diff options
| -rw-r--r-- | src/algebra/Makefile.in | 3 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 2220 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 3996 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1327 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 10213 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 32935 |
6 files changed, 25359 insertions, 25335 deletions
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index fc186f97..5d3fd2ce 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -343,6 +343,7 @@ $(OUT)/DIFFMOD.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT) $(OUT)/PDSPC.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) $(OUT)/DSEXT.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT) $(OUT)/PDSPC.$(FASLEXT) +$(OUT)/ORDTYPE.$(FASLEXT): $(OUT)/BASTYPE.$(FASLEXT) axiom_algebra_layer_0 = \ AHYP ATTREG CFCAT ELTAB KOERCE KONVERT \ @@ -370,7 +371,7 @@ axiom_algebra_layer_0 = \ LIST DIFFDOM DIFFDOM- DIFFSPC DIFFSPC- DIFFMOD \ LINEXP PATMAB REAL CHARZ LOGIC LOGIC- \ RTVALUE SYSPTR PDDOM PDDOM- PDSPC PDSPC- \ - DSEXT DSEXT- + DSEXT DSEXT- ORDTYPE ORDTYPE- axiom_algebra_layer_0_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_0)) diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index b2175999..3afba534 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2293386 . 3486772025) +(2294476 . 3486783785) (-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."))) -((-4463 . T) (-4462 . T)) +((-4465 . T) (-4464 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4459 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4455 . T) (-4460 . T) (-4454 . T)) +((-4461 . T) (-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4457 . T) (-4462 . T) (-4456 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,14 +56,14 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1956) +(-32 R -2117) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) +((|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4462))) +((|HasAttribute| |#1| (QUOTE -4464))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4462 . T) (-4463 . T)) +((-4464 . T) (-4465 . 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"))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -1956 UP UPUP -2005) +(-40 -2117 UP UPUP -1869) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2755 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2755 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) -(-41 R -1956) +((-4457 |has| (-419 |#2|) (-374)) (-4462 |has| (-419 |#2|) (-374)) (-4456 |has| (-419 |#2|) (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-3795 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-3795 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3795 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3795 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-3795 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-3795 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +(-41 R -2117) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-317)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4459 |has| |#1| (-568)) (-4457 . T) (-4456 . T)) +((-4461 |has| |#1| (-568)) (-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) -((-4462 . T) (-4463 . T)) -((-2755 (-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|))))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|))))))) +((-4464 . T) (-4465 . T)) +((-3795 (-12 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|))))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (QUOTE (-576))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4459 . T)) +((-4461 . T)) NIL (-51 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1956) +(-54 |Base| R -2117) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -158,7 +158,7 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4462 . T) (-4463 . T)) +((-4464 . T) (-4465 . T)) NIL (-58 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) @@ -166,65 +166,65 @@ NIL NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -2624) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -4149) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -2624) +(-62 -4149) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -2624) +(-63 -4149) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2624) +(-64 -4149) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -2624) +(-65 -4149) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -2624) +(-66 -4149) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -2624) +(-67 -4149) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -2624) +(-68 -4149) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -2624) +(-69 -4149) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -2624) +(-70 -4149) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -2624) +(-71 -4149) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -2624) +(-72 -4149) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -2624) +(-73 -4149) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -2624) +(-74 -4149) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2624) +(-77 -4149) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2624) +(-78 -4149) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -2624) +(-79 -4149) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -2624) +(-80 -4149) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -2624) +(-81 -4149) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -2624) +(-82 -4149) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2624) +(-83 -4149) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2624) +(-84 -4149) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2624) +(-85 -4149) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2624) +(-86 -4149) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2624) +(-87 -4149) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -2624) +(-88 -4149) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -2624) +(-89 -4149) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -294,8 +294,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-374)))) (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -318,15 +318,15 @@ NIL NIL (-97) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4462 . T)) +((-4464 . T)) NIL (-98) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4462 . T) ((-4464 "*") . T) (-4463 . T) (-4459 . T) (-4457 . T) (-4456 . T) (-4455 . T) (-4460 . T) (-4454 . T) (-4453 . T) (-4452 . T) (-4451 . T) (-4450 . T) (-4458 . T) (-4461 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4449 . T)) +((-4464 . T) ((-4466 "*") . T) (-4465 . T) (-4461 . T) (-4459 . T) (-4458 . T) (-4457 . T) (-4462 . T) (-4456 . T) (-4455 . T) (-4454 . T) (-4453 . T) (-4452 . T) (-4460 . T) (-4463 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4451 . T)) NIL (-99 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-4459 . T)) +((-4461 . T)) NIL (-100 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) @@ -342,15 +342,15 @@ NIL NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4464 "*")))) +((|HasAttribute| |#1| (QUOTE (-4466 "*")))) (-105) ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4462 . T)) +((-4464 . T)) NIL (-106 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -358,23 +358,23 @@ NIL NIL (-107 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4463 . T)) +((-4465 . T)) NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2755 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (-3795 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4463 . T) (-4462 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-112) (QUOTE (-102)))) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-112) (QUOTE (-102)))) (-111 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -392,22 +392,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -1956 UP) +(-116 -2117 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-118 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-926))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1041))) (|HasCategory| (-117 |#1|) (QUOTE (-832))) (-2755 (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-862)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1171))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (|HasCategory| (-117 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-117 |#1|) (QUOTE (-928))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1043))) (|HasCategory| (-117 |#1|) (QUOTE (-832))) (-3795 (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-862)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1173))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (|HasCategory| (-117 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-928)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4463))) +((|HasAttribute| |#1| (QUOTE -4465))) (-120 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -418,15 +418,15 @@ NIL NIL (-122 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-124) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4463 . T) (-4462 . T)) +((-4465 . T) (-4464 . T)) NIL (-125 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -434,20 +434,20 @@ NIL NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4462 . T) (-4463 . T)) +((-4464 . T) (-4465 . T)) NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2755 (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119)))) (-2755 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119)))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-3795 (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1121)))) (-3795 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1121)))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -470,13 +470,13 @@ NIL NIL (-135) ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4464 "*") . T)) +(((-4466 "*") . T)) NIL -(-136 |minix| -2701 S T$) +(-136 |minix| -1911 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -2701 R) +(-137 |minix| -1911 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -498,8 +498,8 @@ NIL NIL (-142) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) -((-4462 . T) (-4452 . T) (-4463 . T)) -((-2755 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-4464 . T) (-4454 . T) (-4465 . T)) +((-3795 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-143 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -514,7 +514,7 @@ NIL NIL (-146) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4459 . T)) +((-4461 . T)) NIL (-147 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -522,9 +522,9 @@ NIL NIL (-148) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4459 . T)) +((-4461 . T)) NIL -(-149 -1956 UP UPUP) +(-149 -2117 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) NIL NIL @@ -535,14 +535,14 @@ NIL (-151 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasAttribute| |#1| (QUOTE -4462))) +((|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasAttribute| |#1| (QUOTE -4464))) (-152 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-153 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((-4457 . T) (-4456 . T) (-4459 . T)) +((-4459 . T) (-4458 . T) (-4461 . T)) NIL (-154) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -564,7 +564,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-159 R -1956) +(-159 R -2117) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -595,10 +595,10 @@ NIL (-166 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (QUOTE (-1221))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasAttribute| |#2| (QUOTE -4461)) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568)))) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-1043))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasAttribute| |#2| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568)))) (-167 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4455 -2755 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-926)))) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4458 |has| |#1| (-6 -4458)) (-4461 |has| |#1| (-6 -4461)) (-4175 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 -3795 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-928)))) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4463 |has| |#1| (-6 -4463)) (-2649 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-168 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4455 -2755 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-926)))) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4458 |has| |#1| (-6 -4458)) (-4461 |has| |#1| (-6 -4461)) (-4175 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . 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T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-3795 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-360)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-928))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-928)))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-928))))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1223)))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-568)))) (-3795 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1223)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4463)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-360))))) (-172 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -626,7 +626,7 @@ NIL NIL (-174) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-175) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -634,7 +634,7 @@ NIL NIL (-176 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-4464 "*") . T) (-4455 . T) (-4460 . T) (-4454 . T) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") . T) (-4457 . T) (-4462 . T) (-4456 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-177) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -651,7 +651,7 @@ NIL (-180 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-969 |#2|) (LIST (QUOTE -899) (|devaluate| |#1|)))) +((|HasCategory| (-971 |#2|) (LIST (QUOTE -901) (|devaluate| |#1|)))) (-181 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) NIL @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1956) +(-190 R -2117) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-217 -1956 UP UPUP R) +(-217 -2117 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-218 -1956 FP) +(-218 -2117 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-219) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2755 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (-3795 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) (-220) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -1956) +(-221 R -2117) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -826,19 +826,19 @@ NIL NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-225 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) -((-4459 . T)) +((-4461 . T)) NIL -(-226 R -1956) +(-226 R -2117) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-227) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4163 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2642 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-228) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -846,19 +846,19 @@ NIL NIL (-229 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4466 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-230 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-231 S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) -((-4463 . T)) +((-4465 . T)) NIL (-232 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((-4459 . T)) +((-4461 . T)) NIL (-233 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -870,7 +870,7 @@ NIL NIL (-235 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) NIL (-236 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) @@ -882,36 +882,36 @@ NIL NIL (-238) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-4459 . T)) +((-4461 . T)) NIL (-239 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -4462))) +((|HasAttribute| |#1| (QUOTE -4464))) (-240 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4463 . T)) +((-4465 . T)) NIL (-241) ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-242 S -2701 R) +(-242 S -1911 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (QUOTE (-862))) (|HasAttribute| |#3| (QUOTE -4459)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (QUOTE (-1119)))) -(-243 -2701 R) +((|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (QUOTE (-862))) (|HasAttribute| |#3| (QUOTE -4461)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (QUOTE (-1121)))) +(-243 -1911 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"))) -((-4456 |has| |#2| (-1068)) (-4457 |has| |#2| (-1068)) (-4459 |has| |#2| (-6 -4459)) (-4462 . T)) +((-4458 |has| |#2| (-1070)) (-4459 |has| |#2| (-1070)) (-4461 |has| |#2| (-6 -4461)) (-4464 . T)) NIL -(-244 -2701 A B) +(-244 -1911 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-245 -2701 R) +(-245 -1911 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) -((-4456 |has| |#2| (-1068)) (-4457 |has| |#2| (-1068)) (-4459 |has| |#2| (-6 -4459)) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-805))) (|HasCategory| |#2| (LIST 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(|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasAttribute| |#2| (QUOTE -4461)) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-1070)))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197))))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))))) (-246) ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -922,7 +922,7 @@ NIL NIL (-248) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4455 . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-249 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) @@ -930,20 +930,20 @@ NIL NIL (-250 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-251 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-252 R) ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) NIL (-253 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#2| (QUOTE (-926))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4466 "*") |has| |#2| (-174)) (-4457 |has| |#2| (-568)) (-4462 |has| |#2| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (-3795 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-3795 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-3795 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3795 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) (-254) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) NIL @@ -958,23 +958,23 @@ NIL NIL (-257 |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((-4459 -2755 (-2669 (|has| |#4| (-1068)) (|has| |#4| (-238))) (|has| |#4| (-6 -4459)) (-2669 (|has| |#4| (-1068)) (|has| |#4| (-915 (-1195))))) (-4456 |has| |#4| (-1068)) (-4457 |has| |#4| (-1068)) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-238))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-374))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-738))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-805))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-862))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST 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category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-238)))) (-260 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL (-261 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4462 . T) (-4463 . T)) +((-4464 . T) (-4465 . T)) NIL (-262) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g),a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -1015,15 +1015,15 @@ NIL (-271 S R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-237)))) +((|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-237)))) (-272 R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL NIL (-273 R S V) ((|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"))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#3| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#3| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#3| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . 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If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1068,11 +1068,11 @@ 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|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-285 R -1956) +(-285 R -2117) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-286 R -1956) +(-286 R -2117) ((|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 @@ -1095,10 +1095,10 @@ NIL (-291 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119)))) +((|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1121)))) (-292 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4463 . T)) +((-4465 . T)) NIL (-293 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1119,18 +1119,18 @@ NIL (-297 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4463))) +((|HasAttribute| |#1| (QUOTE -4465))) (-298 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-299 S R |Mod| -2234 -1872 |exactQuo|) +(-299 S R |Mod| -3565 -3181 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-300) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4455 . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-301) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1146,21 +1146,21 @@ NIL NIL (-304 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4459 -2755 (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4456 |has| |#1| (-1068)) (-4457 |has| |#1| (-1068))) -((|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1068)))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-1068)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1068)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1068)))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1068)))) (-2755 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738)))) (|HasCategory| |#1| (QUOTE (-485))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-312))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-485)))) (-2755 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738)))) (-2755 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-738)))) +((-4461 -3795 (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4458 |has| |#1| (-1070)) (-4459 |has| |#1| (-1070))) +((|HasCategory| |#1| (QUOTE (-374))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3795 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738)))) (|HasCategory| |#1| (QUOTE (-485))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-312))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-485)))) (-3795 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738)))) (-3795 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-738)))) (-305 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|)))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1121))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102)))) (-306) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-307 -1956 S) +(-307 -2117 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-308 E -1956) +(-308 E -2117) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1175,7 +1175,7 @@ NIL (-311 S) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1068)))) +((|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1070)))) (-312) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL @@ -1198,7 +1198,7 @@ NIL NIL (-317) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-318 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1208,7 +1208,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-320 -1956) +(-320 -2117) ((|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 @@ -1222,8 +1222,8 @@ NIL NIL (-323 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-1041))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (-2755 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-862)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-1171))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -319) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -296) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-317))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-862))) (-12 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| $ (QUOTE (-146)))) (-2755 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| $ (QUOTE (-146)))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-1043))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (-3795 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-862)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-1173))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -319) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -296) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-317))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-862))) (-12 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| $ (QUOTE (-146)))) (-3795 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| $ (QUOTE (-146)))))) (-324 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1234,9 +1234,9 @@ NIL NIL (-326 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4459 -2755 (-12 (|has| |#1| (-568)) (-2755 (|has| |#1| (-1068)) (|has| |#1| (-485)))) (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) ((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-568)) (-4454 |has| |#1| (-568))) -((-2755 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-21))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-1068))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -651) 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(|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3795 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3795 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568)))) (-3795 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-3795 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-3795 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1133)))) (-3795 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-3795 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) +(-327 R -2117) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1246,8 +1246,8 @@ NIL NIL (-329 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2092) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1960) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -4114) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1583) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) (-330 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1258,7 +1258,7 @@ NIL NIL (-332 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}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-804)))) (-333 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1274,19 +1274,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) (-336 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-337 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."))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-338 S -1956) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-338 S -2117) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-379)))) -(-339 -1956) +(-339 -2117) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-340) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) @@ -1308,54 +1308,54 @@ 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 -(-345 S -1956 UP UPUP R) +(-345 S -2117 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-346 -1956 UP UPUP R) +(-346 -2117 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-347 -1956 UP UPUP R) +(-347 -2117 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL (-348 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|)))) (-349 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-350 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-390)))) (|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (QUOTE (-576))))) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-390)))) (|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) (-351 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-352 S -1956 UP UPUP) +(-352 S -2117 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-374)))) -(-353 -1956 UP UPUP) +(-353 -2117 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 |has| (-419 |#2|) (-374)) (-4462 |has| (-419 |#2|) (-374)) (-4456 |has| (-419 |#2|) (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-354 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2755 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-3795 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) (-355 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-3795 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-356 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-3795 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-357 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1370,33 +1370,33 @@ NIL NIL (-360) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-361 R UP -1956) +(-361 R UP -2117) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-362 |p| |extdeg|) ((|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."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2755 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-3795 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) (-363 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-3795 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-364 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-3795 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2755 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-3795 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) (-366 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) -(-367 -1956 GF) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-3795 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +(-367 -2117 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1404,21 +1404,21 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-369 -1956 FP FPP) +(-369 -2117 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-370 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-3795 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-371 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL NIL (-372 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4459 . T)) +((-4461 . T)) NIL (-373 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1426,7 +1426,7 @@ NIL NIL (-374) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-375 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1442,7 +1442,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-568)))) (-378 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4459 |has| |#1| (-568)) (-4457 . T) (-4456 . T)) +((-4461 |has| |#1| (-568)) (-4459 . T) (-4458 . T)) NIL (-379) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1454,7 +1454,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-374)))) (-381 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-382 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1463,14 +1463,14 @@ NIL (-383 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119)))) +((|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1121)))) (-384 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4462 . T)) +((-4464 . T)) NIL (-385 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4457 . T) (-4456 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4459 . T) (-4458 . T)) NIL (-386 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1490,7 +1490,7 @@ NIL NIL (-390) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4445 . T) (-4453 . T) (-4163 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4447 . T) (-4455 . T) (-2642 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-391 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1498,11 +1498,11 @@ NIL NIL (-392 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-393 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) NIL (-394) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) @@ -1514,7 +1514,7 @@ NIL NIL (-396 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-397 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1526,7 +1526,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-862)))) (-399) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-400) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1538,13 +1538,13 @@ NIL NIL (-402 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) NIL (-403) ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-404 -1956 UP UPUP R) +(-404 -2117 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 @@ -1568,11 +1568,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-410 -2624 |returnType| -1924 |symbols|) +(-410 -4149 |returnType| -4285 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-411 -1956 UP) +(-411 -2117 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1586,15 +1586,15 @@ NIL NIL (-414) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-415 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4445)) (|HasAttribute| |#1| (QUOTE -4453))) +((|HasAttribute| |#1| (QUOTE -4447)) (|HasAttribute| |#1| (QUOTE -4455))) (-416) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-4163 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2642 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-417 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1606,20 +1606,20 @@ NIL NIL (-419 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4449 -12 (|has| |#1| (-6 -4460)) (|has| |#1| (-464)) (|has| |#1| (-6 -4449))) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-832))) (-2755 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-862)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4449)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +((-4451 -12 (|has| |#1| (-6 -4462)) (|has| |#1| (-464)) (|has| |#1| (-6 -4451))) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (QUOTE (-832))) (-3795 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-862)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4451)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) (-420 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-421 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-422 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) +((|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576))))) (-423 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL @@ -1628,14 +1628,14 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-425 R -1956 UP A) +(-425 R -2117 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)}."))) -((-4459 . T)) +((-4461 . T)) NIL -(-426 R -1956 UP A |ibasis|) +(-426 R -2117 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (LIST (QUOTE -1057) (|devaluate| |#2|)))) +((|HasCategory| |#4| (LIST (QUOTE -1059) (|devaluate| |#2|)))) (-427 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1646,12 +1646,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-429 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4459 |has| |#1| (-568)) (-4457 . T) (-4456 . T)) +((-4461 |has| |#1| (-568)) (-4459 . T) (-4458 . T)) NIL (-430 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1240))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1240)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1242))) (-3795 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1242)))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) (-431 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1678,37 +1678,37 @@ NIL ((|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-379)))) (-437 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4462 . T) (-4452 . T) (-4463 . T)) +((-4464 . T) (-4454 . T) (-4465 . T)) NIL -(-438 R -1956) +(-438 R -2117) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-439 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4449 -12 (|has| |#1| (-6 -4449)) (|has| |#2| (-6 -4449))) (-4456 . T) (-4457 . T) (-4459 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4449)) (|HasAttribute| |#2| (QUOTE -4449)))) -(-440 R -1956) +((-4451 -12 (|has| |#1| (-6 -4451)) (|has| |#2| (-6 -4451))) (-4458 . T) (-4459 . T) (-4461 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4451)) (|HasAttribute| |#2| (QUOTE -4451)))) +(-440 R -2117) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL (-441 S R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) +((|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (-442 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4459 -2755 (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) ((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-568)) (-4454 |has| |#1| (-568))) +((-4461 -3795 (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) ((-4466 "*") |has| |#1| (-568)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-568)) (-4456 |has| |#1| (-568))) NIL -(-443 R -1956) +(-443 R -2117) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-444 R -1956) +(-444 R -2117) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-445 R -1956) +(-445 R -2117) ((|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 @@ -1716,10 +1716,10 @@ 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 -(-447 R -1956 UP) +(-447 R -2117 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-48))))) +((|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-48))))) (-448) ((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) NIL @@ -1748,7 +1748,7 @@ 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\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-455 R UP -1956) +(-455 R UP -2117) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1786,16 +1786,16 @@ NIL NIL (-464) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-465 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4459 |has| (-419 (-969 |#1|)) (-568)) (-4457 . T) (-4456 . T)) -((|HasCategory| (-419 (-969 |#1|)) (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-419 (-969 |#1|)) (QUOTE (-568)))) +((-4461 |has| (-419 (-971 |#1|)) (-568)) (-4459 . T) (-4458 . T)) +((|HasCategory| (-419 (-971 |#1|)) (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-419 (-971 |#1|)) (QUOTE (-568)))) (-466 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#2| (QUOTE (-926))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4466 "*") |has| |#2| (-174)) (-4457 |has| |#2| (-568)) (-4462 |has| |#2| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . 