |Kovacic| |CoercibleFrom| + |KleeneTrivalentLogic| |ConvertibleFrom| |LocalAlgebra| |LeftAlgebra&| + |LeftAlgebra| |LaplaceTransform| |LaurentPolynomial| |LazardSetSolvingPackage| + |LeadingCoefDetermination| |LetAst| |LieExponentials| |LexTriangularPackage| + |LiouvillianFunction| |LiouvillianFunctionCategory| |LinGroebnerPackage| + |Library| |AssociatedLieAlgebra| |LieAlgebra&| |LieAlgebra| + |PowerSeriesLimitPackage| |RationalFunctionLimitPackage| |LinearBasis| + |LinearDependence| |LinearElement| |LinearlyExplicitRingOver| |LinearForm| + |LinearSet| |List| |ListFunctions2| |ListToMap| |ListFunctions3| |Literal| + |LeftLinearSet| |ListMultiDictionary| |LeftModule| |ListMonoidOps| + |LinearAggregate&| |LinearAggregate| |Localize| |ElementaryFunctionLODESolver| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index ee7aa349..76e80a37 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,4042 +1,4039 @@ -(2814603 . 3577395502) -((-1731 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1729 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3787 ((|#2| $ (-483) |#2|) NIL T ELT) ((|#2| $ (-1145 (-483)) |#2|) 44 T ELT)) (-2297 (($ $) 80 T ELT)) (-3841 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3418 (((-483) (-1 (-85) |#2|) $) 27 T ELT) (((-483) |#2| $) NIL T ELT) 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T) ((-653 $) OR (|has| |#1| (-494)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-660 |#1| (-1083 |#1|)) . T) ((-662) . T) ((-805 $ (-1088)) OR (|has| |#1| (-810 (-1088))) (|has| |#1| (-808 (-1088)))) ((-808 (-1088)) |has| |#1| (-808 (-1088))) ((-810 (-1088)) OR (|has| |#1| (-810 (-1088))) (|has| |#1| (-808 (-1088)))) ((-795 (-328)) |has| |#1| (-795 (-328))) ((-795 (-483)) |has| |#1| (-795 (-483))) ((-793 |#1|) . T) ((-820) -12 (|has| |#1| (-258)) (|has| |#1| (-820))) ((-831) OR (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-914) -12 (|has| |#1| (-914)) (|has| |#1| (-1113))) ((-949 (-348 (-483))) |has| |#1| (-949 (-348 (-483)))) ((-949 (-483)) |has| |#1| (-949 (-483))) ((-949 |#1|) . T) ((-962 (-348 (-483))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-962 |#1|) . T) ((-962 $) . T) ((-967 (-348 (-483))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-967 |#1|) . T) ((-967 $) . T) ((-960) . T) ((-969) . T) ((-1024) . T) ((-1059) . T) ((-1012) . 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|t#2| (-6 -3991)) (-6 -3991) |%noBranch|) (IF (|has| |t#2| (-756)) (-6 (-756)) |%noBranch|) (IF (|has| |t#2| (-717)) (-6 (-717)) |%noBranch|) (IF (|has| |t#2| (-312)) (-6 (-1186 |t#2|)) |%noBranch|))) -(((-21) OR (|has| |#2| (-961)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-21))) ((-23) OR (|has| |#2| (-961)) (|has| |#2| (-717)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) OR (|has| |#2| (-961)) (|has| |#2| (-717)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-72) OR (|has| |#2| (-1013)) (|has| |#2| (-961)) (|has| |#2| (-756)) (|has| |#2| (-717)) (|has| |#2| (-663)) (|has| |#2| (-318)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-72)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-82 |#2| |#2|) OR (|has| |#2| (-961)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-104) OR (|has| |#2| (-961)) (|has| |#2| (-717)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-21))) ((-555 (-348 (-483))) -12 (|has| |#2| (-950 (-348 (-483)))) (|has| |#2| (-1013))) ((-555 (-483)) OR (|has| |#2| (-961)) (-12 (|has| |#2| (-950 (-483))) (|has| |#2| (-1013)))) ((-555 |#2|) |has| |#2| (-1013)) ((-552 (-772)) OR (|has| |#2| (-1013)) (|has| |#2| (-961)) (|has| |#2| (-756)) (|has| |#2| (-717)) (|has| |#2| (-663)) (|has| |#2| (-318)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-552 (-772))) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-552 (-1178 |#2|)) . T) ((-186 $) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-961))) (-12 (|has| |#2| (-190)) (|has| |#2| (-961)))) ((-184 |#2|) |has| |#2| (-961)) ((-190) -12 (|has| |#2| (-190)) (|has| |#2| (-961))) ((-189) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-961))) (-12 (|has| |#2| (-190)) (|has| |#2| (-961)))) ((-225 |#2|) |has| |#2| (-961)) ((-241 (-483) |#2|) . T) ((-243 (-483) |#2|) . T) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1013))) ((-318) |has| |#2| (-318)) ((-327 |#2|) |has| |#2| (-961)) ((-353 |#2|) |has| |#2| (-1013)) ((-427 |#2|) . T) ((-538 (-483) |#2|) . T) ((-454 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1013))) ((-13) . T) ((-588 (-483)) OR (|has| |#2| (-961)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-21))) ((-588 |#2|) OR (|has| |#2| (-961)) (|has| |#2| (-663)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-588 $) |has| |#2| (-961)) ((-590 (-483)) -12 (|has| |#2| (-580 (-483))) (|has| |#2| (-961))) ((-590 |#2|) OR (|has| |#2| (-961)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-590 $) |has| |#2| (-961)) ((-582 |#2|) OR (|has| |#2| (-663)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-580 (-483)) -12 (|has| |#2| (-580 (-483))) (|has| |#2| (-961))) ((-580 |#2|) |has| |#2| (-961)) ((-654 |#2|) OR (|has| |#2| (-312)) (|has| |#2| (-146))) ((-663) |has| |#2| (-961)) ((-716) |has| |#2| (-717)) ((-717) |has| |#2| (-717)) ((-718) |has| |#2| (-717)) ((-721) |has| |#2| (-717)) ((-756) OR (|has| |#2| (-756)) (|has| |#2| (-717))) ((-759) OR (|has| |#2| (-756)) (|has| |#2| (-717))) ((-806 $ (-1089)) OR (-12 (|has| |#2| (-811 (-1089))) (|has| |#2| (-961))) (-12 (|has| |#2| (-809 (-1089))) (|has| |#2| (-961)))) ((-809 (-1089)) -12 (|has| |#2| (-809 (-1089))) (|has| |#2| (-961))) ((-811 (-1089)) OR (-12 (|has| |#2| (-811 (-1089))) (|has| |#2| (-961))) (-12 (|has| |#2| (-809 (-1089))) (|has| |#2| (-961)))) ((-950 (-348 (-483))) -12 (|has| |#2| (-950 (-348 (-483)))) (|has| |#2| (-1013))) ((-950 (-483)) -12 (|has| |#2| (-950 (-483))) (|has| |#2| (-1013))) ((-950 |#2|) |has| |#2| (-1013)) ((-963 |#2|) OR (|has| |#2| (-961)) (|has| |#2| (-663)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-968 |#2|) OR (|has| |#2| (-961)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-961) |has| |#2| (-961)) ((-970) |has| |#2| (-961)) ((-1025) |has| |#2| (-961)) ((-1060) |has| |#2| (-961)) ((-1013) OR (|has| |#2| (-1013)) (|has| |#2| (-961)) (|has| |#2| (-756)) (|has| |#2| (-717)) (|has| |#2| (-663)) (|has| |#2| (-318)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1128) . 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T) ((-186 $) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-960))) (-12 (|has| |#2| (-190)) (|has| |#2| (-960)))) ((-184 |#2|) |has| |#2| (-960)) ((-190) -12 (|has| |#2| (-190)) (|has| |#2| (-960))) ((-189) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-960))) (-12 (|has| |#2| (-190)) (|has| |#2| (-960)))) ((-225 |#2|) |has| |#2| (-960)) ((-241 (-483) |#2|) . T) ((-243 (-483) |#2|) . T) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1012))) ((-318) |has| |#2| (-318)) ((-327 |#2|) |has| |#2| (-960)) ((-353 |#2|) |has| |#2| (-1012)) ((-427 |#2|) . T) ((-537 (-483) |#2|) . T) ((-454 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1012))) ((-13) . T) ((-587 (-483)) OR (|has| |#2| (-960)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-21))) ((-587 |#2|) OR (|has| |#2| (-960)) (|has| |#2| (-662)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-587 $) |has| |#2| (-960)) ((-589 (-483)) -12 (|has| |#2| (-579 (-483))) (|has| |#2| (-960))) ((-589 |#2|) OR (|has| |#2| (-960)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-589 $) |has| |#2| (-960)) ((-581 |#2|) OR (|has| |#2| (-662)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-579 (-483)) -12 (|has| |#2| (-579 (-483))) (|has| |#2| (-960))) ((-579 |#2|) |has| |#2| (-960)) ((-653 |#2|) OR (|has| |#2| (-312)) (|has| |#2| (-146))) ((-662) |has| |#2| (-960)) ((-715) |has| |#2| (-716)) ((-716) |has| |#2| (-716)) ((-717) |has| |#2| (-716)) ((-720) |has| |#2| (-716)) ((-755) OR (|has| |#2| (-755)) (|has| |#2| (-716))) ((-758) OR (|has| |#2| (-755)) (|has| |#2| (-716))) ((-805 $ (-1088)) OR (-12 (|has| |#2| (-810 (-1088))) (|has| |#2| (-960))) (-12 (|has| |#2| (-808 (-1088))) (|has| |#2| (-960)))) ((-808 (-1088)) -12 (|has| |#2| (-808 (-1088))) (|has| |#2| (-960))) ((-810 (-1088)) OR (-12 (|has| |#2| (-810 (-1088))) (|has| |#2| (-960))) (-12 (|has| |#2| (-808 (-1088))) (|has| |#2| (-960)))) ((-949 (-348 (-483))) -12 (|has| |#2| (-949 (-348 (-483)))) (|has| |#2| (-1012))) ((-949 (-483)) -12 (|has| |#2| (-949 (-483))) (|has| |#2| (-1012))) ((-949 |#2|) |has| |#2| (-1012)) ((-962 |#2|) OR (|has| |#2| (-960)) (|has| |#2| (-662)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-967 |#2|) OR (|has| |#2| (-960)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-960) |has| |#2| (-960)) ((-969) |has| |#2| (-960)) ((-1024) |has| |#2| (-960)) ((-1059) |has| |#2| (-960)) ((-1012) OR (|has| |#2| (-1012)) (|has| |#2| (-960)) (|has| |#2| (-755)) (|has| |#2| (-716)) (|has| |#2| (-662)) (|has| |#2| (-318)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1127) . 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T) ((-23) . T) ((-47 |#1| (-483)) . T) ((-25) . T) ((-38 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 |#2|) |has| |#1| (-312)) ((-38 $) OR (|has| |#1| (-494)) (|has| |#1| (-312))) ((-35) |has| |#1| (-38 (-348 (-483)))) ((-66) |has| |#1| (-38 (-348 (-483)))) ((-72) . T) ((-82 (-348 (-483)) (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-82 |#1| |#1|) . T) ((-82 |#2| |#2|) |has| |#1| (-312)) ((-82 $ $) OR (|has| |#1| (-494)) (|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| (-740))) (-12 (|has| |#1| (-312)) (|has| |#2| (-120))) (|has| |#1| (-120))) ((-555 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-555 (-483)) . T) ((-555 (-1089)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-1089)))) ((-555 |#1|) |has| |#1| (-146)) ((-555 |#2|) . 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T) ((-590 |#2|) |has| |#1| (-312)) ((-590 $) . T) ((-582 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-582 |#1|) |has| |#1| (-146)) ((-582 |#2|) |has| |#1| (-312)) ((-582 $) OR (|has| |#1| (-494)) (|has| |#1| (-312))) ((-580 (-483)) -12 (|has| |#1| (-312)) (|has| |#2| (-580 (-483)))) ((-580 |#2|) |has| |#1| (-312)) ((-654 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-654 |#1|) |has| |#1| (-146)) ((-654 |#2|) |has| |#1| (-312)) ((-654 $) OR (|has| |#1| (-494)) (|has| |#1| (-312))) ((-663) . 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(NIL NIL T) -8 NIL NIL NIL) (-1077 2389049 2389149 2389313 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1076 2384160 2385442 2386589 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1075 2378618 2380089 2381400 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1074 2371533 2373597 2375388 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1073 2364363 2371445 2371528 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1072 2359057 2364077 2364192 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1071 2358644 2358727 2358871 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1070 2357795 2357996 2358231 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1069 2357535 2357593 2357686 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1068 2350273 2355740 2356346 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1067 2349449 2349654 2349885 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1066 2348694 2349065 2349212 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1065 2348182 2348424 2348454 "STEP" 2348548 STEP (NIL) -9 NIL 2348619 NIL) (-1064 2341285 2348100 2348177 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1063 2335500 2340083 2340126 "STAGG" 2340553 STAGG (NIL T) -9 NIL 2340727 NIL) (-1062 2333879 2334627 2335495 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1061 2332036 2333706 2333798 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1060 2331316 2331855 2331885 "SRING" 2331890 SRING (NIL) -9 NIL 2331910 NIL) (-1059 2323938 2329854 2330293 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2317712 2319151 2320655 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1057 2310137 2315048 2315078 "SRAGG" 2316377 SRAGG (NIL) -9 NIL 2316981 NIL) (-1056 2309434 2309754 2310132 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1055 2303489 2308756 2309179 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1054 2297702 2300871 2301593 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1053 2294131 2294950 2295587 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1052 2293106 2293411 2293441 "SPFCAT" 2293885 SPFCAT (NIL) -9 NIL NIL NIL) (-1051 2292043 2292295 2292559 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1050 2282801 2285075 2285105 "SPADXPT" 2289742 SPADXPT (NIL) -9 NIL 2291866 NIL) (-1049 2282603 2282649 2282718 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1048 2280259 2282567 2282598 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1047 2271933 2274022 2274064 "SPACEC" 2278379 SPACEC (NIL T) -9 NIL 2280184 NIL) (-1046 2269762 2271880 2271928 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1045 2268695 2268884 2269173 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1044 2267099 2267432 2267843 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1043 2266364 2266598 2266859 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1042 2262544 2263504 2264499 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1041 2258902 2259601 2260330 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1040 2252688 2258242 2258338 "SNTSCAT" 2258343 SNTSCAT (NIL T T T T) -9 NIL 2258413 NIL) (-1039 2246509 2251329 2251719 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1038 2240281 2246428 2246504 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1037 2238713 2239044 2239442 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1036 2230318 2235297 2235399 "SMATCAT" 2236742 SMATCAT (NIL NIL T T T) -9 NIL 2237290 NIL) (-1035 2228159 2229143 2230313 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1034 2225751 2227365 2227408 "SKAGG" 2227669 SKAGG (NIL T) -9 NIL 2227803 NIL) (-1033 2221797 2225571 2225682 "SINT" NIL SINT (NIL) -8 NIL NIL 2225723) (-1032 2221607 2221651 2221717 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1031 2220682 2220914 2221182 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1030 2219686 2219848 2220124 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1029 2219032 2219372 2219495 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1028 2218378 2218685 2218825 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1027 2216489 2216981 2217487 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1026 2209929 2216408 2216484 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1025 2209432 2209669 2209699 "SGROUP" 2209792 SGROUP (NIL) -9 NIL 2209854 NIL) (-1024 2209322 2209354 2209427 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1023 2208960 2209000 2209041 "SGPOPC" 2209046 SGPOPC (NIL T) -9 NIL 2209247 NIL) (-1022 2208494 2208771 2208877 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1021 2205917 2206686 2207408 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1020 2199802 2205356 2205452 "SFRTCAT" 2205457 SFRTCAT (NIL T T T T) -9 NIL 2205495 NIL) (-1019 2194194 2195307 2196434 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1018 2188370 2189531 2190695 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1017 2187342 2188244 2188365 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1016 2182950 2183845 2183940 "SEXCAT" 2186553 SEXCAT (NIL T T T T T) -9 NIL 2187104 NIL) (-1015 2181923 2182877 2182945 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1014 2180314 2180899 2181201 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1013 2179837 2180022 2180052 "SETCAT" 2180169 SETCAT (NIL) -9 NIL 2180253 NIL) (-1012 2179669 2179733 2179832 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1011 2175892 2178123 2178166 "SETAGG" 2179034 SETAGG (NIL T) -9 NIL 2179372 NIL) (-1010 2175498 2175650 2175887 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1009 2172452 2175445 2175493 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1008 2171918 2172228 2172328 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1007 2171045 2171411 2171472 "SEGXCAT" 2171758 SEGXCAT (NIL T T) -9 NIL 2171878 NIL) (-1006 2169970 2170238 2170281 "SEGCAT" 2170803 SEGCAT (NIL T) -9 NIL 2171024 NIL) (-1005 2169650 2169715 2169828 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1004 2168716 2169186 2169394 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1003 2168294 2168573 2168649 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1002 2167659 2167795 2167999 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1001 2166725 2167472 2167654 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1000 2165978 2166673 2166720 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-999 2157465 2165847 2165973 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-998 2156325 2156615 2156932 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-997 2155631 2155843 2156031 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-996 2154981 2155138 2155314 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-995 2154554 2154785 2154813 "SASTCAT" 2154818 SASTCAT (NIL) -9 NIL 2154831 NIL) (-994 2154021 2154446 2154520 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-993 2153624 2153665 2153836 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-992 2153255 2153296 2153453 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-991 2146336 2153172 2153250 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-990 2144986 2145315 2145711 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-989 2143747 2144108 2144408 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-988 2143371 2143592 2143673 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-987 2140831 2141465 2141918 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-986 2140670 2140703 2140771 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-985 2140161 2140464 2140555 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-984 2135789 2136657 2137568 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-983 2124608 2130162 2130256 "RSETCAT" 2134312 RSETCAT (NIL T T T T) -9 NIL 2135400 NIL) (-982 2123146 2123788 2124603 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-981 2116920 2118365 2119872 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-980 2114802 2115359 2115431 "RRCC" 2116504 RRCC (NIL T T) -9 NIL 2116845 NIL) (-979 2114327 2114526 2114797 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-978 2113797 2114107 2114205 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-977 2086349 2097062 2097126 "RPOLCAT" 2107600 RPOLCAT (NIL T T T) -9 NIL 2110745 NIL) (-976 2080448 2083271 2086344 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-975 2076615 2080196 2080334 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-974 2074943 2075682 2075938 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-973 2070586 2073398 2073426 "RNS" 2073688 RNS (NIL) -9 NIL 2073940 NIL) (-972 2069489 2069976 2070513 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-971 2068607 2069008 2069208 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-970 2067745 2068307 2068335 "RNG" 2068395 RNG (NIL) -9 NIL 2068449 NIL) (-969 2067634 2067668 2067740 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-968 2066896 2067401 2067441 "RMODULE" 2067446 RMODULE (NIL T) -9 NIL 2067472 NIL) (-967 2065835 2065941 2066271 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-966 2062681 2065425 2065718 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-965 2055330 2057822 2057934 "RMATCAT" 2061239 RMATCAT (NIL NIL NIL T T T) -9 NIL 2062216 NIL) (-964 2054847 2055026 2055325 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-963 2054415 2054626 2054667 "RLINSET" 2054728 RLINSET (NIL T) -9 NIL 2054772 NIL) (-962 2054060 2054141 2054267 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-961 2052906 2053637 2053665 "RING" 2053720 RING (NIL) -9 NIL 2053812 NIL) (-960 2052751 2052807 2052901 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-959 2051805 2052072 2052328 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-958 2042792 2051433 2051634 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-957 2042017 2042528 2042567 "RGBCSPC" 2042624 RGBCSPC (NIL T) -9 NIL 2042675 NIL) (-956 2041051 2041537 2041576 "RGBCMDL" 2041804 RGBCMDL (NIL T) -9 NIL 2041918 NIL) (-955 2040763 2040832 2040933 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-954 2040526 2040567 2040662 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-953 2038950 2039380 2039760 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-952 2036537 2037205 2037873 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-951 2036087 2036185 2036345 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-950 2035709 2035807 2035848 "RETRACT" 2035979 RETRACT (NIL T) -9 NIL 2036066 NIL) (-949 2035589 2035620 2035704 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-948 2035191 2035463 2035530 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-947 2033671 2034562 2034759 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-946 2033362 2033423 2033519 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-945 2033105 2033146 2033251 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-944 2032840 2032881 2032990 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-943 2027911 2029362 2030577 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-942 2025010 2025768 2026576 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-941 2022979 2023601 2024201 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-940 2015614 2021530 2021966 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-939 2014926 2015206 2015355 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-938 2014411 2014526 2014691 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-937 2010004 2013814 2014035 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-936 2009236 2009435 2009648 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-935 2006526 2007364 2008246 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-934 2003108 2004144 2005203 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-933 2002944 2002997 2003025 "REAL" 2003030 REAL (NIL) -9 NIL 2003065 NIL) (-932 2002434 2002738 2002829 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-931 2001914 2001992 2002197 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-930 2001147 2001339 2001550 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-929 2000035 2000332 2000699 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-928 1998302 1998772 1999305 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-927 1997224 1997501 1997888 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-926 1996051 1996360 1996779 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-925 1989399 1992911 1992939 "RCFIELD" 1994216 RCFIELD (NIL) -9 NIL 1994946 NIL) (-924 1988017 1988629 1989326 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-923 1984217 1986109 1986150 "RCAGG" 1987217 RCAGG (NIL T) -9 NIL 1987678 NIL) (-922 1983944 1984054 1984212 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-921 1983389 1983518 1983679 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-920 1983006 1983085 1983204 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-919 1982421 1982571 1982721 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-918 1982203 1982253 1982324 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-917 1974645 1981321 1981629 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-916 1964347 1974512 1974640 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-915 1963981 1964074 1964102 "RADCAT" 1964259 RADCAT (NIL) -9 NIL NIL NIL) (-914 1963819 1963879 1963976 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-913 1961919 1963650 1963739 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-912 1961600 1961649 1961776 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-911 1953887 1957971 1958011 "QUATCAT" 1958789 QUATCAT (NIL T) -9 NIL 1959553 NIL) (-910 1951137 1952417 1953793 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-909 1946977 1951087 1951132 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-908 1944364 1946031 1946072 "QUAGG" 1946447 QUAGG (NIL T) -9 NIL 1946621 NIL) (-907 1943966 1944238 1944305 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-906 1942972 1943602 1943765 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-905 1942653 1942702 1942829 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-904 1932253 1938422 1938462 "QFCAT" 1939120 QFCAT (NIL T) -9 NIL 1940113 NIL) (-903 1929137 1930576 1932159 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-902 1928683 1928817 1928947 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-901 1922879 1924040 1925202 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-900 1922298 1922478 1922710 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-899 1920120 1920648 1921071 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-898 1919019 1919261 1919578 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-897 1917380 1917578 1917931 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-896 1913136 1914352 1914393 "PTRANFN" 1916277 PTRANFN (NIL T) -9 NIL NIL NIL) (-895 1911783 1912128 1912449 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-894 1911476 1911539 1911646 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-893 1905549 1910272 1910312 "PTCAT" 1910604 PTCAT (NIL T) -9 NIL 1910757 NIL) (-892 1905242 1905283 1905407 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-891 1904121 1904437 1904771 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-890 1893000 1895561 1897870 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-889 1885907 1888803 1888897 "PSETCAT" 1891871 PSETCAT (NIL T T T T) -9 NIL 1892678 NIL) (-888 1884357 1885091 1885902 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-887 1883676 1883871 1883899 "PSCURVE" 1884167 PSCURVE (NIL) -9 NIL 1884334 NIL) (-886 1879278 1881098 1881162 "PSCAT" 1881997 PSCAT (NIL T T T) -9 NIL 1882236 NIL) (-885 1878592 1878874 1879273 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-884 1876989 1877904 1878167 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-883 1876480 1876783 1876874 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-882 1867500 1869922 1872110 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-881 1865243 1866820 1866860 "PRQAGG" 1867043 PRQAGG (NIL T) -9 NIL 1867144 NIL) (-880 1864416 1864862 1864890 "PROPLOG" 1865029 PROPLOG (NIL) -9 NIL 1865143 NIL) (-879 1864091 1864154 1864277 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-878 1863527 1863666 1863838 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-877 1861775 1862538 1862835 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-876 1861327 1861459 1861587 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-875 1855768 1860267 1861087 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-874 1855597 1855635 1855694 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-873 1855036 1855176 1855327 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-872 1853504 1853923 1854389 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-871 1853221 1853282 1853310 "PRIMCAT" 1853434 PRIMCAT (NIL) -9 NIL NIL NIL) (-870 1852392 1852588 1852816 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-869 1848270 1852342 1852387 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-868 1847969 1848031 1848142 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-867 1845105 1847618 1847851 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-866 1844556 1844713 1844741 "PPCURVE" 1844946 PPCURVE (NIL) -9 NIL 1845082 NIL) (-865 1844169 1844414 1844497 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-864 1841925 1842346 1842938 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-863 1841368 1841432 1841665 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-862 1838088 1838574 1839185 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-861 1823679 1829808 1829872 "POLYCAT" 1833357 POLYCAT (NIL T T T) -9 NIL 1835234 NIL) (-860 1819189 1821336 1823674 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-859 1818846 1818920 1819039 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-858 1818539 1818602 1818709 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-857 1811902 1818272 1818431 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-856 1810789 1811052 1811328 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-855 1809393 1809706 1810036 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-854 1804555 1809343 1809388 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-853 1803043 1803454 1803829 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-852 1801800 1802109 1802505 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-851 1801471 1801555 1801672 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-850 1801050 1801125 1801299 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-849 1800536 1800632 1800792 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-848 1800008 1800128 1800282 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-847 1798903 1799121 1799498 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-846 1798514 1798599 1798751 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-845 1798065 1798147 1798328 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-844 1797757 1797838 1797951 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-843 1797270 1797345 1797553 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-842 1796618 1796746 1796948 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-841 1795980 1796114 1796277 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-840 1795284 1795466 1795647 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-839 1795007 1795081 1795175 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-838 1791575 1792764 1793680 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-837 1790659 1790860 1791095 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-836 1786224 1787608 1788750 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-835 1766145 1771032 1775879 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-834 1765885 1765938 1766041 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-833 1765326 1765460 1765640 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-832 1763335 1764556 1764584 "PID" 1764781 PID (NIL) -9 NIL 1764908 NIL) (-831 1763123 1763166 1763241 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-830 1762310 1762970 1763057 "PI" NIL PI (NIL) -8 NIL NIL 1763097) (-829 1761762 1761913 1762089 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-828 1758090 1759048 1759953 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-827 1756454 1756743 1757109 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-826 1755896 1756011 1756172 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-825 1752437 1754765 1755118 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-824 1751043 1751323 1751648 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-823 1749808 1750062 1750410 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-822 1748518 1748745 1749097 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-821 1745528 1747088 1747116 "PFECAT" 1747709 PFECAT (NIL) -9 NIL 1748086 NIL) (-820 1745151 1745316 1745523 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-819 1743975 1744257 1744558 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-818 1742157 1742544 1742974 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-817 1738127 1742083 1742152 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-816 1734030 1735177 1736044 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-815 1731962 1733051 1733092 "PERMCAT" 1733491 PERMCAT (NIL T) -9 NIL 1733788 NIL) (-814 1731658 1731705 1731828 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-813 1728107 1729788 1730433 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-812 1725572 1727862 1727983 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-811 1724441 1724704 1724745 "PDSPC" 1725278 PDSPC (NIL T) -9 NIL 1725523 NIL) (-810 1723808 1724074 1724436 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-809 1722443 1723436 1723477 "PDRING" 1723482 PDRING (NIL T) -9 NIL 1723509 NIL) (-808 1721153 1721942 1721995 "PDMOD" 1722000 PDMOD (NIL T T) -9 NIL 1722103 NIL) (-807 1720246 1720458 1720707 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-806 1719851 1719918 1719972 "PDDOM" 1720137 PDDOM (NIL T T) -9 NIL 1720217 NIL) (-805 1719703 1719739 1719846 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-804 1719489 1719528 1719617 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-803 1717806 1718560 1718859 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-802 1717495 1717558 1717667 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-801 1715633 1716063 1716514 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-800 1709253 1711082 1712374 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-799 1708884 1708957 1709089 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-798 1706586 1707266 1707747 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-797 1704790 1705218 1705621 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-796 1704236 1704484 1704525 "PATMAB" 1704632 PATMAB (NIL T) -9 NIL 1704715 NIL) (-795 1702883 1703287 1703544 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-794 1702421 1702552 1702593 "PATAB" 1702598 PATAB (NIL T) -9 NIL 1702770 NIL) (-793 1700964 1701401 1701824 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-792 1700642 1700717 1700819 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-791 1700331 1700394 1700503 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-790 1700136 1700182 1700249 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-789 1699814 1699889 1699991 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-788 1699503 1699566 1699675 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-787 1699194 1699264 1699361 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-786 1698883 1698946 1699055 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-785 1698044 1698423 1698602 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-784 1697651 1697749 1697868 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-783 1696619 1697044 1697263 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-782 1695284 1695938 1696298 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-781 1688374 1694688 1694882 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-780 1680795 1687872 1688056 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-779 1677520 1679435 1679475 "PADICCT" 1680056 PADICCT (NIL NIL) -9 NIL 1680338 NIL) (-778 1675510 1677470 1677515 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-777 1674672 1674882 1675148 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-776 1674014 1674157 1674361 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-775 1672395 1673422 1673700 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-774 1671919 1672178 1672275 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-773 1670978 1671656 1671828 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-772 1661400 1664269 1666468 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-771 1660792 1661106 1661232 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-770 1660069 1660264 1660292 "OUTBCON" 1660610 OUTBCON (NIL) -9 NIL 1660776 NIL) (-769 1659777 1659907 1660064 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-768 1659158 1659303 1659464 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-767 1658529 1658956 1659045 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-766 1657944 1658359 1658387 "OSGROUP" 1658392 OSGROUP (NIL) -9 NIL 1658414 NIL) (-765 1656908 1657169 1657454 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-764 1654177 1656783 1656903 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-763 1651318 1653928 1654054 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-762 1649336 1649864 1650424 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-761 1642678 1645218 1645258 "OREPCAT" 1647579 OREPCAT (NIL T) -9 NIL 1648681 NIL) (-760 1640704 1641638 1642673 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-759 1639901 1640172 1640200 "ORDTYPE" 1640505 ORDTYPE (NIL) -9 NIL 1640663 NIL) (-758 1639435 1639646 1639896 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-757 1638897 1639273 1639430 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-756 1638391 1638754 1638782 "ORDSET" 1638787 ORDSET (NIL) -9 NIL 1638809 NIL) (-755 1636956 1637978 1638006 "ORDRING" 1638011 ORDRING (NIL) -9 NIL 1638039 NIL) (-754 1636204 1636761 1636789 "ORDMON" 1636794 ORDMON (NIL) -9 NIL 1636815 NIL) (-753 1635508 1635670 1635862 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-752 1634719 1635227 1635255 "ORDFIN" 1635320 ORDFIN (NIL) -9 NIL 1635394 NIL) (-751 1634113 1634252 1634438 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-750 1630788 1633081 1633487 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-749 1630195 1630550 1630655 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-748 1630003 1630048 1630114 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-747 1629304 1629580 1629621 "OPERCAT" 1629832 OPERCAT (NIL T) -9 NIL 1629928 NIL) (-746 1629116 1629183 1629299 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-745 1626482 1627918 1628414 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-744 1625903 1626030 1626204 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-743 1622804 1625042 1625408 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-742 1619435 1622234 1622274 "OMSAGG" 1622335 OMSAGG (NIL T) -9 NIL 1622399 NIL) (-741 1617847 1619106 1619274 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-740 1616043 1617284 1617312 "OINTDOM" 1617317 OINTDOM (NIL) -9 NIL 1617338 NIL) (-739 1613473 1615045 1615374 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-738 1612727 1613423 1613468 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-737 1609929 1612568 1612722 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-736 1601466 1609800 1609924 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-735 1594877 1601357 1601461 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-734 1593849 1594086 1594359 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-733 1591483 1592153 1592857 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-732 1587260 1588220 1589243 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-731 1586768 1586856 1587050 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-730 1584217 1584799 1585472 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-729 1581612 1582120 1582716 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-728 1578609 1579148 1579794 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-727 1577964 1578072 1578330 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-726 1577122 1577247 1577468 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-725 1573406 1574202 1575115 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-724 1572846 1572941 1573163 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-723 1572527 1572576 1572703 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-722 1569130 1572326 1572445 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-721 1568290 1568912 1568940 "OCAMON" 1568945 OCAMON (NIL) -9 NIL 1568966 NIL) (-720 1562502 1565316 1565356 "OC" 1566451 OC (NIL T) -9 NIL 1567307 NIL) (-719 1560502 1561428 1562408 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-718 1559918 1560336 1560364 "OASGP" 1560369 OASGP (NIL) -9 NIL 1560389 NIL) (-717 1558981 1559630 1559658 "OAMONS" 1559698 OAMONS (NIL) -9 NIL 1559741 NIL) (-716 1558126 1558707 1558735 "OAMON" 1558792 OAMON (NIL) -9 NIL 1558843 NIL) (-715 1558022 1558054 1558121 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-714 1556773 1557547 1557575 "OAGROUP" 1557721 OAGROUP (NIL) -9 NIL 1557813 NIL) (-713 1556564 1556651 1556768 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-712 1556304 1556360 1556448 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-711 1551366 1552929 1554456 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-710 1548061 1549095 1550130 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-709 1547171 1547404 1547622 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-708 1536032 1539060 1541508 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-707 1529919 1535473 1535567 "NTSCAT" 1535572 NTSCAT (NIL T T T T) -9 NIL 1535610 NIL) (-706 1529260 1529439 1529632 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-705 1528953 1529016 1529123 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-704 1516620 1526573 1527383 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-703 1505629 1516485 1516615 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-702 1504349 1504674 1505031 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-701 1503185 1503449 1503807 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-700 1502352 1502485 1502701 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-699 1500670 1500989 1501395 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-698 1500383 1500417 1500541 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-697 1500202 1500237 1500306 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-696 1499978 1500168 1500197 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-695 1499542 1499609 1499786 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-694 1497828 1498905 1499160 "NNI" NIL NNI (NIL) -8 NIL NIL 1499507) (-693 1496556 1496893 1497257 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-692 1495533 1495785 1496087 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-691 1494620 1495185 1495226 "NETCLT" 1495397 NETCLT (NIL T) -9 NIL 1495478 NIL) (-690 1493524 1493791 1494072 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-689 1493323 1493366 1493441 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-688 1491854 1492242 1492662 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-687 1490487 1491453 1491481 "NASRING" 1491591 NASRING (NIL) -9 NIL 1491671 NIL) (-686 1490332 1490388 1490482 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-685 1489261 1489939 1489967 "NARNG" 1490084 NARNG (NIL) -9 NIL 1490175 NIL) (-684 1489037 1489122 1489256 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-683 1487803 1488557 1488597 "NAALG" 1488676 NAALG (NIL T) -9 NIL 1488737 NIL) (-682 1487673 1487708 1487798 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-681 1482652 1483837 1485023 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-680 1482047 1482134 1482318 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-679 1474057 1478551 1478603 "MTSCAT" 1479663 MTSCAT (NIL T T) -9 NIL 1480177 NIL) (-678 1473823 1473883 1473975 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-677 1473649 1473688 1473748 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-676 1470511 1473200 1473241 "MSETAGG" 1473246 MSETAGG (NIL T) -9 NIL 1473280 NIL) (-675 1466648 1469557 1469875 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-674 1462922 1464745 1465485 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-673 1462559 1462632 1462761 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-672 1462212 1462253 1462397 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-671 1460077 1460414 1460845 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-670 1453475 1459976 1460072 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-669 1453000 1453041 1453249 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-668 1452559 1452608 1452791 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1451833 1451926 1452145 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-666 1450450 1450811 1451201 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-665 1449971 1450038 1450077 "MONOPC" 1450137 MONOPC (NIL T) -9 NIL 1450356 NIL) (-664 1449422 1449758 1449886 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-663 1448564 1448943 1448971 "MONOID" 1449189 MONOID (NIL) -9 NIL 1449333 NIL) (-662 1448223 1448373 1448559 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-661 1437161 1444031 1444090 "MONOGEN" 1444764 MONOGEN (NIL T T) -9 NIL 1445220 NIL) (-660 1435173 1436059 1437042 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-659 1433887 1434431 1434459 "MONADWU" 1434850 MONADWU (NIL) -9 NIL 1435085 NIL) (-658 1433435 1433635 1433882 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-657 1432712 1433013 1433041 "MONAD" 1433248 MONAD (NIL) -9 NIL 1433360 NIL) (-656 1432479 1432575 1432707 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-655 1430869 1431639 1431918 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-654 1430003 1430530 1430570 "MODULE" 1430575 MODULE (NIL T) -9 NIL 1430613 NIL) (-653 1429682 1429808 1429998 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-652 1427393 1428279 1428593 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-651 1424572 1425989 1426502 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-650 1423206 1423780 1424056 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-649 1412425 1421871 1422284 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-648 1409381 1411425 1411694 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-647 1408465 1408832 1409022 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-646 1408034 1408083 1408262 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-645 1405859 1406855 1406895 "MLO" 1407312 MLO (NIL T) -9 NIL 1407552 NIL) (-644 1403740 1404267 1404862 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-643 1403208 1403304 1403458 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-642 1402878 1402954 1403077 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-641 1402090 1402276 1402504 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-640 1401583 1401699 1401855 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-639 1400955 1401069 1401254 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-638 1399982 1400255 1400532 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-637 1399415 1399503 1399674 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-636 1396573 1397452 1398331 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-635 1395240 1395588 1395941 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-634 1391897 1394364 1394405 "MDAGG" 1394662 MDAGG (NIL T) -9 NIL 1394807 NIL) (-633 1391171 1391335 1391535 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-632 1390249 1390535 1390765 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-631 1388346 1388923 1389484 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-630 1384118 1387936 1388183 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-629 1380467 1381236 1381970 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-628 1379220 1379389 1379718 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-627 1368733 1372322 1372398 "MATCAT" 1377386 MATCAT (NIL T T T) -9 NIL 1378854 NIL) (-626 1366014 1367320 1368728 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-625 1364415 1364775 1365159 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-624 1363548 1363745 1363967 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-623 1362299 1362625 1362952 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-622 1361461 1361863 1362039 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-621 1361130 1361194 1361317 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-620 1360778 1360851 1360965 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-619 1360313 1360428 1360570 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-618 1358522 1359290 1359591 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-617 1358016 1358318 1358408 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-616 1351525 1356331 1356372 "LZSTAGG" 1357149 LZSTAGG (NIL T) -9 NIL 1357439 NIL) (-615 1348644 1350078 1351520 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-614 1346031 1346997 1347480 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-613 1345612 1345891 1345965 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-612 1337776 1345473 1345607 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-611 1337139 1337284 1337512 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-610 1334623 1335321 1336033 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-609 1332735 1333058 1333506 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-608 1325904 1331822 1331863 "LSAGG" 1331925 LSAGG (NIL T) -9 NIL 1332003 NIL) (-607 1323598 1324697 1325899 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-606 1321078 1322947 1323196 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-605 1320745 1320836 1320959 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-604 1320416 1320495 1320523 "LOGIC" 1320634 LOGIC (NIL) -9 NIL 1320716 NIL) (-603 1320311 1320340 1320411 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-602 1319630 1319788 1319981 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-601 1318415 1318664 1319015 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-600 1314237 1317036 1317076 "LODOCAT" 1317508 LODOCAT (NIL T) -9 NIL 1317719 NIL) (-599 1314030 1314106 1314232 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-598 1311030 1313907 1314025 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-597 1308128 1310980 1311025 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-596 1305215 1308058 1308123 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-595 1304268 1304443 1304745 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-594 1302400 1303530 1303783 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-593 1297495 1300559 1300600 "LNAGG" 1301462 LNAGG (NIL T) -9 NIL 1301897 NIL) (-592 1296882 1297149 1297490 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-591 1293454 1294395 1295032 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-590 1292716 1293221 1293261 "LMODULE" 1293266 LMODULE (NIL T) -9 NIL 1293292 NIL) (-589 1289895 1292453 1292575 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-588 1289463 1289674 1289715 "LLINSET" 1289776 LLINSET (NIL T) -9 NIL 1289820 NIL) (-587 1289139 1289399 1289458 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-586 1288738 1288818 1288957 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-585 1287189 1287537 1287936 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-584 1286360 1286556 1286784 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-583 1279406 1285616 1285870 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-582 1278983 1279216 1279257 "LINSET" 1279262 LINSET (NIL T) -9 NIL 1279295 NIL) (-581 1277884 1278606 1278773 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-580 1276150 1276905 1276945 "LINEXP" 1277431 LINEXP (NIL T) -9 NIL 1277704 NIL) (-579 1274772 1275759 1275940 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-578 1273599 1273871 1274173 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-577 1272812 1273401 1273511 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-576 1270362 1271084 1271834 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-575 1268992 1269289 1269680 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-574 1267785 1268387 1268427 "LIECAT" 1268567 LIECAT (NIL T) -9 NIL 1268718 NIL) (-573 1267659 1267692 1267780 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-572 1261915 1267349 1267577 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-571 1254264 1261591 1261747 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-570 1250716 1251665 1252600 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-569 1249340 1250248 1250276 "LFCAT" 1250483 LFCAT (NIL) -9 NIL 1250622 NIL) (-568 1247579 1247909 1248254 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-567 1245096 1245761 1246442 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-566 1242108 1243086 1243589 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-565 1241599 1241902 1241993 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-564 1240306 1240630 1241030 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-563 1239572 1239657 1239883 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-562 1234575 1238140 1238676 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-561 1234200 1234250 1234410 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-560 1232971 1233744 1233784 "LALG" 1233845 LALG (NIL T) -9 NIL 1233903 NIL) (-559 1232754 1232831 1232966 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-558 1230607 1232022 1232273 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-557 1230436 1230466 1230507 "KVTFROM" 1230569 KVTFROM (NIL T) -9 NIL NIL NIL) (-556 1229252 1229967 1230156 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-555 1229081 1229111 1229152 "KRCFROM" 1229214 KRCFROM (NIL T) -9 NIL NIL NIL) (-554 1228183 1228380 1228675 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-553 1228012 1228042 1228083 "KONVERT" 1228145 KONVERT (NIL T) -9 NIL NIL NIL) (-552 1227841 1227871 1227912 "KOERCE" 1227974 KOERCE (NIL T) -9 NIL NIL NIL) (-551 1227411 1227504 1227636 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-550 1225464 1226358 1226730 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-549 1218641 1223656 1223710 "KDAGG" 1224086 KDAGG (NIL T T) -9 NIL 1224293 NIL) (-548 1218289 1218431 1218636 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-547 1211119 1218070 1218227 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-546 1210769 1211051 1211114 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-545 1209739 1210238 1210487 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-544 1208865 1209314 1209519 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-543 1207729 1208221 1208521 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-542 1207011 1207410 1207571 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-541 1206721 1206957 1207006 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-540 1200976 1206411 1206639 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-539 1200394 1200727 1200847 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-538 1196556 1198571 1198625 "IXAGG" 1199552 IXAGG (NIL T T) -9 NIL 1200009 NIL) (-537 1195762 1196133 1196551 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-536 1191016 1195698 1195757 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-535 1189983 1190258 1190521 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-534 1188645 1188852 1189145 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-533 1187596 1187818 1188101 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-532 1187271 1187334 1187457 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-531 1186533 1186905 1187079 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-530 1184509 1185809 1186083 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-529 1174057 1179826 1180983 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-528 1173302 1173454 1173690 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-527 1172793 1173096 1173187 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-526 1172086 1172177 1172390 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-525 1171218 1171443 1171683 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-524 1169631 1170012 1170440 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-523 1169416 1169460 1169536 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-522 1168266 1168563 1168858 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-521 1167539 1167890 1168041 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-520 1166742 1166873 1167086 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-519 1164897 1165394 1165938 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-518 1161978 1163246 1163935 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-517 1161803 1161843 1161903 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-516 1157801 1161729 1161798 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-515 1155804 1157740 1157796 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-514 1155175 1155474 1155604 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-513 1154628 1154916 1155048 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-512 1153709 1154334 1154460 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-511 1153119 1153613 1153641 "IOBCON" 1153646 IOBCON (NIL) -9 NIL 1153667 NIL) (-510 1152690 1152754 1152936 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-509 1144734 1147105 1149430 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-508 1141845 1142628 1143492 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-507 1141522 1141619 1141736 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-506 1138964 1141458 1141517 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-505 1137076 1137605 1138172 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-504 1136578 1136692 1136832 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-503 1134962 1135368 1135830 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-502 1132741 1133335 1133946 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-501 1130114 1130724 1131444 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-500 1129518 1129676 1129884 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-499 1129037 1129123 1129311 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-498 1127242 1127763 1128220 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-497 1120324 1121977 1123706 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-496 1119690 1119852 1120025 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-495 1117563 1118027 1118571 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-494 1115689 1116639 1116667 "INTDOM" 1116966 INTDOM (NIL) -9 NIL 1117171 NIL) (-493 1115242 1115444 1115684 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-492 1111049 1113521 1113575 "INTCAT" 1114371 INTCAT (NIL T) -9 NIL 1114687 NIL) (-491 1110614 1110734 1110861 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-490 1109454 1109626 1109932 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-489 1109027 1109123 1109280 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-488 1102067 1108882 1109022 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-487 1101365 1101920 1101985 "INT8" NIL INT8 (NIL) -8 NIL NIL 1102019) (-486 1100662 1101217 1101282 "INT64" NIL INT64 (NIL) -8 NIL NIL 1101316) (-485 1099959 1100514 1100579 "INT32" NIL INT32 (NIL) -8 NIL NIL 1100613) (-484 1099256 1099811 1099876 "INT16" NIL INT16 (NIL) -8 NIL NIL 1099910) (-483 1095719 1099175 1099251 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-482 1089776 1093259 1093287 "INS" 1094217 INS (NIL) -9 NIL 1094876 NIL) (-481 1087838 1088756 1089703 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-480 1086897 1087120 1087395 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-479 1086111 1086252 1086449 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-478 1085101 1085242 1085479 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-477 1084253 1084417 1084677 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-476 1083533 1083648 1083836 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-475 1082272 1082541 1082865 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-474 1081552 1081693 1081876 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-473 1081215 1081287 1081385 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-472 1078293 1079779 1080302 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-471 1077892 1077999 1078113 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-470 1077048 1077693 1077794 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-469 1075898 1076166 1076487 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-468 1074888 1075828 1075893 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-467 1074513 1074593 1074710 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-466 1073427 1073972 1074176 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-465 1069522 1070577 1071520 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-464 1068376 1068699 1068727 "INBCON" 1069240 INBCON (NIL) -9 NIL 1069506 NIL) (-463 1067830 1068095 1068371 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-462 1067324 1067626 1067716 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-461 1066781 1067090 1067195 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-460 1065621 1065760 1066075 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-459 1064045 1064312 1064649 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-458 1058888 1063976 1064040 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-457 1058268 1058602 1058717 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-456 1053075 1057706 1057892 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-455 1052105 1052997 1053070 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-454 1051677 1051754 1051808 "IEVALAB" 1052015 IEVALAB (NIL T T) -9 NIL NIL NIL) (-453 1051432 1051512 1051672 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-452 1050817 1051044 1051201 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-451 1049810 1050737 1050812 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-450 1048873 1049730 1049805 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-449 1047955 1048602 1048739 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-448 1046318 1046889 1046940 "IDPC" 1047446 IDPC (NIL T T) -9 NIL 1047759 NIL) (-447 1045606 1046240 1046313 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-446 1044776 1045528 1045601 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-445 1044469 1044682 1044742 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-444 1044173 1044213 1044252 "IDEMOPC" 1044257 IDEMOPC (NIL T) -9 NIL 1044394 NIL) (-443 1041244 1042125 1043017 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-442 1034870 1036147 1037186 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-441 1034132 1034262 1034461 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-440 1033305 1033804 1033942 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-439 1031694 1032025 1032416 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-438 1027463 1031650 1031689 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-437 1024721 1025345 1026040 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-436 1022947 1023427 1023960 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-435 1020787 1022853 1022942 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-434 1016656 1020725 1020782 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-433 1010235 1015620 1016088 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-432 1009803 1009866 1010039 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-431 1009295 1009444 1009472 "HYPCAT" 1009679 HYPCAT (NIL) -9 NIL NIL NIL) (-430 1008951 1009104 1009290 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-429 1008564 1008809 1008892 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-428 1008397 1008446 1008487 "HOMOTOP" 1008492 HOMOTOP (NIL T) -9 NIL 1008525 NIL) (-427 1004965 1006339 1006380 "HOAGG" 1007355 HOAGG (NIL T) -9 NIL 1008076 NIL) (-426 1003971 1004441 1004960 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-425 997171 1003696 1003844 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-424 996106 996364 996627 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-423 995041 995971 996101 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-422 993235 994874 994962 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-421 992550 992902 993035 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-420 986004 992483 992545 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-419 979143 985740 985891 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-418 978596 978753 978916 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-417 971679 978487 978591 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-416 971170 971473 971564 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-415 968720 970957 971136 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-414 964113 968603 968715 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-413 957199 964010 964108 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-412 949136 956568 956823 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-411 948160 948669 948697 "GROUP" 948900 GROUP (NIL) -9 NIL 949034 NIL) (-410 947703 947904 948155 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-409 946375 946714 947101 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-408 945197 945554 945605 "GRMOD" 946134 GRMOD (NIL T T) -9 NIL 946300 NIL) (-407 945016 945064 945192 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-406 941139 942350 943350 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-405 939861 940185 940500 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-404 939414 939542 939683 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-403 938487 938986 939037 "GRALG" 939190 GRALG (NIL T T) -9 NIL 939280 NIL) (-402 938206 938307 938482 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-401 934923 937888 938064 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-400 934336 934399 934656 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-399 930190 931086 931611 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-398 929365 929567 929805 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-397 924368 925295 926314 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-396 924116 924173 924262 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-395 923598 923687 923852 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-394 923107 923148 923361 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-393 921908 922191 922495 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-392 915183 921598 921759 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-391 904966 909973 911077 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-390 903018 904121 904149 "GCDDOM" 904404 GCDDOM (NIL) -9 NIL 904561 NIL) (-389 902641 902798 903013 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-388 893434 895904 898292 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-387 891569 891894 892312 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-386 890510 890699 890966 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-385 889381 889588 889892 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-384 888844 888986 889134 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-383 887456 887804 