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A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1822,7 +1822,7 @@ NIL NIL (-473 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) NIL (-474 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1830,8 +1830,8 @@ NIL NIL (-475 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4463 . T) (-4462 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#4| (QUOTE (-102)))) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) (-476 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL @@ -1860,7 +1860,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-483 |lv| -1956 R) +(-483 |lv| -2117 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1870,23 +1870,23 @@ NIL NIL (-485) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4459 . T)) +((-4461 . 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T)) +((-12 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121)))) (-488 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) -((-4463 . T) (-4462 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#4| (QUOTE (-102)))) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) (-489) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-490) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1894,29 +1894,29 @@ NIL NIL (-491 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|)))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1121))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102)))) (-492) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-493 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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T) (-4458 . T) (-4461 . 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(|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-496 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}."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-497 -1956 UP UPUP R) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-497 -2117 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1926,12 +1926,12 @@ NIL NIL (-499) ((|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."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . 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T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (-3795 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) (-500 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) +((|HasAttribute| |#1| (QUOTE -4464)) (|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-501 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1952,34 +1952,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-506 -1956 UP |AlExt| |AlPol|) +(-506 -2117 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-507) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (QUOTE (-576))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) (-508 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-509 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-510 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) NIL NIL -(-511 R UP -1956) +(-511 R UP -2117) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-512 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4463 . T) (-4462 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-112) (QUOTE (-102)))) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-112) (QUOTE (-102)))) (-513 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL @@ -1992,10 +1992,10 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-516 -1956 |Expon| |VarSet| |DPoly|) +(-516 -2117 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-1195))))) +((|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-1197))))) (-517 |vl| |nv|) ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) NIL @@ -2042,36 +2042,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-804)))) (-528 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-529) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL (-530 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2755 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-3795 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) (-531 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-532 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-533 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4463))) +((|HasAttribute| |#3| (QUOTE -4465))) (-534 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -4463))) +((|HasAttribute| |#7| (QUOTE -4465))) (-535 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4466 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-536) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2104,7 +2104,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-544 K -1956 |Par|) +(-544 K -2117 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2128,7 +2128,7 @@ 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 -(-550 K -1956 |Par|) +(-550 K -2117 |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 @@ -2158,7 +2158,7 @@ NIL NIL (-557) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-558) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2178,13 +2178,13 @@ NIL NIL (-562 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|)))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102)))) -(-563 R -1956) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1121))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102)))) +(-563 R -2117) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-564 R0 -1956 UP UPUP R) +(-564 R0 -2117 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 @@ -2194,7 +2194,7 @@ NIL NIL (-566 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-4163 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2642 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-567 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2202,9 +2202,9 @@ NIL NIL (-568) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-569 R -1956) +(-569 R -2117) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2216,7 +2216,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-572 R -1956 L) +(-572 R -2117 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -668) (|devaluate| |#2|)))) @@ -2224,31 +2224,31 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-574 -1956 UP UPUP R) +(-574 -2117 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-575 -1956 UP) +(-575 -2117 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL (-576) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4444 . T) (-4450 . T) (-4454 . T) (-4449 . T) (-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4446 . T) (-4452 . T) (-4456 . T) (-4451 . T) (-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-577) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-578 R -1956 L) +(-578 R -2117 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -668) (|devaluate| |#2|)))) -(-579 R -1956) +(-579 R -2117) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1158)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-641))))) -(-580 -1956 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1160)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-641))))) +(-580 -2117 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2256,27 +2256,27 @@ 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 -(-582 -1956) +(-582 -2117) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-583 R) ((|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."))) -((-4163 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2642 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-584) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-585 R -1956) +(-585 R -2117) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-294))) (|HasCategory| |#2| (QUOTE (-641))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) -(-586 -1956 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-294))) (|HasCategory| |#2| (QUOTE (-641))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) +(-586 -2117 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-587 R -1956) +(-587 R -2117) ((|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 @@ -2298,21 +2298,21 @@ NIL NIL (-592 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-593 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) (-594) ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-595 R -1956) +(-595 R -2117) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-596 E -1956) +(-596 E -2117) ((|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 @@ -2320,10 +2320,10 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-598 -1956) +(-598 -2117) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-4457 . T) (-4456 . T)) -((|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1195))))) +((-4459 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-1197))))) (-599 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL @@ -2350,19 +2350,19 @@ NIL NIL (-605 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2755 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (-2755 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-3795 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1121)))) (-3795 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1121)))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-606 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL (-607 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4114) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) (-608 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-568)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-568)))) (-609) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) @@ -2376,7 +2376,7 @@ 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 -(-612 R -1956 FG) +(-612 R -2117 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2386,12 +2386,12 @@ NIL NIL (-614 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-615 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-862))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#3| (QUOTE (-1119)))) +((|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (QUOTE (-862))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#3| (QUOTE (-1121)))) (-616 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2406,19 +2406,19 @@ NIL NIL (-619 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4459 -2755 (-2669 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) -((-2755 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4461 -3795 (-2311 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4459 . T) (-4458 . T)) +((-3795 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-620 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| (-1177) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| (-1179) (QUOTE (-862))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (QUOTE (-102)))) (-621 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL NIL (-622 |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4463 . T)) +((-4465 . T)) NIL (-623 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"))) @@ -2427,7 +2427,7 @@ NIL (-624 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) +((|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-625 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL @@ -2436,7 +2436,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-627 -1956 UP) +(-627 -2117 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2458,20 +2458,20 @@ NIL NIL (-632 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((-4459 . T)) +((-4461 . T)) NIL (-633 A R S) ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-860)))) -(-634 R -1956) +(-634 R -2117) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) NIL NIL (-635 R UP) ((|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"))) -((-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4455 . T) (-4459 . T)) -((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) +((-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4457 . T) (-4461 . T)) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (-636 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) NIL @@ -2486,7 +2486,7 @@ NIL NIL (-639 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4459 . T)) +((-4461 . T)) NIL (-640 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) @@ -2496,30 +2496,30 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-642 R -1956) +(-642 R -2117) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-643 |lv| -1956) +(-643 |lv| -2117) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-644) ((|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."))) -((-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4437) (QUOTE (-52))))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1177) (QUOTE (-862))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-1119)))) +((-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -2904) (QUOTE (-52))))))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1179) (QUOTE (-862))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 (-52))) (QUOTE (-1121)))) (-645 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-646 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4457 . T) (-4456 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4459 . T) (-4458 . T)) NIL (-647 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4459 -2755 (-2669 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) -((-2755 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4461 -3795 (-2311 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4459 . T) (-4458 . T)) +((-3795 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-648 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL @@ -2531,7 +2531,7 @@ NIL (-650 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2658 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) +((-2300 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) (-651 R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|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 @@ -2554,8 +2554,8 @@ NIL NIL (-656 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-657 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2566,8 +2566,8 @@ NIL NIL (-659 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-660 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2579,39 +2579,39 @@ NIL (-662 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4463))) +((|HasAttribute| |#1| (QUOTE -4465))) (-663 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-664 R -1956 L) +(-664 R -2117 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 (-665 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-666 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-667 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-668 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-669 -1956 UP) +(-669 -2117 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)))) -(-670 A -3641) +(-670 A -3629) ((|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}}"))) -((-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-671 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL @@ -2626,7 +2626,7 @@ NIL NIL (-674 M R S) ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-803)))) (-675 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2634,7 +2634,7 @@ NIL NIL (-676 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4457 . T) (-4456 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4459 . T) (-4458 . T)) ((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-174)))) (-677 A S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) @@ -2642,13 +2642,13 @@ NIL NIL (-678 S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) -((-4463 . T) (-4462 . T)) +((-4465 . T) (-4464 . T)) NIL -(-679 -1956) +(-679 -2117) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-680 -1956 |Row| |Col| M) +(-680 -2117 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2658,8 +2658,8 @@ NIL NIL (-682 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) -((-4459 . T) (-4462 . T) (-4456 . T) (-4457 . T)) -((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-2755 (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4461 . T) (-4464 . T) (-4458 . T) (-4459 . T)) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-3795 (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-683) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2679,7 +2679,7 @@ NIL (-687 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) NIL -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-688) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2723,10 +2723,10 @@ NIL (-698 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|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 (-4464 "*"))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568)))) +((|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568)))) (-699 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|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"))) -((-4462 . T) (-4463 . T)) +((-4464 . T) (-4465 . T)) NIL (-700 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) @@ -2734,8 +2734,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568)))) (-701 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) -((-4462 . T) (-4463 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4464 . T) (-4465 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4466 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-702 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2744,7 +2744,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-704 S -1956 FLAF FLAS) +(-704 S -2117 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2754,11 +2754,11 @@ NIL NIL (-706) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4455 . T) (-4460 |has| (-711) (-374)) (-4454 |has| (-711) (-374)) (-4175 . T) (-4461 |has| (-711) (-6 -4461)) (-4458 |has| (-711) (-6 -4458)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-711) (QUOTE (-148))) (|HasCategory| (-711) (QUOTE (-146))) (|HasCategory| (-711) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-379))) (|HasCategory| (-711) (QUOTE (-374))) (-2755 (|HasCategory| (-711) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-237))) (-2755 (-12 (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195))))) (-2755 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (LIST (QUOTE -296) (QUOTE (-711)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -319) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-711) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (-2755 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-711) (QUOTE (-1041))) (|HasCategory| (-711) (QUOTE (-1221))) (-12 (|HasCategory| (-711) (QUOTE (-1021))) (|HasCategory| (-711) (QUOTE (-1221)))) (-2755 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-926))))) (-2755 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (-12 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-926)))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-926))))) (|HasCategory| (-711) (QUOTE (-557))) (-12 (|HasCategory| (-711) (QUOTE (-1079))) (|HasCategory| (-711) (QUOTE (-1221)))) (|HasCategory| (-711) (QUOTE (-1079))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926))) (-2755 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374)))) (-2755 (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (QUOTE (-237)))) (-2755 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-568)))) (-12 (|HasCategory| (-711) (QUOTE (-237))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-568))) (|HasAttribute| (-711) (QUOTE -4461)) (|HasAttribute| (-711) (QUOTE -4458)) (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-146)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-360))))) +((-4457 . T) (-4462 |has| (-711) (-374)) (-4456 |has| (-711) (-374)) (-2649 . T) (-4463 |has| (-711) (-6 -4463)) (-4460 |has| (-711) (-6 -4460)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-711) (QUOTE (-148))) (|HasCategory| (-711) (QUOTE (-146))) (|HasCategory| (-711) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-379))) (|HasCategory| (-711) (QUOTE (-374))) (-3795 (|HasCategory| (-711) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-237))) (-3795 (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197))))) (-3795 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (LIST (QUOTE -296) (QUOTE (-711)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -319) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-711) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (-3795 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-711) (QUOTE (-1043))) (|HasCategory| (-711) (QUOTE (-1223))) (-12 (|HasCategory| (-711) (QUOTE (-1023))) (|HasCategory| (-711) (QUOTE (-1223)))) (-3795 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-374))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-928))))) (-3795 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (-12 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-928)))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-928))))) (|HasCategory| (-711) (QUOTE (-557))) (-12 (|HasCategory| (-711) (QUOTE (-1081))) (|HasCategory| (-711) (QUOTE (-1223)))) (|HasCategory| (-711) (QUOTE (-1081))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928))) (-3795 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-374)))) (-3795 (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (QUOTE (-237)))) (-3795 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-568)))) (-12 (|HasCategory| (-711) (QUOTE (-237))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-568))) (|HasAttribute| (-711) (QUOTE -4463)) (|HasAttribute| (-711) (QUOTE -4460)) (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-146)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-360))))) (-707 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4463 . T)) +((-4465 . T)) NIL (-708 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2768,13 +2768,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-710 OV E -1956 PG) +(-710 OV E -2117 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 (-711) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-4163 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2642 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-712 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2782,7 +2782,7 @@ NIL NIL (-713) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4461 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4463 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-714 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) @@ -2800,7 +2800,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-718 S -2014 I) +(-718 S -3157 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 @@ -2810,7 +2810,7 @@ NIL NIL (-720 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-721 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) @@ -2820,25 +2820,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-723 R |Mod| -2234 -1872 |exactQuo|) +(-723 R |Mod| -3565 -3181 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-724 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4458 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) (-725 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-726 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-727 R |Mod| -2234 -1872 |exactQuo|) +(-727 R |Mod| -3565 -3181 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4459 . T)) +((-4461 . T)) NIL (-728 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2846,11 +2846,11 @@ NIL NIL (-729 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) NIL -(-730 -1956) +(-730 -2117) ((|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]]}."))) -((-4459 . T)) +((-4461 . T)) NIL (-731 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) @@ -2874,7 +2874,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-360))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-379)))) (-736 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((-4455 |has| |#1| (-374)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 |has| |#1| (-374)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-737 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) @@ -2884,7 +2884,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-739 -1956 UP) +(-739 -2117 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 @@ -2902,8 +2902,8 @@ NIL NIL (-743 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) -(((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#2| (QUOTE (-926))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4466 "*") |has| |#2| (-174)) (-4457 |has| |#2| (-568)) (-4462 |has| |#2| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (-3795 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-3795 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-3795 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3795 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) (-744 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2918,16 +2918,16 @@ NIL NIL (-747 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-862)))) (-748 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4452 . T) (-4463 . T)) +((-4454 . T) (-4465 . T)) NIL (-749 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) -((-4462 . T) (-4452 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4454 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-750) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL @@ -2938,7 +2938,7 @@ NIL NIL (-752 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4457 . T) (-4456 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL (-753 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) @@ -2954,7 +2954,7 @@ NIL NIL (-756 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) NIL (-757) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -3036,11 +3036,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-777 -1956) +(-777 -2117) ((|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 -(-778 P -1956) +(-778 P -2117) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -3048,7 +3048,7 @@ NIL NIL NIL NIL -(-780 UP -1956) +(-780 UP -2117) ((|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 @@ -3062,9 +3062,9 @@ NIL NIL (-783) ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) -(((-4464 "*") . T)) +(((-4466 "*") . T)) NIL -(-784 R -1956) +(-784 R -2117) ((|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 @@ -3084,7 +3084,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-789 -1956 |ExtF| |SUEx| |ExtP| |n|) +(-789 -2117 |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 @@ -3098,28 +3098,28 @@ NIL NIL (-792 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . 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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| (((|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 (-794 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4458 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) (-795 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-796 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4463 . T) (-4462 . T)) +((-4465 . T) (-4464 . T)) NIL (-797 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-174)))) +((-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-174)))) (-798) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL @@ -3163,28 +3163,28 @@ NIL (-808 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-379)))) +((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-379)))) (-809 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-810 -2755 R OS S) +(-810 -3795 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-811 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-2755 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-3795 (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3795 (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (-812) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-813 R -1956 L) +(-813 R -2117 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-814 R -1956) +(-814 R -2117) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3192,7 +3192,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-816 R -1956) +(-816 R -2117) ((|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 @@ -3200,11 +3200,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-818 -1956 UP UPUP R) +(-818 -2117 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 -(-819 -1956 UP L LQ) +(-819 -2117 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3212,41 +3212,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-821 -1956 UP L LQ) +(-821 -2117 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-822 -1956 UP) +(-822 -2117 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-823 -1956 L UP A LO) +(-823 -2117 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 -(-824 -1956 UP) +(-824 -2117 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-825 -1956 LO) +(-825 -2117 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}.")) 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(((|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 -(-826 -1956 LODO) +(-826 -2117 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)]}."))) 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T) (-4457 . T) (-4456 . T)) +(((-4466 "*") |has| |#2| (-374)) (-4457 |has| |#2| (-374)) (-4462 |has| |#2| (-374)) (-4456 |has| |#2| (-374)) (-4461 . T) (-4459 . T) (-4458 . T)) ((|HasCategory| |#2| (QUOTE (-374)))) (-830 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) @@ -3258,7 +3258,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-862)))) (-832) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-833) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) @@ -3286,7 +3286,7 @@ NIL NIL (-839 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-238)))) (-840) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3298,7 +3298,7 @@ NIL NIL (-842 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4462 . T) (-4452 . T) (-4463 . T)) +((-4464 . T) (-4454 . T) (-4465 . T)) NIL (-843) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) @@ -3310,8 +3310,8 @@ NIL NIL (-845 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) -((-4459 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2755 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2755 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4461 |has| |#1| (-860))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-3795 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-3795 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-846 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3322,7 +3322,7 @@ NIL NIL (-848 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) (-849) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) @@ -3350,13 +3350,13 @@ NIL NIL (-855 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4459 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2755 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2755 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4461 |has| |#1| (-860))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-3795 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-3795 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-856) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-857 -2701 S) +(-857 -1911 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3370,7 +3370,7 @@ NIL NIL (-860) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4459 . T)) +((-4461 . T)) NIL (-861 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3380,1817 +3380,1825 @@ NIL ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) NIL NIL -(-863 S R) +(-863 S) +((|constructor| (NIL "Category of types equipped with a total 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 +(-864) +((|constructor| (NIL "Category of types equipped with a total ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) +NIL +NIL +(-865 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) NIL ((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) -(-864 R) +(-866 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-865 R C) +(-867 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) -(-866 R |sigma| -3640) +(-868 R |sigma| -1991) ((|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."))) -((-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) -(-867 |x| R |sigma| -3640) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) +(-869 |x| R |sigma| -1991) ((|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}."))) -((-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-374)))) -(-868 R) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-374)))) +(-870 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) -(-869) +(-871) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL NIL -(-870) +(-872) ((|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 -(-871 S) +(-873 S) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-872) +(-874) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-873) +(-875) ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) NIL NIL -(-874) +(-876) ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL -(-875) +(-877) ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-876 |VariableList|) +(-878 |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 -(-877) +(-879) ((|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 -(-878 R |vl| |wl| |wtlevel|) +(-880 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) -(-879 R PS UP) +(-881 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 -(-880 R |x| |pt|) +(-882 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 -(-881 |p|) +(-883 |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}."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-882 |p|) +(-884 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-883 |p|) +(-885 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-882 |#1|) (QUOTE (-926))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-148))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-882 |#1|) (QUOTE (-1041))) (|HasCategory| (-882 |#1|) (QUOTE (-832))) (-2755 (|HasCategory| (-882 |#1|) (QUOTE (-832))) (|HasCategory| (-882 |#1|) (QUOTE (-862)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-1171))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-237))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (QUOTE (-238))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -882) (|devaluate| |#1|)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (QUOTE (-317))) (|HasCategory| (-882 |#1|) (QUOTE (-557))) (|HasCategory| (-882 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))))) -(-884 |p| PADIC) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-884 |#1|) (QUOTE (-928))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-148))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-884 |#1|) (QUOTE (-1043))) (|HasCategory| (-884 |#1|) (QUOTE (-832))) (-3795 (|HasCategory| (-884 |#1|) (QUOTE (-832))) (|HasCategory| (-884 |#1|) (QUOTE (-862)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (QUOTE (-1173))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (QUOTE (-237))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (QUOTE (-238))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -884) (|devaluate| |#1|)) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (QUOTE (-317))) (|HasCategory| (-884 |#1|) (QUOTE (-557))) (|HasCategory| (-884 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-928)))) (|HasCategory| (-884 |#1|) (QUOTE (-146))))) +(-886 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-832))) (-2755 (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) -(-885 S T$) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1043))) (|HasCategory| |#2| (QUOTE (-832))) (-3795 (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-887 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) -(-886) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))))) +(-888) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL NIL -(-887) +(-889) ((|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 -(-888) +(-890) ((|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 -(-889 CF1 CF2) +(-891 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-890 |ComponentFunction|) +(-892 |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 -(-891 CF1 CF2) +(-893 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-892 |ComponentFunction|) +(-894 |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 -(-893) +(-895) ((|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 -(-894 CF1 CF2) +(-896 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-895 |ComponentFunction|) +(-897 |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 -(-896) +(-898) ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'s}.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}\\spad{'s},{} and 4 \\spad{5}\\spad{'s}.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) NIL NIL -(-897 R) +(-899 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 -(-898 R S L) +(-900 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 -(-899 S) +(-901 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 -(-900 |Base| |Subject| |Pat|) +(-902 |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 (-2658 (|HasCategory| |#2| (QUOTE (-1068)))) (-2658 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (-2658 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195))))) -(-901 R A B) +((-12 (-2300 (|HasCategory| |#2| (QUOTE (-1070)))) (-2300 (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197)))))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (-2300 (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197))))) +(-903 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL NIL -(-902 R S) +(-904 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-903 R -2014) +(-905 R -3157) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL -(-904 R S) +(-906 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 -(-905 R) +(-907 R) ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-906 |VarSet|) +(-908 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL NIL -(-907 UP R) +(-909 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) NIL NIL -(-908 A T$ S) +(-910 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 -(-909 T$ S) +(-911 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 -(-910) +(-912) ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-911 UP -1956) +(-913 UP -2117) ((|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 -(-912) +(-914) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st,tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}"))) NIL NIL -(-913) +(-915) ((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-914 R S) +(-916 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) NIL -(-915 S) +(-917 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4459 . T)) +((-4461 . T)) NIL -(-916 A S) +(-918 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 -(-917 S) +(-919 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 -(-918 S) +(-920 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-919 |n| R) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-921 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL -(-920 S) +(-922 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."))) -((-4459 . T)) +((-4461 . T)) NIL -(-921 S) +(-923 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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-922 S) +(-924 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) -((-4459 . T)) -((-2755 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) -(-923 R E |VarSet| S) +((-4461 . T)) +((-3795 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) +(-925 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 -(-924 R S) +(-926 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 -(-925 S) +(-927 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-146)))) -(-926) +(-928) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-927 |p|) +(-929 |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."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) -(-928 R0 -1956 UP UPUP R) +(-930 R0 -2117 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 -(-929 UP UPUP R) +(-931 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 -(-930 UP UPUP) +(-932 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 -(-931 R) +(-933 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-932 R) +(-934 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 -(-933 E OV R P) +(-935 E OV R P) ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}."))) NIL NIL -(-934) +(-936) ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-935 -1956) +(-937 -2117) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL -(-936 R) +(-938 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 -(-937) +(-939) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-938) +(-940) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4464 "*") . T)) +(((-4466 "*") . T)) NIL -(-939 -1956 P) +(-941 -2117 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-940 |xx| -1956) +(-942 |xx| -2117) ((|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 -(-941 R |Var| |Expon| GR) +(-943 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, w, p, r, rm, m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{~=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, w, r, s, m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-942 S) +(-944 S) ((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,theta,seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,t,seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,x,seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-943) +(-945) ((|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 -(-944) +(-946) ((|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 -(-945) +(-947) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-946 R -1956) +(-948 R -2117) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL -(-947) +(-949) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-948 S A B) +(-950 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 -(-949 S R -1956) +(-951 S R -2117) ((|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 -(-950 I) +(-952 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 -(-951 S E) +(-953 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 -(-952 S R L) +(-954 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 -(-953 S E V R P) +(-955 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 -899) (|devaluate| |#1|)))) -(-954 R -1956 -2014) +((|HasCategory| |#3| (LIST (QUOTE -901) (|devaluate| |#1|)))) +(-956 R -2117 -3157) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-955 -2014) +(-957 -3157) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-956 S R Q) +(-958 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 -(-957 S) +(-959 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 -(-958 S R P) +(-960 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 -(-959) +(-961) ((|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 -(-960 R) +(-962 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-961 |lv| R) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-963 |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 -(-962 |TheField| |ThePols|) +(-964 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL ((|HasCategory| |#1| (QUOTE (-860)))) -(-963 R S) +(-965 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 -(-964 |x| R) +(-966 |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 -(-965 S R E |VarSet|) +(-967 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-926))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#4| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) -(-966 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-928))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#4| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) +(-968 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-967 E V R P -1956) +(-969 E V R P -2117) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-968 E |Vars| R P S) +(-970 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 -(-969 R) +(-971 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}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-970 E V R P -1956) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-972 E V R P -2117) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-464)))) -(-971) +(-973) ((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}."))) NIL NIL -(-972) +(-974) ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-973 R L) +(-975 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL NIL -(-974 A B) +(-976 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -(-975 S) +(-977 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-976) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-978) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-977 -1956) +(-979 -2117) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL -(-978 I) +(-980 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-979) +(-981) ((|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 -(-980 R E) +(-982 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}"))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4460))) -(-981 A B) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4462))) +(-983 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) 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(-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) +(-984) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-983 T$) +(-985 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|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-984 T$) +(-986 T$) ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} \\spad{++} returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) NIL NIL -(-985 S T$) +(-987 S T$) ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) NIL NIL -(-986) +(-988) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-987 S) +(-989 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4462 . T) (-4463 . T)) +((-4464 . T) (-4465 . T)) NIL -(-988 R |polR|) +(-990 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) NIL ((|HasCategory| |#1| (QUOTE (-464)))) -(-989) +(-991) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-990) +(-992) ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\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 -(-991 S |Coef| |Expon| |Var|) +(-993 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 -(-992 |Coef| |Expon| |Var|) +(-994 |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}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-993) +(-995) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-994 S R E |VarSet| P) +(-996 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL ((|HasCategory| |#2| (QUOTE (-568)))) -(-995 R E |VarSet| P) +(-997 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4462 . T)) +((-4464 . T)) NIL -(-996 R E V P) +(-998 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-464)))) -(-997 K) +(-999 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 -(-998 |VarSet| E RC P) +(-1000 |VarSet| E RC P) ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{gcd} domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) NIL NIL -(-999 R) +(-1001 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}."))) -((-4463 . T) (-4462 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1000 R1 R2) +(-1002 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-1001 R) +(-1003 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 -(-1002 K) +(-1004 K) ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns \\spad{csc}(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) NIL NIL -(-1003 R E OV PPR) +(-1005 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 -(-1004 K R UP -1956) +(-1006 K R UP -2117) ((|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 -(-1005 |vl| |nv|) +(-1007 |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 -(-1006 R |Var| |Expon| |Dpoly|) +(-1008 R |Var| |Expon| |Dpoly|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-317))))) -(-1007 R E V P TS) +(-1009 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1008) +(-1010) ((|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 -(-1009 A B R S) +(-1011 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 -(-1010 A S) +(-1012 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 (-926))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1171)))) -(-1011 S) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1043))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1173)))) +(-1013 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}."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1012 |n| K) +(-1014 |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 -(-1013) +(-1015) ((|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 -(-1014 S) +(-1016 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4462 . T) (-4463 . T)) +((-4464 . T) (-4465 . T)) NIL -(-1015 S R) +(-1017 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-300)))) -(-1016 R) +((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-300)))) +(-1018 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}."))) -((-4455 |has| |#1| (-300)) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 |has| |#1| (-300)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1017 QR R QS S) +(-1019 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 -(-1018 R) +(-1020 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.}"))) -((-4455 |has| |#1| (-300)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-557)))) -(-1019 S) +((-4457 |has| |#1| (-300)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-557)))) +(-1021 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}."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1020 S) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1022 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1021) +(-1023) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1022 -1956 UP UPUP |radicnd| |n|) +(-1024 -2117 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2755 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2755 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) -(-1023 |bb|) +((-4457 |has| (-419 |#2|) (-374)) (-4462 |has| (-419 |#2|) (-374)) (-4456 |has| (-419 |#2|) (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-3795 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-3795 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3795 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3795 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-3795 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-3795 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +(-1025 |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."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2755 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) -(-1024) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (-3795 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) +(-1026) ((|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 -(-1025) +(-1027) ((|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 -(-1026 RP) +(-1028 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 -(-1027 S) +(-1029 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 -(-1028 A S) +(-1030 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-1119)))) -(-1029 S) +((|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (QUOTE (-1121)))) +(-1031 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL NIL -(-1030 S) +(-1032 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) NIL NIL -(-1031) +(-1033) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-4455 . T) (-4460 . T) (-4454 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4459 . T)) +((-4457 . T) (-4462 . T) (-4456 . T) (-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4461 . T)) NIL -(-1032 R -1956) +(-1034 R -2117) ((|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 -(-1033 R -1956) +(-1035 R -2117) ((|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 -(-1034 -1956 UP) +(-1036 -2117 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 -(-1035 -1956 UP) +(-1037 -2117 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 -(-1036 S) +(-1038 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 -(-1037 F1 UP UPUP R F2) +(-1039 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 -(-1038) +(-1040) ((|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 -(-1039 |Pol|) +(-1041 |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 -(-1040 |Pol|) +(-1042 |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 -(-1041) +(-1043) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-1042) +(-1044) ((|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 -(-1043 |TheField|) +(-1045 |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"))) -((-4455 . T) (-4460 . T) (-4454 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4459 . T)) -((-2755 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576))))) -(-1044 -1956 L) +((-4457 . T) (-4462 . T) (-4456 . T) (-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4461 . T)) +((-3795 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (QUOTE (-576))))) +(-1046 -2117 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 -(-1045 S) +(-1047 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,m)} same as \\spad{setelt(n,m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) NIL -((|HasCategory| |#1| (QUOTE (-1119)))) -(-1046 R E V P) +((|HasCategory| |#1| (QUOTE (-1121)))) +(-1048 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4463 . T) (-4462 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1047 R) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1049 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4464 "*")))) -(-1048 R) +((|HasAttribute| |#1| (QUOTE (-4466 "*")))) +(-1050 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-317)))) -(-1049 S) +(-1051 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 -(-1050) +(-1052) ((|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 -(-1051 S) +(-1053 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 -(-1052 S) +(-1054 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 -(-1053 -1956 |Expon| |VarSet| |FPol| |LFPol|) +(-1055 -2117 |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"))) -(((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1054) +(-1056) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4437) (QUOTE (-52))))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102)))) -(-1055) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (QUOTE (-1197))) (LIST (QUOTE |:|) (QUOTE -2904) (QUOTE (-52))))))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-1197) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1121))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-102)))) +(-1057) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-1056 A S) +(-1058 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 -(-1057 S) +(-1059 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 -(-1058 Q R) +(-1060 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 -(-1059) +(-1061) ((|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 -(-1060 UP) +(-1062 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 -(-1061 R) +(-1063 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 -(-1062 R) +(-1064 R) ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-1063 T$) +(-1065 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of \\spad{`c'}.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of \\spad{`c'}.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) NIL NIL -(-1064 T$) +(-1066 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) NIL NIL -(-1065 R |ls|) +(-1067 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4463 . T) (-4462 . T)) -((-12 (|HasCategory| (-792 |#1| (-876 |#2|)) (QUOTE (-1119))) (|HasCategory| (-792 |#1| (-876 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -792) (|devaluate| |#1|) (LIST (QUOTE -876) (|devaluate| |#2|)))))) (|HasCategory| (-792 |#1| (-876 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-792 |#1| (-876 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-876 |#2|) (QUOTE (-379))) (|HasCategory| (-792 |#1| (-876 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-792 |#1| (-876 |#2|)) (QUOTE (-102)))) -(-1066) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| (-792 |#1| (-878 |#2|)) (QUOTE (-1121))) (|HasCategory| (-792 |#1| (-878 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -792) (|devaluate| |#1|) (LIST (QUOTE -878) (|devaluate| |#2|)))))) (|HasCategory| (-792 |#1| (-878 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-792 |#1| (-878 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-878 |#2|) (QUOTE (-379))) (|HasCategory| (-792 |#1| (-878 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-792 |#1| (-878 |#2|)) (QUOTE (-102)))) +(-1068) ((|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 -(-1067 S) +(-1069 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 -(-1068) +(-1070) ((|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."))) -((-4459 . T)) +((-4461 . T)) NIL -(-1069 |xx| -1956) +(-1071 |xx| -2117) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-1070 S) +(-1072 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 -(-1071 S |m| |n| R |Row| |Col|) +(-1073 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) NIL ((|HasCategory| |#4| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-374))) (|HasCategory| |#4| (QUOTE (-568))) (|HasCategory| |#4| (QUOTE (-174)))) -(-1072 |m| |n| R |Row| |Col|) +(-1074 |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"))) -((-4462 . T) (-4457 . T) (-4456 . T)) +((-4464 . T) (-4459 . T) (-4458 . T)) NIL -(-1073 |m| |n| R) +(-1075 |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}."))) -((-4462 . T) (-4457 . T) (-4456 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2755 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-874))))) -(-1074 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4464 . T) (-4459 . T) (-4458 . T)) +((|HasCategory| |#3| (QUOTE (-174))) (-3795 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-876))))) +(-1076 |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 -(-1075 R) +(-1077 R) ((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline"))) NIL NIL -(-1076 S T$) +(-1078 S T$) ((|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 (-1119)))) -(-1077) +((|HasCategory| |#1| (QUOTE (-1121)))) +(-1079) ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline"))) NIL NIL -(-1078 S) +(-1080 S) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-1079) +(-1081) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1080 |TheField| |ThePolDom|) +(-1082 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1081) +(-1083) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4450 . T) (-4454 . T) (-4449 . T) (-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4452 . T) (-4456 . T) (-4451 . T) (-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1082) +(-1084) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4437) (QUOTE (-52))))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102)))) -(-1083 S R E V) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (QUOTE (-1197))) (LIST (QUOTE |:|) (QUOTE -2904) (QUOTE (-52))))))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-1121))) (|HasCategory| (-1197) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1121))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 (-1197)) (|:| -2904 (-52))) (QUOTE (-102)))) +(-1085 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-1195))))) -(-1084 R E V) +((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1013) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-1197))))) +(-1086 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-1085) +(-1087) ((|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 -(-1086 S |TheField| |ThePols|) +(-1088 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 -(-1087 |TheField| |ThePols|) +(-1089 |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 -(-1088 R E V P TS) +(-1090 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{gcd} need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1089 S R E V P) +(-1091 S R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) NIL NIL -(-1090 R E V P) +(-1092 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4463 . T) (-4462 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1091 R E V P TS) +(-1093 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1092) +(-1094) ((|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 -(-1093) +(-1095) ((|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 -(-1094 |f|) +(-1096 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1095 |Base| R -1956) +(-1097 |Base| R -2117) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1096 |Base| R -1956) +(-1098 |Base| R -2117) ((|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 -(-1097 R |ls|) +(-1099 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 -(-1098 UP SAE UPA) +(-1100 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 -(-1099 R UP M) +(-1101 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."))) -((-4455 |has| |#1| (-374)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))))) -(-1100 UP SAE UPA) +((-4457 |has| |#1| (-374)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) +(-1102 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 -(-1101) +(-1103) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1102) +(-1104) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-1103 S) +(-1105 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 -(-1104) +(-1106) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding \\spad{`b'}.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of \\spad{`n'} in \\spad{`s'}; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) NIL NIL -(-1105 R) +(-1107 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 -(-1106 R) +(-1108 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"))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1107 (-1195)) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1107 (-1195)) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1107 (-1195)) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1107 (-1195)) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1107 (-1195)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-1107 S) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-1109 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 -(-1108 R S) +(-1110 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 (-860)))) -(-1109) +(-1111) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1110 R S) +(-1112 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1111 S) +(-1113 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1113 |#1|) (QUOTE (-1119)))) -(-1112 S) +((|HasCategory| (-1115 |#1|) (QUOTE (-1121)))) +(-1114 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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 -(-1113 S) +(-1115 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1119)))) -(-1114 S L) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) +(-1116 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 -(-1115) +(-1117) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1116 A S) +(-1118 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1117 S) +(-1119 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4452 . T)) +((-4454 . T)) NIL -(-1118 S) +(-1120 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1119) +(-1121) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1120 |m| |n|) +(-1122 |m| |n|) ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1121 S) +(-1123 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)}}"))) -((-4462 . T) (-4452 . T) (-4463 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-1122 |Str| |Sym| |Int| |Flt| |Expr|) +((-4464 . T) (-4454 . T) (-4465 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-1124 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL NIL -(-1123) +(-1125) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1124 |Str| |Sym| |Int| |Flt| |Expr|) +(-1126 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1125 R FS) +(-1127 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,ftype,body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program."))) NIL NIL -(-1126 R E V P TS) +(-1128 R E V P TS) ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(\\spad{ts},{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1127 R E V P TS) +(-1129 R E V P TS) ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1128 R E V P) +(-1130 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4463 . T) (-4462 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1129) +(-1131) ((|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 -(-1130 S) +(-1132 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1131) +(-1133) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) 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(((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-464)))) -(-1134) +(-1136) ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1135 R -1956) +(-1137 R -2117) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1136 R) +(-1138 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1137) +(-1139) ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) NIL NIL -(-1138) +(-1140) ((|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 -(-1139) +(-1141) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4450 . T) (-4454 . T) (-4449 . T) (-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4452 . T) (-4456 . T) (-4451 . T) (-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1140 S) +(-1142 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4462 . T) (-4463 . T)) +((-4464 . T) (-4465 . T)) NIL -(-1141 S |ndim| R |Row| |Col|) +(-1143 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-374))) (|HasAttribute| |#3| (QUOTE (-4464 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) -(-1142 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-374))) (|HasAttribute| |#3| (QUOTE (-4466 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) +(-1144 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-4462 . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4464 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1143 R |Row| |Col| M) +(-1145 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 -(-1144 R |VarSet|) +(-1146 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."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-1145 |Coef| |Var| SMP) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-1147 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) -(-1146 R E V P) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +(-1148 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}"))) -((-4463 . T) (-4462 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1147 UP -1956) +(-1149 UP -2117) ((|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 -(-1148 R) +(-1150 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 -(-1149 R) +(-1151 R) ((|constructor| (NIL "This package finds the function func3 where func1 and func2 \\indented{1}{are given and\\space{2}func1 = func3(func2) .\\space{2}If there is no solution then} \\indented{1}{function func1 will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function func3 where \\spad{func1} = func3(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) NIL NIL -(-1150 R) +(-1152 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 -(-1151 S A) +(-1153 S A) ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,f)} \\undocumented"))) NIL ((|HasCategory| |#1| (QUOTE (-862)))) -(-1152 R) +(-1154 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 -(-1153 R) +(-1155 R) ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); close2 set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through \\spad{pn},{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if close2 is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and close2 indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument close2 equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through \\spad{pn},{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through \\spad{pn} defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through \\spad{pn} to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1154) +(-1156) ((|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 -(-1155) +(-1157) ((|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 -(-1156) +(-1158) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) NIL NIL -(-1157) +(-1159) ((|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 -(-1158) +(-1160) ((|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 -(-1159 V C) +(-1161 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}o2)} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}o1,{}o2)} returns \\spad{true} iff \\axiom{o1(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{vt}.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) NIL NIL -(-1160 V C) +(-1162 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))) (-2755 (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (-2755 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))))) (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-102)))) -(-1161 |ndim| R) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121))) (-3795 (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121)))) (-3795 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-876)))) (-12 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121))))) (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102)))) +(-1163 |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}."))) -((-4459 . T) (-4451 |has| |#2| (-6 (-4464 "*"))) (-4462 . T) (-4456 . T) (-4457 . 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T) (-4453 |has| |#2| (-6 (-4466 "*"))) (-4464 . T) (-4458 . T) (-4459 . T)) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-374))) (-3795 (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +(-1164 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1163) +(-1165) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4463 . T) (-4462 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1164 R E V P TS) +(-1166 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1165 R E V P) +(-1167 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4463 . T) (-4462 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1166 S) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1168 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}."