888117 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-382 886001 886322 886644 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-381 883627 883983 884388 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-380 876879 878540 880118 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-379 876531 876752 876820 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-378 876155 876376 876457 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-377 874252 874935 875395 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-376 872845 873152 873544 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-375 871500 871859 872183 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-374 870803 870927 871114 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-373 869777 870043 870390 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-372 867435 867965 868447 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-371 867018 867078 867247 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-370 865318 866232 866535 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-369 864466 864600 864823 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-368 863637 863798 864025 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-367 859620 862571 862612 "FSAGG" 862982 FSAGG (NIL T) -9 NIL 863241 NIL) (-366 857974 858733 859525 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-365 855930 856226 856770 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-364 854977 855159 855459 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-363 854658 854707 854834 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-362 834814 844315 844356 "FS" 848226 FS (NIL T) -9 NIL 850504 NIL) (-361 827045 830538 834517 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-360 826579 826706 826858 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-359 821102 824260 824300 "FRNAALG" 825620 FRNAALG (NIL T) -9 NIL 826218 NIL) (-358 817843 819094 820352 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-357 817524 817573 817700 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-356 816011 816568 816862 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-355 815297 815390 815677 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-354 813131 813897 814213 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-353 812240 812683 812724 "FRETRCT" 812729 FRETRCT (NIL T) -9 NIL 812900 NIL) (-352 811613 811891 812235 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-351 808357 809877 809936 "FRAMALG" 810818 FRAMALG (NIL T T) -9 NIL 811110 NIL) (-350 806953 807504 808134 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-349 806646 806709 806816 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-348 800287 806451 806641 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-347 799980 800043 800150 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-346 792288 796859 798187 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-345 786066 789569 789597 "FPS" 790716 FPS (NIL) -9 NIL 791272 NIL) (-344 785623 785756 785920 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-343 782433 784476 784504 "FPC" 784729 FPC (NIL) -9 NIL 784871 NIL) (-342 782279 782331 782428 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-341 781056 781765 781806 "FPATMAB" 781811 FPATMAB (NIL T) -9 NIL 781963 NIL) (-340 779486 780082 780429 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-339 779061 779119 779292 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-338 777564 778459 778633 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-337 776179 776684 776712 "FNCAT" 777169 FNCAT (NIL) -9 NIL 777426 NIL) (-336 775636 776146 776174 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-335 774223 775585 775631 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-334 770811 772169 772210 "FMONCAT" 773427 FMONCAT (NIL T) -9 NIL 774031 NIL) (-333 767669 768747 768800 "FMCAT" 769981 FMCAT (NIL T T) -9 NIL 770473 NIL) (-332 766369 767492 767591 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-331 765417 766217 766364 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-330 763604 764056 764550 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-329 761539 762075 762653 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-328 754925 759876 760490 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-327 753406 754507 754547 "FLINEXP" 754552 FLINEXP (NIL T) -9 NIL 754645 NIL) (-326 752815 753074 753401 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-325 752030 752189 752410 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-324 748913 749992 750044 "FLALG" 751271 FLALG (NIL T T) -9 NIL 751738 NIL) (-323 748084 748245 748472 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-322 741493 745503 745544 "FLAGG" 746799 FLAGG (NIL T) -9 NIL 747444 NIL) (-321 740601 741005 741488 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-320 737162 738426 738485 "FINRALG" 739613 FINRALG (NIL T T) -9 NIL 740121 NIL) (-319 736553 736818 737157 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-318 735851 736147 736175 "FINITE" 736371 FINITE (NIL) -9 NIL 736478 NIL) (-317 735759 735785 735846 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-316 727720 730311 730351 "FINAALG" 734003 FINAALG (NIL T) -9 NIL 735441 NIL) (-315 723987 725232 726355 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 722539 722958 723012 "FILECAT" 723696 FILECAT (NIL T T) -9 NIL 723912 NIL) (-313 721890 722364 722467 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 719138 721016 721044 "FIELD" 721084 FIELD (NIL) -9 NIL 721164 NIL) (-311 718163 718624 719133 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 716167 717113 717459 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 715410 715591 715810 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 710680 715348 715405 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 710342 710409 710544 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 709882 709924 710133 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 706562 707439 708216 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 701846 706494 706557 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 696525 701335 701525 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 691006 695806 696064 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 685213 690457 690668 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 684236 684446 684761 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 679676 682381 682409 "FFIELDC" 683028 FFIELDC (NIL) -9 NIL 683403 NIL) (-298 678745 679185 679671 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 678360 678418 678542 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 676504 677027 677544 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 671598 676303 676404 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 666698 671387 671494 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 661364 666489 666597 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 660818 660867 661102 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 639393 650427 650513 "FFCAT" 655663 FFCAT (NIL T T T) -9 NIL 657099 NIL) (-290 635633 636859 638165 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 630476 635564 635628 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 629368 629837 629878 "FEVALAB" 629962 FEVALAB (NIL T) -9 NIL 630223 NIL) (-287 628773 629025 629363 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 625600 626511 626626 "FDIVCAT" 628193 FDIVCAT (NIL T T T T) -9 NIL 628629 NIL) (-285 625394 625426 625595 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 624701 624794 625071 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 623187 624185 624388 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 622280 622664 622866 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 621402 621891 622031 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 612989 617632 617672 "FAXF" 619473 FAXF (NIL T) -9 NIL 620163 NIL) (-279 610905 611709 612524 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 605769 610427 610601 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 600227 602650 602702 "FAMR" 603713 FAMR (NIL T T) -9 NIL 604172 NIL) (-276 599426 599791 600222 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 598447 599368 599421 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 596041 596920 596973 "FAMONC" 597914 FAMONC (NIL T T) -9 NIL 598299 NIL) (-273 594597 595899 596036 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 592677 593038 593440 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 591954 592151 592373 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 583814 591401 591600 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 581833 582403 582989 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 578735 579377 580097 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 573892 574599 575404 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 573581 573644 573753 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 558374 572630 573056 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 548901 557694 557982 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 548395 548697 548787 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 548171 548361 548390 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 547860 547928 548041 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 547377 547519 547560 "EVALAB" 547730 EVALAB (NIL T) -9 NIL 547834 NIL) (-259 547005 547151 547372 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 544048 545643 545671 "EUCDOM" 546225 EUCDOM (NIL) -9 NIL 546574 NIL) (-257 542975 543468 544043 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 542700 542756 542856 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 542388 542452 542561 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 536159 538059 538087 "ES" 540829 ES (NIL) -9 NIL 542213 NIL) (-253 532674 534206 535998 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 532022 532175 532351 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 525111 531926 532017 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 524800 524863 524972 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 518427 521552 522985 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 514730 515826 516919 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 513559 513909 514214 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 512444 513175 513203 "ENTIRER" 513208 ENTIRER (NIL) -9 NIL 513252 NIL) (-245 512333 512367 512439 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 508966 510763 511112 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 508058 508269 508323 "ELTAGG" 508703 ELTAGG (NIL T T) -9 NIL 508914 NIL) (-242 507838 507912 508053 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 507584 507619 507673 "ELTAB" 507757 ELTAB (NIL T T) -9 NIL 507809 NIL) (-240 506835 507005 507204 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 506559 506633 506661 "ELEMFUN" 506766 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 506459 506486 506554 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 501005 504500 504541 "ELAGG" 505478 ELAGG (NIL T) -9 NIL 505938 NIL) (-236 499803 500341 501000 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 499221 499388 499544 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 498134 498453 498732 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 491527 493525 494352 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 485506 487502 488312 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 483320 483726 484197 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 474320 476233 477774 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 473433 473934 474083 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 472131 472805 472845 "DVARCAT" 473128 DVARCAT (NIL T) -9 NIL 473268 NIL) (-227 471550 471814 472126 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 463617 471418 471545 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 461955 462746 462787 "DSEXT" 463150 DSEXT (NIL T) -9 NIL 463444 NIL) (-224 460760 461284 461950 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 460484 460549 460647 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 456635 457851 458982 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 452281 453636 454700 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 450956 451317 451703 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 450642 450701 450819 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 449617 449915 450205 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 449202 449277 449427 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 441615 443727 445842 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 437132 438151 439230 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 433727 435796 435837 "DQAGG" 436466 DQAGG (NIL T) -9 NIL 436739 NIL) (-213 420270 427910 427992 "DPOLCAT" 429829 DPOLCAT (NIL T T T T) -9 NIL 430372 NIL) (-212 416678 418326 420265 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 409683 416576 416673 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 402597 409512 409678 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 402190 402450 402539 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 401604 402052 402132 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 400890 401215 401366 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 394029 400626 400777 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 391778 393095 393135 "DMEXT" 393140 DMEXT (NIL T) -9 NIL 393315 NIL) (-204 391434 391496 391640 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 384759 390919 391109 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 381425 383582 383623 "DLAGG" 384173 DLAGG (NIL T) -9 NIL 384402 NIL) (-201 379776 380647 380675 "DIVRING" 380767 DIVRING (NIL) -9 NIL 380850 NIL) (-200 379227 379471 379771 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 377655 378072 378478 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 376692 376913 377178 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 370166 376624 376687 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 358486 364946 364999 "DIRPCAT" 365255 DIRPCAT (NIL NIL T) -9 NIL 366128 NIL) (-195 356492 357262 358149 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 355939 356105 356291 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 352485 354825 354866 "DIOPS" 355298 DIOPS (NIL T) -9 NIL 355524 NIL) (-192 352145 352289 352480 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 351152 351898 351926 "DIOID" 351931 DIOID (NIL) -9 NIL 351953 NIL) (-190 349980 350809 350837 "DIFRING" 350842 DIFRING (NIL) -9 NIL 350863 NIL) (-189 349616 349714 349742 "DIFFSPC" 349861 DIFFSPC (NIL) -9 NIL 349936 NIL) (-188 349357 349459 349611 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 348260 348885 348925 "DIFFMOD" 348930 DIFFMOD (NIL T) -9 NIL 349027 NIL) (-186 347944 348001 348042 "DIFFDOM" 348163 DIFFDOM (NIL T) -9 NIL 348231 NIL) (-185 347825 347855 347939 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 345498 347019 347059 "DIFEXT" 347064 DIFEXT (NIL T) -9 NIL 347216 NIL) (-183 342659 344999 345040 "DIAGG" 345045 DIAGG (NIL T) -9 NIL 345065 NIL) (-182 342215 342405 342654 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 337427 341405 341682 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 333885 334938 335948 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 328435 333039 333366 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 327001 327293 327668 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 324121 325373 325769 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 321841 323952 324041 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 321224 321369 321551 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 318542 319266 320066 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 316651 317109 317671 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 316034 316367 316481 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 309234 315759 315907 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 307154 307664 308168 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 306793 306842 306993 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 306052 306614 306705 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 304076 304518 304878 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 303368 303657 303803 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 302819 302965 303117 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 300181 300974 301701 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 299620 299766 299937 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 297692 298003 298370 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 297249 297504 297605 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 296450 296833 296861 "CTORCAT" 297042 CTORCAT (NIL) -9 NIL 297154 NIL) (-159 296153 296287 296445 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 295646 295903 296011 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 295062 295493 295566 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 294521 294638 294791 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 290915 291671 292426 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 290406 290709 290800 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 289625 289834 290062 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 289129 289234 289438 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 288882 288916 289022 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 285821 286583 287301 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 285340 285482 285621 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 281233 283803 284295 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 281107 281134 281162 "CONDUIT" 281199 CONDUIT (NIL) -9 NIL NIL NIL) (-146 279986 280717 280745 "COMRING" 280750 COMRING (NIL) -9 NIL 280800 NIL) (-145 279151 279518 279696 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 278847 278888 279016 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 278540 278603 278710 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 267382 278490 278535 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 266843 266982 267142 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 266596 266637 266735 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 248027 260277 260317 "COMPCAT" 261318 COMPCAT (NIL T) -9 NIL 262660 NIL) (-138 240565 244078 247671 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 240324 240358 240460 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 240154 240193 240251 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 239735 240014 240088 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 239312 239553 239640 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 238507 238755 238783 "COMBOPC" 239121 COMBOPC (NIL) -9 NIL 239296 NIL) (-132 237571 237823 238065 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 234503 235187 235810 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 233383 233834 234069 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 232874 233177 233268 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 232561 232614 232739 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 232031 232341 232439 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 228551 229621 230701 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 226846 227831 228069 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 222958 224966 225007 "CLAGG" 225933 CLAGG (NIL T) -9 NIL 226466 NIL) (-123 221851 222378 222953 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 221480 221571 221711 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 219417 219924 220472 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 218378 219109 219137 "CHARZ" 219142 CHARZ (NIL) -9 NIL 219156 NIL) (-119 218172 218218 218296 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 217011 217774 217802 "CHARNZ" 217863 CHARNZ (NIL) -9 NIL 217911 NIL) (-117 214489 215586 216109 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 214197 214276 214304 "CFCAT" 214415 CFCAT (NIL) -9 NIL NIL NIL) (-115 213540 213669 213851 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 209529 212953 213233 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 208907 209094 209271 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 208435 208854 208902 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 207908 208217 208314 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 207399 207702 207793 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 206648 206808 207029 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 202748 204005 204713 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 201114 202145 202396 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 200695 200974 201048 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 200129 200382 200410 "CACHSET" 200542 CACHSET (NIL) -9 NIL 200620 NIL) (-104 199481 199896 199924 "CABMON" 199974 CABMON (NIL) -9 NIL 200030 NIL) (-103 199011 199275 199385 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 194234 198668 198840 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 193204 193908 194043 "BYTE" NIL BYTE (NIL) -8 NIL NIL 194206) (-100 190675 192971 193077 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 188106 190418 190537 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 185346 187550 187589 "BTCAT" 187656 BTCAT (NIL T) -9 NIL 187732 NIL) (-97 185097 185195 185341 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 180207 184328 184354 "BTAGG" 184465 BTAGG (NIL) -9 NIL 184573 NIL) (-95 179838 179999 180202 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176900 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T) ((-589 |#2|) |has| |#1| (-312)) ((-589 $) . T) ((-581 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-581 |#1|) |has| |#1| (-146)) ((-581 |#2|) |has| |#1| (-312)) ((-581 $) OR (|has| |#1| (-494)) (|has| |#1| (-312))) ((-579 (-483)) -12 (|has| |#1| (-312)) (|has| |#2| (-579 (-483)))) ((-579 |#2|) |has| |#1| (-312)) ((-653 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-653 |#1|) |has| |#1| (-146)) ((-653 |#2|) |has| |#1| (-312)) ((-653 $) OR (|has| |#1| (-494)) (|has| |#1| (-312))) ((-662) . 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-494)) ((-72) . T) ((-82 (-348 (-483)) (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-494)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-554 (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-554 (-483)) . T) ((-554 |#1|) |has| |#1| (-146)) ((-554 $) |has| |#1| (-494)) ((-551 (-771)) . T) ((-146) OR (|has| |#1| (-494)) (|has| |#1| (-146))) ((-186 $) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-190) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-189) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-241 |#2| |#1|) . T) ((-241 $ $) |has| |#2| (-1024)) ((-246) |has| |#1| (-494)) ((-494) |has| |#1| (-494)) ((-13) . T) ((-587 (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-587 (-483)) . T) ((-587 |#1|) . T) ((-587 $) . 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2736370 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1178 2734396 2734677 2734993 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1177 2729512 2734223 2734315 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1176 2722614 2727222 2727265 "VECTCAT" 2728253 VECTCAT (NIL T) -9 NIL 2728837 NIL) (-1175 2721893 2722219 2722609 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1174 2721387 2721629 2721749 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1173 2721320 2721325 2721355 "UTYPE" 2721360 UTYPE (NIL) -9 NIL NIL NIL) (-1172 2720307 2720483 2720744 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1171 2718158 2718666 2719190 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1170 2708040 2714010 2714052 "UTSCAT" 2715150 UTSCAT (NIL T) -9 NIL 2715907 NIL) (-1169 2706105 2707048 2708035 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1168 2705779 2705828 2705959 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1167 2697490 2703975 2704454 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2691485 2694298 2694341 "URAGG" 2696411 URAGG (NIL T) -9 NIL 2697133 NIL) (-1165 2689500 2690462 2691480 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1164 2685207 2688476 2688938 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1163 2677636 2685131 2685202 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1162 2666287 2673774 2673835 "UPXSCCA" 2674403 UPXSCCA (NIL T T) -9 NIL 2674635 NIL) (-1161 2666008 2666110 2666282 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1160 2654560 2661772 2661814 "UPXSCAT" 2662454 UPXSCAT (NIL T) -9 NIL 2663062 NIL) (-1159 2654073 2654158 2654335 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1158 2645759 2653664 2653926 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1157 2644654 2644924 2645274 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1156 2637357 2640842 2640896 "UPSCAT" 2641965 UPSCAT (NIL T T) -9 NIL 2642729 NIL) (-1155 2636777 2637029 2637352 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1154 2636451 2636500 2636631 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1153 2620581 2629535 2629577 "UPOLYC" 2631655 UPOLYC (NIL T) -9 NIL 2632875 NIL) (-1152 2614636 2617484 2620576 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1151 2614072 2614197 2614360 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1150 2613706 2613793 2613932 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1149 2612519 2612786 2613090 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1148 2611852 2611982 2612167 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1147 2611444 2611519 2611666 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1146 2602208 2611210 2611338 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1145 2601570 2601707 2601912 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1144 2600171 2601018 2601294 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1143 2599400 2599597 2599822 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1142 2586210 2599324 2599395 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1141 2566016 2579251 2579312 "ULSCCAT" 2579943 ULSCCAT (NIL T T) -9 NIL 2580230 NIL) (-1140 2565351 2565637 2566011 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1139 2553723 2560857 2560899 "ULSCAT" 2561752 ULSCAT (NIL T) -9 NIL 2562482 NIL) (-1138 2553236 2553321 2553498 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1137 2535353 2552735 2552976 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1136 2534387 2535080 2535194 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2535305) (-1135 2533420 2534113 2534227 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2534338) (-1134 2532453 2533146 2533260 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2533371) (-1133 2531486 2532179 2532293 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2532404) (-1132 2529493 2530714 2530744 "UFD" 2530955 UFD (NIL) -9 NIL 2531068 NIL) (-1131 2529337 2529394 2529488 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1130 2528589 2528796 2529012 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1129 2526809 2527262 2527727 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1128 2526534 2526774 2526804 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1127 2526472 2526477 2526507 "TYPE" 2526512 TYPE (NIL) -9 NIL 2526519 NIL) (-1126 2525631 2525851 2526091 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1125 2524809 2525240 2525475 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1124 2522963 2523536 2524075 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1123 2521997 2522233 2522469 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1122 2510351 2514819 2514915 "TSETCAT" 2520130 TSETCAT (NIL T T T T) -9 NIL 2521642 NIL) (-1121 2506688 2508504 2510346 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1120 2501080 2505914 2506196 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1119 2496417 2497430 2498359 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1118 2495914 2495989 2496152 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1117 2493990 2494280 2494635 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1116 2493474 2493623 2493653 "TRIGCAT" 2493866 TRIGCAT (NIL) -9 NIL NIL NIL) (-1115 2493225 2493328 2493469 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1114 2490221 2492334 2492612 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1113 2489327 2490023 2490053 "TRANFUN" 2490088 TRANFUN (NIL) -9 NIL 2490154 NIL) (-1112 2488791 2489042 2489322 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1111 2488628 2488666 2488727 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1110 2488085 2488216 2488367 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1109 2486826 2487483 2487719 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1108 2486638 2486675 2486747 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1107 2484852 2485498 2485927 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1106 2483232 2483569 2483891 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1105 2474290 2481033 2481089 "TBAGG" 2481491 TBAGG (NIL T T) -9 NIL 2481704 NIL) (-1104 2470821 2472513 2474285 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1103 2470298 2470423 2470568 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1102 2469808 2470128 2470218 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1101 2469305 2469422 2469560 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1100 2462392 2469207 2469300 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1099 2458145 2459440 2460685 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1098 2457514 2457673 2457854 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1097 2454668 2455421 2456204 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1096 2454442 2454632 2454663 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1095 2453396 2454081 2454207 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2454393) (-1094 2452660 2453208 2453287 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2453347) (-1093 2449483 2450642 2451342 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1092 2447166 2447849 2448483 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1091 2443244 2444290 2445267 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1090 2440343 2442899 2443128 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1089 2439939 2440026 2440148 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1088 2436563 2438037 2438856 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1087 2429523 2435760 2436053 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1086 2421209 2429114 2429376 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1085 2420488 2420627 2420844 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1084 2420172 2420237 2420348 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1083 2410895 2419884 2420009 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1082 2409625 2409923 2410278 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1081 2409030 2409108 2409299 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1080 2391182 2408529 2408770 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1079 2390781 2391053 2391122 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1078 2390117 2390398 2390538 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1077 2384719 2385978 2386931 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1076 2384251 2384351 2384515 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1075 2379362 2380644 2381791 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1074 2373820 2375291 2376602 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1073 2366735 2368799 2370590 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1072 2359565 2366647 2366730 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1071 2354259 2359279 2359394 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1070 2353846 2353929 2354073 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1069 2352997 2353198 2353433 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1068 2352737 2352795 2352888 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1067 2345475 2350942 2351548 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1066 2344651 2344856 2345087 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1065 2343896 2344267 2344414 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1064 2343384 2343626 2343656 "STEP" 2343750 STEP (NIL) -9 NIL 2343821 NIL) (-1063 2336487 2343302 2343379 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1062 2330702 2335285 2335328 "STAGG" 2335755 STAGG (NIL T) -9 NIL 2335929 NIL) (-1061 2329081 2329829 2330697 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1060 2327238 2328908 2329000 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1059 2326518 2327057 2327087 "SRING" 2327092 SRING (NIL) -9 NIL 2327112 NIL) (-1058 2319140 2325056 2325495 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2312914 2314353 2315857 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1056 2305339 2310250 2310280 "SRAGG" 2311579 SRAGG (NIL) -9 NIL 2312183 NIL) (-1055 2304636 2304956 2305334 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1054 2298691 2303958 2304381 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1053 2292904 2296073 2296795 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1052 2289333 2290152 2290789 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1051 2288308 2288613 2288643 "SPFCAT" 2289087 SPFCAT (NIL) -9 NIL NIL NIL) (-1050 2287245 2287497 2287761 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1049 2278003 2280277 2280307 "SPADXPT" 2284944 SPADXPT (NIL) -9 NIL 2287068 NIL) (-1048 2277805 2277851 2277920 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1047 2275461 2277769 2277800 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1046 2267135 2269224 2269266 "SPACEC" 2273581 SPACEC (NIL T) -9 NIL 2275386 NIL) (-1045 2264964 2267082 2267130 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1044 2263897 2264086 2264375 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1043 2262301 2262634 2263045 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1042 2261566 2261800 2262061 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1041 2257746 2258706 2259701 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1040 2254104 2254803 2255532 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1039 2247890 2253444 2253540 "SNTSCAT" 2253545 SNTSCAT (NIL T T T T) -9 NIL 2253615 NIL) (-1038 2241711 2246531 2246921 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1037 2235483 2241630 2241706 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1036 2233915 2234246 2234644 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1035 2225520 2230499 2230601 "SMATCAT" 2231944 SMATCAT (NIL NIL T T T) -9 NIL 2232492 NIL) (-1034 2223361 2224345 2225515 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1033 2220953 2222567 2222610 "SKAGG" 2222871 SKAGG (NIL T) -9 NIL 2223005 NIL) (-1032 2216999 2220773 2220884 "SINT" NIL SINT (NIL) -8 NIL NIL 2220925) (-1031 2216809 2216853 2216919 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1030 2215884 2216116 2216384 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1029 2214888 2215050 2215326 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1028 2214234 2214574 2214697 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1027 2213580 2213887 2214027 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1026 2211691 2212183 2212689 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1025 2205131 2211610 2211686 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1024 2204634 2204871 2204901 "SGROUP" 2204994 SGROUP (NIL) -9 NIL 2205056 NIL) (-1023 2204524 2204556 2204629 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1022 2204162 2204202 2204243 "SGPOPC" 2204248 SGPOPC (NIL T) -9 NIL 2204449 NIL) (-1021 2203696 2203973 2204079 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1020 2201119 2201888 2202610 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1019 2195004 2200558 2200654 "SFRTCAT" 2200659 SFRTCAT (NIL T T T T) -9 NIL 2200697 NIL) (-1018 2189396 2190509 2191636 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1017 2183572 2184733 2185897 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1016 2182544 2183446 2183567 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1015 2178152 2179047 2179142 "SEXCAT" 2181755 SEXCAT (NIL T T T T T) -9 NIL 2182306 NIL) (-1014 2177125 2178079 2178147 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1013 2175516 2176101 2176403 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1012 2175039 2175224 2175254 "SETCAT" 2175371 SETCAT (NIL) -9 NIL 2175455 NIL) (-1011 2174871 2174935 2175034 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1010 2171094 2173325 2173368 "SETAGG" 2174236 SETAGG (NIL T) -9 NIL 2174574 NIL) (-1009 2170700 2170852 2171089 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1008 2167654 2170647 2170695 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1007 2167120 2167430 2167530 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1006 2166247 2166613 2166674 "SEGXCAT" 2166960 SEGXCAT (NIL T T) -9 NIL 2167080 NIL) (-1005 2165172 2165440 2165483 "SEGCAT" 2166005 SEGCAT (NIL T) -9 NIL 2166226 NIL) (-1004 2164852 2164917 2165030 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1003 2163918 2164388 2164596 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1002 2163496 2163775 2163851 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1001 2162861 2162997 2163201 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1000 2161927 2162674 2162856 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-999 2161182 2161877 2161922 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-998 2152719 2161053 2161177 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-997 2151579 2151869 2152186 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-996 2150885 2151097 2151285 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-995 2150235 2150392 2150568 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-994 2149808 2150039 2150067 "SASTCAT" 2150072 SASTCAT (NIL) -9 NIL 2150085 NIL) (-993 2149275 2149700 2149774 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-992 2148878 2148919 2149090 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-991 2148509 2148550 2148707 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-990 2141590 2148426 2148504 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-989 2140240 2140569 2140965 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-988 2139001 2139362 2139662 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-987 2138625 2138846 2138927 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-986 2136085 2136719 2137172 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-985 2135924 2135957 2136025 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-984 2135415 2135718 2135809 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-983 2131043 2131911 2132822 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-982 2119862 2125416 2125510 "RSETCAT" 2129566 RSETCAT (NIL T T T T) -9 NIL 2130654 NIL) (-981 2118400 2119042 2119857 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-980 2112174 2113619 2115126 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-979 2110056 2110613 2110685 "RRCC" 2111758 RRCC (NIL T T) -9 NIL 2112099 NIL) (-978 2109581 2109780 2110051 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-977 2109051 2109361 2109459 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-976 2081603 2092316 2092380 "RPOLCAT" 2102854 RPOLCAT (NIL T T T) -9 NIL 2105999 NIL) (-975 2075702 2078525 2081598 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-974 2071869 2075450 2075588 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-973 2070197 2070936 2071192 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-972 2065840 2068652 2068680 "RNS" 2068942 RNS (NIL) -9 NIL 2069194 NIL) (-971 2064743 2065230 2065767 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-970 2063861 2064262 2064462 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-969 2062999 2063561 2063589 "RNG" 2063649 RNG (NIL) -9 NIL 2063703 NIL) (-968 2062888 2062922 2062994 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-967 2062150 2062655 2062695 "RMODULE" 2062700 RMODULE (NIL T) -9 NIL 2062726 NIL) (-966 2061089 2061195 2061525 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-965 2057935 2060679 2060972 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-964 2050584 2053076 2053188 "RMATCAT" 2056493 RMATCAT (NIL NIL NIL T T T) -9 NIL 2057470 NIL) (-963 2050101 2050280 2050579 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-962 2049669 2049880 2049921 "RLINSET" 2049982 RLINSET (NIL T) -9 NIL 2050026 NIL) (-961 2049314 2049395 2049521 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-960 2048160 2048891 2048919 "RING" 2048974 RING (NIL) -9 NIL 2049066 NIL) (-959 2048005 2048061 2048155 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-958 2047059 2047326 2047582 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-957 2038046 2046687 2046888 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-956 2037271 2037782 2037821 "RGBCSPC" 2037878 RGBCSPC (NIL T) -9 NIL 2037929 NIL) (-955 2036305 2036791 2036830 "RGBCMDL" 2037058 RGBCMDL (NIL T) -9 NIL 2037172 NIL) (-954 2036017 2036086 2036187 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-953 2035780 2035821 2035916 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-952 2034204 2034634 2035014 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-951 2031791 2032459 2033127 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-950 2031341 2031439 2031599 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-949 2030963 2031061 2031102 "RETRACT" 2031233 RETRACT (NIL T) -9 NIL 2031320 NIL) (-948 2030843 2030874 2030958 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-947 2030445 2030717 2030784 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-946 2028925 2029816 2030013 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-945 2028616 2028677 2028773 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-944 2028359 2028400 2028505 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-943 2028094 2028135 2028244 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-942 2023165 2024616 2025831 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-941 2020264 2021022 2021830 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-940 2018233 2018855 2019455 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-939 2010868 2016784 2017220 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-938 2010180 2010460 2010609 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-937 2009665 2009780 2009945 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-936 2005258 2009068 2009289 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-935 2004490 2004689 2004902 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-934 2001780 2002618 2003500 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-933 1998362 1999398 2000457 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-932 1998198 1998251 1998279 "REAL" 1998284 REAL (NIL) -9 NIL 1998319 NIL) (-931 1997688 1997992 1998083 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-930 1997168 1997246 1997451 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-929 1996401 1996593 1996804 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-928 1995289 1995586 1995953 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-927 1993556 1994026 1994559 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-926 1992478 1992755 1993142 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-925 1991305 1991614 1992033 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-924 1984653 1988165 1988193 "RCFIELD" 1989470 RCFIELD (NIL) -9 NIL 1990200 NIL) (-923 1983271 1983883 1984580 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-922 1979471 1981363 1981404 "RCAGG" 1982471 RCAGG (NIL T) -9 NIL 1982932 NIL) (-921 1979198 1979308 1979466 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-920 1978643 1978772 1978933 