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1167 A S) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1169 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1168 S) +(-1170 S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1169 |Key| |Ent| |dent|) +(-1171 |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."))) -((-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|)))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119)))) -(-1170) +((-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121)))) +(-1172) ((|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 -(-1171) +(-1173) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL NIL -(-1172 |Coef|) +(-1174 |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 -(-1173 S) +(-1175 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 -(-1174 A B) +(-1176 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 -(-1175 A B C) +(-1177 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 -(-1176 S) +(-1178 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."))) -((-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1177) +((-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1179) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2755 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (-2755 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) -(-1178 |Entry|) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-3795 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1121)))) (-3795 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1121)))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +(-1180 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#1|)))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-1119))) (|HasCategory| (-1177) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-102)))) -(-1179 A) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#1|)))))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (QUOTE (-1121))) (|HasCategory| (-1179) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (-3795 (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 (-1179)) (|:| -2904 |#1|)) (QUOTE (-102)))) +(-1181 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) -(-1180 |Coef|) +(-1182 |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 -(-1181 |Coef|) +(-1183 |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 -(-1182 R UP) +(-1184 R UP) ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, q)} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p, q)}."))) NIL ((|HasCategory| |#1| (QUOTE (-317)))) -(-1183 |n| R) +(-1185 |n| R) ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) 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(|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 -(-1190 E OV R P) +(-1192 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.")) 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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}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . 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T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -4114) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1583) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(-1196) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL NIL -(-1195) +(-1197) ((|constructor| (NIL "Basic and scripted symbols.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| (-990) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasAttribute| |#1| (QUOTE -4460))) -(-1198) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| (-992) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasAttribute| |#1| (QUOTE -4462))) +(-1200) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL -(-1199) +(-1201) ((|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 -(-1200) +(-1202) ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if \\spad{`x'} really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The value returned is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax \\spad{`s'}.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1201 N) +(-1203 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1202 N) +(-1204 N) ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}."))) NIL NIL -(-1203) +(-1205) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1204 R) +(-1206 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 -(-1205) +(-1207) ((|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 -(-1206 S) +(-1208 S) ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1207 S) +(-1209 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 -(-1208 |Key| |Entry|) +(-1210 |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}"))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|)))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102)))) -(-1209 S) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2240) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1121))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-3795 (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -2240 |#1|) (|:| -2904 |#2|)) (QUOTE (-102)))) +(-1211 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 -(-1210 R) +(-1212 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 -(-1211 S |Key| |Entry|) +(-1213 S |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) NIL NIL -(-1212 |Key| |Entry|) +(-1214 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4463 . T)) +((-4465 . T)) NIL -(-1213 |Key| |Entry|) +(-1215 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1214) +(-1216) ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) NIL NIL -(-1215 S) +(-1217 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 -(-1216) +(-1218) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL -(-1217) +(-1219) ((|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 -(-1218 R) +(-1220 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 -(-1219) +(-1221) ((|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 -(-1220 S) +(-1222 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1221) +(-1223) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1222 S) +(-1224 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4463 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1223 S) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1225 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1224) +(-1226) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1225 R -1956) +(-1227 R -2117) ((|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 -(-1226 R |Row| |Col| M) +(-1228 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 -(-1227 R -1956) +(-1229 R -2117) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -899) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -899) (|devaluate| |#1|))))) -(-1228 S R E V P) +((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -901) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -901) (|devaluate| |#1|))))) +(-1230 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-379)))) -(-1229 R E V P) +(-1231 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4463 . T) (-4462 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1230 |Coef|) +(-1232 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) -(-1231 |Curve|) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +(-1233 |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 -(-1232) +(-1234) ((|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 -(-1233 S) +(-1235 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL -((|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) -(-1234 -1956) +((|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) +(-1236 -2117) ((|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 -(-1235) +(-1237) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1236) +(-1238) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1237 S) +(-1239 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) NIL ((|HasCategory| |#1| (QUOTE (-862)))) -(-1238) +(-1240) ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,...,bm], [a1,...,an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,...,bm], [a1,...,an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) NIL NIL -(-1239 S) +(-1241 S) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) NIL NIL -(-1240) +(-1242) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1241) +(-1243) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1242) +(-1244) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1243) +(-1245) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1244) +(-1246) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) NIL NIL -(-1245 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1247 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1246 |Coef|) +(-1248 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1247 S |Coef| UTS) +(-1249 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-374)))) -(-1248 |Coef| UTS) +(-1250 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1249 |Coef| UTS) +(-1251 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-926)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1041)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1171)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-146))))) (-2755 (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-148))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-238)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasCategory| (-576) (QUOTE (-1131))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-926)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1041)))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-832)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-862))))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE 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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 -(-1252 R S) +(-1254 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) NIL ((|HasCategory| |#1| (QUOTE (-860)))) -(-1253 S) +(-1255 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 (-860))) (|HasCategory| |#1| (QUOTE (-1119)))) -(-1254 |x| R |y| S) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) +(-1256 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1255 R Q UP) +(-1257 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1256 R UP) +(-1258 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1257 R UP) +(-1259 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 -(-1258 R U) +(-1260 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) NIL NIL -(-1259 |x| R) +(-1261 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4458 |has| |#2| (-374)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) -(-1260 R PR S PS) +(((-4466 "*") |has| |#2| (-174)) (-4457 |has| |#2| (-568)) (-4460 |has| |#2| (-374)) (-4462 |has| |#2| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3795 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-3795 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-3795 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-3795 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-3795 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-3795 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-1262 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 -(-1261 S R) +(-1263 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1171)))) -(-1262 R) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1173)))) +(-1264 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4458 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-1263 S |Coef| |Expon|) +(-1265 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1131))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3567) (LIST (|devaluate| |#2|) (QUOTE (-1195)))))) -(-1264 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4114) (LIST (|devaluate| |#2|) (QUOTE (-1197)))))) +(-1266 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1265 RC P) +(-1267 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1266 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1268 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1267 |Coef|) +(-1269 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1268 S |Coef| ULS) +(-1270 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 -(-1269 |Coef| ULS) +(-1271 |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)}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1270 |Coef| ULS) +(-1272 |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)}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2092) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1960) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) -(-1271 |Coef| |var| |cen|) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -4114) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1583) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) +(-1273 |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."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2092) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1960) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) -(-1272 R FE |var| |cen|) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -4114) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1583) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(-1274 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))}."))) -(((-4464 "*") |has| (-1271 |#2| |#3| |#4|) (-174)) (-4455 |has| (-1271 |#2| |#3| |#4|) (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-174))) (-2755 (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-568)))) -(-1273 A S) +(((-4466 "*") |has| (-1273 |#2| |#3| |#4|) (-174)) (-4457 |has| (-1273 |#2| |#3| |#4|) (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-174))) (-3795 (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-568)))) +(-1275 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4463))) -(-1274 S) +((|HasAttribute| |#1| (QUOTE -4465))) +(-1276 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1275 |Coef1| |Coef2| UTS1 UTS2) +(-1277 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1276 S |Coef|) +(-1278 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-1221))) (|HasSignature| |#2| (LIST (QUOTE -1960) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2092) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1195))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) -(-1277 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasSignature| |#2| (LIST (QUOTE -1583) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1488) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1197))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) +(-1279 |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."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1278 |Coef| |var| |cen|) +(-1280 |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}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1131))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2092) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1960) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) -(-1279 |Coef| UTS) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -4114) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1583) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(-1281 |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 -(-1280 -1956 UP L UTS) +(-1282 -2117 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-568)))) -(-1281) +(-1283) ((|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 -(-1282 |sym|) +(-1284 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1283 S R) +(-1285 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL -((|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1284 R) +((|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1286 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4463 . T) (-4462 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1285 A B) +(-1287 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1286 R) +(-1288 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4463 . T) (-4462 . T)) -((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-1287) +((-4465 . T) (-4464 . T)) +((-3795 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3795 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3795 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3795 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-1289) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1288) +(-1290) ((|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 -(-1289) +(-1291) ((|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 -(-1290) +(-1292) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1291) +(-1293) ((|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| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1292 A S) +(-1294 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1293 S) +(-1295 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}."))) -((-4457 . T) (-4456 . T)) +((-4459 . T) (-4458 . T)) NIL -(-1294 R) +(-1296 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1295 K R UP -1956) +(-1297 K R UP -2117) ((|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 -(-1296) +(-1298) ((|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 -(-1297) +(-1299) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1298 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1300 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) -(-1299 R E V P) +(-1301 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) -((-4463 . T) (-4462 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1300 R) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1302 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})"))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1301 |vl| R) +(-1303 |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."))) -((-4459 . T) (-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4455))) -(-1302 R |VarSet| XPOLY) +((-4461 . T) (-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4457))) +(-1304 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1303 |vl| R) +(-1305 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-1304 S -1956) +(-1306 S -2117) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1305 -1956) +(-1307 -2117) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1306 |VarSet| R) +(-1308 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -729) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasAttribute| |#2| (QUOTE -4455))) -(-1307 |vl| R) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -729) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasAttribute| |#2| (QUOTE -4457))) +(-1309 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-1308 R) +(-1310 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4455 |has| |#1| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4455))) -(-1309 R E) +((-4457 |has| |#1| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4457))) +(-1311 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4459 . T) (-4460 |has| |#1| (-6 -4460)) (-4455 |has| |#1| (-6 -4455)) (-4457 . T) (-4456 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4459)) (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4455))) -(-1310 |VarSet| R) +((-4461 . T) (-4462 |has| |#1| (-6 -4462)) (-4457 |has| |#1| (-6 -4457)) (-4459 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4457))) +(-1312 |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."))) -((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4455))) -(-1311) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4457))) +(-1313) ((|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 -(-1312 A) +(-1314 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 -(-1313 R |ls| |ls2|) +(-1315 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1314 R) +(-1316 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1315 |p|) +(-1317 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL NIL NIL @@ -5208,4 +5216,4 @@ NIL NIL NIL NIL -((-3 NIL 2293366 2293371 2293376 2293381) (-2 NIL 2293346 2293351 2293356 2293361) (-1 NIL 2293326 2293331 2293336 2293341) (0 NIL 2293306 2293311 2293316 2293321) (-1315 "ZMOD.spad" 2293115 2293128 2293244 2293301) (-1314 "ZLINDEP.spad" 2292181 2292192 2293105 2293110) (-1313 "ZDSOLVE.spad" 2282126 2282148 2292171 2292176) (-1312 "YSTREAM.spad" 2281621 2281632 2282116 2282121) (-1311 "YDIAGRAM.spad" 2281255 2281264 2281611 2281616) (-1310 "XRPOLY.spad" 2280475 2280495 2281111 2281180) (-1309 "XPR.spad" 2278270 2278283 2280193 2280292) (-1308 "XPOLY.spad" 2277825 2277836 2278126 2278195) (-1307 "XPOLYC.spad" 2277144 2277160 2277751 2277820) (-1306 "XPBWPOLY.spad" 2275581 2275601 2276924 2276993) (-1305 "XF.spad" 2274044 2274059 2275483 2275576) (-1304 "XF.spad" 2272487 2272504 2273928 2273933) (-1303 "XFALG.spad" 2269535 2269551 2272413 2272482) (-1302 "XEXPPKG.spad" 2268786 2268812 2269525 2269530) (-1301 "XDPOLY.spad" 2268400 2268416 2268642 2268711) (-1300 "XALG.spad" 2268060 2268071 2268356 2268395) (-1299 "WUTSET.spad" 2263863 2263880 2267670 2267697) (-1298 "WP.spad" 2263062 2263106 2263721 2263788) (-1297 "WHILEAST.spad" 2262860 2262869 2263052 2263057) (-1296 "WHEREAST.spad" 2262531 2262540 2262850 2262855) (-1295 "WFFINTBS.spad" 2260194 2260216 2262521 2262526) (-1294 "WEIER.spad" 2258416 2258427 2260184 2260189) (-1293 "VSPACE.spad" 2258089 2258100 2258384 2258411) (-1292 "VSPACE.spad" 2257782 2257795 2258079 2258084) (-1291 "VOID.spad" 2257459 2257468 2257772 2257777) (-1290 "VIEW.spad" 2255139 2255148 2257449 2257454) (-1289 "VIEWDEF.spad" 2250340 2250349 2255129 2255134) (-1288 "VIEW3D.spad" 2234301 2234310 2250330 2250335) (-1287 "VIEW2D.spad" 2222192 2222201 2234291 2234296) (-1286 "VECTOR.spad" 2220713 2220724 2220964 2220991) (-1285 "VECTOR2.spad" 2219352 2219365 2220703 2220708) (-1284 "VECTCAT.spad" 2217256 2217267 2219320 2219347) (-1283 "VECTCAT.spad" 2214967 2214980 2217033 2217038) (-1282 "VARIABLE.spad" 2214747 2214762 2214957 2214962) (-1281 "UTYPE.spad" 2214391 2214400 2214737 2214742) (-1280 "UTSODETL.spad" 2213686 2213710 2214347 2214352) (-1279 "UTSODE.spad" 2211902 2211922 2213676 2213681) (-1278 "UTS.spad" 2206849 2206877 2210369 2210466) (-1277 "UTSCAT.spad" 2204328 2204344 2206747 2206844) (-1276 "UTSCAT.spad" 2201451 2201469 2203872 2203877) (-1275 "UTS2.spad" 2201046 2201081 2201441 2201446) (-1274 "URAGG.spad" 2195719 2195730 2201036 2201041) (-1273 "URAGG.spad" 2190356 2190369 2195675 2195680) (-1272 "UPXSSING.spad" 2188001 2188027 2189437 2189570) (-1271 "UPXS.spad" 2185297 2185325 2186133 2186282) (-1270 "UPXSCONS.spad" 2183056 2183076 2183429 2183578) (-1269 "UPXSCCA.spad" 2181627 2181647 2182902 2183051) (-1268 "UPXSCCA.spad" 2180340 2180362 2181617 2181622) (-1267 "UPXSCAT.spad" 2178929 2178945 2180186 2180335) (-1266 "UPXS2.spad" 2178472 2178525 2178919 2178924) (-1265 "UPSQFREE.spad" 2176886 2176900 2178462 2178467) (-1264 "UPSCAT.spad" 2174673 2174697 2176784 2176881) (-1263 "UPSCAT.spad" 2172166 2172192 2174279 2174284) (-1262 "UPOLYC.spad" 2167206 2167217 2172008 2172161) (-1261 "UPOLYC.spad" 2162138 2162151 2166942 2166947) (-1260 "UPOLYC2.spad" 2161609 2161628 2162128 2162133) (-1259 "UP.spad" 2158715 2158730 2159102 2159255) (-1258 "UPMP.spad" 2157615 2157628 2158705 2158710) (-1257 "UPDIVP.spad" 2157180 2157194 2157605 2157610) (-1256 "UPDECOMP.spad" 2155425 2155439 2157170 2157175) (-1255 "UPCDEN.spad" 2154634 2154650 2155415 2155420) (-1254 "UP2.spad" 2153998 2154019 2154624 2154629) (-1253 "UNISEG.spad" 2153351 2153362 2153917 2153922) (-1252 "UNISEG2.spad" 2152848 2152861 2153307 2153312) (-1251 "UNIFACT.spad" 2151951 2151963 2152838 2152843) (-1250 "ULS.spad" 2141735 2141763 2142680 2143109) (-1249 "ULSCONS.spad" 2132869 2132889 2133239 2133388) (-1248 "ULSCCAT.spad" 2130606 2130626 2132715 2132864) (-1247 "ULSCCAT.spad" 2128451 2128473 2130562 2130567) (-1246 "ULSCAT.spad" 2126683 2126699 2128297 2128446) (-1245 "ULS2.spad" 2126197 2126250 2126673 2126678) (-1244 "UINT8.spad" 2126074 2126083 2126187 2126192) (-1243 "UINT64.spad" 2125950 2125959 2126064 2126069) (-1242 "UINT32.spad" 2125826 2125835 2125940 2125945) (-1241 "UINT16.spad" 2125702 2125711 2125816 2125821) (-1240 "UFD.spad" 2124767 2124776 2125628 2125697) (-1239 "UFD.spad" 2123894 2123905 2124757 2124762) (-1238 "UDVO.spad" 2122775 2122784 2123884 2123889) (-1237 "UDPO.spad" 2120268 2120279 2122731 2122736) (-1236 "TYPE.spad" 2120200 2120209 2120258 2120263) (-1235 "TYPEAST.spad" 2120119 2120128 2120190 2120195) (-1234 "TWOFACT.spad" 2118771 2118786 2120109 2120114) (-1233 "TUPLE.spad" 2118257 2118268 2118670 2118675) (-1232 "TUBETOOL.spad" 2115124 2115133 2118247 2118252) (-1231 "TUBE.spad" 2113771 2113788 2115114 2115119) (-1230 "TS.spad" 2112370 2112386 2113336 2113433) (-1229 "TSETCAT.spad" 2099497 2099514 2112338 2112365) (-1228 "TSETCAT.spad" 2086610 2086629 2099453 2099458) (-1227 "TRMANIP.spad" 2080976 2080993 2086316 2086321) (-1226 "TRIMAT.spad" 2079939 2079964 2080966 2080971) (-1225 "TRIGMNIP.spad" 2078466 2078483 2079929 2079934) (-1224 "TRIGCAT.spad" 2077978 2077987 2078456 2078461) (-1223 "TRIGCAT.spad" 2077488 2077499 2077968 2077973) (-1222 "TREE.spad" 2075946 2075957 2076978 2077005) (-1221 "TRANFUN.spad" 2075785 2075794 2075936 2075941) (-1220 "TRANFUN.spad" 2075622 2075633 2075775 2075780) (-1219 "TOPSP.spad" 2075296 2075305 2075612 2075617) (-1218 "TOOLSIGN.spad" 2074959 2074970 2075286 2075291) (-1217 "TEXTFILE.spad" 2073520 2073529 2074949 2074954) (-1216 "TEX.spad" 2070666 2070675 2073510 2073515) (-1215 "TEX1.spad" 2070222 2070233 2070656 2070661) (-1214 "TEMUTL.spad" 2069777 2069786 2070212 2070217) (-1213 "TBCMPPK.spad" 2067870 2067893 2069767 2069772) (-1212 "TBAGG.spad" 2066920 2066943 2067850 2067865) (-1211 "TBAGG.spad" 2065978 2066003 2066910 2066915) (-1210 "TANEXP.spad" 2065386 2065397 2065968 2065973) (-1209 "TALGOP.spad" 2065110 2065121 2065376 2065381) (-1208 "TABLE.spad" 2063079 2063102 2063349 2063376) (-1207 "TABLEAU.spad" 2062560 2062571 2063069 2063074) (-1206 "TABLBUMP.spad" 2059363 2059374 2062550 2062555) (-1205 "SYSTEM.spad" 2058591 2058600 2059353 2059358) (-1204 "SYSSOLP.spad" 2056074 2056085 2058581 2058586) (-1203 "SYSPTR.spad" 2055973 2055982 2056064 2056069) (-1202 "SYSNNI.spad" 2055155 2055166 2055963 2055968) (-1201 "SYSINT.spad" 2054559 2054570 2055145 2055150) (-1200 "SYNTAX.spad" 2050765 2050774 2054549 2054554) (-1199 "SYMTAB.spad" 2048833 2048842 2050755 2050760) (-1198 "SYMS.spad" 2044856 2044865 2048823 2048828) (-1197 "SYMPOLY.spad" 2043863 2043874 2043945 2044072) (-1196 "SYMFUNC.spad" 2043364 2043375 2043853 2043858) (-1195 "SYMBOL.spad" 2040867 2040876 2043354 2043359) (-1194 "SWITCH.spad" 2037638 2037647 2040857 2040862) (-1193 "SUTS.spad" 2034686 2034714 2036105 2036202) (-1192 "SUPXS.spad" 2031969 2031997 2032818 2032967) (-1191 "SUP.spad" 2028689 2028700 2029462 2029615) (-1190 "SUPFRACF.spad" 2027794 2027812 2028679 2028684) (-1189 "SUP2.spad" 2027186 2027199 2027784 2027789) (-1188 "SUMRF.spad" 2026160 2026171 2027176 2027181) (-1187 "SUMFS.spad" 2025797 2025814 2026150 2026155) (-1186 "SULS.spad" 2015568 2015596 2016526 2016955) (-1185 "SUCHTAST.spad" 2015337 2015346 2015558 2015563) (-1184 "SUCH.spad" 2015019 2015034 2015327 2015332) (-1183 "SUBSPACE.spad" 2007134 2007149 2015009 2015014) (-1182 "SUBRESP.spad" 2006304 2006318 2007090 2007095) (-1181 "STTF.spad" 2002403 2002419 2006294 2006299) (-1180 "STTFNC.spad" 1998871 1998887 2002393 2002398) (-1179 "STTAYLOR.spad" 1991506 1991517 1998752 1998757) (-1178 "STRTBL.spad" 1989557 1989574 1989706 1989733) (-1177 "STRING.spad" 1988344 1988353 1988565 1988592) (-1176 "STREAM.spad" 1985145 1985156 1987752 1987767) (-1175 "STREAM3.spad" 1984718 1984733 1985135 1985140) (-1174 "STREAM2.spad" 1983846 1983859 1984708 1984713) (-1173 "STREAM1.spad" 1983552 1983563 1983836 1983841) (-1172 "STINPROD.spad" 1982488 1982504 1983542 1983547) (-1171 "STEP.spad" 1981689 1981698 1982478 1982483) (-1170 "STEPAST.spad" 1980923 1980932 1981679 1981684) (-1169 "STBL.spad" 1979007 1979035 1979174 1979189) (-1168 "STAGG.spad" 1978082 1978093 1978997 1979002) (-1167 "STAGG.spad" 1977155 1977168 1978072 1978077) (-1166 "STACK.spad" 1976395 1976406 1976645 1976672) (-1165 "SREGSET.spad" 1974063 1974080 1976005 1976032) (-1164 "SRDCMPK.spad" 1972624 1972644 1974053 1974058) (-1163 "SRAGG.spad" 1967767 1967776 1972592 1972619) (-1162 "SRAGG.spad" 1962930 1962941 1967757 1967762) (-1161 "SQMATRIX.spad" 1960473 1960491 1961389 1961476) (-1160 "SPLTREE.spad" 1954869 1954882 1959753 1959780) (-1159 "SPLNODE.spad" 1951457 1951470 1954859 1954864) (-1158 "SPFCAT.spad" 1950266 1950275 1951447 1951452) (-1157 "SPECOUT.spad" 1948818 1948827 1950256 1950261) (-1156 "SPADXPT.spad" 1940413 1940422 1948808 1948813) (-1155 "spad-parser.spad" 1939878 1939887 1940403 1940408) (-1154 "SPADAST.spad" 1939579 1939588 1939868 1939873) (-1153 "SPACEC.spad" 1923778 1923789 1939569 1939574) (-1152 "SPACE3.spad" 1923554 1923565 1923768 1923773) (-1151 "SORTPAK.spad" 1923103 1923116 1923510 1923515) (-1150 "SOLVETRA.spad" 1920866 1920877 1923093 1923098) (-1149 "SOLVESER.spad" 1919394 1919405 1920856 1920861) (-1148 "SOLVERAD.spad" 1915420 1915431 1919384 1919389) (-1147 "SOLVEFOR.spad" 1913882 1913900 1915410 1915415) (-1146 "SNTSCAT.spad" 1913482 1913499 1913850 1913877) (-1145 "SMTS.spad" 1911754 1911780 1913047 1913144) (-1144 "SMP.spad" 1909229 1909249 1909619 1909746) (-1143 "SMITH.spad" 1908074 1908099 1909219 1909224) (-1142 "SMATCAT.spad" 1906184 1906214 1908018 1908069) (-1141 "SMATCAT.spad" 1904226 1904258 1906062 1906067) (-1140 "SKAGG.spad" 1903189 1903200 1904194 1904221) (-1139 "SINT.spad" 1902129 1902138 1903055 1903184) (-1138 "SIMPAN.spad" 1901857 1901866 1902119 1902124) (-1137 "SIG.spad" 1901187 1901196 1901847 1901852) (-1136 "SIGNRF.spad" 1900305 1900316 1901177 1901182) (-1135 "SIGNEF.spad" 1899584 1899601 1900295 1900300) (-1134 "SIGAST.spad" 1898969 1898978 1899574 1899579) (-1133 "SHP.spad" 1896897 1896912 1898925 1898930) (-1132 "SHDP.spad" 1884575 1884602 1885084 1885183) (-1131 "SGROUP.spad" 1884183 1884192 1884565 1884570) (-1130 "SGROUP.spad" 1883789 1883800 1884173 1884178) (-1129 "SGCF.spad" 1876928 1876937 1883779 1883784) (-1128 "SFRTCAT.spad" 1875858 1875875 1876896 1876923) (-1127 "SFRGCD.spad" 1874921 1874941 1875848 1875853) (-1126 "SFQCMPK.spad" 1869558 1869578 1874911 1874916) (-1125 "SFORT.spad" 1868997 1869011 1869548 1869553) (-1124 "SEXOF.spad" 1868840 1868880 1868987 1868992) (-1123 "SEX.spad" 1868732 1868741 1868830 1868835) (-1122 "SEXCAT.spad" 1866504 1866544 1868722 1868727) (-1121 "SET.spad" 1864792 1864803 1865889 1865928) (-1120 "SETMN.spad" 1863242 1863259 1864782 1864787) (-1119 "SETCAT.spad" 1862564 1862573 1863232 1863237) (-1118 "SETCAT.spad" 1861884 1861895 1862554 1862559) (-1117 "SETAGG.spad" 1858433 1858444 1861864 1861879) (-1116 "SETAGG.spad" 1854990 1855003 1858423 1858428) (-1115 "SEQAST.spad" 1854693 1854702 1854980 1854985) (-1114 "SEGXCAT.spad" 1853849 1853862 1854683 1854688) (-1113 "SEG.spad" 1853662 1853673 1853768 1853773) (-1112 "SEGCAT.spad" 1852587 1852598 1853652 1853657) (-1111 "SEGBIND.spad" 1852345 1852356 1852534 1852539) (-1110 "SEGBIND2.spad" 1852043 1852056 1852335 1852340) (-1109 "SEGAST.spad" 1851757 1851766 1852033 1852038) (-1108 "SEG2.spad" 1851192 1851205 1851713 1851718) (-1107 "SDVAR.spad" 1850468 1850479 1851182 1851187) (-1106 "SDPOL.spad" 1847801 1847812 1848092 1848219) (-1105 "SCPKG.spad" 1845890 1845901 1847791 1847796) (-1104 "SCOPE.spad" 1845043 1845052 1845880 1845885) (-1103 "SCACHE.spad" 1843739 1843750 1845033 1845038) (-1102 "SASTCAT.spad" 1843648 1843657 1843729 1843734) (-1101 "SAOS.spad" 1843520 1843529 1843638 1843643) (-1100 "SAERFFC.spad" 1843233 1843253 1843510 1843515) (-1099 "SAE.spad" 1840703 1840719 1841314 1841449) (-1098 "SAEFACT.spad" 1840404 1840424 1840693 1840698) (-1097 "RURPK.spad" 1838063 1838079 1840394 1840399) (-1096 "RULESET.spad" 1837516 1837540 1838053 1838058) (-1095 "RULE.spad" 1835756 1835780 1837506 1837511) (-1094 "RULECOLD.spad" 1835608 1835621 1835746 1835751) (-1093 "RTVALUE.spad" 1835343 1835352 1835598 1835603) (-1092 "RSTRCAST.spad" 1835060 1835069 1835333 1835338) (-1091 "RSETGCD.spad" 1831438 1831458 1835050 1835055) (-1090 "RSETCAT.spad" 1821374 1821391 1831406 1831433) (-1089 "RSETCAT.spad" 1811330 1811349 1821364 1821369) (-1088 "RSDCMPK.spad" 1809782 1809802 1811320 1811325) (-1087 "RRCC.spad" 1808166 1808196 1809772 1809777) (-1086 "RRCC.spad" 1806548 1806580 1808156 1808161) (-1085 "RPTAST.spad" 1806250 1806259 1806538 1806543) (-1084 "RPOLCAT.spad" 1785610 1785625 1806118 1806245) (-1083 "RPOLCAT.spad" 1764683 1764700 1785193 1785198) (-1082 "ROUTINE.spad" 1760104 1760113 1762868 1762895) (-1081 "ROMAN.spad" 1759432 1759441 1759970 1760099) (-1080 "ROIRC.spad" 1758512 1758544 1759422 1759427) (-1079 "RNS.spad" 1757415 1757424 1758414 1758507) (-1078 "RNS.spad" 1756404 1756415 1757405 1757410) (-1077 "RNG.spad" 1756139 1756148 1756394 1756399) (-1076 "RNGBIND.spad" 1755299 1755313 1756094 1756099) (-1075 "RMODULE.spad" 1755064 1755075 1755289 1755294) (-1074 "RMCAT2.spad" 1754484 1754541 1755054 1755059) (-1073 "RMATRIX.spad" 1753272 1753291 1753615 1753654) (-1072 "RMATCAT.spad" 1748851 1748882 1753228 1753267) (-1071 "RMATCAT.spad" 1744320 1744353 1748699 1748704) (-1070 "RLINSET.spad" 1744024 1744035 1744310 1744315) (-1069 "RINTERP.spad" 1743912 1743932 1744014 1744019) (-1068 "RING.spad" 1743382 1743391 1743892 1743907) (-1067 "RING.spad" 1742860 1742871 1743372 1743377) (-1066 "RIDIST.spad" 1742252 1742261 1742850 1742855) (-1065 "RGCHAIN.spad" 1740780 1740796 1741682 1741709) (-1064 "RGBCSPC.spad" 1740561 1740573 1740770 1740775) (-1063 "RGBCMDL.spad" 1740091 1740103 1740551 1740556) (-1062 "RF.spad" 1737733 1737744 1740081 1740086) (-1061 "RFFACTOR.spad" 1737195 1737206 1737723 1737728) (-1060 "RFFACT.spad" 1736930 1736942 1737185 1737190) (-1059 "RFDIST.spad" 1735926 1735935 1736920 1736925) (-1058 "RETSOL.spad" 1735345 1735358 1735916 1735921) (-1057 "RETRACT.spad" 1734773 1734784 1735335 1735340) (-1056 "RETRACT.spad" 1734199 1734212 1734763 1734768) (-1055 "RETAST.spad" 1734011 1734020 1734189 1734194) (-1054 "RESULT.spad" 1731609 1731618 1732196 1732223) (-1053 "RESRING.spad" 1730956 1731003 1731547 1731604) (-1052 "RESLATC.spad" 1730280 1730291 1730946 1730951) (-1051 "REPSQ.spad" 1730011 1730022 1730270 1730275) (-1050 "REP.spad" 1727565 1727574 1730001 1730006) (-1049 "REPDB.spad" 1727272 1727283 1727555 1727560) (-1048 "REP2.spad" 1716930 1716941 1727114 1727119) (-1047 "REP1.spad" 1711126 1711137 1716880 1716885) (-1046 "REGSET.spad" 1708887 1708904 1710736 1710763) (-1045 "REF.spad" 1708222 1708233 1708842 1708847) (-1044 "REDORDER.spad" 1707428 1707445 1708212 1708217) (-1043 "RECLOS.spad" 1706211 1706231 1706915 1707008) (-1042 "REALSOLV.spad" 1705351 1705360 1706201 1706206) (-1041 "REAL.spad" 1705223 1705232 1705341 1705346) (-1040 "REAL0Q.spad" 1702521 1702536 1705213 1705218) (-1039 "REAL0.spad" 1699365 1699380 1702511 1702516) (-1038 "RDUCEAST.spad" 1699086 1699095 1699355 1699360) (-1037 "RDIV.spad" 1698741 1698766 1699076 1699081) (-1036 "RDIST.spad" 1698308 1698319 1698731 1698736) (-1035 "RDETRS.spad" 1697172 1697190 1698298 1698303) (-1034 "RDETR.spad" 1695311 1695329 1697162 1697167) (-1033 "RDEEFS.spad" 1694410 1694427 1695301 1695306) (-1032 "RDEEF.spad" 1693420 1693437 1694400 1694405) (-1031 "RCFIELD.spad" 1690606 1690615 1693322 1693415) (-1030 "RCFIELD.spad" 1687878 1687889 1690596 1690601) (-1029 "RCAGG.spad" 1685806 1685817 1687868 1687873) (-1028 "RCAGG.spad" 1683661 1683674 1685725 1685730) (-1027 "RATRET.spad" 1683021 1683032 1683651 1683656) (-1026 "RATFACT.spad" 1682713 1682725 1683011 1683016) (-1025 "RANDSRC.spad" 1682032 1682041 1682703 1682708) (-1024 "RADUTIL.spad" 1681788 1681797 1682022 1682027) (-1023 "RADIX.spad" 1678612 1678626 1680158 1680251) (-1022 "RADFF.spad" 1676351 1676388 1676470 1676626) (-1021 "RADCAT.spad" 1675946 1675955 1676341 1676346) (-1020 "RADCAT.spad" 1675539 1675550 1675936 1675941) (-1019 "QUEUE.spad" 1674770 1674781 1675029 1675056) (-1018 "QUAT.spad" 1673258 1673269 1673601 1673666) (-1017 "QUATCT2.spad" 1672878 1672897 1673248 1673253) (-1016 "QUATCAT.spad" 1671048 1671059 1672808 1672873) (-1015 "QUATCAT.spad" 1668969 1668982 1670731 1670736) (-1014 "QUAGG.spad" 1667796 1667807 1668937 1668964) (-1013 "QQUTAST.spad" 1667564 1667573 1667786 1667791) (-1012 "QFORM.spad" 1667182 1667197 1667554 1667559) (-1011 "QFCAT.spad" 1665884 1665895 1667084 1667177) (-1010 "QFCAT.spad" 1664177 1664190 1665379 1665384) (-1009 "QFCAT2.spad" 1663869 1663886 1664167 1664172) (-1008 "QEQUAT.spad" 1663427 1663436 1663859 1663864) (-1007 "QCMPACK.spad" 1658173 1658193 1663417 1663422) (-1006 "QALGSET.spad" 1654251 1654284 1658087 1658092) (-1005 "QALGSET2.spad" 1652246 1652265 1654241 1654246) (-1004 "PWFFINTB.spad" 1649661 1649683 1652236 1652241) (-1003 "PUSHVAR.spad" 1648999 1649019 1649651 1649656) (-1002 "PTRANFN.spad" 1645126 1645137 1648989 1648994) (-1001 "PTPACK.spad" 1642213 1642224 1645116 1645121) (-1000 "PTFUNC2.spad" 1642035 1642050 1642203 1642208) (-999 "PTCAT.spad" 1641290 1641300 1642003 1642030) (-998 "PSQFR.spad" 1640597 1640621 1641280 1641285) (-997 "PSEUDLIN.spad" 1639483 1639493 1640587 1640592) (-996 "PSETPK.spad" 1624916 1624932 1639361 1639366) (-995 "PSETCAT.spad" 1618836 1618859 1624896 1624911) (-994 "PSETCAT.spad" 1612730 1612755 1618792 1618797) (-993 "PSCURVE.spad" 1611713 1611721 1612720 1612725) (-992 "PSCAT.spad" 1610496 1610525 1611611 1611708) (-991 "PSCAT.spad" 1609369 1609400 1610486 1610491) (-990 "PRTITION.spad" 1608067 1608075 1609359 1609364) (-989 "PRTDAST.spad" 1607786 1607794 1608057 1608062) (-988 "PRS.spad" 1597348 1597365 1607742 1607747) (-987 "PRQAGG.spad" 1596783 1596793 1597316 1597343) (-986 "PROPLOG.spad" 1596355 1596363 1596773 1596778) (-985 "PROPFUN2.spad" 1595978 1595991 1596345 1596350) (-984 "PROPFUN1.spad" 1595376 1595387 1595968 1595973) (-983 "PROPFRML.spad" 1593944 1593955 1595366 1595371) (-982 "PROPERTY.spad" 1593432 1593440 1593934 1593939) (-981 "PRODUCT.spad" 1591114 1591126 1591398 1591453) (-980 "PR.spad" 1589506 1589518 1590205 1590332) (-979 "PRINT.spad" 1589258 1589266 1589496 1589501) (-978 "PRIMES.spad" 1587511 1587521 1589248 1589253) (-977 "PRIMELT.spad" 1585592 1585606 1587501 1587506) (-976 "PRIMCAT.spad" 1585219 1585227 1585582 1585587) (-975 "PRIMARR.spad" 1584071 1584081 1584249 1584276) (-974 "PRIMARR2.spad" 1582838 1582850 1584061 1584066) (-973 "PREASSOC.spad" 1582220 1582232 1582828 1582833) (-972 "PPCURVE.spad" 1581357 1581365 1582210 1582215) (-971 "PORTNUM.spad" 1581132 1581140 1581347 1581352) (-970 "POLYROOT.spad" 1579981 1580003 1581088 1581093) (-969 "POLY.spad" 1577316 1577326 1577831 1577958) (-968 "POLYLIFT.spad" 1576581 1576604 1577306 1577311) (-967 "POLYCATQ.spad" 1574699 1574721 1576571 1576576) (-966 "POLYCAT.spad" 1568169 1568190 1574567 1574694) (-965 "POLYCAT.spad" 1560977 1561000 1567377 1567382) (-964 "POLY2UP.spad" 1560429 1560443 1560967 1560972) (-963 "POLY2.spad" 1560026 1560038 1560419 1560424) (-962 "POLUTIL.spad" 1558967 1558996 1559982 1559987) (-961 "POLTOPOL.spad" 1557715 1557730 1558957 1558962) (-960 "POINT.spad" 1556400 1556410 1556487 1556514) (-959 "PNTHEORY.spad" 1553102 1553110 1556390 1556395) (-958 "PMTOOLS.spad" 1551877 1551891 1553092 1553097) (-957 "PMSYM.spad" 1551426 1551436 1551867 1551872) (-956 "PMQFCAT.spad" 1551017 1551031 1551416 1551421) (-955 "PMPRED.spad" 1550496 1550510 1551007 1551012) (-954 "PMPREDFS.spad" 1549950 1549972 1550486 1550491) (-953 "PMPLCAT.spad" 1549030 1549048 1549882 1549887) (-952 "PMLSAGG.spad" 1548615 1548629 1549020 1549025) (-951 "PMKERNEL.spad" 1548194 1548206 1548605 1548610) (-950 "PMINS.spad" 1547774 1547784 1548184 1548189) (-949 "PMFS.spad" 1547351 1547369 1547764 1547769) (-948 "PMDOWN.spad" 1546641 1546655 1547341 1547346) (-947 "PMASS.spad" 1545651 1545659 1546631 1546636) (-946 "PMASSFS.spad" 1544618 1544634 1545641 1545646) (-945 "PLOTTOOL.spad" 1544398 1544406 1544608 1544613) (-944 "PLOT.spad" 1539321 1539329 1544388 1544393) (-943 "PLOT3D.spad" 1535785 1535793 1539311 1539316) (-942 "PLOT1.spad" 1534942 1534952 1535775 1535780) (-941 "PLEQN.spad" 1522232 1522259 1534932 1534937) (-940 "PINTERP.spad" 1521854 1521873 1522222 1522227) (-939 "PINTERPA.spad" 1521638 1521654 1521844 1521849) (-938 "PI.spad" 1521247 1521255 1521612 1521633) (-937 "PID.spad" 1520217 1520225 1521173 1521242) (-936 "PICOERCE.spad" 1519874 1519884 1520207 1520212) (-935 "PGROEB.spad" 1518475 1518489 1519864 1519869) (-934 "PGE.spad" 1510092 1510100 1518465 1518470) (-933 "PGCD.spad" 1508982 1508999 1510082 1510087) (-932 "PFRPAC.spad" 1508131 1508141 1508972 1508977) (-931 "PFR.spad" 1504794 1504804 1508033 1508126) (-930 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520502) (-342 "FCPAK1.spad" 518082 518090 519505 519510) (-341 "FCOMP.spad" 517461 517471 518072 518077) (-340 "FC.spad" 507468 507476 517451 517456) (-339 "FAXF.spad" 500439 500453 507370 507463) (-338 "FAXF.spad" 493462 493478 500395 500400) (-337 "FARRAY.spad" 491459 491469 492492 492519) (-336 "FAMR.spad" 489595 489607 491357 491454) (-335 "FAMR.spad" 487715 487729 489479 489484) (-334 "FAMONOID.spad" 487383 487393 487669 487674) (-333 "FAMONC.spad" 485679 485691 487373 487378) (-332 "FAGROUP.spad" 485303 485313 485575 485602) (-331 "FACUTIL.spad" 483507 483524 485293 485298) (-330 "FACTFUNC.spad" 482701 482711 483497 483502) (-329 "EXPUPXS.spad" 479534 479557 480833 480982) (-328 "EXPRTUBE.spad" 476822 476830 479524 479529) (-327 "EXPRODE.spad" 473982 473998 476812 476817) (-326 "EXPR.spad" 469157 469167 469871 470166) (-325 "EXPR2UPS.spad" 465279 465292 469147 469152) (-324 "EXPR2.spad" 464984 464996 465269 465274) (-323 "EXPEXPAN.spad" 461785 461810 462417 462510) (-322 "EXIT.spad" 461456 461464 461775 461780) (-321 "EXITAST.spad" 461192 461200 461446 461451) (-320 "EVALCYC.spad" 460652 460666 461182 461187) (-319 "EVALAB.spad" 460224 460234 460642 460647) (-318 "EVALAB.spad" 459794 459806 460214 460219) (-317 "EUCDOM.spad" 457368 457376 459720 459789) (-316 "EUCDOM.spad" 455004 455014 457358 457363) (-315 "ESTOOLS.spad" 446850 446858 454994 454999) (-314 "ESTOOLS2.spad" 446453 446467 446840 446845) (-313 "ESTOOLS1.spad" 446138 446149 446443 446448) (-312 "ES.spad" 438953 438961 446128 446133) (-311 "ES.spad" 431674 431684 438851 438856) (-310 "ESCONT.spad" 428467 428475 431664 431669) (-309 "ESCONT1.spad" 428216 428228 428457 428462) (-308 "ES2.spad" 427721 427737 428206 428211) (-307 "ES1.spad" 427291 427307 427711 427716) (-306 "ERROR.spad" 424618 424626 427281 427286) (-305 "EQTBL.spad" 422648 422670 422857 422884) (-304 "EQ.spad" 417453 417463 420240 420352) (-303 "EQ2.spad" 417171 417183 417443 417448) (-302 "EP.spad" 413497 413507 417161 417166) (-301 "ENV.spad" 412175 412183 413487 413492) (-300 "ENTIRER.spad" 411843 411851 412119 412170) (-299 "EMR.spad" 411131 411172 411769 411838) (-298 "ELTAGG.spad" 409385 409404 411121 411126) (-297 "ELTAGG.spad" 407603 407624 409341 409346) (-296 "ELTAB.spad" 407078 407091 407593 407598) (-295 "ELFUTS.spad" 406465 406484 407068 407073) (-294 "ELEMFUN.spad" 406154 406162 406455 406460) (-293 "ELEMFUN.spad" 405841 405851 406144 406149) (-292 "ELAGG.spad" 403812 403822 405821 405836) (-291 "ELAGG.spad" 401720 401732 403731 403736) (-290 "ELABOR.spad" 401066 401074 401710 401715) (-289 "ELABEXPR.spad" 399998 400006 401056 401061) (-288 "EFUPXS.spad" 396774 396804 399954 399959) (-287 "EFULS.spad" 393610 393633 396730 396735) (-286 "EFSTRUC.spad" 391625 391641 393600 393605) (-285 "EF.spad" 386401 386417 391615 391620) (-284 "EAB.spad" 384677 384685 386391 386396) (-283 "E04UCFA.spad" 384213 384221 384667 384672) (-282 "E04NAFA.spad" 383790 383798 384203 384208) (-281 "E04MBFA.spad" 383370 383378 383780 383785) (-280 "E04JAFA.spad" 382906 382914 383360 383365) (-279 "E04GCFA.spad" 382442 382450 382896 382901) (-278 "E04FDFA.spad" 381978 381986 382432 382437) (-277 "E04DGFA.spad" 381514 381522 381968 381973) (-276 "E04AGNT.spad" 377364 377372 381504 381509) (-275 "DVARCAT.spad" 374254 374264 377354 377359) (-274 "DVARCAT.spad" 371142 371154 374244 374249) (-273 "DSMP.spad" 368516 368530 368821 368948) (-272 "DSEXT.spad" 367818 367828 368506 368511) (-271 "DSEXT.spad" 367027 367039 367717 367722) (-270 "DROPT.spad" 360986 360994 367017 367022) (-269 "DROPT1.spad" 360651 360661 360976 360981) (-268 "DROPT0.spad" 355508 355516 360641 360646) (-267 "DRAWPT.spad" 353681 353689 355498 355503) (-266 "DRAW.spad" 346557 346570 353671 353676) (-265 "DRAWHACK.spad" 345865 345875 346547 346552) (-264 "DRAWCX.spad" 343335 343343 345855 345860) (-263 "DRAWCURV.spad" 342882 342897 343325 343330) (-262 "DRAWCFUN.spad" 332414 332422 342872 342877) (-261 "DQAGG.spad" 330592 330602 332382 332409) (-260 "DPOLCAT.spad" 325941 325957 330460 330587) (-259 "DPOLCAT.spad" 321376 321394 325897 325902) (-258 "DPMO.spad" 313136 313152 313274 313487) (-257 "DPMM.spad" 304909 304927 305034 305247) (-256 "DOMTMPLT.spad" 304680 304688 304899 304904) (-255 "DOMCTOR.spad" 304435 304443 304670 304675) (-254 "DOMAIN.spad" 303522 303530 304425 304430) (-253 "DMP.spad" 300782 300797 301352 301479) (-252 "DMEXT.spad" 300649 300659 300750 300777) (-251 "DLP.spad" 300001 300011 300639 300644) (-250 "DLIST.spad" 298427 298437 299031 299058) (-249 "DLAGG.spad" 296844 296854 298417 298422) (-248 "DIVRING.spad" 296386 296394 296788 296839) (-247 "DIVRING.spad" 295972 295982 296376 296381) (-246 "DISPLAY.spad" 294162 294170 295962 295967) (-245 "DIRPROD.spad" 281709 281725 282349 282448) (-244 "DIRPROD2.spad" 280527 280545 281699 281704) (-243 "DIRPCAT.spad" 279720 279736 280423 280522) (-242 "DIRPCAT.spad" 278540 278558 279245 279250) (-241 "DIOSP.spad" 277365 277373 278530 278535) (-240 "DIOPS.spad" 276361 276371 277345 277360) (-239 "DIOPS.spad" 275331 275343 276317 276322) (-238 "DIFRING.spad" 275169 275177 275311 275326) (-237 "DIFFSPC.spad" 274748 274756 275159 275164) (-236 "DIFFSPC.spad" 274325 274335 274738 274743) (-235 "DIFFMOD.spad" 273814 273824 274293 274320) (-234 "DIFFDOM.spad" 272979 272990 273804 273809) (-233 "DIFFDOM.spad" 272142 272155 272969 272974) (-232 "DIFEXT.spad" 271961 271971 272122 272137) (-231 "DIAGG.spad" 271591 271601 271941 271956) (-230 "DIAGG.spad" 271229 271241 271581 271586) (-229 "DHMATRIX.spad" 269424 269434 270569 270596) (-228 "DFSFUN.spad" 263064 263072 269414 269419) (-227 "DFLOAT.spad" 259795 259803 262954 263059) (-226 "DFINTTLS.spad" 258026 258042 259785 259790) (-225 "DERHAM.spad" 255940 255972 258006 258021) (-224 "DEQUEUE.spad" 255147 255157 255430 255457) (-223 "DEGRED.spad" 254764 254778 255137 255142) (-222 "DEFINTRF.spad" 252301 252311 254754 254759) (-221 "DEFINTEF.spad" 250811 250827 252291 252296) (-220 "DEFAST.spad" 250179 250187 250801 250806) (-219 "DECIMAL.spad" 248188 248196 248549 248642) (-218 "DDFACT.spad" 246001 246018 248178 248183) (-217 "DBLRESP.spad" 245601 245625 245991 245996) (-216 "DBASE.spad" 244265 244275 245591 245596) (-215 "DATAARY.spad" 243727 243740 244255 244260) (-214 "D03FAFA.spad" 243555 243563 243717 243722) (-213 "D03EEFA.spad" 243375 243383 243545 243550) (-212 "D03AGNT.spad" 242461 242469 243365 243370) (-211 "D02EJFA.spad" 241923 241931 242451 242456) (-210 "D02CJFA.spad" 241401 241409 241913 241918) (-209 "D02BHFA.spad" 240891 240899 241391 241396) (-208 "D02BBFA.spad" 240381 240389 240881 240886) (-207 "D02AGNT.spad" 235195 235203 240371 240376) (-206 "D01WGTS.spad" 233514 233522 235185 235190) (-205 "D01TRNS.spad" 233491 233499 233504 233509) (-204 "D01GBFA.spad" 233013 233021 233481 233486) (-203 "D01FCFA.spad" 232535 232543 233003 233008) (-202 "D01ASFA.spad" 232003 232011 232525 232530) (-201 "D01AQFA.spad" 231449 231457 231993 231998) (-200 "D01APFA.spad" 230873 230881 231439 231444) (-199 "D01ANFA.spad" 230367 230375 230863 230868) (-198 "D01AMFA.spad" 229877 229885 230357 230362) (-197 "D01ALFA.spad" 229417 229425 229867 229872) (-196 "D01AKFA.spad" 228943 228951 229407 229412) (-195 "D01AJFA.spad" 228466 228474 228933 228938) (-194 "D01AGNT.spad" 224533 224541 228456 228461) (-193 "CYCLOTOM.spad" 224039 224047 224523 224528) (-192 "CYCLES.spad" 220831 220839 224029 224034) (-191 "CVMP.spad" 220248 220258 220821 220826) (-190 "CTRIGMNP.spad" 218748 218764 220238 220243) (-189 "CTOR.spad" 218439 218447 218738 218743) (-188 "CTORKIND.spad" 218042 218050 218429 218434) (-187 "CTORCAT.spad" 217291 217299 218032 218037) (-186 "CTORCAT.spad" 216538 216548 217281 217286) (-185 "CTORCALL.spad" 216127 216137 216528 216533) (-184 "CSTTOOLS.spad" 215372 215385 216117 216122) (-183 "CRFP.spad" 209096 209109 215362 215367) (-182 "CRCEAST.spad" 208816 208824 209086 209091) (-181 "CRAPACK.spad" 207867 207877 208806 208811) (-180 "CPMATCH.spad" 207371 207386 207792 207797) (-179 "CPIMA.spad" 207076 207095 207361 207366) (-178 "COORDSYS.spad" 202085 202095 207066 207071) (-177 "CONTOUR.spad" 201496 201504 202075 202080) (-176 "CONTFRAC.spad" 197246 197256 201398 201491) (-175 "CONDUIT.spad" 197004 197012 197236 197241) (-174 "COMRING.spad" 196678 196686 196942 196999) (-173 "COMPPROP.spad" 196196 196204 196668 196673) (-172 "COMPLPAT.spad" 195963 195978 196186 196191) (-171 "COMPLEX.spad" 191340 191350 191584 191845) (-170 "COMPLEX2.spad" 191055 191067 191330 191335) (-169 "COMPILER.spad" 190604 190612 191045 191050) (-168 "COMPFACT.spad" 190206 190220 190594 190599) (-167 "COMPCAT.spad" 188278 188288 189940 190201) (-166 "COMPCAT.spad" 186078 186090 187742 187747) (-165 "COMMUPC.spad" 185826 185844 186068 186073) (-164 "COMMONOP.spad" 185359 185367 185816 185821) (-163 "COMM.spad" 185170 185178 185349 185354) (-162 "COMMAAST.spad" 184933 184941 185160 185165) (-161 "COMBOPC.spad" 183848 183856 184923 184928) (-160 "COMBINAT.spad" 182615 182625 183838 183843) (-159 "COMBF.spad" 179997 180013 182605 182610) (-158 "COLOR.spad" 178834 178842 179987 179992) (-157 "COLONAST.spad" 178500 178508 178824 178829) (-156 "CMPLXRT.spad" 178211 178228 178490 178495) (-155 "CLLCTAST.spad" 177873 177881 178201 178206) (-154 "CLIP.spad" 173981 173989 177863 177868) (-153 "CLIF.spad" 172636 172652 173937 173976) (-152 "CLAGG.spad" 169141 169151 172626 172631) (-151 "CLAGG.spad" 165517 165529 169004 169009) (-150 "CINTSLPE.spad" 164848 164861 165507 165512) (-149 "CHVAR.spad" 162986 163008 164838 164843) (-148 "CHARZ.spad" 162901 162909 162966 162981) (-147 "CHARPOL.spad" 162411 162421 162891 162896) (-146 "CHARNZ.spad" 162164 162172 162391 162406) (-145 "CHAR.spad" 160038 160046 162154 162159) (-144 "CFCAT.spad" 159366 159374 160028 160033) (-143 "CDEN.spad" 158562 158576 159356 159361) (-142 "CCLASS.spad" 156673 156681 157935 157974) (-141 "CATEGORY.spad" 155715 155723 156663 156668) (-140 "CATCTOR.spad" 155606 155614 155705 155710) (-139 "CATAST.spad" 155224 155232 155596 155601) (-138 "CASEAST.spad" 154938 154946 155214 155219) (-137 "CARTEN.spad" 150305 150329 154928 154933) (-136 "CARTEN2.spad" 149695 149722 150295 150300) (-135 "CARD.spad" 146990 146998 149669 149690) (-134 "CAPSLAST.spad" 146764 146772 146980 146985) (-133 "CACHSET.spad" 146388 146396 146754 146759) (-132 "CABMON.spad" 145943 145951 146378 146383) (-131 "BYTEORD.spad" 145618 145626 145933 145938) (-130 "BYTE.spad" 145045 145053 145608 145613) (-129 "BYTEBUF.spad" 142743 142751 144053 144080) (-128 "BTREE.spad" 141699 141709 142233 142260) (-127 "BTOURN.spad" 140587 140597 141189 141216) (-126 "BTCAT.spad" 139979 139989 140555 140582) (-125 "BTCAT.spad" 139391 139403 139969 139974) (-124 "BTAGG.spad" 138857 138865 139359 139386) (-123 "BTAGG.spad" 138343 138353 138847 138852) (-122 "BSTREE.spad" 136967 136977 137833 137860) (-121 "BRILL.spad" 135164 135175 136957 136962) (-120 "BRAGG.spad" 134104 134114 135154 135159) (-119 "BRAGG.spad" 133008 133020 134060 134065) (-118 "BPADICRT.spad" 130882 130894 131137 131230) (-117 "BPADIC.spad" 130546 130558 130808 130877) (-116 "BOUNDZRO.spad" 130202 130219 130536 130541) (-115 "BOP.spad" 125384 125392 130192 130197) (-114 "BOP1.spad" 122850 122860 125374 125379) (-113 "BOOLE.spad" 122500 122508 122840 122845) (-112 "BOOLEAN.spad" 121938 121946 122490 122495) (-111 "BMODULE.spad" 121650 121662 121906 121933) (-110 "BITS.spad" 121033 121041 121248 121275) (-109 "BINDING.spad" 120446 120454 121023 121028) (-108 "BINARY.spad" 118460 118468 118816 118909) (-107 "BGAGG.spad" 117665 117675 118440 118455) (-106 "BGAGG.spad" 116878 116890 117655 117660) (-105 "BFUNCT.spad" 116442 116450 116858 116873) (-104 "BEZOUT.spad" 115582 115609 116392 116397) (-103 "BBTREE.spad" 112310 112320 115072 115099) (-102 "BASTYPE.spad" 111982 111990 112300 112305) (-101 "BASTYPE.spad" 111652 111662 111972 111977) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2294456 2294461 2294466 2294471) (-2 NIL 2294436 2294441 2294446 2294451) (-1 NIL 2294416 2294421 2294426 2294431) (0 NIL 2294396 2294401 2294406 2294411) (-1317 "ZMOD.spad" 2294205 2294218 2294334 2294391) (-1316 "ZLINDEP.spad" 2293271 2293282 2294195 2294200) (-1315 "ZDSOLVE.spad" 2283216 2283238 2293261 2293266) (-1314 "YSTREAM.spad" 2282711 2282722 2283206 2283211) (-1313 "YDIAGRAM.spad" 2282345 2282354 2282701 2282706) (-1312 "XRPOLY.spad" 2281565 2281585 2282201 2282270) (-1311 "XPR.spad" 2279360 2279373 2281283 2281382) (-1310 "XPOLY.spad" 2278915 2278926 2279216 2279285) (-1309 "XPOLYC.spad" 2278234 2278250 2278841 2278910) (-1308 "XPBWPOLY.spad" 2276671 2276691 2278014 2278083) (-1307 "XF.spad" 2275134 2275149 2276573 2276666) (-1306 "XF.spad" 2273577 2273594 2275018 2275023) (-1305 "XFALG.spad" 2270625 2270641 2273503 2273572) (-1304 "XEXPPKG.spad" 2269876 2269902 2270615 2270620) (-1303 "XDPOLY.spad" 2269490 2269506 2269732 2269801) (-1302 "XALG.spad" 2269150 2269161 2269446 2269485) (-1301 "WUTSET.spad" 2264953 2264970 2268760 2268787) (-1300 "WP.spad" 2264152 2264196 2264811 2264878) (-1299 "WHILEAST.spad" 2263950 2263959 2264142 2264147) (-1298 "WHEREAST.spad" 2263621 2263630 2263940 2263945) (-1297 "WFFINTBS.spad" 2261284 2261306 2263611 2263616) (-1296 "WEIER.spad" 2259506 2259517 2261274 2261279) (-1295 "VSPACE.spad" 2259179 2259190 2259474 2259501) (-1294 "VSPACE.spad" 2258872 2258885 2259169 2259174) (-1293 "VOID.spad" 2258549 2258558 2258862 2258867) (-1292 "VIEW.spad" 2256229 2256238 2258539 2258544) (-1291 "VIEWDEF.spad" 2251430 2251439 2256219 2256224) (-1290 "VIEW3D.spad" 2235391 2235400 2251420 2251425) (-1289 "VIEW2D.spad" 2223282 2223291 2235381 2235386) (-1288 "VECTOR.spad" 2221803 2221814 2222054 2222081) (-1287 "VECTOR2.spad" 2220442 2220455 2221793 2221798) (-1286 "VECTCAT.spad" 2218346 2218357 2220410 2220437) (-1285 "VECTCAT.spad" 2216057 2216070 2218123 2218128) (-1284 "VARIABLE.spad" 2215837 2215852 2216047 2216052) (-1283 "UTYPE.spad" 2215481 2215490 2215827 2215832) (-1282 "UTSODETL.spad" 2214776 2214800 2215437 2215442) (-1281 "UTSODE.spad" 2212992 2213012 2214766 2214771) (-1280 "UTS.spad" 2207939 2207967 2211459 2211556) (-1279 "UTSCAT.spad" 2205418 2205434 2207837 2207934) (-1278 "UTSCAT.spad" 2202541 2202559 2204962 2204967) (-1277 "UTS2.spad" 2202136 2202171 2202531 2202536) (-1276 "URAGG.spad" 2196809 2196820 2202126 2202131) (-1275 "URAGG.spad" 2191446 2191459 2196765 2196770) (-1274 "UPXSSING.spad" 2189091 2189117 2190527 2190660) (-1273 "UPXS.spad" 2186387 2186415 2187223 2187372) (-1272 "UPXSCONS.spad" 2184146 2184166 2184519 2184668) (-1271 "UPXSCCA.spad" 2182717 2182737 2183992 2184141) (-1270 "UPXSCCA.spad" 2181430 2181452 2182707 2182712) (-1269 "UPXSCAT.spad" 2180019 2180035 2181276 2181425) (-1268 "UPXS2.spad" 2179562 2179615 2180009 2180014) (-1267 "UPSQFREE.spad" 2177976 2177990 2179552 2179557) (-1266 "UPSCAT.spad" 2175763 2175787 2177874 2177971) (-1265 "UPSCAT.spad" 2173256 2173282 2175369 2175374) (-1264 "UPOLYC.spad" 2168296 2168307 2173098 2173251) (-1263 "UPOLYC.spad" 2163228 2163241 2168032 2168037) (-1262 "UPOLYC2.spad" 2162699 2162718 2163218 2163223) (-1261 "UP.spad" 2159805 2159820 2160192 2160345) (-1260 "UPMP.spad" 2158705 2158718 2159795 2159800) (-1259 "UPDIVP.spad" 2158270 2158284 2158695 2158700) (-1258 "UPDECOMP.spad" 2156515 2156529 2158260 2158265) (-1257 "UPCDEN.spad" 2155724 2155740 2156505 2156510) (-1256 "UP2.spad" 2155088 2155109 2155714 2155719) (-1255 "UNISEG.spad" 2154441 2154452 2155007 2155012) (-1254 "UNISEG2.spad" 2153938 2153951 2154397 2154402) (-1253 "UNIFACT.spad" 2153041 2153053 2153928 2153933) (-1252 "ULS.spad" 2142825 2142853 2143770 2144199) (-1251 "ULSCONS.spad" 2133959 2133979 2134329 2134478) (-1250 "ULSCCAT.spad" 2131696 2131716 2133805 2133954) (-1249 "ULSCCAT.spad" 2129541 2129563 2131652 2131657) (-1248 "ULSCAT.spad" 2127773 2127789 2129387 2129536) (-1247 "ULS2.spad" 2127287 2127340 2127763 2127768) (-1246 "UINT8.spad" 2127164 2127173 2127277 2127282) (-1245 "UINT64.spad" 2127040 2127049 2127154 2127159) (-1244 "UINT32.spad" 2126916 2126925 2127030 2127035) (-1243 "UINT16.spad" 2126792 2126801 2126906 2126911) (-1242 "UFD.spad" 2125857 2125866 2126718 2126787) (-1241 "UFD.spad" 2124984 2124995 2125847 2125852) (-1240 "UDVO.spad" 2123865 2123874 2124974 2124979) (-1239 "UDPO.spad" 2121358 2121369 2123821 2123826) (-1238 "TYPE.spad" 2121290 2121299 2121348 2121353) (-1237 "TYPEAST.spad" 2121209 2121218 2121280 2121285) (-1236 "TWOFACT.spad" 2119861 2119876 2121199 2121204) (-1235 "TUPLE.spad" 2119347 2119358 2119760 2119765) (-1234 "TUBETOOL.spad" 2116214 2116223 2119337 2119342) (-1233 "TUBE.spad" 2114861 2114878 2116204 2116209) (-1232 "TS.spad" 2113460 2113476 2114426 2114523) (-1231 "TSETCAT.spad" 2100587 2100604 2113428 2113455) (-1230 "TSETCAT.spad" 2087700 2087719 2100543 2100548) (-1229 "TRMANIP.spad" 2082066 2082083 2087406 2087411) (-1228 "TRIMAT.spad" 2081029 2081054 2082056 2082061) (-1227 "TRIGMNIP.spad" 2079556 2079573 2081019 2081024) (-1226 "TRIGCAT.spad" 2079068 2079077 2079546 2079551) (-1225 "TRIGCAT.spad" 2078578 2078589 2079058 2079063) (-1224 "TREE.spad" 2077036 2077047 2078068 2078095) (-1223 "TRANFUN.spad" 2076875 2076884 2077026 2077031) (-1222 "TRANFUN.spad" 2076712 2076723 2076865 2076870) (-1221 "TOPSP.spad" 2076386 2076395 2076702 2076707) (-1220 "TOOLSIGN.spad" 2076049 2076060 2076376 2076381) (-1219 "TEXTFILE.spad" 2074610 2074619 2076039 2076044) (-1218 "TEX.spad" 2071756 2071765 2074600 2074605) (-1217 "TEX1.spad" 2071312 2071323 2071746 2071751) (-1216 "TEMUTL.spad" 2070867 2070876 2071302 2071307) (-1215 "TBCMPPK.spad" 2068960 2068983 2070857 2070862) (-1214 "TBAGG.spad" 2068010 2068033 2068940 2068955) (-1213 "TBAGG.spad" 2067068 2067093 2068000 2068005) (-1212 "TANEXP.spad" 2066476 2066487 2067058 2067063) (-1211 "TALGOP.spad" 2066200 2066211 2066466 2066471) (-1210 "TABLE.spad" 2064169 2064192 2064439 2064466) (-1209 "TABLEAU.spad" 2063650 2063661 2064159 2064164) (-1208 "TABLBUMP.spad" 2060453 2060464 2063640 2063645) (-1207 "SYSTEM.spad" 2059681 2059690 2060443 2060448) (-1206 "SYSSOLP.spad" 2057164 2057175 2059671 2059676) (-1205 "SYSPTR.spad" 2057063 2057072 2057154 2057159) (-1204 "SYSNNI.spad" 2056245 2056256 2057053 2057058) (-1203 "SYSINT.spad" 2055649 2055660 2056235 2056240) (-1202 "SYNTAX.spad" 2051855 2051864 2055639 2055644) (-1201 "SYMTAB.spad" 2049923 2049932 2051845 2051850) (-1200 "SYMS.spad" 2045946 2045955 2049913 2049918) (-1199 "SYMPOLY.spad" 2044953 2044964 2045035 2045162) (-1198 "SYMFUNC.spad" 2044454 2044465 2044943 2044948) (-1197 "SYMBOL.spad" 2041957 2041966 2044444 2044449) (-1196 "SWITCH.spad" 2038728 2038737 2041947 2041952) (-1195 "SUTS.spad" 2035776 2035804 2037195 2037292) (-1194 "SUPXS.spad" 2033059 2033087 2033908 2034057) (-1193 "SUP.spad" 2029779 2029790 2030552 2030705) (-1192 "SUPFRACF.spad" 2028884 2028902 2029769 2029774) (-1191 "SUP2.spad" 2028276 2028289 2028874 2028879) (-1190 "SUMRF.spad" 2027250 2027261 2028266 2028271) (-1189 "SUMFS.spad" 2026887 2026904 2027240 2027245) (-1188 "SULS.spad" 2016658 2016686 2017616 2018045) (-1187 "SUCHTAST.spad" 2016427 2016436 2016648 2016653) (-1186 "SUCH.spad" 2016109 2016124 2016417 2016422) (-1185 "SUBSPACE.spad" 2008224 2008239 2016099 2016104) (-1184 "SUBRESP.spad" 2007394 2007408 2008180 2008185) (-1183 "STTF.spad" 2003493 2003509 2007384 2007389) (-1182 "STTFNC.spad" 1999961 1999977 2003483 2003488) (-1181 "STTAYLOR.spad" 1992596 1992607 1999842 1999847) (-1180 "STRTBL.spad" 1990647 1990664 1990796 1990823) (-1179 "STRING.spad" 1989434 1989443 1989655 1989682) (-1178 "STREAM.spad" 1986235 1986246 1988842 1988857) (-1177 "STREAM3.spad" 1985808 1985823 1986225 1986230) (-1176 "STREAM2.spad" 1984936 1984949 1985798 1985803) (-1175 "STREAM1.spad" 1984642 1984653 1984926 1984931) (-1174 "STINPROD.spad" 1983578 1983594 1984632 1984637) (-1173 "STEP.spad" 1982779 1982788 1983568 1983573) (-1172 "STEPAST.spad" 1982013 1982022 1982769 1982774) (-1171 "STBL.spad" 1980097 1980125 1980264 1980279) (-1170 "STAGG.spad" 1979172 1979183 1980087 1980092) (-1169 "STAGG.spad" 1978245 1978258 1979162 1979167) (-1168 "STACK.spad" 1977485 1977496 1977735 1977762) (-1167 "SREGSET.spad" 1975153 1975170 1977095 1977122) (-1166 "SRDCMPK.spad" 1973714 1973734 1975143 1975148) (-1165 "SRAGG.spad" 1968857 1968866 1973682 1973709) (-1164 "SRAGG.spad" 1964020 1964031 1968847 1968852) (-1163 "SQMATRIX.spad" 1961563 1961581 1962479 1962566) (-1162 "SPLTREE.spad" 1955959 1955972 1960843 1960870) (-1161 "SPLNODE.spad" 1952547 1952560 1955949 1955954) (-1160 "SPFCAT.spad" 1951356 1951365 1952537 1952542) (-1159 "SPECOUT.spad" 1949908 1949917 1951346 1951351) (-1158 "SPADXPT.spad" 1941503 1941512 1949898 1949903) (-1157 "spad-parser.spad" 1940968 1940977 1941493 1941498) (-1156 "SPADAST.spad" 1940669 1940678 1940958 1940963) (-1155 "SPACEC.spad" 1924868 1924879 1940659 1940664) (-1154 "SPACE3.spad" 1924644 1924655 1924858 1924863) (-1153 "SORTPAK.spad" 1924193 1924206 1924600 1924605) (-1152 "SOLVETRA.spad" 1921956 1921967 1924183 1924188) (-1151 "SOLVESER.spad" 1920484 1920495 1921946 1921951) (-1150 "SOLVERAD.spad" 1916510 1916521 1920474 1920479) (-1149 "SOLVEFOR.spad" 1914972 1914990 1916500 1916505) (-1148 "SNTSCAT.spad" 1914572 1914589 1914940 1914967) (-1147 "SMTS.spad" 1912844 1912870 1914137 1914234) (-1146 "SMP.spad" 1910319 1910339 1910709 1910836) (-1145 "SMITH.spad" 1909164 1909189 1910309 1910314) (-1144 "SMATCAT.spad" 1907274 1907304 1909108 1909159) (-1143 "SMATCAT.spad" 1905316 1905348 1907152 1907157) (-1142 "SKAGG.spad" 1904279 1904290 1905284 1905311) (-1141 "SINT.spad" 1903219 1903228 1904145 1904274) (-1140 "SIMPAN.spad" 1902947 1902956 1903209 1903214) (-1139 "SIG.spad" 1902277 1902286 1902937 1902942) (-1138 "SIGNRF.spad" 1901395 1901406 1902267 1902272) (-1137 "SIGNEF.spad" 1900674 1900691 1901385 1901390) (-1136 "SIGAST.spad" 1900059 1900068 1900664 1900669) (-1135 "SHP.spad" 1897987 1898002 1900015 1900020) (-1134 "SHDP.spad" 1885665 1885692 1886174 1886273) (-1133 "SGROUP.spad" 1885273 1885282 1885655 1885660) (-1132 "SGROUP.spad" 1884879 1884890 1885263 1885268) (-1131 "SGCF.spad" 1878018 1878027 1884869 1884874) (-1130 "SFRTCAT.spad" 1876948 1876965 1877986 1878013) (-1129 "SFRGCD.spad" 1876011 1876031 1876938 1876943) (-1128 "SFQCMPK.spad" 1870648 1870668 1876001 1876006) (-1127 "SFORT.spad" 1870087 1870101 1870638 1870643) (-1126 "SEXOF.spad" 1869930 1869970 1870077 1870082) (-1125 "SEX.spad" 1869822 1869831 1869920 1869925) (-1124 "SEXCAT.spad" 1867594 1867634 1869812 1869817) (-1123 "SET.spad" 1865882 1865893 1866979 1867018) (-1122 "SETMN.spad" 1864332 1864349 1865872 1865877) (-1121 "SETCAT.spad" 1863654 1863663 1864322 1864327) (-1120 "SETCAT.spad" 1862974 1862985 1863644 1863649) (-1119 "SETAGG.spad" 1859523 1859534 1862954 1862969) (-1118 "SETAGG.spad" 1856080 1856093 1859513 1859518) (-1117 "SEQAST.spad" 1855783 1855792 1856070 1856075) (-1116 "SEGXCAT.spad" 1854939 1854952 1855773 1855778) (-1115 "SEG.spad" 1854752 1854763 1854858 1854863) (-1114 "SEGCAT.spad" 1853677 1853688 1854742 1854747) (-1113 "SEGBIND.spad" 1853435 1853446 1853624 1853629) (-1112 "SEGBIND2.spad" 1853133 1853146 1853425 1853430) (-1111 "SEGAST.spad" 1852847 1852856 1853123 1853128) (-1110 "SEG2.spad" 1852282 1852295 1852803 1852808) (-1109 "SDVAR.spad" 1851558 1851569 1852272 1852277) (-1108 "SDPOL.spad" 1848891 1848902 1849182 1849309) (-1107 "SCPKG.spad" 1846980 1846991 1848881 1848886) (-1106 "SCOPE.spad" 1846133 1846142 1846970 1846975) (-1105 "SCACHE.spad" 1844829 1844840 1846123 1846128) (-1104 "SASTCAT.spad" 1844738 1844747 1844819 1844824) (-1103 "SAOS.spad" 1844610 1844619 1844728 1844733) (-1102 "SAERFFC.spad" 1844323 1844343 1844600 1844605) (-1101 "SAE.spad" 1841793 1841809 1842404 1842539) (-1100 "SAEFACT.spad" 1841494 1841514 1841783 1841788) (-1099 "RURPK.spad" 1839153 1839169 1841484 1841489) (-1098 "RULESET.spad" 1838606 1838630 1839143 1839148) (-1097 "RULE.spad" 1836846 1836870 1838596 1838601) (-1096 "RULECOLD.spad" 1836698 1836711 1836836 1836841) (-1095 "RTVALUE.spad" 1836433 1836442 1836688 1836693) (-1094 "RSTRCAST.spad" 1836150 1836159 1836423 1836428) (-1093 "RSETGCD.spad" 1832528 1832548 1836140 1836145) (-1092 "RSETCAT.spad" 1822464 1822481 1832496 1832523) (-1091 "RSETCAT.spad" 1812420 1812439 1822454 1822459) (-1090 "RSDCMPK.spad" 1810872 1810892 1812410 1812415) (-1089 "RRCC.spad" 1809256 1809286 1810862 1810867) (-1088 "RRCC.spad" 1807638 1807670 1809246 1809251) (-1087 "RPTAST.spad" 1807340 1807349 1807628 1807633) (-1086 "RPOLCAT.spad" 1786700 1786715 1807208 1807335) (-1085 "RPOLCAT.spad" 1765773 1765790 1786283 1786288) (-1084 "ROUTINE.spad" 1761194 1761203 1763958 1763985) (-1083 "ROMAN.spad" 1760522 1760531 1761060 1761189) (-1082 "ROIRC.spad" 1759602 1759634 1760512 1760517) (-1081 "RNS.spad" 1758505 1758514 1759504 1759597) (-1080 "RNS.spad" 1757494 1757505 1758495 1758500) (-1079 "RNG.spad" 1757229 1757238 1757484 1757489) (-1078 "RNGBIND.spad" 1756389 1756403 1757184 1757189) (-1077 "RMODULE.spad" 1756154 1756165 1756379 1756384) (-1076 "RMCAT2.spad" 1755574 1755631 1756144 1756149) (-1075 "RMATRIX.spad" 1754362 1754381 1754705 1754744) (-1074 "RMATCAT.spad" 1749941 1749972 1754318 1754357) (-1073 "RMATCAT.spad" 1745410 1745443 1749789 1749794) (-1072 "RLINSET.spad" 1745114 1745125 1745400 1745405) (-1071 "RINTERP.spad" 1745002 1745022 1745104 1745109) (-1070 "RING.spad" 1744472 1744481 1744982 1744997) (-1069 "RING.spad" 1743950 1743961 1744462 1744467) (-1068 "RIDIST.spad" 1743342 1743351 1743940 1743945) (-1067 "RGCHAIN.spad" 1741870 1741886 1742772 1742799) (-1066 "RGBCSPC.spad" 1741651 1741663 1741860 1741865) (-1065 "RGBCMDL.spad" 1741181 1741193 1741641 1741646) (-1064 "RF.spad" 1738823 1738834 1741171 1741176) (-1063 "RFFACTOR.spad" 1738285 1738296 1738813 1738818) (-1062 "RFFACT.spad" 1738020 1738032 1738275 1738280) (-1061 "RFDIST.spad" 1737016 1737025 1738010 1738015) (-1060 "RETSOL.spad" 1736435 1736448 1737006 1737011) (-1059 "RETRACT.spad" 1735863 1735874 1736425 1736430) (-1058 "RETRACT.spad" 1735289 1735302 1735853 1735858) (-1057 "RETAST.spad" 1735101 1735110 1735279 1735284) (-1056 "RESULT.spad" 1732699 1732708 1733286 1733313) (-1055 "RESRING.spad" 1732046 1732093 1732637 1732694) (-1054 "RESLATC.spad" 1731370 1731381 1732036 1732041) (-1053 "REPSQ.spad" 1731101 1731112 1731360 1731365) (-1052 "REP.spad" 1728655 1728664 1731091 1731096) (-1051 "REPDB.spad" 1728362 1728373 1728645 1728650) (-1050 "REP2.spad" 1718020 1718031 1728204 1728209) (-1049 "REP1.spad" 1712216 1712227 1717970 1717975) (-1048 "REGSET.spad" 1709977 1709994 1711826 1711853) (-1047 "REF.spad" 1709312 1709323 1709932 1709937) (-1046 "REDORDER.spad" 1708518 1708535 1709302 1709307) (-1045 "RECLOS.spad" 1707301 1707321 1708005 1708098) (-1044 "REALSOLV.spad" 1706441 1706450 1707291 1707296) (-1043 "REAL.spad" 1706313 1706322 1706431 1706436) (-1042 "REAL0Q.spad" 1703611 1703626 1706303 1706308) (-1041 "REAL0.spad" 1700455 1700470 1703601 1703606) (-1040 "RDUCEAST.spad" 1700176 1700185 1700445 1700450) (-1039 "RDIV.spad" 1699831 1699856 1700166 1700171) (-1038 "RDIST.spad" 1699398 1699409 1699821 1699826) (-1037 "RDETRS.spad" 1698262 1698280 1699388 1699393) (-1036 "RDETR.spad" 1696401 1696419 1698252 1698257) (-1035 "RDEEFS.spad" 1695500 1695517 1696391 1696396) (-1034 "RDEEF.spad" 1694510 1694527 1695490 1695495) (-1033 "RCFIELD.spad" 1691696 1691705 1694412 1694505) (-1032 "RCFIELD.spad" 1688968 1688979 1691686 1691691) (-1031 "RCAGG.spad" 1686896 1686907 1688958 1688963) (-1030 "RCAGG.spad" 1684751 1684764 1686815 1686820) (-1029 "RATRET.spad" 1684111 1684122 1684741 1684746) (-1028 "RATFACT.spad" 1683803 1683815 1684101 1684106) (-1027 "RANDSRC.spad" 1683122 1683131 1683793 1683798) (-1026 "RADUTIL.spad" 1682878 1682887 1683112 1683117) (-1025 "RADIX.spad" 1679702 1679716 1681248 1681341) (-1024 "RADFF.spad" 1677441 1677478 1677560 1677716) (-1023 "RADCAT.spad" 1677036 1677045 1677431 1677436) (-1022 "RADCAT.spad" 1676629 1676640 1677026 1677031) (-1021 "QUEUE.spad" 1675860 1675871 1676119 1676146) (-1020 "QUAT.spad" 1674348 1674359 1674691 1674756) (-1019 "QUATCT2.spad" 1673968 1673987 1674338 1674343) (-1018 "QUATCAT.spad" 1672138 1672149 1673898 1673963) (-1017 "QUATCAT.spad" 1670059 1670072 1671821 1671826) (-1016 "QUAGG.spad" 1668886 1668897 1670027 1670054) (-1015 "QQUTAST.spad" 1668654 1668663 1668876 1668881) (-1014 "QFORM.spad" 1668272 1668287 1668644 1668649) (-1013 "QFCAT.spad" 1666974 1666985 1668174 1668267) (-1012 "QFCAT.spad" 1665267 1665280 1666469 1666474) (-1011 "QFCAT2.spad" 1664959 1664976 1665257 1665262) (-1010 "QEQUAT.spad" 1664517 1664526 1664949 1664954) (-1009 "QCMPACK.spad" 1659263 1659283 1664507 1664512) (-1008 "QALGSET.spad" 1655341 1655374 1659177 1659182) (-1007 "QALGSET2.spad" 1653336 1653355 1655331 1655336) (-1006 "PWFFINTB.spad" 1650751 1650773 1653326 1653331) (-1005 "PUSHVAR.spad" 1650089 1650109 1650741 1650746) (-1004 "PTRANFN.spad" 1646216 1646227 1650079 1650084) (-1003 "PTPACK.spad" 1643303 1643314 1646206 1646211) (-1002 "PTFUNC2.spad" 1643125 1643140 1643293 1643298) (-1001 "PTCAT.spad" 1642379 1642390 1643093 1643120) (-1000 "PSQFR.spad" 1641685 1641710 1642369 1642374) (-999 "PSEUDLIN.spad" 1640571 1640581 1641675 1641680) (-998 "PSETPK.spad" 1626004 1626020 1640449 1640454) (-997 "PSETCAT.spad" 1619924 1619947 1625984 1625999) (-996 "PSETCAT.spad" 1613818 1613843 1619880 1619885) (-995 "PSCURVE.spad" 1612801 1612809 1613808 1613813) (-994 "PSCAT.spad" 1611584 1611613 1612699 1612796) (-993 "PSCAT.spad" 1610457 1610488 1611574 1611579) (-992 "PRTITION.spad" 1609155 1609163 1610447 1610452) (-991 "PRTDAST.spad" 1608874 1608882 1609145 1609150) (-990 "PRS.spad" 1598436 1598453 1608830 1608835) (-989 "PRQAGG.spad" 1597871 1597881 1598404 1598431) (-988 "PROPLOG.spad" 1597443 1597451 1597861 1597866) (-987 "PROPFUN2.spad" 1597066 1597079 1597433 1597438) (-986 "PROPFUN1.spad" 1596464 1596475 1597056 1597061) (-985 "PROPFRML.spad" 1595032 1595043 1596454 1596459) (-984 "PROPERTY.spad" 1594520 1594528 1595022 1595027) (-983 "PRODUCT.spad" 1592202 1592214 1592486 1592541) (-982 "PR.spad" 1590594 1590606 1591293 1591420) (-981 "PRINT.spad" 1590346 1590354 1590584 1590589) (-980 "PRIMES.spad" 1588599 1588609 1590336 1590341) (-979 "PRIMELT.spad" 1586680 1586694 1588589 1588594) (-978 "PRIMCAT.spad" 1586307 1586315 1586670 1586675) (-977 "PRIMARR.spad" 1585159 1585169 1585337 1585364) (-976 "PRIMARR2.spad" 1583926 1583938 1585149 1585154) (-975 "PREASSOC.spad" 1583308 1583320 1583916 1583921) (-974 "PPCURVE.spad" 1582445 1582453 1583298 1583303) (-973 "PORTNUM.spad" 1582220 1582228 1582435 1582440) (-972 "POLYROOT.spad" 1581069 1581091 1582176 1582181) (-971 "POLY.spad" 1578404 1578414 1578919 1579046) (-970 "POLYLIFT.spad" 1577669 1577692 1578394 1578399) (-969 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1072329 1072334) (-687 "M3D.spad" 1069521 1069531 1071179 1071184) (-686 "LZSTAGG.spad" 1066759 1066769 1069511 1069516) (-685 "LZSTAGG.spad" 1063995 1064007 1066749 1066754) (-684 "LWORD.spad" 1060700 1060717 1063985 1063990) (-683 "LSTAST.spad" 1060484 1060492 1060690 1060695) (-682 "LSQM.spad" 1058641 1058655 1059035 1059086) (-681 "LSPP.spad" 1058176 1058193 1058631 1058636) (-680 "LSMP.spad" 1057026 1057054 1058166 1058171) (-679 "LSMP1.spad" 1054844 1054858 1057016 1057021) (-678 "LSAGG.spad" 1054513 1054523 1054812 1054839) (-677 "LSAGG.spad" 1054202 1054214 1054503 1054508) (-676 "LPOLY.spad" 1053156 1053175 1054058 1054127) (-675 "LPEFRAC.spad" 1052427 1052437 1053146 1053151) (-674 "LO.spad" 1051828 1051842 1052361 1052388) (-673 "LOGIC.spad" 1051430 1051438 1051818 1051823) (-672 "LOGIC.spad" 1051030 1051040 1051420 1051425) (-671 "LODOOPS.spad" 1049960 1049972 1051020 1051025) (-670 "LODO.spad" 1049344 1049360 1049640 1049679) (-669 "LODOF.spad" 1048390 1048407 1049301 1049306) (-668 "LODOCAT.spad" 1047056 1047066 1048346 1048385) (-667 "LODOCAT.spad" 1045720 1045732 1047012 1047017) (-666 "LODO2.spad" 1044993 1045005 1045400 1045439) (-665 "LODO1.spad" 1044393 1044403 1044673 1044712) (-664 "LODEEF.spad" 1043195 1043213 1044383 1044388) (-663 "LNAGG.spad" 1039342 1039352 1043185 1043190) (-662 "LNAGG.spad" 1035453 1035465 1039298 1039303) (-661 "LMOPS.spad" 1032221 1032238 1035443 1035448) (-660 "LMODULE.spad" 1031989 1031999 1032211 1032216) (-659 "LMDICT.spad" 1031159 1031169 1031423 1031450) (-658 "LLINSET.spad" 1030866 1030876 1031149 1031154) (-657 "LITERAL.spad" 1030772 1030783 1030856 1030861) (-656 "LIST.spad" 1028354 1028364 1029766 1029793) (-655 "LIST3.spad" 1027665 1027679 1028344 1028349) (-654 "LIST2.spad" 1026367 1026379 1027655 1027660) (-653 "LIST2MAP.spad" 1023270 1023282 1026357 1026362) (-652 "LINSET.spad" 1023049 1023059 1023260 1023265) (-651 "LINEXP.spad" 1021792 1021802 1023039 1023044) (-650 "LINDEP.spad" 1020601 1020613 1021704 1021709) (-649 "LIMITRF.spad" 1018529 1018539 1020591 1020596) (-648 "LIMITPS.spad" 1017432 1017445 1018519 1018524) (-647 "LIE.spad" 1015448 1015460 1016722 1016867) (-646 "LIECAT.spad" 1014924 1014934 1015374 1015443) (-645 "LIECAT.spad" 1014428 1014440 1014880 1014885) (-644 "LIB.spad" 1012179 1012187 1012625 1012640) (-643 "LGROBP.spad" 1009532 1009551 1012169 1012174) (-642 "LF.spad" 1008487 1008503 1009522 1009527) (-641 "LFCAT.spad" 1007546 1007554 1008477 1008482) (-640 "LEXTRIPK.spad" 1003049 1003064 1007536 1007541) (-639 "LEXP.spad" 1001052 1001079 1003029 1003044) (-638 "LETAST.spad" 1000751 1000759 1001042 1001047) (-637 "LEADCDET.spad" 999149 999166 1000741 1000746) (-636 "LAZM3PK.spad" 997853 997875 999139 999144) (-635 "LAUPOL.spad" 996453 996466 997353 997422) (-634 "LAPLACE.spad" 996036 996052 996443 996448) (-633 "LA.spad" 995476 995490 995958 995997) (-632 "LALG.spad" 995252 995262 995456 995471) (-631 "LALG.spad" 995036 995048 995242 995247) (-630 "KVTFROM.spad" 994771 994781 995026 995031) (-629 "KTVLOGIC.spad" 994283 994291 994761 994766) (-628 "KRCFROM.spad" 994021 994031 994273 994278) (-627 "KOVACIC.spad" 992744 992761 994011 994016) (-626 "KONVERT.spad" 992466 992476 992734 992739) (-625 "KOERCE.spad" 992203 992213 992456 992461) (-624 "KERNEL.spad" 990858 990868 991987 991992) (-623 "KERNEL2.spad" 990561 990573 990848 990853) (-622 "KDAGG.spad" 989670 989692 990541 990556) (-621 "KDAGG.spad" 988787 988811 989660 989665) (-620 "KAFILE.spad" 987641 987657 987876 987903) (-619 "JORDAN.spad" 985470 985482 986931 987076) (-618 "JOINAST.spad" 985164 985172 985460 985465) (-617 "JAVACODE.spad" 985030 985038 985154 985159) (-616 "IXAGG.spad" 983163 983187 985020 985025) (-615 "IXAGG.spad" 981151 981177 983010 983015) (-614 "IVECTOR.spad" 979768 979783 979923 979950) (-613 "ITUPLE.spad" 978929 978939 979758 979763) (-612 "ITRIGMNP.spad" 977768 977787 978919 978924) (-611 "ITFUN3.spad" 977274 977288 977758 977763) (-610 "ITFUN2.spad" 977018 977030 977264 977269) (-609 "ITFORM.spad" 976373 976381 977008 977013) (-608 "ITAYLOR.spad" 974367 974382 976237 976334) (-607 "ISUPS.spad" 966804 966819 973341 973438) (-606 "ISUMP.spad" 966305 966321 966794 966799) (-605 "ISTRING.spad" 965232 965245 965313 965340) (-604 "ISAST.spad" 964951 964959 965222 965227) (-603 "IRURPK.spad" 963668 963687 964941 964946) (-602 "IRSN.spad" 961640 961648 963658 963663) (-601 "IRRF2F.spad" 960125 960135 961596 961601) (-600 "IRREDFFX.spad" 959726 959737 960115 960120) (-599 "IROOT.spad" 958065 958075 959716 959721) (-598 "IR.spad" 955866 955880 957920 957947) (-597 "IRFORM.spad" 955190 955198 955856 955861) (-596 "IR2.spad" 954218 954234 955180 955185) (-595 "IR2F.spad" 953424 953440 954208 954213) (-594 "IPRNTPK.spad" 953184 953192 953414 953419) (-593 "IPF.spad" 952749 952761 952989 953082) (-592 "IPADIC.spad" 952510 952536 952675 952744) (-591 "IP4ADDR.spad" 952067 952075 952500 952505) (-590 "IOMODE.spad" 951589 951597 952057 952062) (-589 "IOBFILE.spad" 950950 950958 951579 951584) (-588 "IOBCON.spad" 950815 950823 950940 950945) (-587 "INVLAPLA.spad" 950464 950480 950805 950810) (-586 "INTTR.spad" 943846 943863 950454 950459) (-585 "INTTOOLS.spad" 941601 941617 943420 943425) (-584 "INTSLPE.spad" 940921 940929 941591 941596) (-583 "INTRVL.spad" 940487 940497 940835 940916) (-582 "INTRF.spad" 938911 938925 940477 940482) (-581 "INTRET.spad" 938343 938353 938901 938906) (-580 "INTRAT.spad" 937070 937087 938333 938338) (-579 "INTPM.spad" 935455 935471 936713 936718) (-578 "INTPAF.spad" 933319 933337 935387 935392) (-577 "INTPACK.spad" 923693 923701 933309 933314) (-576 "INT.spad" 923141 923149 923547 923688) (-575 "INTHERTR.spad" 922415 922432 923131 923136) (-574 "INTHERAL.spad" 922085 922109 922405 922410) (-573 "INTHEORY.spad" 918524 918532 922075 922080) (-572 "INTG0.spad" 912257 912275 918456 918461) (-571 "INTFTBL.spad" 906286 906294 912247 912252) (-570 "INTFACT.spad" 905345 905355 906276 906281) (-569 "INTEF.spad" 903730 903746 905335 905340) (-568 "INTDOM.spad" 902353 902361 903656 903725) (-567 "INTDOM.spad" 901038 901048 902343 902348) (-566 "INTCAT.spad" 899297 899307 900952 901033) (-565 "INTBIT.spad" 898804 898812 899287 899292) (-564 "INTALG.spad" 897992 898019 898794 898799) (-563 "INTAF.spad" 897492 897508 897982 897987) (-562 "INTABL.spad" 895568 895599 895731 895758) (-561 "INT8.spad" 895448 895456 895558 895563) (-560 "INT64.spad" 895327 895335 895438 895443) (-559 "INT32.spad" 895206 895214 895317 895322) (-558 "INT16.spad" 895085 895093 895196 895201) (-557 "INS.spad" 892588 892596 894987 895080) (-556 "INS.spad" 890177 890187 892578 892583) (-555 "INPSIGN.spad" 889625 889638 890167 890172) (-554 "INPRODPF.spad" 888721 888740 889615 889620) (-553 "INPRODFF.spad" 887809 887833 888711 888716) (-552 "INNMFACT.spad" 886784 886801 887799 887804) (-551 "INMODGCD.spad" 886272 886302 886774 886779) (-550 "INFSP.spad" 884569 884591 886262 886267) (-549 "INFPROD0.spad" 883649 883668 884559 884564) (-548 "INFORM.spad" 880848 880856 883639 883644) (-547 "INFORM1.spad" 880473 880483 880838 880843) (-546 "INFINITY.spad" 880025 880033 880463 880468) (-545 "INETCLTS.spad" 880002 880010 880015 880020) (-544 "INEP.spad" 878540 878562 879992 879997) (-543 "INDE.spad" 878269 878286 878530 878535) (-542 "INCRMAPS.spad" 877690 877700 878259 878264) (-541 "INBFILE.spad" 876762 876770 877680 877685) (-540 "INBFF.spad" 872556 872567 876752 876757) (-539 "INBCON.spad" 870846 870854 872546 872551) (-538 "INBCON.spad" 869134 869144 870836 870841) (-537 "INAST.spad" 868795 868803 869124 869129) (-536 "IMPTAST.spad" 868503 868511 868785 868790) (-535 "IMATRIX.spad" 867331 867357 867843 867870) (-534 "IMATQF.spad" 866425 866469 867287 867292) (-533 "IMATLIN.spad" 865030 865054 866381 866386) (-532 "ILIST.spad" 863535 863550 864060 864087) (-531 "IIARRAY2.spad" 862806 862844 863025 863052) (-530 "IFF.spad" 862216 862232 862487 862580) (-529 "IFAST.spad" 861830 861838 862206 862211) (-528 "IFARRAY.spad" 859170 859185 860860 860887) (-527 "IFAMON.spad" 859032 859049 859126 859131) (-526 "IEVALAB.spad" 858437 858449 859022 859027) (-525 "IEVALAB.spad" 857840 857854 858427 858432) (-524 "IDPO.spad" 857653 857665 857830 857835) (-523 "IDPOAMS.spad" 857409 857421 857643 857648) (-522 "IDPOAM.spad" 857129 857141 857399 857404) (-521 "IDPC.spad" 855858 855870 857119 857124) (-520 "IDPAM.spad" 855603 855615 855848 855853) (-519 "IDPAG.spad" 855350 855362 855593 855598) (-518 "IDENT.spad" 855000 855008 855340 855345) (-517 "IDECOMP.spad" 852239 852257 854990 854995) (-516 "IDEAL.spad" 847188 847227 852174 852179) (-515 "ICDEN.spad" 846377 846393 847178 847183) (-514 "ICARD.spad" 845568 845576 846367 846372) (-513 "IBPTOOLS.spad" 844175 844192 845558 845563) (-512 "IBITS.spad" 843340 843353 843773 843800) (-511 "IBATOOL.spad" 840317 840336 843330 843335) (-510 "IBACHIN.spad" 838824 838839 840307 840312) (-509 "IARRAY2.spad" 837695 837721 838314 838341) (-508 "IARRAY1.spad" 836587 836602 836725 836752) (-507 "IAN.spad" 834810 834818 836403 836496) (-506 "IALGFACT.spad" 834413 834446 834800 834805) (-505 "HYPCAT.spad" 833837 833845 834403 834408) (-504 "HYPCAT.spad" 833259 833269 833827 833832) (-503 "HOSTNAME.spad" 833067 833075 833249 833254) (-502 "HOMOTOP.spad" 832810 832820 833057 833062) (-501 "HOAGG.spad" 830092 830102 832800 832805) (-500 "HOAGG.spad" 827113 827125 829823 829828) (-499 "HEXADEC.spad" 825118 825126 825483 825576) (-498 "HEUGCD.spad" 824153 824164 825108 825113) (-497 "HELLFDIV.spad" 823743 823767 824143 824148) (-496 "HEAP.spad" 823018 823028 823233 823260) (-495 "HEADAST.spad" 822551 822559 823008 823013) (-494 "HDP.spad" 810361 810377 810738 810837) (-493 "HDMP.spad" 807575 807590 808191 808318) (-492 "HB.spad" 805826 805834 807565 807570) (-491 "HASHTBL.spad" 803854 803885 804065 804092) (-490 "HASAST.spad" 803570 803578 803844 803849) (-489 "HACKPI.spad" 803061 803069 803472 803565) (-488 "GTSET.spad" 801964 801980 802671 802698) (-487 "GSTBL.spad" 800041 800076 800215 800230) (-486 "GSERIES.spad" 797354 797381 798173 798322) (-485 "GROUP.spad" 796627 796635 797334 797349) (-484 "GROUP.spad" 795908 795918 796617 796622) (-483 "GROEBSOL.spad" 794402 794423 795898 795903) (-482 "GRMOD.spad" 792973 792985 794392 794397) (-481 "GRMOD.spad" 791542 791556 792963 792968) (-480 "GRIMAGE.spad" 784431 784439 791532 791537) (-479 "GRDEF.spad" 782810 782818 784421 784426) (-478 "GRAY.spad" 781273 781281 782800 782805) (-477 "GRALG.spad" 780350 780362 781263 781268) (-476 "GRALG.spad" 779425 779439 780340 780345) (-475 "GPOLSET.spad" 778843 778866 779071 779098) (-474 "GOSPER.spad" 778112 778130 778833 778838) (-473 "GMODPOL.spad" 777260 777287 778080 778107) (-472 "GHENSEL.spad" 776343 776357 777250 777255) (-471 "GENUPS.spad" 772636 772649 776333 776338) (-470 "GENUFACT.spad" 772213 772223 772626 772631) (-469 "GENPGCD.spad" 771799 771816 772203 772208) (-468 "GENMFACT.spad" 771251 771270 771789 771794) (-467 "GENEEZ.spad" 769202 769215 771241 771246) (-466 "GDMP.spad" 766258 766275 767032 767159) (-465 "GCNAALG.spad" 760181 760208 766052 766119) (-464 "GCDDOM.spad" 759357 759365 760107 760176) (-463 "GCDDOM.spad" 758595 758605 759347 759352) (-462 "GB.spad" 756121 756159 758551 758556) (-461 "GBINTERN.spad" 752141 752179 756111 756116) (-460 "GBF.spad" 747908 747946 752131 752136) (-459 "GBEUCLID.spad" 745790 745828 747898 747903) (-458 "GAUSSFAC.spad" 745103 745111 745780 745785) (-457 "GALUTIL.spad" 743429 743439 745059 745064) (-456 "GALPOLYU.spad" 741883 741896 743419 743424) (-455 "GALFACTU.spad" 740056 740075 741873 741878) (-454 "GALFACT.spad" 730245 730256 740046 740051) (-453 "FVFUN.spad" 727268 727276 730235 730240) (-452 "FVC.spad" 726320 726328 727258 727263) (-451 "FUNDESC.spad" 725998 726006 726310 726315) (-450 "FUNCTION.spad" 725847 725859 725988 725993) (-449 "FT.spad" 724144 724152 725837 725842) (-448 "FTEM.spad" 723309 723317 724134 724139) (-447 "FSUPFACT.spad" 722209 722228 723245 723250) (-446 "FST.spad" 720295 720303 722199 722204) (-445 "FSRED.spad" 719775 719791 720285 720290) (-444 "FSPRMELT.spad" 718657 718673 719732 719737) (-443 "FSPECF.spad" 716748 716764 718647 718652) (-442 "FS.spad" 711016 711026 716523 716743) (-441 "FS.spad" 705062 705074 710571 710576) (-440 "FSINT.spad" 704722 704738 705052 705057) (-439 "FSERIES.spad" 703913 703925 704542 704641) (-438 "FSCINT.spad" 703230 703246 703903 703908) (-437 "FSAGG.spad" 702347 702357 703186 703225) (-436 "FSAGG.spad" 701426 701438 702267 702272) (-435 "FSAGG2.spad" 700169 700185 701416 701421) (-434 "FS2UPS.spad" 694660 694694 700159 700164) (-433 "FS2.spad" 694307 694323 694650 694655) (-432 "FS2EXPXP.spad" 693432 693455 694297 694302) (-431 "FRUTIL.spad" 692386 692396 693422 693427) (-430 "FR.spad" 686009 686019 691317 691386) (-429 "FRNAALG.spad" 681278 681288 685951 686004) (-428 "FRNAALG.spad" 676559 676571 681234 681239) (-427 "FRNAAF2.spad" 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(-406 "FORMULA.spad" 648048 648056 650564 650569) (-405 "FORMULA1.spad" 647527 647537 648038 648043) (-404 "FORDER.spad" 647218 647242 647517 647522) (-403 "FOP.spad" 646419 646427 647208 647213) (-402 "FNLA.spad" 645843 645865 646387 646414) (-401 "FNCAT.spad" 644438 644446 645833 645838) (-400 "FNAME.spad" 644330 644338 644428 644433) (-399 "FMTC.spad" 644128 644136 644256 644325) (-398 "FMONOID.spad" 643793 643803 644084 644089) (-397 "FMONCAT.spad" 640946 640956 643783 643788) (-396 "FM.spad" 640641 640653 640880 640907) (-395 "FMFUN.spad" 637671 637679 640631 640636) (-394 "FMC.spad" 636723 636731 637661 637666) (-393 "FMCAT.spad" 634391 634409 636691 636718) (-392 "FM1.spad" 633748 633760 634325 634352) (-391 "FLOATRP.spad" 631483 631497 633738 633743) (-390 "FLOAT.spad" 624797 624805 631349 631478) (-389 "FLOATCP.spad" 622228 622242 624787 624792) (-388 "FLINEXP.spad" 621950 621960 622218 622223) (-387 "FLINEXP.spad" 621616 621628 621886 621891) (-386 "FLASORT.spad" 620942 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(-365 "FF.spad" 567238 567254 567471 567564) (-364 "FFNBX.spad" 565750 565770 566954 567047) (-363 "FFNBP.spad" 564263 564280 565466 565559) (-362 "FFNB.spad" 562728 562749 563944 564037) (-361 "FFINTBAS.spad" 560242 560261 562718 562723) (-360 "FFIELDC.spad" 557819 557827 560144 560237) (-359 "FFIELDC.spad" 555482 555492 557809 557814) (-358 "FFHOM.spad" 554230 554247 555472 555477) (-357 "FFF.spad" 551665 551676 554220 554225) (-356 "FFCGX.spad" 550512 550532 551381 551474) (-355 "FFCGP.spad" 549401 549421 550228 550321) (-354 "FFCG.spad" 548193 548214 549082 549175) (-353 "FFCAT.spad" 541366 541388 548032 548188) (-352 "FFCAT.spad" 534618 534642 541286 541291) (-351 "FFCAT2.spad" 534365 534405 534608 534613) (-350 "FEXPR.spad" 526082 526128 534121 534160) (-349 "FEVALAB.spad" 525790 525800 526072 526077) (-348 "FEVALAB.spad" 525283 525295 525567 525572) (-347 "FDIV.spad" 524725 524749 525273 525278) (-346 "FDIVCAT.spad" 522789 522813 524715 524720) (-345 "FDIVCAT.spad" 520851 520877 522779 522784) (-344 "FDIV2.spad" 520507 520547 520841 520846) (-343 "FCTRDATA.spad" 519515 519523 520497 520502) (-342 "FCPAK1.spad" 518082 518090 519505 519510) (-341 "FCOMP.spad" 517461 517471 518072 518077) (-340 "FC.spad" 507468 507476 517451 517456) (-339 "FAXF.spad" 500439 500453 507370 507463) (-338 "FAXF.spad" 493462 493478 500395 500400) (-337 "FARRAY.spad" 491459 491469 492492 492519) (-336 "FAMR.spad" 489595 489607 491357 491454) (-335 "FAMR.spad" 487715 487729 489479 489484) (-334 "FAMONOID.spad" 487383 487393 487669 487674) (-333 "FAMONC.spad" 485679 485691 487373 487378) (-332 "FAGROUP.spad" 485303 485313 485575 485602) (-331 "FACUTIL.spad" 483507 483524 485293 485298) (-330 "FACTFUNC.spad" 482701 482711 483497 483502) (-329 "EXPUPXS.spad" 479534 479557 480833 480982) (-328 "EXPRTUBE.spad" 476822 476830 479524 479529) (-327 "EXPRODE.spad" 473982 473998 476812 476817) (-326 "EXPR.spad" 469157 469167 469871 470166) (-325 "EXPR2UPS.spad" 465279 465292 469147 469152) (-324 "EXPR2.spad" 464984 464996 465269 465274) (-323 "EXPEXPAN.spad" 461785 461810 462417 462510) (-322 "EXIT.spad" 461456 461464 461775 461780) (-321 "EXITAST.spad" 461192 461200 461446 461451) (-320 "EVALCYC.spad" 460652 460666 461182 461187) (-319 "EVALAB.spad" 460224 460234 460642 460647) (-318 "EVALAB.spad" 459794 459806 460214 460219) (-317 "EUCDOM.spad" 457368 457376 459720 459789) (-316 "EUCDOM.spad" 455004 455014 457358 457363) (-315 "ESTOOLS.spad" 446850 446858 454994 454999) (-314 "ESTOOLS2.spad" 446453 446467 446840 446845) (-313 "ESTOOLS1.spad" 446138 446149 446443 446448) (-312 "ES.spad" 438953 438961 446128 446133) (-311 "ES.spad" 431674 431684 438851 438856) (-310 "ESCONT.spad" 428467 428475 431664 431669) (-309 "ESCONT1.spad" 428216 428228 428457 428462) (-308 "ES2.spad" 427721 427737 428206 428211) (-307 "ES1.spad" 427291 427307 427711 427716) (-306 "ERROR.spad" 424618 424626 427281 427286) (-305 "EQTBL.spad" 422648 422670 422857 422884) (-304 "EQ.spad" 417453 417463 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343325 343330) (-262 "DRAWCFUN.spad" 332414 332422 342872 342877) (-261 "DQAGG.spad" 330592 330602 332382 332409) (-260 "DPOLCAT.spad" 325941 325957 330460 330587) (-259 "DPOLCAT.spad" 321376 321394 325897 325902) (-258 "DPMO.spad" 313136 313152 313274 313487) (-257 "DPMM.spad" 304909 304927 305034 305247) (-256 "DOMTMPLT.spad" 304680 304688 304899 304904) (-255 "DOMCTOR.spad" 304435 304443 304670 304675) (-254 "DOMAIN.spad" 303522 303530 304425 304430) (-253 "DMP.spad" 300782 300797 301352 301479) (-252 "DMEXT.spad" 300649 300659 300750 300777) (-251 "DLP.spad" 300001 300011 300639 300644) (-250 "DLIST.spad" 298427 298437 299031 299058) (-249 "DLAGG.spad" 296844 296854 298417 298422) (-248 "DIVRING.spad" 296386 296394 296788 296839) (-247 "DIVRING.spad" 295972 295982 296376 296381) (-246 "DISPLAY.spad" 294162 294170 295962 295967) (-245 "DIRPROD.spad" 281709 281725 282349 282448) (-244 "DIRPROD2.spad" 280527 280545 281699 281704) (-243 "DIRPCAT.spad" 279720 279736 280423 280522) (-242 "DIRPCAT.spad" 278540 278558 279245 279250) (-241 "DIOSP.spad" 277365 277373 278530 278535) (-240 "DIOPS.spad" 276361 276371 277345 277360) (-239 "DIOPS.spad" 275331 275343 276317 276322) (-238 "DIFRING.spad" 275169 275177 275311 275326) (-237 "DIFFSPC.spad" 274748 274756 275159 275164) (-236 "DIFFSPC.spad" 274325 274335 274738 274743) (-235 "DIFFMOD.spad" 273814 273824 274293 274320) (-234 "DIFFDOM.spad" 272979 272990 273804 273809) (-233 "DIFFDOM.spad" 272142 272155 272969 272974) (-232 "DIFEXT.spad" 271961 271971 272122 272137) (-231 "DIAGG.spad" 271591 271601 271941 271956) (-230 "DIAGG.spad" 271229 271241 271581 271586) (-229 "DHMATRIX.spad" 269424 269434 270569 270596) (-228 "DFSFUN.spad" 263064 263072 269414 269419) (-227 "DFLOAT.spad" 259795 259803 262954 263059) (-226 "DFINTTLS.spad" 258026 258042 259785 259790) (-225 "DERHAM.spad" 255940 255972 258006 258021) (-224 "DEQUEUE.spad" 255147 255157 255430 255457) (-223 "DEGRED.spad" 254764 254778 255137 255142) (-222 "DEFINTRF.spad" 252301 252311 254754 254759) (-221 "DEFINTEF.spad" 250811 250827 252291 252296) (-220 "DEFAST.spad" 250179 250187 250801 250806) (-219 "DECIMAL.spad" 248188 248196 248549 248642) (-218 "DDFACT.spad" 246001 246018 248178 248183) (-217 "DBLRESP.spad" 245601 245625 245991 245996) (-216 "DBASE.spad" 244265 244275 245591 245596) (-215 "DATAARY.spad" 243727 243740 244255 244260) (-214 "D03FAFA.spad" 243555 243563 243717 243722) (-213 "D03EEFA.spad" 243375 243383 243545 243550) (-212 "D03AGNT.spad" 242461 242469 243365 243370) (-211 "D02EJFA.spad" 241923 241931 242451 242456) (-210 "D02CJFA.spad" 241401 241409 241913 241918) (-209 "D02BHFA.spad" 240891 240899 241391 241396) (-208 "D02BBFA.spad" 240381 240389 240881 240886) (-207 "D02AGNT.spad" 235195 235203 240371 240376) (-206 "D01WGTS.spad" 233514 233522 235185 235190) (-205 "D01TRNS.spad" 233491 233499 233504 233509) (-204 "D01GBFA.spad" 233013 233021 233481 233486) (-203 "D01FCFA.spad" 232535 232543 233003 233008) (-202 "D01ASFA.spad" 232003 232011 232525 232530) (-201 "D01AQFA.spad" 231449 231457 231993 231998) (-200 "D01APFA.spad" 230873 230881 231439 231444) (-199 "D01ANFA.spad" 230367 230375 230863 230868) (-198 "D01AMFA.spad" 229877 229885 230357 230362) (-197 "D01ALFA.spad" 229417 229425 229867 229872) (-196 "D01AKFA.spad" 228943 228951 229407 229412) (-195 "D01AJFA.spad" 228466 228474 228933 228938) (-194 "D01AGNT.spad" 224533 224541 228456 228461) (-193 "CYCLOTOM.spad" 224039 224047 224523 224528) (-192 "CYCLES.spad" 220831 220839 224029 224034) (-191 "CVMP.spad" 220248 220258 220821 220826) (-190 "CTRIGMNP.spad" 218748 218764 220238 220243) (-189 "CTOR.spad" 218439 218447 218738 218743) (-188 "CTORKIND.spad" 218042 218050 218429 218434) (-187 "CTORCAT.spad" 217291 217299 218032 218037) (-186 "CTORCAT.spad" 216538 216548 217281 217286) (-185 "CTORCALL.spad" 216127 216137 216528 216533) (-184 "CSTTOOLS.spad" 215372 215385 216117 216122) (-183 "CRFP.spad" 209096 209109 215362 215367) (-182 "CRCEAST.spad" 208816 208824 209086 209091) (-181 "CRAPACK.spad" 207867 207877 208806 208811) (-180 "CPMATCH.spad" 207371 207386 207792 207797) (-179 "CPIMA.spad" 207076 207095 207361 207366) (-178 "COORDSYS.spad" 202085 202095 207066 207071) (-177 "CONTOUR.spad" 201496 201504 202075 202080) (-176 "CONTFRAC.spad" 197246 197256 201398 201491) (-175 "CONDUIT.spad" 197004 197012 197236 197241) (-174 "COMRING.spad" 196678 196686 196942 196999) (-173 "COMPPROP.spad" 196196 196204 196668 196673) (-172 "COMPLPAT.spad" 195963 195978 196186 196191) (-171 "COMPLEX.spad" 191340 191350 191584 191845) (-170 "COMPLEX2.spad" 191055 191067 191330 191335) (-169 "COMPILER.spad" 190604 190612 191045 191050) (-168 "COMPFACT.spad" 190206 190220 190594 190599) (-167 "COMPCAT.spad" 188278 188288 189940 190201) (-166 "COMPCAT.spad" 186078 186090 187742 187747) (-165 "COMMUPC.spad" 185826 185844 186068 186073) (-164 "COMMONOP.spad" 185359 185367 185816 185821) (-163 "COMM.spad" 185170 185178 185349 185354) (-162 "COMMAAST.spad" 184933 184941 185160 185165) (-161 "COMBOPC.spad" 183848 183856 184923 184928) (-160 "COMBINAT.spad" 182615 182625 183838 183843) (-159 "COMBF.spad" 179997 180013 182605 182610) (-158 "COLOR.spad" 178834 178842 179987 179992) (-157 "COLONAST.spad" 178500 178508 178824 178829) (-156 "CMPLXRT.spad" 178211 178228 178490 178495) (-155 "CLLCTAST.spad" 177873 177881 178201 178206) (-154 "CLIP.spad" 173981 173989 177863 177868) (-153 "CLIF.spad" 172636 172652 173937 173976) (-152 "CLAGG.spad" 169141 169151 172626 172631) (-151 "CLAGG.spad" 165517 165529 169004 169009) (-150 "CINTSLPE.spad" 164848 164861 165507 165512) (-149 "CHVAR.spad" 162986 163008 164838 164843) (-148 "CHARZ.spad" 162901 162909 162966 162981) (-147 "CHARPOL.spad" 162411 162421 162891 162896) (-146 "CHARNZ.spad" 162164 162172 162391 162406) (-145 "CHAR.spad" 160038 160046 162154 162159) (-144 "CFCAT.spad" 159366 159374 160028 160033) (-143 "CDEN.spad" 158562 158576 159356 159361) (-142 "CCLASS.spad" 156673 156681 157935 157974) (-141 "CATEGORY.spad" 155715 155723 156663 156668) (-140 "CATCTOR.spad" 155606 155614 155705 155710) (-139 "CATAST.spad" 155224 155232 155596 155601) (-138 "CASEAST.spad" 154938 154946 155214 155219) (-137 "CARTEN.spad" 150305 150329 154928 154933) (-136 "CARTEN2.spad" 149695 149722 150295 150300) (-135 "CARD.spad" 146990 146998 149669 149690) (-134 "CAPSLAST.spad" 146764 146772 146980 146985) (-133 "CACHSET.spad" 146388 146396 146754 146759) (-132 "CABMON.spad" 145943 145951 146378 146383) (-131 "BYTEORD.spad" 145618 145626 145933 145938) (-130 "BYTE.spad" 145045 145053 145608 145613) (-129 "BYTEBUF.spad" 142743 142751 144053 144080) (-128 "BTREE.spad" 141699 141709 142233 142260) (-127 "BTOURN.spad" 140587 140597 141189 141216) (-126 "BTCAT.spad" 139979 139989 140555 140582) (-125 "BTCAT.spad" 139391 139403 139969 139974) (-124 "BTAGG.spad" 138857 138865 139359 139386) (-123 "BTAGG.spad" 138343 138353 138847 138852) (-122 "BSTREE.spad" 136967 136977 137833 137860) (-121 "BRILL.spad" 135164 135175 136957 136962) (-120 "BRAGG.spad" 134104 134114 135154 135159) (-119 "BRAGG.spad" 133008 133020 134060 134065) (-118 "BPADICRT.spad" 130882 130894 131137 131230) (-117 "BPADIC.spad" 130546 130558 130808 130877) (-116 "BOUNDZRO.spad" 130202 130219 130536 130541) (-115 "BOP.spad" 125384 125392 130192 130197) (-114 "BOP1.spad" 122850 122860 125374 125379) (-113 "BOOLE.spad" 122500 122508 122840 122845) (-112 "BOOLEAN.spad" 121938 121946 122490 122495) (-111 "BMODULE.spad" 121650 121662 121906 121933) (-110 "BITS.spad" 121033 121041 121248 121275) (-109 "BINDING.spad" 120446 120454 121023 121028) (-108 "BINARY.spad" 118460 118468 118816 118909) (-107 "BGAGG.spad" 117665 117675 118440 118455) (-106 "BGAGG.spad" 116878 116890 117655 117660) (-105 "BFUNCT.spad" 116442 116450 116858 116873) (-104 "BEZOUT.spad" 115582 115609 116392 116397) (-103 "BBTREE.spad" 112310 112320 115072 115099) (-102 "BASTYPE.spad" 111982 111990 112300 112305) (-101 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192464) ((-508 . -616) 192441) ((-792 . -1119) T) ((-792 . -1084) 192408) ((-473 . -1119) T) ((-466 . -1119) T) ((-598 . -729) 192383) ((-661 . -1119) T) ((-1278 . -47) 192360) ((-1272 . -102) T) ((-1271 . -47) 192330) ((-1250 . -47) 192307) ((-1230 . -174) 192258) ((-1192 . -317) 192237) ((-1186 . -317) 192216) ((-1115 . -628) 192197) ((-1109 . -628) 192178) ((-1099 . -568) 192129) ((-1099 . -1240) 192080) ((-1023 . -915) NIL) ((-1092 . -628) 192061) ((-682 . -132) T) ((-639 . -1131) T) ((-1085 . -628) 192042) ((-1055 . -628) 192023) ((-1038 . -628) 192004) ((-726 . -1075) 191974) ((-711 . -658) 191924) ((-284 . -1119) T) ((-85 . -453) T) ((-85 . -407) T) ((-724 . -909) 191827) ((-723 . -174) T) ((-50 . -1119) T) ((-607 . -47) 191804) ((-227 . -660) 191769) ((-593 . -1119) T) ((-530 . -1119) T) ((-499 . -832) T) ((-499 . -937) T) ((-370 . -1240) T) ((-364 . -1240) T) ((-356 . -1240) T) ((-329 . -1131) T) ((-326 . -1070) 191679) ((-323 . -1070) 191608) ((-108 . -1240) T) ((-638 . -628) 191589) ((-370 . -568) T) ((-219 . -937) T) ((-219 . -832) T) ((-326 . -652) 191499) ((-323 . -652) 191428) ((-364 . -568) T) ((-356 . -568) T) ((-495 . -628) 191409) ((-108 . -568) T) ((-670 . -729) 191379) ((-1186 . -1041) NIL) ((-220 . -628) 191360) ((-329 . -23) T) ((-67 . -1236) T) ((-1019 . -625) 191292) ((-706 . -272) 191274) ((-706 . -232) 191256) ((-1315 . -1171) T) ((-726 . -111) 191221) ((-1310 . -21) T) ((-656 . -34) T) ((-250 . -501) 191205) ((-1310 . -25) T) ((-1308 . -132) T) ((-1306 . -132) T) ((-1299 . -102) T) ((-1121 . -1117) 191189) ((-173 . -1119) T) ((-1282 . -625) 191155) ((-1278 . -1236) T) ((-1271 . -1236) T) ((-1271 . -1057) 191090) ((-1250 . -1236) T) ((-969 . -926) 191069) ((-1250 . -899) NIL) ((-1250 . -897) 191021) ((-1250 . -1057) 190987) ((-527 . -628) 190971) ((-1230 . -526) 190938) ((-1208 . -626) NIL) ((-1208 . -625) 190920) ((-493 . -926) 190899) ((-1161 . -1142) 190844) ((-1106 . -729) 190693) ((-1081 . -660) 190665) ((-969 . -660) 190554) ((-794 . -729) 190383) ((-609 . -502) 190364) ((-597 . -502) 190345) ((-609 . -625) 190311) ((-597 . -625) 190277) ((-548 . -625) 190259) ((-591 . -1236) T) ((-548 . -626) 190240) ((-792 . -729) 190089) ((-1096 . -102) T) ((-635 . -658) 190061) ((-392 . -25) T) ((-392 . -21) T) ((-493 . -660) 189950) ((-473 . -729) 189921) ((-466 . -729) 189770) ((-1006 . -102) T) ((-1065 . -1229) 189699) ((-918 . -319) 189637) ((-888 . -93) T) ((-749 . -102) T) ((-118 . -658) 189567) ((-617 . -628) 189549) ((-726 . -628) 189503) ((-693 . -93) T) ((-543 . -25) T) ((-688 . -93) T) ((-676 . -625) 189485) ((-657 . -502) 189466) ((-657 . -625) 189419) ((-142 . -102) T) ((-44 . -132) T) ((-608 . -1236) T) ((-607 . -1236) T) ((-354 . -1077) T) ((-299 . -1131) T) ((-490 . -93) T) ((-419 . -237) 189370) ((-366 . -625) 189352) ((-363 . -625) 189334) ((-355 . -625) 189316) ((-273 . -626) 189064) ((-273 . -625) 189046) ((-253 . -625) 189028) ((-253 . -626) 188889) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1160 . -625) 188871) ((-1139 . -652) 188858) ((-1139 . -1070) 188845) ((-831 . -738) T) ((-831 . -869) T) ((-614 . -298) 188822) ((-593 . -729) 188787) ((-491 . -626) NIL) ((-491 . -625) 188769) ((-530 . -729) 188714) ((-326 . -102) T) ((-323 . -102) T) ((-299 . -23) T) ((-153 . -132) T) ((-927 . -625) 188696) ((-927 . -626) 188678) ((-398 . -738) T) ((-884 . -1075) 188630) ((-884 . -111) 188568) ((-726 . -1068) T) ((-724 . -1262) 188552) ((-706 . -360) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-531 . -625) 188484) ((-390 . -807) T) ((-169 . -1236) T) ((-225 . -1119) T) ((-390 . -804) T) ((-59 . -626) 188445) ((-227 . -806) T) ((-227 . -803) T) ((-59 . -625) 188357) ((-227 . -738) T) ((-528 . -626) 188318) ((-528 . -625) 188230) ((-509 . -625) 188162) ((-508 . -626) 188123) ((-508 . -625) 188035) ((-1099 . -374) 187986) ((-40 . -423) 187963) ((-77 . -1236) T) ((-883 . -926) NIL) ((-370 . -339) 187947) ((-370 . -374) T) ((-364 . -339) 187931) ((-364 . -374) T) ((-356 . -339) 187915) ((-356 . -374) T) ((-326 . -294) 187894) ((-108 . -374) T) ((-70 . -1236) T) ((-1250 . -349) 187846) ((-883 . -660) 187791) ((-1250 . -388) 187743) ((-981 . -132) 187598) ((-827 . -132) 187469) ((-975 . -663) 187453) ((-1106 . -174) 187364) ((-975 . -384) 187348) ((-1081 . -806) T) ((-1081 . -803) T) ((-884 . -628) 187246) ((-794 . -174) 187137) ((-792 . -174) 187048) ((-828 . -47) 187010) ((-1081 . -738) T) ((-337 . -501) 186994) ((-969 . -738) T) ((-1299 . -319) 186932) ((-1278 . -915) 186845) ((-466 . -174) 186756) ((-250 . -296) 186708) ((-1271 . -915) 186614) ((-1270 . -1075) 186449) ((-1250 . -915) 186282) ((-493 . -738) T) ((-1249 . -1075) 186090) ((-1230 . -300) 186069) ((-1205 . -1236) T) ((-1202 . -379) T) ((-1201 . -379) T) ((-1165 . -152) 186053) ((-1139 . -102) T) ((-1137 . -1119) T) ((-1099 . -23) T) ((-1099 . -1131) T) ((-1094 . -102) T) ((-1076 . -625) 186020) ((-1022 . -421) 185992) ((-944 . -972) T) ((-749 . -319) 185930) ((-75 . -1236) T) ((-676 . -393) 185902) ((-171 . -926) 185855) ((-30 . -972) T) ((-112 . -856) T) ((-1 . -625) 185837) ((-1018 . -909) 185758) ((-129 . -663) 185740) ((-50 . -632) 185724) ((-706 . -658) 185659) ((-607 . -915) 185572) ((-450 . -102) T) ((-129 . -384) 185554) ((-142 . -319) NIL) ((-884 . -1068) T) ((-845 . -862) 185533) ((-81 . -1236) T) ((-723 . -300) T) ((-40 . -1077) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 185515) ((-171 . -660) 185389) ((-519 . -625) 185371) ((-362 . -148) 185353) ((-362 . -146) T) ((-370 . -1131) T) ((-364 . -1131) T) ((-356 . -1131) T) ((-1023 . -317) T) ((-931 . -317) T) ((-884 . -248) T) ((-108 . -1131) T) ((-884 . -238) 185332) ((-1270 . -111) 185153) ((-1249 . -111) 184942) ((-250 . -1274) 184926) ((-576 . -860) T) ((-370 . -23) T) ((-365 . -360) T) ((-326 . -319) 184913) ((-323 . -319) 184854) ((-364 . -23) T) ((-329 . -132) T) ((-356 . -23) T) ((-1023 . -1041) T) ((-31 . -628) 184835) ((-108 . -23) T) ((-666 . -1070) 184819) ((-250 . -616) 184796) ((-343 . -1119) T) ((-666 . -652) 184766) ((-1272 . -38) 184658) ((-1259 . -926) 184637) ((-112 . -1119) T) ((-828 . -1236) T) ((-425 . -1236) T) ((-1054 . -102) T) ((-1259 . -660) 184526) ((-883 . -806) NIL) ((-867 . -660) 184500) ((-883 . -803) NIL) ((-828 . -899) NIL) ((-883 . -738) T) ((-1106 . -526) 184373) ((-794 . -526) 184320) ((-792 . -526) 184272) ((-583 . -660) 184259) ((-828 . -1057) 184087) ((-466 . -526) 184030) ((-400 . -401) T) ((-1270 . -628) 183843) ((-1249 . -628) 183591) ((-60 . -1236) T) ((-633 . -862) 183570) ((-512 . -673) T) ((-1165 . -995) 183539) ((-1043 . -658) 183476) ((-1022 . -464) T) ((-711 . -860) T) ((-522 . -804) T) ((-486 . -1075) 183311) ((-512 . -113) T) ((-354 . -1119) T) ((-323 . -1171) NIL) ((-299 . -132) T) ((-406 . -1119) T) ((-882 . -1077) T) ((-706 . -381) 183278) ((-365 . -658) 183208) ((-225 . -632) 183185) ((-337 . -296) 183137) ((-486 . -111) 182958) ((-1270 . -1068) T) ((-1249 . -1068) T) ((-828 . -388) 182942) ((-836 . -1236) T) ((-171 . -738) T) ((-1301 . -1236) T) ((-666 . -102) T) ((-1270 . -248) 182921) ((-1270 . -238) 182873) ((-1249 . -238) 182778) ((-1249 . -248) 182757) ((-1022 . -414) NIL) ((-682 . -651) 182705) ((-326 . -38) 182615) ((-323 . -38) 182544) ((-69 . -625) 182526) ((-329 . -505) 182492) ((-48 . -658) 182442) ((-1208 . -298) 182421) ((-1244 . -862) T) ((-1132 . -1131) 182399) ((-83 . -1236) T) ((-61 . -625) 182381) ((-491 . -298) 182360) ((-1301 . -1057) 182337) ((-1183 . -1119) T) ((-1132 . -23) 182189) ((-828 . -915) 182125) ((-1259 . -738) T) ((-1121 . -1236) T) ((-486 . -628) 181951) ((-362 . -237) T) ((-1106 . -300) 181882) ((-983 . -1119) T) ((-906 . -102) T) ((-794 . -300) 181793) ((-337 . -19) 181777) ((-59 . -298) 181754) ((-792 . -300) 181685) ((-867 . -738) T) ((-118 . -860) NIL) ((-528 . -298) 181662) ((-337 . -616) 181639) ((-508 . -298) 181616) ((-466 . -300) 181547) ((-1054 . -319) 181398) ((-888 . -502) 181379) ((-888 . -625) 181345) ((-693 . -502) 181326) ((-583 . -738) T) ((-688 . -502) 181307) ((-693 . -625) 181257) ((-688 . -625) 181223) ((-674 . -625) 181205) ((-490 . -502) 181186) ((-490 . -625) 181152) ((-250 . -626) 181113) ((-250 . -502) 181090) ((-139 . -502) 181071) ((-138 . -502) 181052) ((-134 . -502) 181033) ((-250 . -625) 180925) ((-215 . -102) T) ((-139 . -625) 180891) ((-138 . -625) 180857) ((-134 . -625) 180823) ((-1166 . -34) T) ((-960 . -1236) T) ((-354 . -729) 180768) ((-682 . -25) T) ((-682 . -21) T) ((-1195 . -628) 180749) ((-341 . -1236) T) ((-486 . -1068) T) ((-647 . -429) 180714) ((-619 . -429) 180679) ((-1139 . -1171) T) ((-1271 . -317) 180658) ((-724 . -1070) 180481) ((-593 . -300) T) ((-530 . -300) T) ((-1250 . -317) 180460) ((-486 . -238) 180412) ((-486 . -248) 180391) ((-451 . -1236) T) ((-724 . -652) 180220) ((-1250 . -1041) NIL) ((-1099 . -132) T) ((-884 . -807) 180199) ((-145 . -102) T) ((-40 . -1119) T) ((-884 . -804) 180178) ((-656 . -1029) 180162) ((-592 . -1077) T) ((-576 . -1077) T) ((-507 . -1077) T) ((-419 . -464) T) ((-370 . -132) T) ((-326 . -412) 180146) ((-323 . -412) 180107) ((-364 . -132) T) ((-356 . -132) T) ((-1200 . -1119) T) ((-1139 . -38) 180094) ((-1113 . -625) 180061) ((-108 . -132) T) ((-971 . -1119) T) ((-938 . -1119) T) ((-783 . -1119) T) ((-684 . -1119) T) ((-713 . -148) T) ((-117 . -148) T) ((-1308 . -21) T) ((-1308 . -25) T) ((-1306 . -21) T) ((-1306 . -25) T) ((-676 . -1075) 180045) ((-543 . -862) T) ((-512 . -862) T) ((-376 . -1236) T) ((-366 . -1075) 179997) ((-363 . -1075) 179949) ((-355 . -1075) 179901) ((-258 . -1236) T) ((-257 . -1236) T) ((-273 . -1075) 179744) ((-253 . -1075) 179587) ((-676 . -111) 179566) ((-829 . -1240) 179545) ((-559 . -856) T) ((-326 . -917) 179511) ((-366 . -111) 179449) ((-363 . -111) 179387) ((-355 . -111) 179325) ((-273 . -111) 179154) ((-253 . -111) 178983) ((-323 . -917) NIL) ((-635 . -423) 178967) ((-44 . -21) T) ((-44 . -25) T) ((-827 . -651) 178873) ((-829 . -568) 178852) ((-258 . -1057) 178679) ((-257 . -1057) 178506) ((-127 . -120) 178490) ((-927 . -1075) 178455) ((-724 . -102) T) ((-711 . -1077) T) ((-609 . -628) 178436) ((-597 . -628) 178417) ((-548 . -630) 178320) ((-354 . -174) T) ((-153 . -21) T) ((-153 . -25) T) ((-88 . -625) 178302) ((-927 . -111) 178258) ((-40 . -729) 178203) ((-882 . -1119) T) ((-676 . -628) 178180) ((-657 . -628) 178161) ((-366 . -628) 178098) ((-363 . -628) 178035) ((-355 . -628) 177972) ((-559 . -1119) T) ((-337 . -626) 177933) ((-337 . -625) 177845) ((-273 . -628) 177598) ((-253 . -628) 177383) ((-188 . -1236) T) ((-1249 . -804) 177336) ((-1249 . -807) 177289) ((-258 . -388) 177258) ((-257 . -388) 177227) ((-666 . -38) 177197) ((-620 . -34) T) ((-494 . -1131) 177175) ((-487 . -34) T) ((-1132 . -132) 177046) ((-981 . -25) 176857) ((-927 . -628) 176807) ((-886 . -625) 176789) ((-981 . -21) 176744) ((-827 . -25) 176577) ((-827 . -21) 176488) ((-1242 . -379) T) ((-635 . -1077) T) ((-1197 . -568) 176467) ((-1191 . -47) 176444) ((-366 . -1068) T) ((-363 . -1068) T) ((-494 . -23) 176296) ((-355 . -1068) T) ((-273 . -1068) T) ((-253 . -1068) T) ((-1144 . -47) 176268) ((-118 . -1077) T) ((-1053 . -660) 176242) ((-975 . -34) T) ((-366 . -238) 176221) ((-366 . -248) T) ((-363 . -238) 176200) ((-363 . -248) T) ((-355 . -238) 176179) ((-355 . -248) T) ((-273 . -336) 176151) ((-253 . -336) 176108) ((-273 . -238) 176087) ((-1176 . -152) 176071) ((-258 . -915) 176003) ((-257 . -915) 175935) ((-1161 . -909) 175856) ((-1101 . -862) T) ((-1253 . -1236) 175834) ((-426 . -1131) T) ((-1073 . -23) T) ((-1043 . -860) T) ((-927 . -1068) T) ((-332 . -660) 175816) ((-713 . -237) T) ((-682 . -234) 175761) ((-1230 . -1021) 175727) ((-1192 . -937) 175706) ((-1186 . -937) 175685) ((-1186 . -832) NIL) ((-1018 . -1070) 175581) ((-984 . -1236) T) ((-927 . -248) T) ((-829 . -374) 175560) ((-396 . -23) T) ((-128 . -1119) 175538) ((-122 . -1119) 175516) ((-927 . -238) T) ((-129 . -34) T) ((-390 . -660) 175481) ((-1018 . -652) 175429) ((-882 . -729) 175416) ((-1315 . -658) 175388) ((-1065 . -152) 175353) ((-1012 . -1236) T) ((-874 . -1236) T) ((-40 . -174) T) ((-706 . -423) 175335) ((-724 . -319) 175322) ((-848 . -660) 175282) ((-839 . -660) 175256) ((-329 . -25) T) ((-329 . -21) T) ((-670 . -296) 175235) ((-592 . -1119) T) ((-576 . -1119) T) ((-507 . -1119) T) ((-1191 . -1236) T) ((-250 . -298) 175212) ((-1144 . -1236) T) ((-866 . -1236) T) ((-323 . -272) 175173) ((-323 . -232) 175134) ((-1191 . -899) NIL) ((-55 . -1119) T) ((-1144 . -899) 174993) ((-130 . -862) T) ((-1191 . -1057) 174873) ((-1144 . -1057) 174756) ((-185 . -625) 174738) ((-866 . -1057) 174634) ((-794 . -296) 174561) ((-829 . -1131) T) ((-1053 . -738) T) ((-1065 . -995) 174490) ((-614 . -663) 174474) ((-1022 . -909) 174381) ((-1018 . -102) T) ((-829 . -23) T) ((-724 . -1171) 174359) ((-706 . -1077) T) ((-614 . -384) 174343) ((-362 . -464) T) ((-354 . -300) T) ((-1287 . -1119) T) ((-254 . -1119) T) ((-411 . -102) T) ((-299 . -21) T) ((-299 . -25) T) ((-372 . -738) T) ((-722 . -1119) T) ((-711 . -1119) T) ((-372 . -485) T) ((-1230 . -625) 174325) ((-1191 . -388) 174309) ((-1144 . -388) 174293) ((-1043 . -423) 174255) ((-142 . -231) 174237) ((-390 . -806) T) ((-390 . -803) T) ((-882 . -174) T) ((-390 . -738) T) ((-723 . -625) 174219) ((-724 . -38) 174048) ((-1286 . -1284) 174032) ((-362 . -414) T) ((-1286 . -1119) 173982) ((-1209 . -1119) T) ((-592 . -729) 173969) ((-576 . -729) 173956) ((-507 . -729) 173921) ((-1272 . -658) 173811) ((-326 . -641) 173790) ((-848 . -738) T) ((-839 . -738) T) ((-1134 . -1236) T) ((-656 . -1236) T) ((-1099 . -651) 173738) ((-1191 . -915) 173681) ((-1144 . -915) 173665) ((-827 . -234) 173556) ((-674 . -1075) 173540) ((-108 . -651) 173522) ((-494 . -132) 173393) ((-1197 . -1131) T) ((-831 . -1236) T) ((-969 . -47) 173362) ((-635 . -1119) T) ((-674 . -111) 173341) ((-503 . -625) 173307) ((-337 . -298) 173284) ((-398 . -1236) T) ((-334 . -1236) T) ((-493 . -47) 173241) ((-1197 . -23) T) ((-118 . -1119) T) ((-103 . -102) 173191) ((-1298 . -1131) T) ((-560 . -862) T) ((-227 . -1236) T) 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T) ((-48 . -1077) T) ((-592 . -174) T) ((-576 . -174) T) ((-507 . -174) T) ((-1081 . -1236) T) ((-969 . -1236) T) ((-725 . -1236) T) ((-670 . -625) 172173) ((-493 . -1236) T) ((-749 . -748) 172157) ((-347 . -625) 172139) ((-68 . -394) T) ((-68 . -407) T) ((-1121 . -107) 172123) ((-1081 . -899) 172105) ((-969 . -899) 172030) ((-665 . -1131) T) ((-635 . -729) 172017) ((-493 . -899) NIL) ((-1165 . -102) T) ((-1113 . -630) 172001) ((-1081 . -1057) 171983) ((-97 . -625) 171965) ((-489 . -148) T) ((-969 . -1057) 171845) ((-118 . -729) 171790) ((-724 . -917) 171697) ((-665 . -23) T) ((-493 . -1057) 171573) ((-1106 . -626) NIL) ((-1106 . -625) 171555) ((-794 . -626) NIL) ((-794 . -625) 171516) ((-792 . -626) 171150) ((-792 . -625) 171064) ((-1132 . -651) 170970) ((-473 . -625) 170952) ((-466 . -625) 170934) ((-466 . -626) 170795) ((-1054 . -231) 170741) ((-884 . -926) 170720) ((-127 . -34) T) ((-829 . -132) T) ((-661 . -625) 170702) ((-590 . -102) T) ((-366 . -1305) 170686) ((-363 . -1305) 170670) ((-355 . -1305) 170654) ((-128 . -526) 170587) ((-122 . -526) 170520) ((-523 . -804) T) ((-523 . -807) T) ((-522 . -806) T) ((-103 . -319) 170458) ((-224 . -102) 170408) ((-711 . -174) T) ((-706 . -1119) T) ((-884 . -660) 170324) ((-65 . -395) T) ((-284 . -625) 170306) ((-65 . -407) T) ((-969 . -388) 170290) ((-882 . -300) T) ((-50 . -625) 170272) ((-1018 . -38) 170220) ((-1139 . -658) 170192) ((-593 . -625) 170174) ((-493 . -388) 170158) ((-593 . -626) 170140) ((-530 . -625) 170122) ((-927 . -1305) 170109) ((-883 . -1236) T) ((-713 . -464) T) ((-507 . -526) 170075) ((-1297 . -1236) T) ((-1296 . -1236) T) ((-499 . -374) T) ((-366 . -379) 170054) ((-363 . -379) 170033) ((-355 . -379) 170012) ((-726 . -738) T) ((-219 . -374) T) ((-117 . -464) T) ((-1309 . -1300) 169996) ((-883 . -897) 169973) ((-883 . -899) NIL) ((-981 . -862) 169872) ((-827 . -862) 169823) ((-1243 . -102) T) ((-666 . -668) 169807) ((-1222 . -34) T) ((-173 . -625) 169789) ((-1132 . -25) 169622) ((-1132 . -21) 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168628) ((-1099 . -234) 168501) ((-499 . -1131) T) ((-365 . -1119) T) ((-219 . -1131) T) ((-76 . -453) T) ((-76 . -407) T) ((-171 . -1057) 168397) ((-304 . -909) 168354) ((-329 . -862) T) ((-1249 . -660) 168162) ((-884 . -806) 168141) ((-884 . -803) 168120) ((-884 . -738) T) ((-499 . -23) T) ((-370 . -234) 168093) ((-364 . -234) 168066) ((-356 . -234) 168039) ((-176 . -464) T) ((-86 . -453) T) ((-224 . -319) 167977) ((-86 . -407) T) ((-225 . -625) 167959) ((-108 . -234) 167946) ((-219 . -23) T) ((-1310 . -1303) 167925) ((-689 . -1057) 167909) ((-592 . -300) T) ((-576 . -300) T) ((-507 . -300) T) ((-1259 . -1236) T) ((-137 . -482) 167864) ((-867 . -1236) T) ((-666 . -658) 167823) ((-48 . -1119) T) ((-724 . -272) 167807) ((-724 . -232) 167791) ((-883 . -915) NIL) ((-583 . -1236) T) ((-1259 . -899) NIL) ((-902 . -102) T) ((-898 . -102) T) ((-400 . -1119) T) ((-171 . -388) 167775) ((-171 . -349) 167759) ((-1259 . -1057) 167639) ((-867 . -1057) 167535) ((-1161 . -102) T) ((-1018 . -917) 167458) ((-674 . -804) 167437) ((-665 . -132) T) ((-674 . -807) 167416) ((-118 . -526) 167324) ((-583 . -1057) 167306) ((-304 . -1293) 167276) ((-878 . -102) T) ((-980 . -568) 167255) ((-1230 . -1075) 167138) ((-1022 . -1070) 167083) ((-494 . -651) 166989) ((-921 . -1119) T) ((-1043 . -729) 166926) ((-723 . -1075) 166891) ((-1022 . -652) 166836) ((-629 . -102) T) ((-614 . -34) T) ((-1166 . -1236) T) ((-1230 . -111) 166705) ((-486 . -660) 166602) ((-365 . -729) 166547) ((-171 . -915) 166506) ((-711 . -300) T) ((-706 . -174) T) ((-723 . -111) 166462) ((-1315 . -1077) T) ((-1259 . -388) 166446) ((-430 . -1240) 166424) ((-1137 . -625) 166406) ((-323 . -860) NIL) ((-430 . -568) T) ((-227 . -317) T) ((-1249 . -803) 166359) ((-1249 . -806) 166312) ((-1270 . -738) T) ((-1249 . -738) T) ((-48 . -729) 166277) ((-227 . -1041) T) ((-1272 . -423) 166243) ((-362 . -1293) 166220) ((-1259 . -915) 166163) ((-730 . -738) T) ((-343 . -625) 166145) ((-1230 . -628) 166027) ((-1132 . -234) 165918) ((-112 . 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. -1119) T) ((-250 . -678) 165043) ((-250 . -663) 165027) ((-670 . -111) 165006) ((-598 . -628) 164990) ((-326 . -423) 164974) ((-250 . -384) 164958) ((-1178 . -240) 164905) ((-1018 . -272) 164889) ((-1018 . -232) 164873) ((-74 . -1236) T) ((-48 . -174) T) ((-713 . -399) T) ((-713 . -144) T) ((-1309 . -102) T) ((-1217 . -1236) T) ((-1216 . -628) 164855) ((-1107 . -1236) T) ((-1106 . -1075) 164698) ((-1095 . -1236) T) ((-273 . -926) 164677) ((-253 . -926) 164656) ((-794 . -1075) 164479) ((-792 . -1075) 164322) ((-620 . -1236) T) ((-1183 . -625) 164304) ((-1106 . -111) 164133) ((-1065 . -102) T) ((-487 . -1236) T) ((-473 . -1075) 164104) ((-466 . -1075) 163947) ((-676 . -660) 163931) ((-883 . -317) T) ((-794 . -111) 163740) ((-792 . -111) 163569) ((-366 . -660) 163521) ((-363 . -660) 163473) ((-355 . -660) 163425) ((-273 . -660) 163314) ((-253 . -660) 163203) ((-1177 . -862) T) ((-1107 . -1057) 163187) ((-473 . -111) 163148) ((-466 . -111) 162977) ((-1095 . -1057) 162954) ((-1019 . -34) 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. -317) 161262) ((-430 . -23) T) ((-40 . -625) 161244) ((-40 . -626) 161228) ((-108 . -1011) 161210) ((-117 . -881) 161194) ((-661 . -628) 161178) ((-48 . -526) 161144) ((-1222 . -1029) 161128) ((-1200 . -625) 161095) ((-1208 . -34) T) ((-971 . -625) 161061) ((-938 . -625) 161043) ((-1132 . -862) 160994) ((-783 . -625) 160976) ((-684 . -625) 160958) ((-529 . -1236) T) ((-1259 . -317) 160937) ((-1176 . -319) 160875) ((-1160 . -34) T) ((-491 . -34) T) ((-1111 . -1236) T) ((-489 . -464) T) ((-1053 . -1236) T) ((-1106 . -1068) T) ((-50 . -628) 160844) ((-794 . -1068) T) ((-792 . -1068) T) ((-659 . -240) 160828) ((-644 . -240) 160774) ((-1197 . -21) T) ((-593 . -628) 160724) ((-530 . -628) 160654) ((-494 . -234) 160545) ((-1197 . -25) T) ((-1106 . -336) 160506) ((-466 . -1068) T) ((-1106 . -238) 160485) ((-794 . -336) 160462) ((-794 . -238) T) ((-792 . -336) 160434) ((-743 . -1240) 160413) ((-531 . -34) T) ((-337 . -663) 160397) ((-528 . -34) T) ((-59 . -34) T) ((-509 . -34) T) ((-508 . 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159644) ((-1139 . -1077) T) ((-103 . -126) 159628) ((-304 . -652) 159570) ((-811 . -23) T) ((-1308 . -1303) 159546) ((-1306 . -1303) 159525) ((-1286 . -296) 159477) ((-419 . -319) 159442) ((-1272 . -1119) T) ((-1161 . -917) 159365) ((-882 . -625) 159347) ((-848 . -1057) 159316) ((-205 . -799) T) ((-204 . -799) T) ((-203 . -799) T) ((-202 . -799) T) ((-201 . -799) T) ((-200 . -799) T) ((-199 . -799) T) ((-198 . -799) T) ((-197 . -799) T) ((-196 . -799) T) ((-559 . -625) 159298) ((-507 . -1021) T) ((-283 . -851) T) ((-282 . -851) T) ((-281 . -851) T) ((-280 . -851) T) ((-48 . -300) T) ((-279 . -851) T) ((-278 . -851) T) ((-277 . -851) T) ((-195 . -799) T) ((-624 . -862) T) ((-666 . -423) 159282) ((-682 . -237) 159233) ((-225 . -628) 159195) ((-110 . -862) T) ((-665 . -21) T) ((-665 . -25) T) ((-1309 . -38) 159165) ((-118 . -296) 159116) ((-1286 . -19) 159100) ((-1286 . -616) 159077) ((-1299 . -1119) T) ((-362 . -1070) 159022) ((-1096 . -1119) T) ((-1006 . -1119) T) ((-980 . -132) T) 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T) ((-494 . -862) 158035) ((-499 . -651) 158017) ((-982 . -625) 157999) ((-1022 . -917) 157908) ((-219 . -651) 157890) ((-227 . -416) T) ((-674 . -660) 157874) ((-55 . -625) 157856) ((-1191 . -937) 157835) ((-743 . -1131) T) ((-527 . -1236) T) ((-522 . -1236) T) ((-520 . -1236) T) ((-362 . -102) T) ((-1235 . -1102) T) ((-1139 . -856) T) ((-830 . -862) T) ((-743 . -23) T) ((-354 . -1075) 157780) ((-1166 . -107) 157764) ((-1287 . -625) 157746) ((-1193 . -23) T) ((-1193 . -1131) T) ((-1192 . -1131) T) ((-1192 . -23) T) ((-527 . -1057) 157730) ((-1186 . -1131) T) ((-1145 . -1131) T) ((-354 . -111) 157659) ((-1023 . -1240) T) ((-127 . -1236) T) ((-931 . -1240) T) ((-1186 . -23) T) ((-1161 . -272) 157643) ((-706 . -296) NIL) ((-726 . -1236) T) ((-1161 . -232) 157627) ((-1145 . -23) T) ((-1094 . -1119) T) ((-1023 . -568) T) ((-931 . -568) T) ((-255 . -1236) T) ((-189 . -1236) T) ((-163 . -1236) T) ((-158 . -1236) T) ((-254 . -625) 157609) ((-827 . -237) 157506) ((-811 . -132) T) ((-722 . 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. -1236) T) ((-657 . -1236) T) ((-794 . -926) 150067) ((-792 . -926) 150046) ((-1208 . -1236) T) ((-366 . -1236) T) ((-363 . -1236) T) ((-355 . -1236) T) ((-273 . -1236) T) ((-253 . -1236) T) ((-466 . -926) 150025) ((-749 . -501) 150009) ((-1106 . -660) 149898) ((-711 . -628) 149833) ((-794 . -660) 149722) ((-635 . -1075) 149709) ((-491 . -1236) T) ((-354 . -379) T) ((-142 . -501) 149691) ((-792 . -660) 149580) ((-1160 . -1236) T) ((-561 . -862) T) ((-473 . -660) 149551) ((-273 . -899) 149410) ((-253 . -899) NIL) ((-118 . -1075) 149355) ((-466 . -660) 149244) ((-676 . -1057) 149221) ((-635 . -111) 149206) ((-402 . -1070) 149190) ((-366 . -1057) 149174) ((-363 . -1057) 149158) ((-355 . -1057) 149142) ((-273 . -1057) 148986) ((-253 . -1057) 148862) ((-927 . -1236) T) ((-118 . -111) 148791) ((-59 . -1236) T) ((-402 . -652) 148775) ((-633 . -1070) 148759) ((-531 . -1236) T) ((-528 . -1236) T) ((-509 . -1236) T) ((-508 . -1236) T) ((-449 . -625) 148741) ((-446 . -625) 148723) ((-633 . -652) 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. -1240) 141341) ((-493 . -1240) 141320) ((-1081 . -568) T) ((-969 . -568) 141251) ((-1191 . -23) T) ((-1170 . -1102) T) ((-1144 . -23) T) ((-866 . -23) T) ((-493 . -568) 141182) ((-1161 . -729) 141114) ((-682 . -1070) 141098) ((-1165 . -526) 141031) ((-682 . -652) 141015) ((-1054 . -626) NIL) ((-1054 . -625) 140997) ((-96 . -1102) T) ((-1315 . -1075) 140984) ((-878 . -729) 140954) ((-1315 . -111) 140939) ((-1230 . -47) 140908) ((-1186 . -862) NIL) ((-258 . -132) T) ((-257 . -132) T) ((-1123 . -1119) T) ((-1022 . -1119) T) ((-62 . -625) 140890) ((-1099 . -909) 140759) ((-1043 . -804) T) ((-1043 . -807) T) ((-1278 . -25) T) ((-1278 . -21) T) ((-1271 . -21) T) ((-1271 . -25) T) ((-882 . -660) 140746) ((-1250 . -21) T) ((-1250 . -25) T) ((-1046 . -152) 140730) ((-1023 . -234) 140717) ((-884 . -832) 140696) ((-884 . -937) T) ((-724 . -296) 140623) ((-608 . -21) T) ((-350 . -658) 140582) ((-108 . -909) NIL) ((-608 . -25) T) ((-607 . -21) T) ((-176 . -658) 140499) ((-40 . -738) T) ((-224 . 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-34) T) ((-794 . -47) 138509) ((-792 . -47) 138481) ((-1259 . -568) 138392) ((-1216 . -1236) T) ((-365 . -379) T) ((-493 . -1131) T) ((-1191 . -132) T) ((-1144 . -132) T) ((-466 . -47) 138371) ((-883 . -374) T) ((-866 . -132) T) ((-153 . -102) T) ((-1081 . -23) T) ((-969 . -23) T) ((-583 . -568) T) ((-828 . -25) T) ((-828 . -21) T) ((-1161 . -526) 138304) ((-604 . -1102) T) ((-598 . -1057) 138288) ((-1272 . -628) 138162) ((-493 . -23) T) ((-362 . -1077) T) ((-1230 . -915) 138143) ((-682 . -319) 138081) ((-1278 . -234) 138034) ((-1132 . -1293) 138004) ((-711 . -660) 137969) ((-1023 . -862) T) ((-1022 . -174) T) ((-980 . -146) 137948) ((-647 . -1119) T) ((-619 . -1119) T) ((-980 . -148) 137927) ((-747 . -148) 137906) ((-747 . -146) 137885) ((-670 . -1236) T) ((-990 . -862) T) ((-1271 . -234) 137831) ((-1250 . -234) 137648) ((-845 . -658) 137565) ((-486 . -937) 137544) ((-347 . -1236) T) ((-329 . -1070) 137379) ((-326 . -1075) 137289) ((-323 . -1075) 137218) ((-1018 . -296) 137176) ((-419 . -729) 137128) ((-329 . -652) 136969) ((-607 . -234) 136922) ((-713 . -860) T) ((-1272 . -1068) T) ((-326 . -111) 136818) ((-323 . -111) 136731) ((-97 . -1236) T) ((-981 . -102) T) ((-827 . -102) 136463) ((-724 . -626) NIL) ((-724 . -625) 136445) ((-1272 . -336) 136389) ((-670 . -1057) 136285) ((-1106 . -1236) T) ((-1054 . -298) 136260) ((-592 . -738) T) ((-576 . -806) T) ((-171 . -374) 136211) ((-576 . -803) T) ((-576 . -738) T) ((-507 . -738) T) ((-794 . -1236) T) ((-792 . -1236) T) ((-1165 . -501) 136195) ((-473 . -1236) T) ((-466 . -1236) T) ((-1308 . -1307) 136171) ((-1106 . -899) NIL) ((-883 . -1131) T) ((-118 . -926) NIL) ((-1306 . -1307) 136150) ((-661 . -1236) T) ((-794 . -899) NIL) ((-792 . -899) 136009) ((-1301 . -25) T) ((-1301 . -21) T) ((-1233 . -102) 135987) ((-1125 . -407) T) ((-635 . -660) 135974) ((-466 . -899) NIL) ((-687 . -102) 135924) ((-1106 . -1057) 135751) ((-883 . -23) T) ((-794 . -1057) 135610) ((-792 . -1057) 135467) ((-118 . -660) 135412) ((-466 . -1057) 135288) ((-284 . -1236) T) ((-326 . -628) 134852) ((-323 . -628) 134735) ((-50 . -1236) T) ((-402 . -658) 134704) ((-661 . -1057) 134688) ((-639 . -102) T) ((-593 . -1236) T) ((-530 . -1236) T) ((-224 . -501) 134672) ((-1286 . -34) T) ((-633 . -658) 134631) ((-299 . -1070) 134618) ((-137 . -628) 134602) ((-299 . -652) 134589) ((-647 . -729) 134573) ((-619 . -729) 134557) ((-682 . -38) 134517) ((-329 . -102) T) ((-1139 . -1075) 134504) ((-85 . -625) 134486) ((-50 . -1057) 134470) ((-1106 . -388) 134454) ((-794 . -388) 134438) ((-711 . -738) T) ((-711 . -806) T) ((-711 . -803) T) ((-60 . -57) 134400) ((-593 . -1057) 134387) ((-530 . -1057) 134364) ((-173 . -1236) T) ((-334 . -132) T) ((-326 . -1068) 134254) ((-323 . -1068) T) ((-171 . -1131) T) ((-792 . -388) 134238) ((-45 . -152) 134188) ((-1023 . -1011) 134170) ((-466 . -388) 134154) ((-419 . -174) T) ((-326 . -248) 134133) ((-323 . -248) T) ((-323 . -238) NIL) ((-304 . -1119) 133915) ((-227 . -132) T) ((-1139 . -111) 133900) ((-171 . -23) T) ((-811 . -148) 133879) ((-811 . -146) 133858) ((-258 . -651) 133764) ((-257 . -651) 133670) ((-329 . -294) 133636) ((-1176 . -526) 133569) ((-489 . -658) 133519) ((-494 . -909) 133386) ((-1152 . -1119) T) ((-227 . -1079) T) ((-827 . -319) 133324) ((-1106 . -915) 133259) ((-794 . -915) 133202) ((-792 . -915) 133186) ((-1308 . -38) 133156) ((-1306 . -38) 133126) ((-1259 . -1131) T) ((-867 . -1131) T) ((-466 . -915) 133103) ((-870 . -1119) T) ((-1259 . -23) T) ((-1139 . -628) 133075) ((-1081 . -132) T) ((-583 . -1131) T) ((-867 . -23) T) ((-635 . -738) T) ((-366 . -937) T) ((-363 . -937) T) ((-299 . -102) T) ((-355 . -937) T) ((-989 . -1102) T) ((-969 . -132) T) ((-828 . -234) 133020) ((-118 . -806) NIL) ((-118 . -803) NIL) ((-118 . -738) T) ((-1065 . -526) 132921) ((-706 . -926) NIL) ((-583 . -23) T) ((-493 . -132) T) ((-430 . -237) 132872) ((-687 . -319) 132810) ((-225 . -1236) T) ((-647 . -773) T) ((-619 . -773) T) ((-1250 . -862) NIL) ((-1099 . -1070) 132720) ((-1022 . -300) T) ((-706 . -660) 132670) ((-258 . -25) T) ((-362 . -1119) T) ((-258 . -21) T) ((-257 . -25) T) ((-257 . -21) T) ((-153 . -38) 132654) ((-2 . -102) T) ((-927 . -937) T) ((-1099 . -652) 132522) ((-494 . -1293) 132492) ((-1139 . -1068) T) ((-723 . -317) T) ((-370 . -1070) 132444) ((-364 . -1070) 132396) ((-356 . -1070) 132348) ((-370 . -652) 132300) ((-225 . -1057) 132277) ((-364 . -652) 132229) ((-108 . -1070) 132179) ((-356 . -652) 132131) ((-304 . -729) 132073) ((-713 . -1077) T) ((-499 . -464) T) ((-419 . -526) 131985) ((-108 . -652) 131935) ((-219 . -464) T) ((-1139 . -238) T) ((-305 . -152) 131885) ((-1018 . -626) 131846) ((-1018 . -625) 131828) ((-1008 . -625) 131810) ((-117 . -1077) T) ((-666 . -1075) 131794) ((-227 . -505) T) ((-411 . -625) 131776) ((-411 . -626) 131753) ((-1073 . -1293) 131723) ((-666 . -111) 131702) ((-682 . -917) 131625) ((-1161 . -501) 131609) ((-1310 . -658) 131568) ((-392 . -658) 131537) ((-63 . -453) T) ((-63 . -407) T) ((-1178 . -102) T) ((-883 . -132) 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130263) ((-1132 . -652) 130185) ((-1185 . -102) T) ((-1013 . -102) T) ((-1012 . -21) T) ((-128 . -1029) 130169) ((-122 . -1029) 130153) ((-1012 . -25) T) ((-918 . -120) 130137) ((-1177 . -102) T) ((-1259 . -132) T) ((-1191 . -25) T) ((-1191 . -21) T) ((-354 . -1236) T) ((-1144 . -25) T) ((-867 . -132) T) ((-406 . -1236) T) ((-1144 . -21) T) ((-866 . -25) T) ((-866 . -21) T) ((-794 . -317) 130116) ((-1178 . -319) 129911) ((-1176 . -501) 129895) ((-1169 . -152) 129845) ((-659 . -102) 129795) ((-644 . -102) T) ((-1165 . -625) 129757) ((-583 . -132) T) ((-633 . -860) 129736) ((-1165 . -626) 129697) ((-1043 . -803) T) ((-1043 . -806) T) ((-1043 . -738) T) ((-827 . -917) 129566) ((-724 . -1075) 129389) ((-496 . -319) 129327) ((-465 . -429) 129297) ((-362 . -174) T) ((-299 . -38) 129284) ((-258 . -234) 129175) ((-257 . -234) 129066) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-279 . -102) T) ((-278 . -102) T) ((-354 . -1057) 129043) ((-277 . -102) T) ((-214 . 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126511) ((-1023 . -148) T) ((-1023 . -146) NIL) ((-390 . -1131) T) ((-334 . -25) T) ((-332 . -23) T) ((-960 . -862) 126490) ((-724 . -336) 126467) ((-493 . -651) 126415) ((-40 . -1057) 126303) ((-724 . -238) T) ((-713 . -729) 126290) ((-350 . -1119) T) ((-176 . -1119) T) ((-341 . -862) T) ((-430 . -464) 126240) ((-390 . -23) T) ((-370 . -38) 126205) ((-364 . -38) 126170) ((-356 . -38) 126135) ((-80 . -453) T) ((-80 . -407) T) ((-227 . -25) T) ((-227 . -21) T) ((-848 . -1131) T) ((-108 . -38) 126085) ((-839 . -1131) T) ((-786 . -1119) T) ((-117 . -729) 126072) ((-684 . -1057) 126056) ((-624 . -102) T) ((-848 . -23) T) ((-839 . -23) T) ((-1176 . -296) 126008) ((-1132 . -319) 125946) ((-494 . -1070) 125847) ((-1121 . -240) 125831) ((-64 . -408) T) ((-64 . -407) T) ((-1170 . -102) T) ((-110 . -102) T) ((-494 . -652) 125753) ((-40 . -388) 125730) ((-96 . -102) T) ((-665 . -864) 125714) ((-1191 . -234) 125701) ((-1154 . -1102) T) ((-1081 . -21) T) ((-1081 . -25) T) ((-1073 . -1070) 125685) 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123147) ((-1018 . -248) 123126) ((-1018 . -238) 123105) ((-1278 . -148) 123084) ((-1271 . -148) 123063) ((-845 . -1119) T) ((-1271 . -146) 123042) ((-1270 . -1240) 123021) ((-1250 . -146) 122928) ((-1250 . -148) 122835) ((-1249 . -1240) 122814) ((-390 . -132) T) ((-227 . -234) 122801) ((-176 . -174) T) ((-576 . -899) 122783) ((0 . -1119) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1236) T) ((-49 . -1119) T) ((-1272 . -660) 122688) ((-1270 . -568) 122639) ((-726 . -1131) T) ((-1249 . -568) 122590) ((-576 . -1057) 122572) ((-607 . -148) 122551) ((-607 . -146) 122530) ((-507 . -1057) 122473) ((-1154 . -1156) T) ((-87 . -395) T) ((-87 . -407) T) ((-884 . -374) T) ((-848 . -132) T) ((-839 . -132) T) ((-981 . -658) 122417) ((-726 . -23) T) ((-518 . -625) 122383) ((-514 . -625) 122365) ((-827 . -658) 122144) ((-1310 . -1077) T) ((-390 . -1079) T) ((-1045 . -1119) 122122) ((-55 . -1057) 122104) ((-918 . -34) T) ((-494 . -319) 122042) ((-604 . -102) T) ((-1176 . -626) 122003) ((-1176 . -625) 121935) ((-1197 . -1070) 121818) ((-45 . -102) T) ((-829 . -102) T) ((-1197 . -652) 121715) ((-1287 . -1236) T) ((-1259 . -25) T) ((-1259 . -21) T) ((-1081 . -234) 121702) ((-867 . -25) T) ((-254 . -1236) T) ((-44 . -378) 121686) ((-867 . -21) T) ((-743 . -464) 121637) ((-1309 . -625) 121619) ((-722 . -1236) T) ((-711 . -1236) T) ((-1298 . -1070) 121589) ((-1073 . -319) 121527) ((-683 . -1102) T) ((-618 . -1102) T) ((-402 . -1119) T) ((-583 . -25) T) ((-583 . -21) T) ((-182 . -1102) T) ((-162 . -1102) T) ((-157 . -1102) T) ((-155 . -1102) T) ((-1298 . -652) 121497) ((-633 . -1119) T) ((-711 . -899) 121479) ((-1286 . -1236) T) ((-229 . -319) 121417) ((-145 . -379) T) ((-1209 . -1236) T) ((-1065 . -626) 121359) ((-1065 . -625) 121302) ((-323 . -926) NIL) ((-1244 . -856) T) ((-1132 . -917) 121171) ((-711 . -1057) 121116) ((-723 . -937) T) ((-486 . -1240) 121095) ((-1192 . -464) 121074) ((-1186 . -464) 121053) ((-340 . -102) T) ((-884 . -1131) T) ((-329 . -658) 120935) ((-326 . -660) 120664) ((-323 . -660) 120593) ((-486 . -568) 120544) ((-350 . -526) 120510) ((-562 . -152) 120460) ((-40 . -317) T) ((-855 . -625) 120442) ((-713 . -300) T) ((-884 . -23) T) ((-390 . -505) T) ((-1099 . -272) 120412) ((-1099 . -232) 120382) ((-524 . -102) T) ((-419 . -626) 120189) ((-419 . -625) 120171) ((-270 . -625) 120153) ((-117 . -300) T) ((-1272 . -738) T) ((-635 . -1236) T) ((-1311 . -1119) T) ((-1270 . -374) 120132) ((-1249 . -374) 120111) ((-1299 . -34) T) ((-1244 . -1119) T) ((-118 . -1236) T) ((-108 . -272) 120093) ((-108 . -232) 120075) ((-1197 . -102) T) ((-489 . -1119) T) ((-535 . -501) 120059) ((-749 . -34) T) ((-665 . -1070) 120043) ((-665 . -652) 120013) ((-883 . -234) NIL) ((-142 . -34) T) ((-118 . -897) 119990) ((-118 . -899) NIL) ((-635 . -1057) 119873) ((-1298 . -102) T) ((-1278 . -237) 119832) ((-656 . -862) 119811) ((-1271 . -237) 119763) ((-1250 . -237) 119586) ((-305 . -102) T) ((-724 . -379) 119565) ((-118 . -1057) 119542) ((-402 . -729) 119526) ((-607 . -237) 119485) ((-633 . -729) 119469) ((-1124 . -1236) T) ((-45 . -319) 119273) ((-828 . -146) 119252) ((-828 . -148) 119231) ((-299 . -658) 119203) ((-1309 . -393) 119182) ((-831 . -862) T) ((-1288 . -1119) T) ((-1178 . -231) 119129) ((-398 . -862) 119108) ((-1278 . -35) 119074) ((-1278 . -1224) 119040) ((-1278 . -1221) 119006) ((-1271 . -1221) 118972) ((-527 . -132) T) ((-1271 . -1224) 118938) ((-1250 . -1221) 118904) ((-1250 . -1224) 118870) ((-1278 . -95) 118836) ((-1271 . -95) 118802) ((-430 . -909) 118723) ((-647 . -625) 118692) ((-619 . -625) 118661) ((-227 . -862) T) ((-1271 . -35) 118627) ((-1270 . -1131) T) ((-1250 . -95) 118593) ((-1139 . -660) 118565) ((-1250 . -35) 118531) ((-1249 . -1131) T) ((-605 . -152) 118513) ((-1099 . -360) 118492) ((-176 . -300) T) ((-118 . -388) 118469) ((-118 . -349) 118446) ((-171 . -234) 118371) ((-882 . -317) T) ((-323 . -806) NIL) ((-323 . -803) NIL) ((-326 . -738) 118220) ((-323 . -738) T) ((-486 . -374) 118199) ((-370 . -360) 118178) ((-364 . -360) 118157) ((-356 . -360) 118136) ((-326 . -485) 118115) ((-1270 . -23) T) ((-1249 . -23) T) ((-730 . -1131) T) ((-726 . -132) T) ((-665 . -102) T) ((-489 . -729) 118080) ((-45 . -292) 118030) ((-105 . -1119) T) ((-68 . -625) 118012) ((-989 . -102) T) ((-876 . -102) T) ((-635 . -915) 117971) ((-1310 . -1119) T) ((-392 . -1119) T) ((-1259 . -234) 117958) ((-1235 . -1119) T) ((-82 . -1236) T) ((-1132 . -272) 117927) ((-1081 . -862) T) ((-118 . -915) NIL) ((-794 . -937) 117906) ((-725 . -862) T) ((-543 . -1119) T) ((-512 . -1119) T) ((-366 . -1240) T) ((-363 . -1240) T) ((-355 . -1240) T) ((-273 . -1240) 117885) ((-253 . -1240) 117864) ((-545 . -872) T) ((-1132 . -232) 117833) ((-1177 . -840) T) ((-1161 . -1075) 117817) ((-402 . -773) T) ((-706 . -1236) T) ((-703 . -1057) 117801) ((-366 . -568) T) ((-363 . -568) T) ((-355 . -568) T) ((-273 . -568) 117732) ((-253 . -568) 117663) ((-537 . -1102) T) ((-1161 . -111) 117642) ((-465 . -756) 117612) ((-878 . -1075) 117582) ((-829 . -38) 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. -628) 115800) ((-883 . -862) NIL) ((-576 . -1041) T) ((-507 . -1041) T) ((-1152 . -625) 115782) ((-1132 . -243) 115761) ((-216 . -102) T) ((-1169 . -102) T) ((-71 . -625) 115743) ((-1043 . -1236) T) ((-1161 . -1068) T) ((-1197 . -38) 115640) ((-870 . -625) 115622) ((-576 . -557) T) ((-682 . -1077) T) ((-743 . -966) 115575) ((-365 . -1236) T) ((-1161 . -238) 115554) ((-1101 . -1119) T) ((-1053 . -25) T) ((-1053 . -21) T) ((-1022 . -1075) 115499) ((-922 . -102) T) ((-878 . -1068) T) ((-706 . -915) NIL) ((-366 . -339) 115483) ((-366 . -374) T) ((-363 . -339) 115467) ((-363 . -374) T) ((-355 . -339) 115451) ((-355 . -374) T) ((-499 . -102) T) ((-1298 . -38) 115421) ((-558 . -862) T) ((-535 . -699) 115371) ((-219 . -102) T) ((-1043 . -1057) 115251) ((-1022 . -111) 115180) ((-1193 . -992) 115149) ((-1192 . -992) 115111) ((-532 . -152) 115095) ((-1099 . -381) 115074) ((-362 . -625) 115056) ((-332 . -21) T) ((-365 . -1057) 115033) ((-332 . -25) T) ((-1186 . -992) 115002) ((-48 . -1236) T) 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. -628) 112547) ((-512 . -526) NIL) ((-494 . -243) 112526) ((-419 . -628) 112424) ((-980 . -1070) 112307) ((-747 . -1070) 112277) ((-980 . -652) 112174) ((-1191 . -146) 112153) ((-747 . -652) 112123) ((-465 . -1070) 112093) ((-1191 . -148) 112072) ((-1144 . -148) 112051) ((-1144 . -146) 112030) ((-647 . -1075) 112014) ((-619 . -1075) 111998) ((-465 . -652) 111968) ((-1193 . -1277) 111952) ((-1193 . -1264) 111929) ((-1192 . -1269) 111890) ((-682 . -1119) T) ((-682 . -1072) 111830) ((-1192 . -1264) 111800) ((-560 . -1119) T) ((-499 . -1171) T) ((-1192 . -1267) 111784) ((-1186 . -1248) 111745) ((-830 . -275) 111729) ((-219 . -1171) T) ((-354 . -937) T) ((-99 . -1236) T) ((-647 . -111) 111708) ((-619 . -111) 111687) ((-1186 . -1264) 111664) ((-855 . -1068) 111643) ((-1186 . -1246) 111627) ((-527 . -25) T) ((-507 . -312) T) ((-523 . -23) T) ((-522 . -25) T) ((-520 . -25) T) ((-519 . -23) T) ((-430 . -1070) 111601) ((-419 . -1068) T) ((-329 . -1077) T) ((-706 . -317) T) ((-430 . -652) 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106274) ((-1193 . -652) 106171) ((-1192 . -652) 106012) ((-723 . -1240) T) ((-1186 . -652) 105808) ((-1176 . -663) 105792) ((-1145 . -652) 105689) ((-831 . -397) 105673) ((-723 . -568) T) ((-607 . -909) 105584) ((-326 . -897) 105568) ((-326 . -899) 105493) ((-323 . -897) 105454) ((-140 . -1236) T) ((-137 . -1236) T) ((-115 . -1236) T) ((-323 . -899) NIL) ((-811 . -319) 105419) ((-329 . -729) 105260) ((-398 . -397) 105244) ((-334 . -333) 105221) ((-497 . -102) T) ((-486 . -25) T) ((-486 . -21) T) ((-430 . -38) 105195) ((-326 . -1057) 104858) ((-227 . -1221) T) ((-227 . -1224) T) ((-3 . -625) 104840) ((-323 . -1057) 104770) ((-884 . -234) 104715) ((-2 . -1119) T) ((-2 . |RecordCategory|) T) ((-1132 . -1077) 104693) ((-845 . -625) 104675) ((-1081 . -237) T) ((-592 . -937) T) ((-576 . -832) T) ((-576 . -937) T) ((-507 . -937) T) ((-137 . -1057) 104659) ((-227 . -95) T) ((-171 . -148) 104638) ((-75 . -453) T) ((0 . -625) 104620) ((-75 . -407) T) ((-171 . -146) 104571) ((-227 . -35) T) ((-49 . -625) 104553) ((-489 . -1077) T) ((-499 . -272) 104535) ((-499 . -232) 104517) ((-496 . -987) 104501) ((-219 . -272) 104483) ((-219 . -232) 104465) ((-81 . -453) T) ((-81 . -407) T) ((-1165 . -34) T) ((-743 . -102) T) ((-665 . -658) 104424) ((-1045 . -625) 104391) ((-512 . -296) 104341) ((-326 . -388) 104310) ((-323 . -388) 104271) ((-323 . -349) 104232) ((-1104 . -625) 104214) ((-828 . -966) 104161) ((-674 . -132) T) ((-1259 . -146) 104140) ((-1259 . -148) 104119) ((-1193 . -102) T) ((-1192 . -102) T) ((-1186 . -102) T) ((-1178 . -1119) T) ((-1145 . -102) T) ((-1094 . -1236) T) ((-224 . -34) T) ((-299 . -729) 104106) ((-1178 . -622) 104082) ((-605 . -319) NIL) ((-1278 . -1277) 104066) ((-1169 . -231) 104016) ((-496 . -1119) 103994) ((-450 . -1236) T) ((-402 . -625) 103976) ((-522 . -862) T) ((-1139 . -1236) T) ((-1278 . -1264) 103953) ((-1271 . -1269) 103914) ((-1271 . -1264) 103884) ((-1271 . -1267) 103868) ((-1250 . -1248) 103829) ((-1250 . -1264) 103806) ((-1250 . -1246) 103790) 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-1119) T) ((-280 . -1119) T) ((-279 . -1119) T) ((-278 . -1119) T) ((-277 . -1119) T) ((-214 . -1119) T) ((-213 . -1119) T) ((-171 . -1224) 100186) ((-171 . -1221) 100164) ((-211 . -1119) T) ((-210 . -1119) T) ((-117 . -1068) T) ((-209 . -1119) T) ((-208 . -1119) T) ((-205 . -1119) T) ((-204 . -1119) T) ((-203 . -1119) T) ((-202 . -1119) T) ((-201 . -1119) T) ((-200 . -1119) T) ((-199 . -1119) T) ((-198 . -1119) T) ((-197 . -1119) T) ((-196 . -1119) T) ((-195 . -1119) T) ((-245 . -102) 99896) ((-171 . -35) 99874) ((-171 . -95) 99852) ((-666 . -1057) 99748) ((-494 . -1077) 99726) ((-1132 . -1119) 99478) ((-1161 . -34) T) ((-682 . -501) 99462) ((-73 . -1236) T) ((-105 . -625) 99444) ((-906 . -1236) T) ((-1310 . -625) 99426) ((-392 . -625) 99408) ((-350 . -628) 99360) ((-176 . -628) 99277) ((-1235 . -502) 99258) ((-743 . -38) 99107) ((-583 . -1224) T) ((-583 . -1221) T) ((-543 . -625) 99089) ((-532 . -319) 99027) ((-512 . -625) 99009) ((-512 . -626) 98991) ((-1235 . -625) 98957) ((-1186 . -1171) NIL) ((-215 . -1236) T) ((-1046 . -1090) 98926) ((-1046 . -1119) T) ((-1023 . -102) T) ((-990 . -102) T) ((-931 . -102) T) ((-906 . -1057) 98903) ((-1161 . -738) T) ((-1022 . -660) 98810) ((-488 . -1119) T) ((-475 . -1119) T) ((-598 . -23) T) ((-583 . -35) T) ((-583 . -95) T) ((-439 . -102) T) ((-1082 . -231) 98756) ((-1193 . -38) 98653) ((-1192 . -38) 98494) ((-878 . -738) T) ((-706 . -937) T) ((-523 . -25) T) ((-519 . -21) T) ((-519 . -25) T) ((-1186 . -38) 98290) ((-350 . -1068) T) ((-145 . -1236) T) ((-1099 . -174) T) ((-176 . -1068) T) ((-1145 . -38) 98187) ((-724 . -47) 98164) ((-370 . -174) T) ((-364 . -174) T) ((-531 . -57) 98138) ((-509 . -57) 98088) ((-362 . -1305) 98065) ((-227 . -464) T) ((-329 . -300) 98016) ((-356 . -174) T) ((-176 . -248) T) ((-1249 . -862) 97915) ((-108 . -174) T) ((-884 . -1011) 97899) ((-670 . -1131) T) ((-593 . -374) T) ((-593 . -339) 97886) ((-530 . -339) 97863) ((-530 . -374) T) ((-326 . -317) 97842) ((-323 . -317) T) ((-614 . -862) 97821) 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95998) ((-299 . -300) T) ((-1250 . -1070) 95788) ((-1101 . -625) 95770) ((-1101 . -626) 95751) ((-419 . -926) 95730) ((-1230 . -132) T) ((-50 . -1131) T) ((-1186 . -412) 95682) ((-1043 . -937) T) ((-1022 . -738) T) ((-855 . -660) 95655) ((-724 . -899) NIL) ((-608 . -1070) 95615) ((-593 . -1131) T) ((-530 . -1131) T) ((-607 . -1070) 95498) ((-1176 . -34) T) ((-1023 . -319) NIL) ((-827 . -501) 95482) ((-608 . -652) 95455) ((-365 . -937) T) ((-607 . -652) 95352) ((-927 . -234) 95339) ((-419 . -660) 95255) ((-50 . -23) T) ((-723 . -132) T) ((-724 . -1057) 95135) ((-593 . -23) T) ((-108 . -526) NIL) ((-530 . -23) T) ((-171 . -421) 95106) ((-1159 . -1119) T) ((-1301 . -1300) 95090) ((-743 . -917) 95067) ((-713 . -807) T) ((-713 . -804) T) ((-1139 . -317) T) ((-390 . -148) T) ((-290 . -625) 95049) ((-289 . -625) 95031) ((-1249 . -1011) 95001) ((-48 . -937) T) ((-687 . -501) 94985) ((-258 . -1293) 94955) ((-257 . -1293) 94925) ((-1107 . -237) T) ((-1195 . -862) T) ((-1139 . -1041) T) ((-1065 . -34) T) ((-848 . -148) 94904) ((-848 . -146) 94883) ((-749 . -107) 94867) ((-624 . -133) T) ((-1197 . -1077) T) ((-494 . -1119) 94619) ((-1193 . -917) 94532) ((-1192 . -917) 94438) ((-1186 . -917) 94199) ((-883 . -464) T) ((-85 . -1236) T) ((-142 . -107) 94181) ((-1145 . -917) 94165) ((-724 . -388) 94149) ((-845 . -628) 94017) ((-1309 . -738) T) ((-1298 . -1077) T) ((-1278 . -102) T) ((-1139 . -557) T) ((-591 . -102) T) ((-130 . -502) 93999) ((-1271 . -102) T) ((-402 . -1075) 93983) ((-1191 . -966) 93952) ((-44 . -296) 93929) ((-130 . -625) 93896) ((-52 . -625) 93878) ((-1144 . -966) 93845) ((-665 . -423) 93829) ((-1250 . -102) T) ((-1177 . -526) NIL) ((-674 . -25) T) ((-633 . -1075) 93813) ((-674 . -21) T) ((-980 . -658) 93723) ((-747 . -658) 93668) ((-727 . -658) 93640) ((-402 . -111) 93619) ((-224 . -261) 93603) ((-1073 . -1072) 93543) ((-1073 . -1119) T) ((-1023 . -1171) T) ((-830 . -1119) T) ((-465 . -658) 93458) ((-647 . -660) 93442) ((-633 . -111) 93421) ((-619 . -660) 93405) ((-354 . -1240) T) ((-608 . -102) T) ((-321 . -502) 93386) ((-598 . -132) T) ((-607 . -102) T) ((-426 . -1119) T) ((-396 . -1119) T) ((-321 . -625) 93352) ((-229 . -1119) 93330) ((-659 . -526) 93263) ((-644 . -526) 93107) ((-845 . -1068) 93086) ((-656 . -152) 93070) ((-354 . -568) T) ((-724 . -915) 93013) ((-562 . -231) 92963) ((-1278 . -294) 92929) ((-1271 . -294) 92895) ((-1099 . -300) 92846) ((-499 . -860) T) ((-225 . -1131) T) ((-1250 . -294) 92812) ((-1230 . -505) 92778) ((-1023 . -38) 92728) ((-219 . -860) T) ((-430 . -658) 92687) ((-931 . -38) 92639) ((-855 . -806) 92618) ((-855 . -803) 92597) ((-855 . -738) 92576) ((-370 . -300) T) ((-364 . -300) T) ((-356 . -300) T) ((-171 . -464) 92507) ((-439 . -38) 92491) ((-225 . -23) T) ((-108 . -300) T) ((-419 . -806) 92470) ((-419 . -803) 92449) ((-419 . -738) T) ((-512 . -298) 92424) ((-489 . -1075) 92389) ((-670 . -132) T) ((-633 . -628) 92358) ((-1132 . -526) 92291) ((-347 . -132) T) ((-171 . -414) 92270) ((-494 . -729) 92212) ((-827 . -296) 92189) ((-489 . -111) 92145) ((-665 . -1077) T) ((-1191 . -909) 92048) ((-1144 . -909) 92030) ((-828 . -1070) 91873) ((-1297 . -1102) T) ((-1259 . -464) 91804) ((-828 . -652) 91653) ((-1296 . -1102) T) ((-1106 . -132) T) ((-1073 . -729) 91595) ((-1046 . -526) 91528) ((-794 . -132) T) ((-792 . -132) T) ((-583 . -464) T) ((-633 . -1068) T) ((-604 . -1119) T) ((-545 . -175) T) ((-473 . -132) T) ((-466 . -132) T) ((-390 . -237) T) ((-1018 . -1236) T) ((-45 . -1119) T) ((-396 . -729) 91498) ((-829 . -1119) T) ((-488 . -526) 91431) ((-475 . -526) 91364) ((-1311 . -628) 91346) ((-465 . -378) 91316) ((-45 . -622) 91295) ((-411 . -1236) T) ((-326 . -312) T) ((-839 . -237) 91274) ((-489 . -628) 91224) ((-1250 . -319) 91109) ((-682 . -625) 91071) ((-59 . -862) 91050) ((-1023 . -412) 91032) ((-560 . -625) 91014) ((-811 . -658) 90973) ((-827 . -616) 90950) ((-528 . -862) 90929) ((-508 . -862) 90908) ((-1018 . -1057) 90804) ((-40 . -1240) T) ((-245 . -917) 90673) ((-50 . -132) T) ((-593 . -132) T) ((-530 . -132) T) ((-304 . -660) 90533) ((-354 . -339) 90510) ((-354 . -374) T) ((-332 . -333) 90487) ((-329 . -296) 90445) ((-40 . -568) T) ((-390 . -1221) T) ((-390 . -1224) T) ((-1054 . -1212) 90420) ((-1208 . -240) 90370) ((-1186 . -232) 90322) ((-1186 . -272) 90274) ((-340 . -1119) T) ((-390 . -95) T) ((-390 . -35) T) ((-1054 . -107) 90220) ((-489 . -1068) T) ((-1310 . -1075) 90204) ((-491 . -240) 90154) ((-1178 . -501) 90088) ((-1301 . -1070) 90072) ((-392 . -1075) 90056) ((-1301 . -652) 90026) ((-489 . -248) T) ((-828 . -102) T) ((-726 . -148) 90005) ((-726 . -146) 89984) ((-496 . -501) 89968) ((-497 . -346) 89937) ((-524 . -1119) T) ((-1310 . -111) 89916) ((-1018 . -388) 89900) ((-425 . -102) T) ((-392 . -111) 89879) ((-1018 . -349) 89863) ((-288 . -1002) 89847) ((-287 . -1002) 89831) ((-1023 . -917) NIL) ((-1308 . -625) 89813) ((-1306 . -625) 89795) ((-110 . -526) NIL) ((-1191 . -1262) 89779) ((-866 . -864) 89763) ((-1197 . -1119) T) ((-103 . -1236) T) ((-969 . -966) 89724) ((-829 . -729) 89666) ((-1250 . -1171) NIL) ((-493 . -966) 89611) ((-1081 . -144) T) ((-60 . -102) 89561) ((-44 . -625) 89543) ((-78 . -625) 89525) ((-362 . -660) 89470) ((-1298 . -1119) T) ((-523 . -862) T) ((-299 . -296) 89449) ((-354 . -1131) T) ((-305 . -1119) T) ((-1018 . -915) 89408) ((-305 . -622) 89387) ((-1310 . -628) 89336) ((-1278 . -38) 89233) ((-1271 . -38) 89074) ((-1250 . -38) 88870) ((-499 . -1077) T) ((-392 . -628) 88854) ((-219 . -1077) T) ((-354 . -23) T) ((-153 . -625) 88836) ((-845 . -807) 88815) ((-845 . -804) 88794) ((-1235 . -628) 88775) ((-608 . -38) 88748) ((-607 . -38) 88645) ((-882 . -568) T) ((-225 . -132) T) ((-329 . -1021) 88611) ((-79 . -625) 88593) ((-724 . -317) 88572) ((-304 . -738) 88474) ((-836 . -102) T) ((-876 . -856) T) ((-304 . -485) 88453) ((-1301 . -102) T) ((-40 . -374) T) ((-884 . -148) 88432) ((-497 . -658) 88414) ((-884 . -146) 88393) ((-1177 . -501) 88375) ((-1310 . -1068) T) ((-494 . -526) 88308) ((-1165 . -1236) T) ((-981 . -625) 88290) ((-659 . -501) 88274) ((-644 . -501) 88205) ((-827 . -625) 87898) ((-48 . -27) T) ((-1197 . -729) 87795) ((-969 . -909) 87774) ((-665 . -1119) T) ((-873 . -872) T) ((-448 . -375) 87748) ((-743 . -658) 87658) ((-493 . -909) 87633) ((-1121 . -102) T) ((-989 . -1119) T) ((-876 . -1119) T) ((-828 . -319) 87620) ((-545 . -539) T) ((-545 . -588) T) ((-1306 . -393) 87592) ((-1073 . -526) 87525) ((-1178 . -296) 87501) ((-245 . -272) 87470) ((-245 . -232) 87439) ((-258 . -1070) 87340) ((-257 . -1070) 87241) ((-1298 . -729) 87211) ((-1185 . -93) T) ((-1013 . -93) T) ((-829 . -174) 87190) ((-258 . -652) 87112) ((-257 . -652) 87034) ((-1233 . -502) 87011) ((-590 . -1236) T) ((-229 . -526) 86944) ((-633 . -807) 86923) ((-633 . -804) 86902) ((-1233 . -625) 86814) ((-224 . -1236) T) ((-687 . -625) 86746) ((-1193 . -658) 86656) ((-1176 . -1029) 86640) ((-960 . -102) 86570) ((-362 . -738) T) ((-873 . -625) 86552) ((-1192 . -658) 86434) ((-1186 . -658) 86271) ((-1145 . -658) 86181) ((-1250 . -412) 86133) ((-1132 . -501) 86117) ((-60 . -319) 86055) ((-341 . -102) T) ((-1230 . -21) T) ((-1230 . -25) T) ((-40 . -1131) T) ((-723 . -21) T) ((-639 . -625) 86037) ((-527 . -333) 86016) ((-723 . -25) T) ((-451 . -102) T) ((-108 . -296) NIL) ((-938 . -1131) T) ((-40 . -23) T) ((-783 . -1131) T) ((-576 . -1240) T) ((-507 . -1240) T) ((-1023 . -272) 85998) ((-329 . -625) 85980) ((-1023 . -232) 85962) ((-171 . -167) 85946) ((-592 . -568) T) ((-576 . -568) T) ((-507 . -568) T) ((-783 . -23) T) ((-1270 . -148) 85925) ((-1270 . -146) 85904) ((-1178 . -616) 85880) ((-1249 . -146) 85805) ((-1046 . -501) 85789) ((-1243 . -1236) T) ((-1249 . -148) 85714) ((-1301 . -1307) 85693) ((-883 . -909) NIL) ((-488 . -501) 85677) ((-475 . -501) 85661) ((-535 . -34) T) ((-665 . -729) 85631) ((-1278 . -917) 85544) ((-1271 . -917) 85450) ((-1250 . -917) 85211) ((-112 . -986) T) ((-1197 . -174) 85162) ((-674 . -862) 85141) ((-376 . -102) T) ((-607 . -917) 85054) ((-245 . -243) 