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-919 1978260 1978339 1978458 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-918 1977675 1977825 1977975 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-917 1977457 1977507 1977578 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-916 1969899 1976575 1976883 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-915 1959601 1969766 1969894 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-914 1959235 1959328 1959356 "RADCAT" 1959513 RADCAT (NIL) -9 NIL NIL NIL) (-913 1959073 1959133 1959230 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-912 1957173 1958904 1958993 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-911 1956854 1956903 1957030 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-910 1949141 1953225 1953265 "QUATCAT" 1954043 QUATCAT (NIL T) -9 NIL 1954807 NIL) (-909 1946391 1947671 1949047 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-908 1942231 1946341 1946386 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-907 1939618 1941285 1941326 "QUAGG" 1941701 QUAGG (NIL T) -9 NIL 1941875 NIL) (-906 1939220 1939492 1939559 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-905 1938226 1938856 1939019 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-904 1937907 1937956 1938083 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-903 1927507 1933676 1933716 "QFCAT" 1934374 QFCAT (NIL T) -9 NIL 1935367 NIL) (-902 1924391 1925830 1927413 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-901 1923937 1924071 1924201 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-900 1918133 1919294 1920456 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-899 1917552 1917732 1917964 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-898 1915374 1915902 1916325 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-897 1914273 1914515 1914832 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-896 1912634 1912832 1913185 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-895 1908390 1909606 1909647 "PTRANFN" 1911531 PTRANFN (NIL T) -9 NIL NIL NIL) (-894 1907037 1907382 1907703 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-893 1906730 1906793 1906900 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-892 1900803 1905526 1905566 "PTCAT" 1905858 PTCAT (NIL T) -9 NIL 1906011 NIL) (-891 1900496 1900537 1900661 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-890 1899375 1899691 1900025 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-889 1888254 1890815 1893124 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-888 1881161 1884057 1884151 "PSETCAT" 1887125 PSETCAT (NIL T T T T) -9 NIL 1887932 NIL) (-887 1879611 1880345 1881156 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-886 1878930 1879125 1879153 "PSCURVE" 1879421 PSCURVE (NIL) -9 NIL 1879588 NIL) (-885 1874532 1876352 1876416 "PSCAT" 1877251 PSCAT (NIL T T T) -9 NIL 1877490 NIL) (-884 1873846 1874128 1874527 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-883 1872243 1873158 1873421 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-882 1871734 1872037 1872128 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-881 1862754 1865176 1867364 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-880 1860497 1862074 1862114 "PRQAGG" 1862297 PRQAGG (NIL T) -9 NIL 1862398 NIL) (-879 1859670 1860116 1860144 "PROPLOG" 1860283 PROPLOG (NIL) -9 NIL 1860397 NIL) (-878 1859345 1859408 1859531 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-877 1858781 1858920 1859092 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-876 1857029 1857792 1858089 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-875 1856581 1856713 1856841 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-874 1851022 1855521 1856341 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-873 1850851 1850889 1850948 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-872 1850290 1850430 1850581 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-871 1848758 1849177 1849643 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-870 1848475 1848536 1848564 "PRIMCAT" 1848688 PRIMCAT (NIL) -9 NIL NIL NIL) (-869 1847646 1847842 1848070 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-868 1843524 1847596 1847641 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-867 1843223 1843285 1843396 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-866 1840359 1842872 1843105 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-865 1839810 1839967 1839995 "PPCURVE" 1840200 PPCURVE (NIL) -9 NIL 1840336 NIL) (-864 1839423 1839668 1839751 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-863 1837179 1837600 1838192 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-862 1836622 1836686 1836919 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-861 1833342 1833828 1834439 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-860 1818933 1825062 1825126 "POLYCAT" 1828611 POLYCAT (NIL T T T) -9 NIL 1830488 NIL) (-859 1814443 1816590 1818928 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-858 1814100 1814174 1814293 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-857 1813793 1813856 1813963 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-856 1807156 1813526 1813685 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-855 1806043 1806306 1806582 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-854 1804647 1804960 1805290 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-853 1799809 1804597 1804642 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-852 1798297 1798708 1799083 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-851 1797054 1797363 1797759 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-850 1796725 1796809 1796926 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-849 1796304 1796379 1796553 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-848 1795790 1795886 1796046 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-847 1795262 1795382 1795536 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-846 1794157 1794375 1794752 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-845 1793768 1793853 1794005 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-844 1793319 1793401 1793582 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-843 1793011 1793092 1793205 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-842 1792524 1792599 1792807 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-841 1791872 1792000 1792202 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-840 1791234 1791368 1791531 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-839 1790538 1790720 1790901 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-838 1790261 1790335 1790429 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-837 1786829 1788018 1788934 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-836 1785913 1786114 1786349 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-835 1781478 1782862 1784004 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-834 1761399 1766286 1771133 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-833 1761139 1761192 1761295 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-832 1760580 1760714 1760894 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-831 1758589 1759810 1759838 "PID" 1760035 PID (NIL) -9 NIL 1760162 NIL) (-830 1758377 1758420 1758495 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-829 1757564 1758224 1758311 "PI" NIL PI (NIL) -8 NIL NIL 1758351) (-828 1757016 1757167 1757343 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-827 1753344 1754302 1755207 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-826 1751708 1751997 1752363 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-825 1751150 1751265 1751426 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-824 1747691 1750019 1750372 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-823 1746297 1746577 1746902 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-822 1745062 1745316 1745664 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-821 1743772 1743999 1744351 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-820 1740782 1742342 1742370 "PFECAT" 1742963 PFECAT (NIL) -9 NIL 1743340 NIL) (-819 1740405 1740570 1740777 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-818 1739229 1739511 1739812 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-817 1737411 1737798 1738228 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-816 1733381 1737337 1737406 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-815 1729284 1730431 1731298 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-814 1727216 1728305 1728346 "PERMCAT" 1728745 PERMCAT (NIL T) -9 NIL 1729042 NIL) (-813 1726912 1726959 1727082 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-812 1723361 1725042 1725687 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-811 1720826 1723116 1723237 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-810 1719695 1719958 1719999 "PDSPC" 1720532 PDSPC (NIL T) -9 NIL 1720777 NIL) (-809 1719062 1719328 1719690 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-808 1717697 1718690 1718731 "PDRING" 1718736 PDRING (NIL T) -9 NIL 1718763 NIL) (-807 1716407 1717196 1717249 "PDMOD" 1717254 PDMOD (NIL T T) -9 NIL 1717357 NIL) (-806 1715500 1715712 1715961 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-805 1715105 1715172 1715226 "PDDOM" 1715391 PDDOM (NIL T T) -9 NIL 1715471 NIL) (-804 1714957 1714993 1715100 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-803 1714743 1714782 1714871 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-802 1713060 1713814 1714113 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-801 1712749 1712812 1712921 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-800 1710887 1711317 1711768 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-799 1704507 1706336 1707628 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-798 1704138 1704211 1704343 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-797 1701840 1702520 1703001 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-796 1700044 1700472 1700875 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-795 1699490 1699738 1699779 "PATMAB" 1699886 PATMAB (NIL T) -9 NIL 1699969 NIL) (-794 1698137 1698541 1698798 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-793 1697675 1697806 1697847 "PATAB" 1697852 PATAB (NIL T) -9 NIL 1698024 NIL) (-792 1696218 1696655 1697078 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-791 1695896 1695971 1696073 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-790 1695585 1695648 1695757 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-789 1695390 1695436 1695503 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-788 1695068 1695143 1695245 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-787 1694757 1694820 1694929 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-786 1694448 1694518 1694615 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-785 1694137 1694200 1694309 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-784 1693298 1693677 1693856 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-783 1692905 1693003 1693122 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-782 1691873 1692298 1692517 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-781 1690538 1691192 1691552 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-780 1683628 1689942 1690136 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-779 1676049 1683126 1683310 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-778 1672774 1674689 1674729 "PADICCT" 1675310 PADICCT (NIL NIL) -9 NIL 1675592 NIL) (-777 1670764 1672724 1672769 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-776 1669926 1670136 1670402 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-775 1669268 1669411 1669615 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-774 1667649 1668676 1668954 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-773 1667173 1667432 1667529 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-772 1666232 1666910 1667082 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-771 1656654 1659523 1661722 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-770 1656046 1656360 1656486 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-769 1655323 1655518 1655546 "OUTBCON" 1655864 OUTBCON (NIL) -9 NIL 1656030 NIL) (-768 1655031 1655161 1655318 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-767 1654412 1654557 1654718 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-766 1653783 1654210 1654299 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-765 1653198 1653613 1653641 "OSGROUP" 1653646 OSGROUP (NIL) -9 NIL 1653668 NIL) (-764 1652162 1652423 1652708 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-763 1649431 1652037 1652157 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-762 1646572 1649182 1649308 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-761 1644590 1645118 1645678 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-760 1637932 1640472 1640512 "OREPCAT" 1642833 OREPCAT (NIL T) -9 NIL 1643935 NIL) (-759 1635958 1636892 1637927 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-758 1635155 1635426 1635454 "ORDTYPE" 1635759 ORDTYPE (NIL) -9 NIL 1635917 NIL) (-757 1634689 1634900 1635150 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-756 1634151 1634527 1634684 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-755 1633645 1634008 1634036 "ORDSET" 1634041 ORDSET (NIL) -9 NIL 1634063 NIL) (-754 1632210 1633232 1633260 "ORDRING" 1633265 ORDRING (NIL) -9 NIL 1633293 NIL) (-753 1631458 1632015 1632043 "ORDMON" 1632048 ORDMON (NIL) -9 NIL 1632069 NIL) (-752 1630762 1630924 1631116 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-751 1629973 1630481 1630509 "ORDFIN" 1630574 ORDFIN (NIL) -9 NIL 1630648 NIL) (-750 1629367 1629506 1629692 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-749 1626042 1628335 1628741 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-748 1625449 1625804 1625909 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-747 1625257 1625302 1625368 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-746 1624558 1624834 1624875 "OPERCAT" 1625086 OPERCAT (NIL T) -9 NIL 1625182 NIL) (-745 1624370 1624437 1624553 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-744 1621736 1623172 1623668 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-743 1621157 1621284 1621458 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-742 1618058 1620296 1620662 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-741 1614689 1617488 1617528 "OMSAGG" 1617589 OMSAGG (NIL T) -9 NIL 1617653 NIL) (-740 1613101 1614360 1614528 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-739 1611297 1612538 1612566 "OINTDOM" 1612571 OINTDOM (NIL) -9 NIL 1612592 NIL) (-738 1608727 1610299 1610628 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-737 1607981 1608677 1608722 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-736 1605183 1607822 1607976 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-735 1596720 1605054 1605178 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-734 1590131 1596611 1596715 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-733 1589103 1589340 1589613 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-732 1586737 1587407 1588111 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-731 1582514 1583474 1584497 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-730 1582022 1582110 1582304 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-729 1579471 1580053 1580726 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-728 1576866 1577374 1577970 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-727 1573863 1574402 1575048 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-726 1573218 1573326 1573584 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-725 1572376 1572501 1572722 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-724 1568660 1569456 1570369 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-723 1568100 1568195 1568417 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-722 1567781 1567830 1567957 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-721 1564384 1567580 1567699 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-720 1563544 1564166 1564194 "OCAMON" 1564199 OCAMON (NIL) -9 NIL 1564220 NIL) (-719 1557756 1560570 1560610 "OC" 1561705 OC (NIL T) -9 NIL 1562561 NIL) (-718 1555756 1556682 1557662 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-717 1555172 1555590 1555618 "OASGP" 1555623 OASGP (NIL) -9 NIL 1555643 NIL) (-716 1554235 1554884 1554912 "OAMONS" 1554952 OAMONS (NIL) -9 NIL 1554995 NIL) (-715 1553380 1553961 1553989 "OAMON" 1554046 OAMON (NIL) -9 NIL 1554097 NIL) (-714 1553276 1553308 1553375 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-713 1552027 1552801 1552829 "OAGROUP" 1552975 OAGROUP (NIL) -9 NIL 1553067 NIL) (-712 1551818 1551905 1552022 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-711 1551558 1551614 1551702 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-710 1546620 1548183 1549710 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-709 1543315 1544349 1545384 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-708 1542425 1542658 1542876 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-707 1531286 1534314 1536762 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-706 1525173 1530727 1530821 "NTSCAT" 1530826 NTSCAT (NIL T T T T) -9 NIL 1530864 NIL) (-705 1524514 1524693 1524886 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-704 1524207 1524270 1524377 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-703 1511874 1521827 1522637 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-702 1500883 1511739 1511869 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-701 1499603 1499928 1500285 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-700 1498439 1498703 1499061 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-699 1497606 1497739 1497955 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-698 1495924 1496243 1496649 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-697 1495637 1495671 1495795 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-696 1495456 1495491 1495560 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-695 1495232 1495422 1495451 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-694 1494796 1494863 1495040 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-693 1493082 1494159 1494414 "NNI" NIL NNI (NIL) -8 NIL NIL 1494761) (-692 1491810 1492147 1492511 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-691 1490787 1491039 1491341 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-690 1489874 1490439 1490480 "NETCLT" 1490651 NETCLT (NIL T) -9 NIL 1490732 NIL) (-689 1488778 1489045 1489326 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-688 1488577 1488620 1488695 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-687 1487108 1487496 1487916 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-686 1485741 1486707 1486735 "NASRING" 1486845 NASRING (NIL) -9 NIL 1486925 NIL) (-685 1485586 1485642 1485736 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-684 1484515 1485193 1485221 "NARNG" 1485338 NARNG (NIL) -9 NIL 1485429 NIL) (-683 1484291 1484376 1484510 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-682 1483057 1483811 1483851 "NAALG" 1483930 NAALG (NIL T) -9 NIL 1483991 NIL) (-681 1482927 1482962 1483052 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-680 1477906 1479091 1480277 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-679 1477301 1477388 1477572 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-678 1469311 1473805 1473857 "MTSCAT" 1474917 MTSCAT (NIL T T) -9 NIL 1475431 NIL) (-677 1469077 1469137 1469229 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-676 1468903 1468942 1469002 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-675 1465765 1468454 1468495 "MSETAGG" 1468500 MSETAGG (NIL T) -9 NIL 1468534 NIL) (-674 1461902 1464811 1465129 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-673 1458176 1459999 1460739 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-672 1457813 1457886 1458015 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-671 1457466 1457507 1457651 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-670 1455331 1455668 1456099 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-669 1448729 1455230 1455326 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-668 1448254 1448295 1448503 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-667 1447813 1447862 1448045 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-666 1447087 1447180 1447399 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-665 1445704 1446065 1446455 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-664 1445225 1445292 1445331 "MONOPC" 1445391 MONOPC (NIL T) -9 NIL 1445610 NIL) (-663 1444676 1445012 1445140 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-662 1443818 1444197 1444225 "MONOID" 1444443 MONOID (NIL) -9 NIL 1444587 NIL) (-661 1443477 1443627 1443813 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-660 1432415 1439285 1439344 "MONOGEN" 1440018 MONOGEN (NIL T T) -9 NIL 1440474 NIL) (-659 1430427 1431313 1432296 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-658 1429141 1429685 1429713 "MONADWU" 1430104 MONADWU (NIL) -9 NIL 1430339 NIL) (-657 1428689 1428889 1429136 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-656 1427966 1428267 1428295 "MONAD" 1428502 MONAD (NIL) -9 NIL 1428614 NIL) (-655 1427733 1427829 1427961 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-654 1426123 1426893 1427172 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-653 1425257 1425784 1425824 "MODULE" 1425829 MODULE (NIL T) -9 NIL 1425867 NIL) (-652 1424936 1425062 1425252 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-651 1422647 1423533 1423847 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-650 1419826 1421243 1421756 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-649 1418460 1419034 1419310 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-648 1407679 1417125 1417538 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-647 1404635 1406679 1406948 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-646 1403719 1404086 1404276 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-645 1403288 1403337 1403516 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-644 1401113 1402109 1402149 "MLO" 1402566 MLO (NIL T) -9 NIL 1402806 NIL) (-643 1398994 1399521 1400116 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-642 1398462 1398558 1398712 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-641 1398132 1398208 1398331 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-640 1397344 1397530 1397758 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-639 1396837 1396953 1397109 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-638 1396209 1396323 1396508 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-637 1395236 1395509 1395786 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-636 1394669 1394757 1394928 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-635 1391827 1392706 1393585 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-634 1390494 1390842 1391195 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-633 1387151 1389618 1389659 "MDAGG" 1389916 MDAGG (NIL T) -9 NIL 1390061 NIL) (-632 1386425 1386589 1386789 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-631 1385503 1385789 1386019 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-630 1383600 1384177 1384738 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-629 1379372 1383190 1383437 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-628 1375721 1376490 1377224 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-627 1374474 1374643 1374972 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-626 1363987 1367576 1367652 "MATCAT" 1372640 MATCAT (NIL T T T) -9 NIL 1374108 NIL) (-625 1361268 1362574 1363982 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-624 1359669 1360029 1360413 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-623 1358802 1358999 1359221 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-622 1357553 1357879 1358206 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-621 1356715 1357117 1357293 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-620 1356384 1356448 1356571 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-619 1356032 1356105 1356219 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-618 1355567 1355682 1355824 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-617 1353776 1354544 1354845 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-616 1353270 1353572 1353662 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-615 1346779 1351585 1351626 "LZSTAGG" 1352403 LZSTAGG (NIL T) -9 NIL 1352693 NIL) (-614 1343898 1345332 1346774 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-613 1341285 1342251 1342734 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-612 1340866 1341145 1341219 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-611 1333030 1340727 1340861 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-610 1332393 1332538 1332766 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-609 1329877 1330575 1331287 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-608 1327989 1328312 1328760 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-607 1321158 1327076 1327117 "LSAGG" 1327179 LSAGG (NIL T) -9 NIL 1327257 NIL) (-606 1318852 1319951 1321153 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-605 1316332 1318201 1318450 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-604 1315999 1316090 1316213 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-603 1315670 1315749 1315777 "LOGIC" 1315888 LOGIC (NIL) -9 NIL 1315970 NIL) (-602 1315565 1315594 1315665 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-601 1314884 1315042 1315235 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-600 1313669 1313918 1314269 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-599 1309491 1312290 1312330 "LODOCAT" 1312762 LODOCAT (NIL T) -9 NIL 1312973 NIL) (-598 1309284 1309360 1309486 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-597 1306284 1309161 1309279 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-596 1303382 1306234 1306279 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-595 1300469 1303312 1303377 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-594 1299522 1299697 1299999 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-593 1297654 1298784 1299037 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-592 1292749 1295813 1295854 "LNAGG" 1296716 LNAGG (NIL T) -9 NIL 1297151 NIL) (-591 1292136 1292403 1292744 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-590 1288708 1289649 1290286 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-589 1287970 1288475 1288515 "LMODULE" 1288520 LMODULE (NIL T) -9 NIL 1288546 NIL) (-588 1285149 1287707 1287829 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-587 1284717 1284928 1284969 "LLINSET" 1285030 LLINSET (NIL T) -9 NIL 1285074 NIL) (-586 1284393 1284653 1284712 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-585 1283992 1284072 1284211 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-584 1282443 1282791 1283190 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-583 1281614 1281810 1282038 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-582 1274660 1280870 1281124 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-581 1274237 1274470 1274511 "LINSET" 1274516 LINSET (NIL T) -9 NIL 1274549 NIL) (-580 1273138 1273860 1274027 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-579 1271404 1272159 1272199 "LINEXP" 1272685 LINEXP (NIL T) -9 NIL 1272958 NIL) (-578 1270026 1271013 1271194 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-577 1268853 1269125 1269427 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-576 1268066 1268655 1268765 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-575 1265616 1266338 1267088 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-574 1264246 1264543 1264934 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-573 1263039 1263641 1263681 "LIECAT" 1263821 LIECAT (NIL T) -9 NIL 1263972 NIL) (-572 1262913 1262946 1263034 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-571 1257169 1262603 1262831 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-570 1249518 1256845 1257001 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-569 1245970 1246919 1247854 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-568 1244594 1245502 1245530 "LFCAT" 1245737 LFCAT (NIL) -9 NIL 1245876 NIL) (-567 1242833 1243163 1243508 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-566 1240350 1241015 1241696 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-565 1237362 1238340 1238843 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-564 1236853 1237156 1237247 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-563 1235560 1235884 1236284 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-562 1234826 1234911 1235137 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-561 1229829 1233394 1233930 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-560 1229454 1229504 1229664 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-559 1228225 1228998 1229038 "LALG" 1229099 LALG (NIL T) -9 NIL 1229157 NIL) (-558 1228008 1228085 1228220 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-557 1225861 1227276 1227527 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-556 1225690 1225720 1225761 "KVTFROM" 1225823 KVTFROM (NIL T) -9 NIL NIL NIL) (-555 1224506 1225221 1225410 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-554 1224335 1224365 1224406 "KRCFROM" 1224468 KRCFROM (NIL T) -9 NIL NIL NIL) (-553 1223437 1223634 1223929 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-552 1223266 1223296 1223337 "KONVERT" 1223399 KONVERT (NIL T) -9 NIL NIL NIL) (-551 1223095 1223125 1223166 "KOERCE" 1223228 KOERCE (NIL T) -9 NIL NIL NIL) (-550 1222665 1222758 1222890 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-549 1220718 1221612 1221984 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-548 1213895 1218910 1218964 "KDAGG" 1219340 KDAGG (NIL T T) -9 NIL 1219547 NIL) (-547 1213543 1213685 1213890 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-546 1206373 1213324 1213481 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-545 1206023 1206305 1206368 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-544 1204993 1205492 1205741 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-543 1204119 1204568 1204773 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-542 1202983 1203475 1203775 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-541 1202265 1202664 1202825 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-540 1201975 1202211 1202260 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-539 1196230 1201665 1201893 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-538 1195648 1195981 1196101 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-537 1191810 1193825 1193879 "IXAGG" 1194806 IXAGG (NIL T T) -9 NIL 1195263 NIL) (-536 1191016 1191387 1191805 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-535 1189983 1190258 1190521 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-534 1188645 1188852 1189145 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-533 1187596 1187818 1188101 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-532 1187271 1187334 1187457 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-531 1186533 1186905 1187079 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-530 1184509 1185809 1186083 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-529 1174057 1179826 1180983 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-528 1173302 1173454 1173690 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-527 1172793 1173096 1173187 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-526 1172086 1172177 1172390 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-525 1171218 1171443 1171683 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-524 1169631 1170012 1170440 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-523 1169416 1169460 1169536 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-522 1168266 1168563 1168858 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-521 1167539 1167890 1168041 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-520 1166742 1166873 1167086 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-519 1164897 1165394 1165938 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-518 1161978 1163246 1163935 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-517 1161803 1161843 1161903 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-516 1157801 1161729 1161798 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-515 1155804 1157740 1157796 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-514 1155175 1155474 1155604 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-513 1154628 1154916 1155048 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-512 1153709 1154334 1154460 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-511 1153119 1153613 1153641 "IOBCON" 1153646 IOBCON (NIL) -9 NIL 1153667 NIL) (-510 1152690 1152754 1152936 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-509 1144734 1147105 1149430 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-508 1141845 1142628 1143492 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-507 1141522 1141619 1141736 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-506 1138964 1141458 1141517 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-505 1137076 1137605 1138172 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-504 1136578 1136692 1136832 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-503 1134962 1135368 1135830 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-502 1132741 1133335 1133946 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-501 1130114 1130724 1131444 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-500 1129518 1129676 1129884 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-499 1129037 1129123 1129311 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-498 1127242 1127763 1128220 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-497 1120324 1121977 1123706 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-496 1119690 1119852 1120025 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-495 1117563 1118027 1118571 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-494 1115689 1116639 1116667 "INTDOM" 1116966 INTDOM (NIL) -9 NIL 1117171 NIL) (-493 1115242 1115444 1115684 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-492 1111049 1113521 1113575 "INTCAT" 1114371 INTCAT (NIL T) -9 NIL 1114687 NIL) (-491 1110614 1110734 1110861 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-490 1109454 1109626 1109932 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-489 1109027 1109123 1109280 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-488 1102067 1108882 1109022 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-487 1101365 1101920 1101985 "INT8" NIL INT8 (NIL) -8 NIL NIL 1102019) (-486 1100662 1101217 1101282 "INT64" NIL INT64 (NIL) -8 NIL NIL 1101316) (-485 1099959 1100514 1100579 "INT32" NIL INT32 (NIL) -8 NIL NIL 1100613) (-484 1099256 1099811 1099876 "INT16" NIL INT16 (NIL) -8 NIL NIL 1099910) (-483 1095719 1099175 1099251 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-482 1089776 1093259 1093287 "INS" 1094217 INS (NIL) -9 NIL 1094876 NIL) (-481 1087838 1088756 1089703 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-480 1086897 1087120 1087395 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-479 1086111 1086252 1086449 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-478 1085101 1085242 1085479 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-477 1084253 1084417 1084677 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-476 1083533 1083648 1083836 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-475 1082272 1082541 1082865 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-474 1081552 1081693 1081876 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-473 1081215 1081287 1081385 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-472 1078293 1079779 1080302 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-471 1077892 1077999 1078113 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-470 1077048 1077693 1077794 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-469 1075898 1076166 1076487 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-468 1074888 1075828 1075893 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-467 1074513 1074593 1074710 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-466 1073427 1073972 1074176 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-465 1069522 1070577 1071520 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-464 1068376 1068699 1068727 "INBCON" 1069240 INBCON (NIL) -9 NIL 1069506 NIL) (-463 1067830 1068095 1068371 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-462 1067324 1067626 1067716 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-461 1066781 1067090 1067195 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-460 1065621 1065760 1066075 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-459 1064045 1064312 1064649 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-458 1058888 1063976 1064040 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-457 1058268 1058602 1058717 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-456 1053075 1057706 1057892 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-455 1052105 1052997 1053070 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-454 1051677 1051754 1051808 "IEVALAB" 1052015 IEVALAB (NIL T T) -9 NIL NIL NIL) (-453 1051432 1051512 1051672 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-452 1050817 1051044 1051201 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-451 1049810 1050737 1050812 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-450 1048873 1049730 1049805 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-449 1047955 1048602 1048739 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-448 1046318 1046889 1046940 "IDPC" 1047446 IDPC (NIL T T) -9 NIL 1047759 NIL) (-447 1045606 1046240 1046313 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-446 1044776 1045528 1045601 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-445 1044469 1044682 1044742 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-444 1044173 1044213 1044252 "IDEMOPC" 1044257 IDEMOPC (NIL T) -9 NIL 1044394 NIL) (-443 1041244 1042125 1043017 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-442 1034870 1036147 1037186 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-441 1034132 1034262 1034461 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-440 1033305 1033804 1033942 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-439 1031694 1032025 1032416 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-438 1027463 1031650 1031689 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-437 1024721 1025345 1026040 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-436 1022947 1023427 1023960 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-435 1020787 1022853 1022942 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-434 1016656 1020725 1020782 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-433 1010235 1015620 1016088 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-432 1009803 1009866 1010039 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-431 1009295 1009444 1009472 "HYPCAT" 1009679 HYPCAT (NIL) -9 NIL NIL NIL) (-430 1008951 1009104 1009290 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-429 1008564 1008809 1008892 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-428 1008397 1008446 1008487 "HOMOTOP" 1008492 HOMOTOP (NIL T) -9 NIL 1008525 NIL) (-427 1004965 1006339 1006380 "HOAGG" 1007355 HOAGG (NIL T) -9 NIL 1008076 NIL) (-426 1003971 1004441 1004960 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-425 997171 1003696 1003844 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-424 996106 996364 996627 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-423 995041 995971 996101 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-422 993235 994874 994962 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-421 992550 992902 993035 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-420 986004 992483 992545 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-419 979143 985740 985891 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-418 978596 978753 978916 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-417 971679 978487 978591 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-416 971170 971473 971564 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-415 968720 970957 971136 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-414 964113 968603 968715 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-413 957199 964010 964108 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-412 949136 956568 956823 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-411 948160 948669 948697 "GROUP" 948900 GROUP (NIL) -9 NIL 949034 NIL) (-410 947703 947904 948155 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-409 946375 946714 947101 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-408 945197 945554 945605 "GRMOD" 946134 GRMOD (NIL T T) -9 NIL 946300 NIL) (-407 945016 945064 945192 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-406 941139 942350 943350 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-405 939861 940185 940500 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-404 939414 939542 939683 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-403 938487 938986 939037 "GRALG" 939190 GRALG (NIL T T) -9 NIL 939280 NIL) (-402 938206 938307 938482 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-401 934923 937888 938064 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-400 934336 934399 934656 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-399 930190 931086 931611 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-398 929365 929567 929805 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-397 924368 925295 926314 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-396 924116 924173 924262 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-395 923598 923687 923852 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-394 923107 923148 923361 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-393 921908 922191 922495 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-392 915183 921598 921759 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-391 904966 909973 911077 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-390 903018 904121 904149 "GCDDOM" 904404 GCDDOM (NIL) -9 NIL 904561 NIL) (-389 902641 902798 903013 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-388 893434 895904 898292 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-387 891569 891894 892312 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-386 890510 890699 890966 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-385 889381 889588 889892 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-384 888844 888986 889134 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-383 887456 887804 888117 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-382 886001 886322 886644 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-381 883627 883983 884388 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-380 876879 878540 880118 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-379 876531 876752 876820 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-378 876155 876376 876457 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-377 874252 874935 875395 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-376 872845 873152 873544 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-375 871500 871859 872183 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-374 870803 870927 871114 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-373 869777 870043 870390 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-372 867435 867965 868447 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-371 867018 867078 867247 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-370 865318 866232 866535 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-369 864466 864600 864823 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-368 863637 863798 864025 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-367 859620 862571 862612 "FSAGG" 862982 FSAGG (NIL T) -9 NIL 863241 NIL) (-366 857974 858733 859525 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-365 855930 856226 856770 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-364 854977 855159 855459 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-363 854658 854707 854834 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-362 834814 844315 844356 "FS" 848226 FS (NIL T) -9 NIL 850504 NIL) (-361 827045 830538 834517 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-360 826579 826706 826858 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-359 821102 824260 824300 "FRNAALG" 825620 FRNAALG (NIL T) -9 NIL 826218 NIL) (-358 817843 819094 820352 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-357 817524 817573 817700 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-356 816011 816568 816862 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-355 815297 815390 815677 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-354 813131 813897 814213 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-353 812240 812683 812724 "FRETRCT" 812729 FRETRCT (NIL T) -9 NIL 812900 NIL) (-352 811613 811891 812235 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-351 808357 809877 809936 "FRAMALG" 810818 FRAMALG (NIL T T) -9 NIL 811110 NIL) (-350 806953 807504 808134 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-349 806646 806709 806816 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-348 800287 806451 806641 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-347 799980 800043 800150 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-346 792288 796859 798187 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-345 786066 789569 789597 "FPS" 790716 FPS (NIL) -9 NIL 791272 NIL) (-344 785623 785756 785920 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-343 782433 784476 784504 "FPC" 784729 FPC (NIL) -9 NIL 784871 NIL) (-342 782279 782331 782428 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-341 781056 781765 781806 "FPATMAB" 781811 FPATMAB (NIL T) -9 NIL 781963 NIL) (-340 779486 780082 780429 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-339 779061 779119 779292 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-338 777564 778459 778633 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-337 776179 776684 776712 "FNCAT" 777169 FNCAT (NIL) -9 NIL 777426 NIL) (-336 775636 776146 776174 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-335 774223 775585 775631 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-334 770811 772169 772210 "FMONCAT" 773427 FMONCAT (NIL T) -9 NIL 774031 NIL) (-333 767669 768747 768800 "FMCAT" 769981 FMCAT (NIL T T) -9 NIL 770473 NIL) (-332 766369 767492 767591 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-331 765417 766217 766364 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-330 763604 764056 764550 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-329 761539 762075 762653 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-328 754925 759876 760490 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-327 753406 754507 754547 "FLINEXP" 754552 FLINEXP (NIL T) -9 NIL 754645 NIL) (-326 752815 753074 753401 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-325 752030 752189 752410 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-324 748913 749992 750044 "FLALG" 751271 FLALG (NIL T T) -9 NIL 751738 NIL) (-323 748084 748245 748472 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-322 741493 745503 745544 "FLAGG" 746799 FLAGG (NIL T) -9 NIL 747444 NIL) (-321 740601 741005 741488 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-320 737162 738426 738485 "FINRALG" 739613 FINRALG (NIL T T) -9 NIL 740121 NIL) (-319 736553 736818 737157 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-318 735851 736147 736175 "FINITE" 736371 FINITE (NIL) -9 NIL 736478 NIL) (-317 735759 735785 735846 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-316 727720 730311 730351 "FINAALG" 734003 FINAALG (NIL T) -9 NIL 735441 NIL) (-315 723987 725232 726355 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 722539 722958 723012 "FILECAT" 723696 FILECAT (NIL T T) -9 NIL 723912 NIL) (-313 721890 722364 722467 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 719138 721016 721044 "FIELD" 721084 FIELD (NIL) -9 NIL 721164 NIL) (-311 718163 718624 719133 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 716167 717113 717459 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 715410 715591 715810 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 710680 715348 715405 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 710342 710409 710544 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 709882 709924 710133 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 706562 707439 708216 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 701846 706494 706557 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 696525 701335 701525 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 691006 695806 696064 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 685213 690457 690668 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 684236 684446 684761 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 679676 682381 682409 "FFIELDC" 683028 FFIELDC (NIL) -9 NIL 683403 NIL) (-298 678745 679185 679671 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 678360 678418 678542 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 676504 677027 677544 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 671598 676303 676404 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 666698 671387 671494 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 661364 666489 666597 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 660818 660867 661102 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 639393 650427 650513 "FFCAT" 655663 FFCAT (NIL T T T) -9 NIL 657099 NIL) (-290 635633 636859 638165 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 630476 635564 635628 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 629368 629837 629878 "FEVALAB" 629962 FEVALAB (NIL T) -9 NIL 630223 NIL) (-287 628773 629025 629363 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 625600 626511 626626 "FDIVCAT" 628193 FDIVCAT (NIL T T T T) -9 NIL 628629 NIL) (-285 625394 625426 625595 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 624701 624794 625071 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 623187 624185 624388 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 622280 622664 622866 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 621402 621891 622031 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 612989 617632 617672 "FAXF" 619473 FAXF (NIL T) -9 NIL 620163 NIL) (-279 610905 611709 612524 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 605769 610427 610601 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 600227 602650 602702 "FAMR" 603713 FAMR (NIL T T) -9 NIL 604172 NIL) (-276 599426 599791 600222 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 598447 599368 599421 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 596041 596920 596973 "FAMONC" 597914 FAMONC (NIL T T) -9 NIL 598299 NIL) (-273 594597 595899 596036 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 592677 593038 593440 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 591954 592151 592373 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 583814 591401 591600 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 581833 582403 582989 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 578735 579377 580097 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 573892 574599 575404 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 573581 573644 573753 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 558374 572630 573056 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 548901 557694 557982 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 548395 548697 548787 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 548171 548361 548390 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 547860 547928 548041 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 547377 547519 547560 "EVALAB" 547730 EVALAB (NIL T) -9 NIL 547834 NIL) (-259 547005 547151 547372 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 544048 545643 545671 "EUCDOM" 546225 EUCDOM (NIL) -9 NIL 546574 NIL) (-257 542975 543468 544043 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 542700 542756 542856 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 542388 542452 542561 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 536159 538059 538087 "ES" 540829 ES (NIL) -9 NIL 542213 NIL) (-253 532674 534206 535998 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 532022 532175 532351 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 525111 531926 532017 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 524800 524863 524972 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 518427 521552 522985 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 514730 515826 516919 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 513559 513909 514214 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 512444 513175 513203 "ENTIRER" 513208 ENTIRER (NIL) -9 NIL 513252 NIL) (-245 512333 512367 512439 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 508966 510763 511112 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 508058 508269 508323 "ELTAGG" 508703 ELTAGG (NIL T T) -9 NIL 508914 NIL) (-242 507838 507912 508053 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 507584 507619 507673 "ELTAB" 507757 ELTAB (NIL T T) -9 NIL 507809 NIL) (-240 506835 507005 507204 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 506559 506633 506661 "ELEMFUN" 506766 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 506459 506486 506554 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 501005 504500 504541 "ELAGG" 505478 ELAGG (NIL T) -9 NIL 505938 NIL) (-236 499803 500341 501000 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 499221 499388 499544 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 498134 498453 498732 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 491527 493525 494352 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 485506 487502 488312 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 483320 483726 484197 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 474320 476233 477774 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 473433 473934 474083 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 472131 472805 472845 "DVARCAT" 473128 DVARCAT (NIL T) -9 NIL 473268 NIL) (-227 471550 471814 472126 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 463617 471418 471545 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 461955 462746 462787 "DSEXT" 463150 DSEXT (NIL T) -9 NIL 463444 NIL) (-224 460760 461284 461950 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 460484 460549 460647 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 456635 457851 458982 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 452281 453636 454700 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 450956 451317 451703 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 450642 450701 450819 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 449617 449915 450205 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 449202 449277 449427 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 441615 443727 445842 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL 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"CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 281107 281134 281162 "CONDUIT" 281199 CONDUIT (NIL) -9 NIL NIL NIL) (-146 279986 280717 280745 "COMRING" 280750 COMRING (NIL) -9 NIL 280800 NIL) (-145 279151 279518 279696 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 278847 278888 279016 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 278540 278603 278710 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 267382 278490 278535 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 266843 266982 267142 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 266596 266637 266735 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 248027 260277 260317 "COMPCAT" 261318 COMPCAT (NIL T) -9 NIL 262660 NIL) (-138 240565 244078 247671 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 240324 240358 240460 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 240154 240193 240251 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 239735 240014 240088 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 239312 239553 239640 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 238507 238755 238783 "COMBOPC" 239121 COMBOPC (NIL) -9 NIL 239296 NIL) (-132 237571 237823 238065 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 234503 235187 235810 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 233383 233834 234069 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 232874 233177 233268 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 232561 232614 232739 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 232031 232341 232439 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 228551 229621 230701 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 226846 227831 228069 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 222958 224966 225007 "CLAGG" 225933 CLAGG (NIL T) -9 NIL 226466 NIL) (-123 221851 222378 222953 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 221480 221571 221711 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 219417 219924 220472 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 218378 219109 219137 "CHARZ" 219142 CHARZ (NIL) -9 NIL 219156 NIL) (-119 218172 218218 218296 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 217011 217774 217802 "CHARNZ" 217863 CHARNZ (NIL) -9 NIL 217911 NIL) (-117 214489 215586 216109 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 214197 214276 214304 "CFCAT" 214415 CFCAT (NIL) -9 NIL NIL NIL) (-115 213540 213669 213851 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 209529 212953 213233 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 208907 209094 209271 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 208435 208854 208902 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 207908 208217 208314 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 207399 207702 207793 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 206648 206808 207029 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 202748 204005 204713 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 201114 202145 202396 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 200695 200974 201048 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 200129 200382 200410 "CACHSET" 200542 CACHSET (NIL) -9 NIL 200620 NIL) (-104 199481 199896 199924 "CABMON" 199974 CABMON (NIL) -9 NIL 200030 NIL) (-103 199011 199275 199385 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 194234 198668 198840 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 193204 193908 194043 "BYTE" NIL BYTE (NIL) -8 NIL NIL 194206) (-100 190675 192971 193077 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 188106 190418 190537 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 185346 187550 187589 "BTCAT" 187656 BTCAT (NIL T) -9 NIL 187732 NIL) (-97 185097 185195 185341 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 180207 184328 184354 "BTAGG" 184465 BTAGG (NIL) -9 NIL 184573 NIL) (-95 179838 179999 180202 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176900 179308 179520 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 176170 176322 176500 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 172703 174876 174915 "BRAGG" 175556 BRAGG (NIL T) -9 NIL 175813 NIL) (-91 171658 172153 172698 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 164192 171163 171344 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 162184 164144 164187 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 161917 161953 162064 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 160156 160589 161037 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 156122 157538 158428 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 154998 155889 156011 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 154584 154741 154767 "BOOLE" 154875 BOOLE (NIL) -9 NIL 154956 NIL) (-83 154377 154458 154579 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 153515 154042 154092 "BMODULE" 154097 BMODULE (NIL T T) -9 NIL 154161 NIL) (-81 149132 153372 153441 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 148945 148985 149024 "BINOPC" 149029 BINOPC (NIL T) -9 NIL 149074 NIL) (-79 148487 148760 148862 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 148008 148152 148290 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 141214 147738 147883 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 138948 140443 140482 "BGAGG" 140738 BGAGG (NIL T) -9 NIL 140875 NIL) (-75 138817 138855 138943 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 137668 137869 138154 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 134306 136826 137153 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 133891 133984 134010 "BASTYPE" 134181 BASTYPE (NIL) -9 NIL 134277 NIL) (-71 133661 133757 133886 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 133176 133264 133414 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 132075 132750 132935 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 131801 131806 131832 "ATTREG" 131837 ATTREG (NIL) -9 NIL NIL NIL) (-67 131406 131678 131743 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 130906 131055 131081 "ATRIG" 131282 ATRIG (NIL) -9 NIL NIL NIL) (-65 130761 130814 130901 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 130331 130562 130588 "ASTCAT" 130593 ASTCAT (NIL) -9 NIL 130623 NIL) (-63 130130 130207 130326 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 128289 129963 130051 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 127096 127409 127774 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 124896 127000 127091 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 124087 124278 124499 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 119674 123818 123932 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 113840 115872 115947 "ARR2CAT" 118577 ARR2CAT (NIL T T T) -9 NIL 119335 NIL) (-56 112217 112987 113835 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 111585 111956 112078 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 110517 110685 110981 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 110218 110272 110390 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 109601 109747 109903 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 109006 109296 109416 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 106574 107735 108058 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 106099 106359 106455 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 99794 105161 105603 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 95328 96991 97041 "AMR" 97779 AMR (NIL T T) -9 NIL 98376 NIL) (-46 94682 94962 95323 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 77862 94616 94677 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 74265 77538 77707 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 71275 71935 72542 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 70654 70767 70951 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 67066 67691 68283 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 56555 66759 66909 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55872 56026 56204 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54585 55380 55418 "ALGEBRA" 55423 ALGEBRA (NIL T) -9 NIL 55463 NIL) (-37 54371 54448 54580 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 34368 51577 51629 "ALAGG" 51767 ALAGG (NIL T T) -9 NIL 51932 NIL) (-35 33868 34017 34043 "AHYP" 34244 AHYP (NIL) -9 NIL NIL NIL) (-34 33164 33345 33371 "AGG" 33652 AGG (NIL) -9 NIL 33839 NIL) (-33 32953 33040 33159 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 31092 31552 31952 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30587 30890 30979 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29957 30252 30408 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17515 26794 26832 "ACFS" 27439 ACFS (NIL T) -9 NIL 27678 NIL) (-28 16138 16748 17510 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11690 14069 14095 "ACF" 14974 ACF (NIL) -9 NIL 15386 NIL) (-26 10786 11192 11685 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10288 10528 10554 "ABELSG" 10646 ABELSG (NIL) -9 NIL 10711 NIL) (-24 10186 10217 10283 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9341 9715 9741 "ABELMON" 9966 ABELMON (NIL) -9 NIL 10099 NIL) (-22 9023 9163 9336 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8235 8718 8744 "ABELGRP" 8816 ABELGRP (NIL) -9 NIL 8891 NIL) (-20 7788 7984 8230 "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 bd0c4436..4c1e431a 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,400 +1,400 @@ -(631058 . 3577395495) +(631058 . 3577398027) (((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-961) (-580 (-483)))) - (-5 *2 (-1178 (-348 (-483)))) (-5 *1 (-1207 *4))))) + (|partial| -12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-960) (-579 (-483)))) + (-5 *2 (-1177 (-348 (-483)))) (-5 *1 (-1206 *4))))) (((*1 *2 *3) - (|partial| -12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-961) (-580 (-483)))) - (-5 *2 (-1178 (-483))) (-5 *1 (-1207 *4))))) + (|partial| -12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-960) (-579 (-483)))) + (-5 *2 (-1177 (-483))) (-5 *1 (-1206 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-961) (-580 (-483)))) (-5 *2 (-85)) - (-5 *1 (-1207 *4))))) + (-12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-960) (-579 (-483)))) (-5 *2 (-85)) + (-5 *1 (-1206 *4))))) (((*1 *2 *3) - 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