85033) ((-258 . -102) T) 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-616) 83758) ((-670 . -21) T) ((-670 . -25) T) ((-605 . -1163) T) ((-1132 . -296) 83735) ((-347 . -25) T) ((-347 . -21) T) ((-902 . -1236) T) ((-898 . -1236) T) ((-1308 . -1075) 83719) ((-245 . -658) 83498) ((-507 . -374) T) ((-1306 . -1075) 83482) ((-1301 . -38) 83452) ((-1270 . -1221) 83418) ((-1270 . -1224) 83384) ((-1259 . -909) 83287) ((-1191 . -1070) 83110) ((-1161 . -1236) T) ((-1144 . -1070) 82953) ((-866 . -1070) 82937) ((-644 . -616) 82912) ((-1270 . -95) 82878) ((-1270 . -237) 82830) ((-1253 . -102) 82808) ((-1191 . -652) 82637) ((-1144 . -652) 82486) ((-866 . -652) 82456) ((-1250 . -232) 82408) ((-1106 . -25) T) ((-561 . -1119) T) ((-1106 . -21) T) ((-980 . -1077) T) ((-543 . -804) T) ((-543 . -807) T) ((-118 . -1240) T) ((-878 . -1236) T) ((-635 . -568) T) ((-794 . -25) T) ((-794 . -21) T) ((-792 . -21) T) ((-792 . -25) T) ((-747 . -1077) T) ((-727 . -1077) T) ((-682 . -1075) 82392) ((-529 . -1102) T) ((-473 . -25) T) ((-118 . -568) T) ((-473 . -21) T) ((-466 . -25) T) ((-466 . -21) T) ((-1250 . -272) 82344) ((-1170 . -93) T) ((-1161 . -1057) 82240) ((-829 . -300) 82219) ((-1249 . -1221) 82185) ((-835 . -1119) T) ((-983 . -986) T) ((-682 . -111) 82164) ((-629 . -1236) T) ((-305 . -526) 81956) ((-1249 . -1224) 81922) ((-1249 . -237) 81781) ((-1244 . -379) T) ((-258 . -319) 81719) ((-257 . -319) 81657) ((-1241 . -856) T) ((-1178 . -626) NIL) ((-1178 . -625) 81639) ((-1161 . -388) 81623) ((-1139 . -832) T) ((-1139 . -937) T) ((-96 . -93) T) ((-1132 . -616) 81600) ((-1099 . -626) 81584) ((-1099 . -625) 81566) ((-1023 . -658) 81516) ((-931 . -658) 81453) ((-827 . -298) 81430) ((-496 . -625) 81362) ((-620 . -152) 81309) ((-499 . -729) 81259) ((-430 . -1077) T) ((-494 . -501) 81243) ((-439 . -658) 81202) ((-337 . -862) 81181) ((-350 . -660) 81155) ((-50 . -21) T) ((-50 . -25) T) ((-219 . -729) 81105) ((-171 . -736) 81076) ((-176 . -660) 81008) ((-593 . -21) T) ((-593 . -25) T) ((-530 . -25) T) ((-530 . -21) T) ((-487 . -152) 80958) ((-1080 . -625) 80940) ((-1012 . -102) T) ((-874 . -102) T) ((-828 . -917) 80840) ((-811 . -423) 80803) ((-40 . -132) T) ((-711 . -374) T) ((-713 . -738) T) ((-713 . -806) T) ((-713 . -803) T) ((-214 . -910) T) ((-592 . -1131) T) ((-576 . -1131) T) ((-507 . -1131) T) ((-370 . -625) 80785) ((-364 . -625) 80767) ((-356 . -625) 80749) ((-66 . -408) T) ((-66 . -407) T) ((-108 . -626) 80679) ((-108 . -625) 80621) ((-213 . -910) T) ((-975 . -152) 80605) ((-783 . -132) T) ((-682 . -628) 80523) ((-135 . -738) T) ((-117 . -738) T) ((-1270 . -35) 80489) ((-1073 . -501) 80473) ((-592 . -23) T) ((-576 . -23) T) ((-507 . -23) T) ((-1249 . -95) 80439) ((-1249 . -35) 80405) ((-1191 . -102) T) ((-1144 . -102) T) ((-866 . -102) T) ((-229 . -501) 80389) ((-1308 . -111) 80368) ((-1306 . -111) 80347) ((-44 . -1075) 80331) ((-1309 . -1236) T) ((-1308 . -628) 80277) ((-1308 . -1068) T) ((-1306 . -628) 80206) ((-1306 . -1068) T) ((-1259 . -1262) 80190) ((-867 . -864) 80174) ((-1197 . -300) 80153) ((-1123 . -1236) T) ((-110 . -296) 80103) ((-1022 . -1236) T) ((-129 . -152) 80085) ((-1161 . -915) 80044) ((-44 . -111) 80023) ((-1241 . -1119) T) ((-1200 . -1281) T) ((-1186 . -860) NIL) ((-1185 . -502) 80004) ((-682 . -1068) T) ((-1185 . -625) 79970) ((-1177 . -625) 79952) ((-486 . -237) 79904) ((-1082 . -622) 79879) ((-1013 . -502) 79860) ((-74 . -453) T) ((-74 . -407) T) ((-1082 . -1119) T) ((-153 . -1075) 79844) ((-1013 . -625) 79810) ((-682 . -238) 79789) ((-583 . -566) 79773) ((-366 . -148) 79752) ((-366 . -146) 79703) ((-363 . -148) 79682) ((-363 . -146) 79633) ((-355 . -148) 79612) ((-355 . -146) 79563) ((-273 . -146) 79542) ((-273 . -148) 79521) ((-253 . -148) 79500) ((-118 . -374) T) ((-253 . -146) 79479) ((-1177 . -626) NIL) ((-153 . -111) 79458) ((-1022 . -1057) 79346) ((-1176 . -1236) T) ((-706 . -1240) T) ((-811 . -1077) T) ((-711 . -1131) T) ((-1022 . -388) 79323) ((-518 . -1236) T) ((-514 . -1236) T) ((-927 . -146) T) ((-927 . -148) 79305) ((-882 . -132) T) ((-827 . -1075) 79226) ((-711 . -23) T) 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. -399) T) ((-430 . -738) T) ((-713 . -1240) T) ((-1161 . -651) 18771) ((-592 . -881) 18755) ((-1301 . -1075) 18739) ((-1178 . -1212) 18715) ((-713 . -568) T) ((-127 . -1119) 18693) ((-726 . -1119) T) ((-670 . -38) 18663) ((-494 . -915) 18595) ((-255 . -1119) T) ((-189 . -1119) T) ((-365 . -414) T) ((-326 . -148) 18574) ((-326 . -146) 18553) ((-117 . -568) T) ((-129 . -526) NIL) ((-323 . -148) 18509) ((-323 . -146) 18465) ((-48 . -464) T) ((-163 . -1119) T) ((-158 . -1119) T) ((-1178 . -107) 18412) ((-794 . -1171) 18390) ((-1301 . -111) 18369) ((-701 . -34) T) ((-604 . -1236) T) ((-562 . -34) T) ((-496 . -107) 18353) ((-258 . -298) 18330) ((-257 . -298) 18307) ((-1242 . -856) T) ((-883 . -296) 18258) ((-45 . -1236) T) ((-1230 . -917) 18239) ((-829 . -1236) T) ((-828 . -1068) T) ((-674 . -658) 18208) ((-1197 . -47) 18185) ((-828 . -336) 18147) ((-1106 . -38) 17996) ((-828 . -238) 17975) ((-794 . -38) 17804) ((-792 . -38) 17653) ((-1134 . -502) 17634) ((-466 . -38) 17483) ((-1134 . -625) 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-1242) T) ((-638 . -628) 191589) ((-370 . -568) T) ((-219 . -939) T) ((-219 . -832) T) ((-326 . -652) 191499) ((-323 . -652) 191428) ((-364 . -568) T) ((-356 . -568) T) ((-495 . -628) 191409) ((-108 . -568) T) ((-670 . -729) 191379) ((-1188 . -1043) NIL) ((-220 . -628) 191360) ((-329 . -23) T) ((-67 . -1238) T) ((-1021 . -625) 191292) ((-706 . -272) 191274) ((-706 . -232) 191256) ((-1317 . -1173) T) ((-726 . -111) 191221) ((-1312 . -21) T) ((-656 . -34) T) ((-250 . -501) 191205) ((-1312 . -25) T) ((-1310 . -132) T) ((-1308 . -132) T) ((-1301 . -102) T) ((-1123 . -1119) 191189) ((-173 . -1121) T) ((-1284 . -625) 191155) ((-1280 . -1238) T) ((-1273 . -1238) T) ((-1273 . -1059) 191090) ((-1252 . -1238) T) ((-971 . -928) 191069) ((-1252 . -901) NIL) ((-1252 . -899) 191021) ((-1252 . -1059) 190987) ((-527 . -628) 190971) ((-1232 . -526) 190938) ((-1210 . -626) NIL) ((-1210 . -625) 190920) ((-493 . -928) 190899) ((-1163 . -1144) 190844) ((-1108 . -729) 190693) ((-1083 . -660) 190665) ((-971 . -660) 190554) ((-794 . -729) 190383) ((-609 . -502) 190364) ((-597 . -502) 190345) ((-609 . -625) 190311) ((-597 . -625) 190277) ((-548 . -625) 190259) ((-591 . -1238) T) ((-548 . -626) 190240) ((-792 . -729) 190089) ((-1098 . -102) T) ((-635 . -658) 190061) ((-392 . -25) T) ((-392 . -21) T) ((-493 . -660) 189950) ((-473 . -729) 189921) ((-466 . -729) 189770) ((-1008 . -102) T) ((-1067 . -1231) 189699) ((-920 . -319) 189637) ((-890 . -93) T) ((-749 . -102) T) ((-118 . -658) 189567) ((-617 . -628) 189549) ((-726 . -628) 189503) ((-693 . -93) T) ((-543 . -25) T) ((-688 . -93) T) ((-676 . -625) 189485) ((-657 . -502) 189466) ((-657 . -625) 189419) ((-142 . -102) T) ((-44 . -132) T) ((-608 . -1238) T) ((-607 . -1238) T) ((-354 . -1079) T) ((-299 . -1133) T) ((-490 . -93) T) ((-419 . -237) 189370) ((-366 . -625) 189352) ((-363 . -625) 189334) ((-355 . -625) 189316) ((-273 . -626) 189064) ((-273 . -625) 189046) ((-253 . -625) 189028) ((-253 . -626) 188889) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1162 . -625) 188871) ((-1141 . -652) 188858) ((-1141 . -1072) 188845) ((-831 . -738) T) ((-831 . -871) T) ((-614 . -298) 188822) ((-593 . -729) 188787) ((-491 . -626) NIL) ((-491 . -625) 188769) ((-530 . -729) 188714) ((-326 . -102) T) ((-323 . -102) T) ((-299 . -23) T) ((-153 . -132) T) ((-929 . -625) 188696) ((-929 . -626) 188678) ((-398 . -738) T) ((-886 . -1077) 188630) ((-886 . -111) 188568) ((-726 . -1070) T) ((-724 . -1264) 188552) ((-706 . -360) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-531 . -625) 188484) ((-390 . -807) T) ((-169 . -1238) T) ((-225 . -1121) T) ((-390 . -804) T) ((-59 . -626) 188445) ((-227 . -806) T) ((-227 . -803) T) ((-59 . -625) 188357) ((-227 . -738) T) ((-528 . -626) 188318) ((-528 . -625) 188230) ((-509 . -625) 188162) ((-508 . -626) 188123) ((-508 . -625) 188035) ((-1101 . -374) 187986) ((-40 . -423) 187963) ((-77 . -1238) T) ((-885 . -928) NIL) ((-370 . -339) 187947) ((-370 . -374) T) ((-364 . -339) 187931) ((-364 . -374) T) ((-356 . -339) 187915) ((-356 . -374) T) ((-326 . -294) 187894) ((-108 . -374) T) ((-70 . -1238) T) ((-1252 . -349) 187846) ((-885 . -660) 187791) ((-1252 . -388) 187743) ((-983 . -132) 187598) ((-827 . -132) 187469) ((-977 . -663) 187453) ((-1108 . -174) 187364) ((-977 . -384) 187348) ((-1083 . -806) T) ((-1083 . -803) T) ((-886 . -628) 187246) ((-794 . -174) 187137) ((-792 . -174) 187048) ((-828 . -47) 187010) ((-1083 . -738) T) ((-337 . -501) 186994) ((-971 . -738) T) ((-1301 . -319) 186932) ((-1280 . -917) 186845) ((-466 . -174) 186756) ((-250 . -296) 186708) ((-1273 . -917) 186614) ((-1272 . -1077) 186449) ((-1252 . -917) 186282) ((-493 . -738) T) ((-1251 . -1077) 186090) ((-1232 . -300) 186069) ((-1207 . -1238) T) ((-1204 . -379) T) ((-1203 . -379) T) ((-1167 . -152) 186053) ((-1141 . -102) T) ((-1139 . -1121) T) ((-1101 . -23) T) ((-1101 . -1133) T) ((-1096 . -102) T) ((-1078 . -625) 186020) ((-1024 . -421) 185992) ((-946 . -974) T) ((-749 . -319) 185930) ((-75 . -1238) T) ((-676 . -393) 185902) ((-171 . -928) 185855) ((-30 . -974) T) ((-112 . -856) T) ((-1 . -625) 185837) ((-1020 . -911) 185758) ((-129 . -663) 185740) ((-50 . -632) 185724) ((-706 . -658) 185659) ((-607 . -917) 185572) ((-450 . -102) T) ((-129 . -384) 185554) ((-142 . -319) NIL) ((-886 . -1070) T) ((-845 . -862) 185533) ((-81 . -1238) T) ((-723 . -300) T) ((-40 . -1079) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 185515) ((-171 . -660) 185389) ((-519 . -625) 185371) ((-362 . -148) 185353) ((-362 . -146) T) ((-370 . -1133) T) ((-364 . -1133) T) ((-356 . -1133) T) ((-1025 . -317) T) ((-933 . -317) T) ((-886 . -248) T) ((-108 . -1133) T) ((-886 . -238) 185332) ((-1272 . -111) 185153) ((-1251 . -111) 184942) ((-250 . -1276) 184926) ((-576 . -860) T) ((-370 . -23) T) ((-365 . -360) T) ((-326 . -319) 184913) ((-323 . -319) 184854) ((-364 . -23) T) ((-329 . -132) T) ((-356 . -23) T) ((-1025 . -1043) T) ((-31 . -628) 184835) ((-108 . -23) T) ((-666 . -1072) 184819) ((-250 . -616) 184796) ((-343 . -1121) T) ((-666 . -652) 184766) ((-1274 . -38) 184658) ((-1261 . -928) 184637) ((-112 . -1121) T) ((-828 . -1238) T) ((-425 . -1238) T) ((-1056 . -102) T) ((-1261 . -660) 184526) ((-885 . -806) NIL) ((-869 . -660) 184500) ((-885 . -803) NIL) ((-828 . -901) NIL) ((-885 . -738) T) ((-1108 . -526) 184373) ((-794 . -526) 184320) ((-792 . -526) 184272) ((-583 . -660) 184259) ((-828 . -1059) 184087) ((-466 . -526) 184030) ((-400 . -401) T) ((-1272 . -628) 183843) ((-1251 . -628) 183591) ((-60 . -1238) T) ((-633 . -862) 183570) ((-512 . -673) T) ((-1167 . -997) 183539) ((-1045 . -658) 183476) ((-1024 . -464) T) ((-711 . -860) T) ((-522 . -804) T) ((-486 . -1077) 183311) ((-512 . -113) T) ((-354 . -1121) T) ((-323 . -1173) NIL) ((-299 . -132) T) ((-406 . -1121) T) ((-884 . -1079) T) ((-706 . -381) 183278) ((-365 . -658) 183208) ((-225 . -632) 183185) ((-337 . -296) 183137) ((-486 . -111) 182958) ((-1272 . -1070) T) ((-1251 . -1070) T) ((-828 . -388) 182942) ((-836 . -1238) T) ((-171 . -738) T) ((-1303 . -1238) T) ((-666 . -102) T) ((-1272 . -248) 182921) ((-1272 . -238) 182873) ((-1251 . -238) 182778) ((-1251 . -248) 182757) ((-1024 . -414) NIL) ((-682 . -651) 182705) ((-326 . -38) 182615) ((-323 . -38) 182544) ((-69 . -625) 182526) ((-329 . -505) 182492) ((-48 . -658) 182442) ((-1210 . -298) 182421) ((-1246 . -862) T) ((-1134 . -1133) 182399) ((-83 . -1238) T) ((-61 . -625) 182381) ((-491 . -298) 182360) ((-1303 . -1059) 182337) ((-1185 . -1121) T) ((-1134 . -23) 182189) ((-828 . -917) 182125) ((-1261 . -738) T) ((-1123 . -1238) T) ((-486 . -628) 181951) ((-362 . -237) T) ((-1108 . -300) 181882) ((-985 . -1121) T) ((-908 . -102) T) ((-794 . -300) 181793) ((-337 . -19) 181777) ((-59 . -298) 181754) ((-792 . -300) 181685) ((-869 . -738) T) ((-118 . -860) NIL) ((-528 . -298) 181662) ((-337 . -616) 181639) ((-508 . -298) 181616) ((-466 . -300) 181547) ((-1056 . -319) 181398) ((-890 . -502) 181379) ((-890 . -625) 181345) ((-693 . -502) 181326) ((-583 . -738) T) ((-688 . -502) 181307) ((-693 . -625) 181257) ((-688 . -625) 181223) ((-674 . -625) 181205) ((-490 . -502) 181186) ((-490 . -625) 181152) ((-250 . -626) 181113) ((-250 . -502) 181090) ((-139 . -502) 181071) ((-138 . -502) 181052) ((-134 . -502) 181033) ((-250 . -625) 180925) ((-215 . -102) T) ((-139 . -625) 180891) ((-138 . -625) 180857) ((-134 . -625) 180823) ((-1168 . -34) T) ((-962 . -1238) T) ((-354 . -729) 180768) ((-682 . -25) T) ((-682 . -21) T) ((-1197 . -628) 180749) ((-341 . -1238) T) ((-486 . -1070) T) ((-647 . -429) 180714) ((-619 . -429) 180679) ((-1141 . -1173) T) ((-1273 . -317) 180658) ((-724 . -1072) 180481) ((-593 . -300) T) ((-530 . -300) T) ((-1252 . -317) 180460) ((-486 . -238) 180412) ((-486 . -248) 180391) ((-451 . -1238) T) ((-724 . -652) 180220) ((-1252 . -1043) NIL) ((-1101 . -132) T) ((-886 . -807) 180199) ((-145 . -102) T) ((-40 . -1121) T) ((-886 . -804) 180178) ((-656 . -1031) 180162) ((-592 . -1079) T) ((-576 . -1079) T) ((-507 . -1079) T) ((-419 . -464) T) ((-370 . -132) T) ((-326 . -412) 180146) ((-323 . -412) 180107) ((-364 . -132) T) ((-356 . -132) T) ((-1202 . -1121) T) ((-1141 . -38) 180094) ((-1115 . -625) 180061) ((-108 . -132) T) ((-973 . -1121) T) ((-940 . -1121) T) ((-783 . -1121) T) ((-684 . -1121) T) ((-713 . -148) T) ((-117 . -148) T) ((-1310 . -21) T) ((-1310 . -25) T) ((-1308 . -21) T) ((-1308 . -25) T) ((-676 . -1077) 180045) ((-543 . -862) T) ((-512 . -862) T) ((-376 . -1238) T) ((-366 . -1077) 179997) ((-363 . -1077) 179949) ((-355 . -1077) 179901) ((-258 . -1238) T) ((-257 . -1238) T) ((-273 . -1077) 179744) ((-253 . -1077) 179587) ((-676 . -111) 179566) ((-829 . -1242) 179545) ((-559 . -856) T) ((-326 . -919) 179511) ((-366 . -111) 179449) ((-363 . -111) 179387) ((-355 . -111) 179325) ((-273 . -111) 179154) ((-253 . -111) 178983) ((-323 . -919) NIL) ((-635 . -423) 178967) ((-44 . -21) T) ((-44 . -25) T) ((-827 . -651) 178873) ((-829 . -568) 178852) ((-258 . -1059) 178679) ((-257 . -1059) 178506) ((-127 . -120) 178490) ((-929 . -1077) 178455) ((-724 . -102) T) ((-711 . -1079) T) ((-609 . -628) 178436) ((-597 . -628) 178417) ((-548 . -630) 178320) ((-354 . -174) T) ((-153 . -21) T) ((-153 . -25) T) ((-88 . -625) 178302) ((-929 . -111) 178258) ((-40 . -729) 178203) ((-884 . -1121) T) ((-676 . -628) 178180) ((-657 . -628) 178161) ((-366 . -628) 178098) ((-363 . -628) 178035) ((-355 . -628) 177972) ((-559 . -1121) T) ((-337 . -626) 177933) ((-337 . -625) 177845) ((-273 . -628) 177598) ((-253 . -628) 177383) ((-188 . -1238) T) ((-1251 . -804) 177336) ((-1251 . -807) 177289) ((-258 . -388) 177258) ((-257 . -388) 177227) ((-666 . -38) 177197) ((-620 . -34) T) ((-494 . -1133) 177175) ((-487 . -34) T) ((-1134 . -132) 177046) ((-983 . -25) 176857) ((-929 . -628) 176807) ((-888 . -625) 176789) ((-983 . -21) 176744) ((-827 . -25) 176577) ((-827 . -21) 176488) ((-1244 . -379) T) ((-635 . -1079) T) ((-1199 . -568) 176467) ((-1193 . -47) 176444) ((-366 . -1070) T) ((-363 . -1070) T) ((-494 . -23) 176296) ((-355 . -1070) T) ((-273 . -1070) T) ((-253 . -1070) T) ((-1146 . -47) 176268) ((-118 . -1079) T) ((-1055 . -660) 176242) ((-977 . -34) T) ((-366 . -238) 176221) ((-366 . -248) T) ((-363 . -238) 176200) ((-363 . -248) T) ((-355 . -238) 176179) ((-355 . -248) T) ((-273 . -336) 176151) ((-253 . -336) 176108) ((-273 . -238) 176087) ((-1178 . -152) 176071) ((-258 . -917) 176003) ((-257 . -917) 175935) ((-1163 . -911) 175856) ((-1103 . -862) T) ((-1255 . -1238) 175834) ((-426 . -1133) T) ((-1075 . -23) T) ((-1045 . -860) T) ((-929 . -1070) T) ((-332 . -660) 175816) ((-713 . -237) T) ((-682 . -234) 175761) ((-1232 . -1023) 175727) ((-1194 . -939) 175706) ((-1188 . -939) 175685) ((-1188 . -832) NIL) ((-1020 . -1072) 175581) ((-986 . -1238) T) ((-929 . -248) T) ((-829 . -374) 175560) ((-396 . -23) T) ((-128 . -1121) 175538) ((-122 . -1121) 175516) ((-929 . -238) T) ((-129 . -34) T) ((-390 . -660) 175481) ((-1020 . -652) 175429) ((-884 . -729) 175416) ((-1317 . -658) 175388) ((-1067 . -152) 175353) ((-1014 . -1238) T) ((-876 . -1238) T) ((-40 . -174) T) ((-706 . -423) 175335) ((-724 . -319) 175322) ((-848 . -660) 175282) ((-839 . -660) 175256) ((-329 . -25) T) ((-329 . -21) T) ((-670 . -296) 175235) ((-592 . -1121) T) ((-576 . -1121) T) ((-507 . -1121) T) ((-1193 . -1238) T) ((-250 . -298) 175212) ((-1146 . -1238) T) ((-868 . -1238) T) ((-323 . -272) 175173) ((-323 . -232) 175134) ((-1193 . -901) NIL) ((-55 . -1121) T) ((-1146 . -901) 174993) ((-130 . -862) T) ((-1193 . -1059) 174873) ((-1146 . -1059) 174756) ((-185 . -625) 174738) ((-868 . -1059) 174634) ((-794 . -296) 174561) ((-829 . -1133) T) ((-1055 . -738) T) ((-1067 . -997) 174490) ((-614 . -663) 174474) ((-1024 . -911) 174381) ((-1020 . -102) T) ((-829 . -23) T) ((-724 . -1173) 174359) ((-706 . -1079) T) ((-614 . -384) 174343) ((-362 . -464) T) ((-354 . -300) T) ((-1289 . -1121) T) ((-254 . -1121) T) ((-411 . -102) T) ((-299 . -21) T) ((-299 . -25) T) ((-372 . -738) T) ((-722 . -1121) T) ((-711 . -1121) T) ((-372 . -485) T) ((-1232 . -625) 174325) ((-1193 . -388) 174309) ((-1146 . -388) 174293) ((-1045 . -423) 174255) ((-142 . -231) 174237) ((-390 . -806) T) ((-390 . -803) T) ((-884 . -174) T) ((-390 . -738) T) ((-723 . -625) 174219) ((-724 . -38) 174048) ((-1288 . -1286) 174032) ((-362 . -414) T) ((-1288 . -1121) 173982) ((-1211 . -1121) T) ((-592 . -729) 173969) ((-576 . -729) 173956) ((-507 . -729) 173921) ((-1274 . -658) 173811) ((-326 . -641) 173790) ((-848 . -738) T) ((-839 . -738) T) ((-1136 . -1238) T) ((-656 . -1238) T) ((-1101 . -651) 173738) ((-1193 . -917) 173681) ((-1146 . -917) 173665) ((-827 . -234) 173556) ((-674 . -1077) 173540) ((-108 . -651) 173522) ((-494 . -132) 173393) ((-1199 . -1133) T) ((-831 . -1238) T) ((-971 . -47) 173362) ((-635 . -1121) T) ((-674 . -111) 173341) ((-503 . -625) 173307) ((-337 . -298) 173284) ((-398 . -1238) T) ((-334 . -1238) T) ((-493 . -47) 173241) ((-1199 . -23) T) ((-118 . -1121) T) ((-103 . -102) 173191) ((-1300 . -1133) T) ((-560 . -862) T) ((-227 . -1238) T) ((-1075 . -132) T) ((-1045 . -1079) T) ((-1300 . -23) T) ((-831 . -1059) 173175) ((-1218 . -625) 173157) ((-1024 . -736) 173129) ((-1141 . -840) T) ((-711 . -729) 173094) ((-598 . -625) 173076) ((-398 . -1059) 173060) ((-365 . -1079) T) ((-396 . -132) T) ((-334 . -1059) 173044) ((-1126 . -1121) T) ((-1101 . -21) T) ((-1101 . -25) T) ((-227 . -901) 173026) ((-1025 . -939) T) ((-91 . -34) T) ((-1025 . -832) T) ((-933 . -939) T) ((-1020 . -319) 172991) ((-890 . -628) 172972) ((-499 . -1242) T) ((-726 . -660) 172932) ((-693 . -628) 172913) ((-688 . -628) 172894) ((-219 . -1242) T) ((-419 . -911) 172815) ((-227 . -1059) 172775) ((-40 . -300) T) ((-499 . -568) T) ((-490 . -628) 172756) ((-370 . -25) T) ((-326 . -658) 172411) ((-323 . -658) 172325) ((-370 . -21) T) ((-364 . -25) T) ((-364 . -21) T) ((-219 . -568) T) ((-356 . -25) T) ((-356 . -21) T) ((-329 . -234) 172271) ((-250 . -628) 172248) ((-139 . -628) 172229) ((-138 . -628) 172210) ((-134 . -628) 172191) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1079) T) ((-592 . -174) T) ((-576 . -174) T) ((-507 . -174) T) ((-1083 . -1238) T) ((-971 . -1238) T) ((-725 . -1238) T) ((-670 . -625) 172173) ((-493 . -1238) T) ((-749 . -748) 172157) ((-347 . -625) 172139) ((-68 . -394) T) ((-68 . -407) T) ((-1123 . -107) 172123) ((-1083 . -901) 172105) ((-971 . -901) 172030) ((-665 . -1133) T) ((-635 . -729) 172017) ((-493 . -901) NIL) ((-1167 . -102) T) ((-1115 . -630) 172001) ((-1083 . -1059) 171983) ((-97 . -625) 171965) ((-489 . -148) T) ((-971 . -1059) 171845) ((-118 . -729) 171790) ((-724 . -919) 171697) ((-665 . -23) T) ((-493 . -1059) 171573) ((-1108 . -626) NIL) ((-1108 . -625) 171555) ((-794 . -626) NIL) ((-794 . -625) 171516) ((-792 . -626) 171150) ((-792 . -625) 171064) ((-1134 . -651) 170970) ((-473 . -625) 170952) ((-466 . -625) 170934) ((-466 . -626) 170795) ((-1056 . -231) 170741) ((-886 . -928) 170720) ((-127 . -34) T) ((-829 . -132) T) ((-661 . -625) 170702) ((-590 . -102) T) 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167535) ((-1163 . -102) T) ((-1020 . -919) 167458) ((-674 . -804) 167437) ((-665 . -132) T) ((-674 . -807) 167416) ((-118 . -526) 167324) ((-583 . -1059) 167306) ((-304 . -1295) 167276) ((-880 . -102) T) ((-982 . -568) 167255) ((-1232 . -1077) 167138) ((-1024 . -1072) 167083) ((-494 . -651) 166989) ((-923 . -1121) T) ((-1045 . -729) 166926) ((-723 . -1077) 166891) ((-1024 . -652) 166836) ((-629 . -102) T) ((-614 . -34) T) ((-1168 . -1238) T) ((-1232 . -111) 166705) ((-486 . -660) 166602) ((-365 . -729) 166547) ((-171 . -917) 166506) ((-711 . -300) T) ((-706 . -174) T) ((-723 . -111) 166462) ((-1317 . -1079) T) ((-1261 . -388) 166446) ((-430 . -1242) 166424) ((-1139 . -625) 166406) ((-323 . -860) NIL) ((-430 . -568) T) ((-227 . -317) T) ((-1251 . -803) 166359) ((-1251 . -806) 166312) ((-1272 . -738) T) ((-1251 . -738) T) ((-48 . -729) 166277) ((-227 . -1043) T) ((-1274 . -423) 166243) ((-362 . -1295) 166220) ((-1261 . -917) 166163) ((-730 . -738) T) ((-343 . -625) 166145) ((-1232 . 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162977) ((-1097 . -1059) 162954) ((-1021 . -34) T) ((-985 . -625) 162936) ((-977 . -1238) T) ((-127 . -1031) 162920) ((-982 . -1133) T) ((-885 . -1043) NIL) ((-747 . -1133) T) ((-727 . -1133) T) ((-670 . -628) 162838) ((-1288 . -501) 162822) ((-1205 . -1238) T) ((-1204 . -1238) T) ((-1163 . -38) 162782) ((-982 . -23) T) ((-929 . -660) 162747) ((-879 . -1121) T) ((-855 . -102) T) ((-829 . -21) T) ((-647 . -1072) 162731) ((-619 . -1072) 162715) ((-829 . -25) T) ((-747 . -23) T) ((-727 . -23) T) ((-647 . -652) 162699) ((-110 . -673) T) ((-619 . -652) 162683) ((-593 . -1077) 162648) ((-530 . -1077) 162593) ((-229 . -57) 162551) ((-465 . -23) T) ((-419 . -102) T) ((-1203 . -1238) T) ((-270 . -102) T) ((-110 . -113) T) ((-706 . -300) T) ((-880 . -38) 162521) ((-1108 . -628) 162257) ((-593 . -111) 162213) ((-530 . -111) 162142) ((-430 . -1133) T) ((-326 . -1079) 162032) ((-323 . -1079) T) ((-129 . -1238) T) ((-131 . -1238) T) ((-794 . -628) 161780) ((-792 . -628) 161546) ((-670 . -1070) T) 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-34) T) ((-59 . -34) T) ((-509 . -34) T) ((-508 . -34) T) ((-466 . -336) 160376) ((-337 . -384) 160360) ((-372 . -1238) T) ((-332 . -1238) T) ((-1024 . -1173) NIL) ((-743 . -568) 160291) ((-647 . -102) T) ((-619 . -102) T) ((-366 . -738) T) ((-363 . -738) T) ((-355 . -738) T) ((-273 . -738) T) ((-253 . -738) T) ((-390 . -1238) T) ((-1300 . -21) T) ((-1067 . -319) 160199) ((-1300 . -25) T) ((-920 . -1121) 160177) ((-830 . -234) 160164) ((-50 . -1070) T) ((-1195 . -568) 160143) ((-1194 . -1242) 160122) ((-1194 . -568) 160073) ((-1188 . -1242) 160052) ((-1188 . -568) 160003) ((-1045 . -300) T) ((-593 . -1070) T) ((-530 . -1070) T) ((-1024 . -38) 159948) ((-372 . -1059) 159932) ((-332 . -1059) 159916) ((-1020 . -658) 159839) ((-390 . -901) 159821) ((-848 . -1238) T) ((-839 . -1238) T) ((-837 . -1238) T) ((-811 . -1133) T) ((-929 . -738) T) ((-593 . -248) T) ((-593 . -238) T) ((-530 . -238) T) ((-530 . -248) T) ((-1147 . -568) 159800) ((-365 . -300) T) ((-659 . -707) 159784) ((-390 . -1059) 159744) ((-304 . -1072) 159665) ((-350 . -911) 159644) ((-1141 . -1079) T) ((-103 . -126) 159628) ((-304 . -652) 159570) ((-811 . -23) T) ((-1310 . -1305) 159546) ((-1308 . -1305) 159525) ((-1288 . -296) 159477) ((-419 . -319) 159442) ((-1274 . -1121) T) ((-1163 . -919) 159365) ((-884 . -625) 159347) ((-848 . -1059) 159316) ((-205 . -799) T) ((-204 . -799) T) ((-203 . -799) T) ((-202 . -799) T) ((-201 . -799) T) ((-200 . -799) T) ((-199 . -799) T) ((-198 . -799) T) ((-197 . -799) T) ((-196 . -799) T) ((-559 . -625) 159298) ((-507 . -1023) T) ((-283 . -851) T) ((-282 . -851) T) ((-281 . -851) T) ((-280 . -851) T) ((-48 . -300) T) ((-279 . -851) T) ((-278 . -851) T) ((-277 . -851) T) ((-195 . -799) T) ((-624 . -862) T) ((-666 . -423) 159282) ((-682 . -237) 159233) ((-225 . -628) 159195) ((-110 . -862) T) ((-665 . -21) T) ((-665 . -25) T) ((-1311 . -38) 159165) ((-118 . -296) 159116) ((-1288 . -19) 159100) ((-1288 . -616) 159077) ((-1301 . -1121) T) ((-362 . -1072) 159022) ((-1098 . 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. -626) 158084) ((-497 . -23) T) ((-220 . -1238) T) ((-494 . -862) 158035) ((-499 . -651) 158017) ((-984 . -625) 157999) ((-1024 . -919) 157908) ((-219 . -651) 157890) ((-227 . -416) T) ((-674 . -660) 157874) ((-55 . -625) 157856) ((-1193 . -939) 157835) ((-743 . -1133) T) ((-527 . -1238) T) ((-522 . -1238) T) ((-520 . -1238) T) ((-362 . -102) T) ((-1237 . -1104) T) ((-1141 . -856) T) ((-830 . -862) T) ((-743 . -23) T) ((-354 . -1077) 157780) ((-1168 . -107) 157764) ((-1289 . -625) 157746) ((-1195 . -23) T) ((-1195 . -1133) T) ((-1194 . -1133) T) ((-1194 . -23) T) ((-527 . -1059) 157730) ((-1188 . -1133) T) ((-1147 . -1133) T) ((-354 . -111) 157659) ((-1025 . -1242) T) ((-127 . -1238) T) ((-933 . -1242) T) ((-1188 . -23) T) ((-1163 . -272) 157643) ((-706 . -296) NIL) ((-726 . -1238) T) ((-1163 . -232) 157627) ((-1147 . -23) T) ((-1096 . -1121) T) ((-1025 . -568) T) ((-933 . -568) T) ((-255 . -1238) T) ((-189 . -1238) T) ((-163 . -1238) T) ((-158 . -1238) T) ((-254 . -625) 157609) 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|EnumerationCategory|) T) ((-329 . -95) 155387) ((-390 . -1043) T) ((-108 . -148) T) ((-108 . -146) NIL) ((-45 . -240) 155337) ((-666 . -1121) T) ((-620 . -107) 155284) ((-497 . -132) T) ((-487 . -107) 155234) ((-245 . -1133) 155212) ((-31 . -1238) T) ((-886 . -388) 155196) ((-886 . -349) 155180) ((-245 . -23) 155032) ((-40 . -628) 154962) ((-1083 . -939) T) ((-1083 . -832) T) ((-593 . -379) T) ((-530 . -379) T) ((-1301 . -526) 154895) ((-1280 . -568) 154874) ((-1273 . -1242) 154853) ((-1273 . -568) 154804) ((-362 . -1173) T) ((-337 . -34) T) ((-44 . -429) 154788) ((-1202 . -628) 154724) ((-887 . -1238) T) ((-402 . -756) 154708) ((-1272 . -1238) T) ((-1252 . -1242) 154687) ((-1163 . -658) 154646) ((-743 . -132) T) ((-684 . -628) 154630) ((-1252 . -568) 154581) ((-1251 . -1238) T) ((-1251 . -901) 154454) ((-1251 . -899) 154424) ((-1195 . -132) T) ((-1194 . -132) T) ((-321 . -1104) T) ((-1188 . -132) T) ((-749 . -526) 154357) ((-1147 . -132) T) ((-1045 . -1023) T) ((-908 . -1121) T) 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-234) 141362) ((-321 . -102) T) ((-868 . -1133) T) ((-971 . -1242) 141341) ((-493 . -1242) 141320) ((-1083 . -568) T) ((-971 . -568) 141251) ((-1193 . -23) T) ((-1172 . -1104) T) ((-1146 . -23) T) ((-868 . -23) T) ((-493 . -568) 141182) ((-1163 . -729) 141114) ((-682 . -1072) 141098) ((-1167 . -526) 141031) ((-682 . -652) 141015) ((-1056 . -626) NIL) ((-1056 . -625) 140997) ((-96 . -1104) T) ((-1317 . -1077) 140984) ((-880 . -729) 140954) ((-1317 . -111) 140939) ((-1232 . -47) 140908) ((-1188 . -862) NIL) ((-258 . -132) T) ((-257 . -132) T) ((-1125 . -1121) T) ((-1024 . -1121) T) ((-62 . -625) 140890) ((-1101 . -911) 140759) ((-1045 . -804) T) ((-1045 . -807) T) ((-1280 . -25) T) ((-1280 . -21) T) ((-1273 . -21) T) ((-1273 . -25) T) ((-884 . -660) 140746) ((-1252 . -21) T) ((-1252 . -25) T) ((-1048 . -152) 140730) ((-1025 . -234) 140717) ((-886 . -832) 140696) ((-886 . -939) T) ((-724 . -296) 140623) ((-608 . -21) T) ((-350 . -658) 140582) ((-108 . -911) NIL) ((-608 . -25) T) ((-607 . -21) T) ((-176 . -658) 140499) ((-40 . -738) T) ((-224 . -526) 140432) ((-607 . -25) T) ((-488 . -152) 140416) ((-475 . -152) 140400) ((-185 . -1238) T) ((-940 . -806) T) ((-940 . -738) T) ((-783 . -805) T) ((-783 . -806) T) ((-518 . -1121) T) ((-514 . -1121) T) ((-783 . -738) T) ((-227 . -374) T) ((-1310 . -1072) 140384) ((-1308 . -1072) 140368) ((-1310 . -652) 140338) ((-1178 . -1121) 140316) ((-885 . -1242) T) ((-1308 . -652) 140286) ((-666 . -625) 140268) ((-885 . -568) T) ((-706 . -379) NIL) ((-44 . -1072) 140252) ((-1317 . -628) 140234) ((-1311 . -1121) T) ((-682 . -102) T) ((-370 . -1295) 140218) ((-364 . -1295) 140202) ((-44 . -652) 140186) ((-356 . -1295) 140170) ((-560 . -102) T) ((-1232 . -1238) T) ((-532 . -862) 140149) ((-723 . -1238) T) ((-499 . -237) T) ((-219 . -237) T) ((-1067 . -1121) T) ((-829 . -464) 140128) ((-153 . -1072) 140112) ((-1067 . -1092) 140041) ((-1048 . -997) 140010) ((-831 . -1133) T) ((-1024 . -729) 139955) ((-153 . -652) 139939) ((-398 . -1133) T) 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-1059) 135467) ((-118 . -660) 135412) ((-466 . -1059) 135288) ((-284 . -1238) T) ((-326 . -628) 134852) ((-323 . -628) 134735) ((-50 . -1238) T) ((-402 . -658) 134704) ((-661 . -1059) 134688) ((-639 . -102) T) ((-593 . -1238) T) ((-530 . -1238) T) ((-224 . -501) 134672) ((-1288 . -34) T) ((-633 . -658) 134631) ((-299 . -1072) 134618) ((-137 . -628) 134602) ((-299 . -652) 134589) ((-647 . -729) 134573) ((-619 . -729) 134557) ((-682 . -38) 134517) ((-329 . -102) T) ((-1141 . -1077) 134504) ((-85 . -625) 134486) ((-50 . -1059) 134470) ((-1108 . -388) 134454) ((-794 . -388) 134438) ((-711 . -738) T) ((-711 . -806) T) ((-711 . -803) T) ((-60 . -57) 134400) ((-593 . -1059) 134387) ((-530 . -1059) 134364) ((-173 . -1238) T) ((-334 . -132) T) ((-326 . -1070) 134254) ((-323 . -1070) T) ((-171 . -1133) T) ((-792 . -388) 134238) ((-45 . -152) 134188) ((-1025 . -1013) 134170) ((-466 . -388) 134154) ((-419 . -174) T) ((-326 . -248) 134133) ((-323 . -248) T) ((-323 . -238) NIL) ((-304 . -1121) 133915) ((-227 . -132) T) ((-1141 . -111) 133900) ((-171 . -23) T) ((-811 . -148) 133879) ((-811 . -146) 133858) ((-258 . -651) 133764) ((-257 . -651) 133670) ((-329 . -294) 133636) ((-1178 . -526) 133569) ((-489 . -658) 133519) ((-494 . -911) 133386) ((-1154 . -1121) T) ((-227 . -1081) T) ((-827 . -319) 133324) ((-1108 . -917) 133259) ((-794 . -917) 133202) ((-792 . -917) 133186) ((-1310 . -38) 133156) ((-1308 . -38) 133126) ((-1261 . -1133) T) ((-869 . -1133) T) ((-466 . -917) 133103) ((-872 . -1121) T) ((-1261 . -23) T) ((-1141 . -628) 133075) ((-1083 . -132) T) ((-583 . -1133) T) ((-869 . -23) T) ((-635 . -738) T) ((-366 . -939) T) ((-363 . -939) T) ((-299 . -102) T) ((-355 . -939) T) ((-991 . -1104) T) ((-971 . -132) T) ((-828 . -234) 133020) ((-118 . -806) NIL) ((-118 . -803) NIL) ((-118 . -738) T) ((-1067 . -526) 132921) ((-706 . -928) NIL) ((-583 . -23) T) ((-493 . -132) T) ((-430 . -237) 132872) ((-687 . -319) 132810) ((-225 . -1238) T) ((-647 . -773) T) ((-619 . -773) T) 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-453) T) ((-63 . -407) T) ((-1180 . -102) T) ((-885 . -132) T) ((-496 . -102) 131487) ((-1139 . -1238) T) ((-1317 . -379) T) ((-1101 . -102) T) ((-1082 . -102) T) ((-362 . -729) 131432) ((-743 . -148) 131411) ((-743 . -146) 131390) ((-666 . -628) 131308) ((-1045 . -660) 131245) ((-535 . -1121) 131223) ((-370 . -102) T) ((-364 . -102) T) ((-356 . -102) T) ((-108 . -102) T) ((-516 . -1121) T) ((-365 . -660) 131168) ((-1193 . -651) 131116) ((-1146 . -651) 131064) ((-396 . -521) 131043) ((-845 . -860) 131022) ((-706 . -738) T) ((-390 . -1242) T) ((-343 . -1238) T) ((-1252 . -1013) 130974) ((-350 . -1079) T) ((-112 . -1238) T) ((-176 . -1079) T) ((-103 . -625) 130906) ((-1195 . -146) 130885) ((-1195 . -148) 130864) ((-390 . -568) T) ((-1194 . -148) 130843) ((-1194 . -146) 130822) ((-1188 . -146) 130729) ((-419 . -300) T) ((-1188 . -148) 130636) ((-1147 . -148) 130615) ((-1147 . -146) 130594) ((-329 . -38) 130435) ((-171 . -132) T) ((-323 . -807) NIL) ((-323 . -804) NIL) ((-666 . -1070) T) 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-102) T) ((-354 . -1059) 129043) ((-277 . -102) T) ((-214 . -102) T) ((-213 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-205 . -102) T) ((-204 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-724 . -111) 128852) ((-365 . -738) T) ((-682 . -272) 128836) ((-682 . -232) 128820) ((-593 . -317) T) ((-530 . -317) T) ((-304 . -526) 128769) ((-1185 . -1238) T) ((-108 . -319) NIL) ((-72 . -407) T) ((-1134 . -102) 128501) ((-845 . -423) 128485) ((-1141 . -807) T) ((-1141 . -804) T) ((-713 . -1121) T) ((-590 . -625) 128467) ((-390 . -374) T) ((-171 . -505) 128445) ((-224 . -625) 128377) ((-135 . -1121) T) ((-117 . -1121) T) ((-985 . -1238) T) ((-48 . -738) T) ((-1067 . -501) 128342) ((-142 . -437) 128324) ((-142 . -379) T) ((-1048 . -102) T) ((-524 . -521) 128303) ((-724 . -628) 128059) ((-1245 . -625) 128041) ((-1202 . -1238) T) 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. -651) 126695) ((-1101 . -38) 126563) ((-971 . -651) 126511) ((-1025 . -148) T) ((-1025 . -146) NIL) ((-390 . -1133) T) ((-334 . -25) T) ((-332 . -23) T) ((-962 . -862) 126490) ((-724 . -336) 126467) ((-493 . -651) 126415) ((-40 . -1059) 126303) ((-724 . -238) T) ((-713 . -729) 126290) ((-350 . -1121) T) ((-176 . -1121) T) ((-341 . -862) T) ((-430 . -464) 126240) ((-390 . -23) T) ((-370 . -38) 126205) ((-364 . -38) 126170) ((-356 . -38) 126135) ((-80 . -453) T) ((-80 . -407) T) ((-227 . -25) T) ((-227 . -21) T) ((-848 . -1133) T) ((-108 . -38) 126085) ((-839 . -1133) T) ((-786 . -1121) T) ((-117 . -729) 126072) ((-684 . -1059) 126056) ((-624 . -102) T) ((-848 . -23) T) ((-839 . -23) T) ((-1178 . -296) 126008) ((-1134 . -319) 125946) ((-494 . -1072) 125847) ((-1123 . -240) 125831) ((-64 . -408) T) ((-64 . -407) T) ((-1172 . -102) T) ((-110 . -102) T) ((-494 . -652) 125753) ((-40 . -388) 125730) ((-96 . -102) T) ((-665 . -866) 125714) ((-1193 . -234) 125701) ((-1156 . -1104) T) ((-1083 . -21) T) ((-1083 . -25) T) ((-1075 . -1072) 125685) ((-827 . -272) 125654) ((-827 . -232) 125623) ((-971 . -25) T) ((-971 . -21) T) ((-1141 . -379) T) ((-1075 . -652) 125565) ((-633 . -1079) T) ((-1048 . -319) 125503) ((-904 . -625) 125485) ((-682 . -658) 125444) ((-493 . -25) T) ((-493 . -21) T) ((-396 . -1072) 125428) ((-900 . -625) 125410) ((-884 . -1238) T) ((-535 . -526) 125343) ((-258 . -862) 125294) ((-257 . -862) 125245) ((-396 . -652) 125215) ((-885 . -651) 125192) ((-488 . -319) 125130) ((-559 . -1238) T) ((-475 . -319) 125068) ((-362 . -300) T) ((-1178 . -1276) 125052) ((-1163 . -625) 125014) ((-1163 . -626) 124975) ((-1161 . -102) T) ((-1020 . -1077) 124871) ((-40 . -917) 124823) ((-1178 . -616) 124800) ((-1317 . -660) 124787) ((-1084 . -152) 124733) ((-499 . -911) NIL) ((-880 . -502) 124710) ((-1020 . -111) 124592) ((-886 . -1242) T) ((-219 . -911) NIL) ((-350 . -729) 124576) ((-880 . -625) 124538) ((-176 . -729) 124470) ((-886 . -568) T) ((-419 . -296) 124428) ((-245 . -237) 124325) ((-108 . -412) 124307) ((-84 . -395) T) ((-84 . -407) T) ((-713 . -174) T) ((-629 . -625) 124289) ((-99 . -738) T) ((-494 . -102) 124021) ((-99 . -485) T) ((-117 . -174) T) ((-1310 . -658) 123980) ((-1308 . -658) 123939) ((-171 . -651) 123887) ((-1101 . -919) 123758) ((-1075 . -102) T) ((-1020 . -628) 123648) ((-885 . -25) T) ((-827 . -243) 123627) ((-885 . -21) T) ((-830 . -102) T) ((-44 . -658) 123570) ((-1025 . -237) T) ((-426 . -102) T) ((-396 . -102) T) ((-110 . -319) NIL) ((-229 . -102) 123520) ((-128 . -1238) T) ((-122 . -1238) T) ((-108 . -919) NIL) ((-829 . -1072) 123471) ((-829 . -652) 123413) ((-1055 . -132) T) ((-682 . -378) 123397) ((-153 . -658) 123356) ((-1317 . -738) T) ((-647 . -296) 123314) ((-619 . -296) 123272) ((-1280 . -146) 123251) ((-1261 . -651) 123199) ((-1020 . -1070) T) ((-1125 . -625) 123181) ((-1024 . -625) 123163) ((-592 . -1238) T) ((-576 . -1238) T) ((-507 . -1238) T) ((-527 . -23) T) ((-522 . -23) T) ((-354 . -317) T) ((-520 . -23) T) ((-332 . -132) T) ((-3 . -1121) T) ((-1024 . -626) 123147) ((-1020 . -248) 123126) ((-1020 . -238) 123105) ((-1280 . -148) 123084) ((-1273 . -148) 123063) ((-845 . -1121) T) ((-1273 . -146) 123042) ((-1272 . -1242) 123021) ((-1252 . -146) 122928) ((-1252 . -148) 122835) ((-1251 . -1242) 122814) ((-390 . -132) T) ((-227 . -234) 122801) ((-176 . -174) T) ((-576 . -901) 122783) ((0 . -1121) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1238) T) ((-49 . -1121) T) ((-1274 . -660) 122688) ((-1272 . -568) 122639) ((-726 . -1133) T) ((-1251 . -568) 122590) ((-576 . -1059) 122572) ((-607 . -148) 122551) ((-607 . -146) 122530) ((-507 . -1059) 122473) ((-1156 . -1158) T) ((-87 . -395) T) ((-87 . -407) T) ((-886 . -374) T) ((-848 . -132) T) ((-839 . -132) T) ((-983 . -658) 122417) ((-726 . -23) T) ((-518 . -625) 122383) ((-514 . -625) 122365) ((-827 . -658) 122144) ((-1312 . -1079) T) ((-390 . -1081) T) ((-1047 . -1121) 122122) ((-55 . -1059) 122104) ((-920 . -34) T) ((-494 . -319) 122042) ((-604 . -102) T) ((-1178 . -626) 122003) ((-1178 . -625) 121935) ((-1199 . -1072) 121818) ((-45 . -102) T) ((-829 . -102) T) ((-1199 . -652) 121715) ((-1289 . -1238) T) ((-1261 . -25) T) ((-1261 . -21) T) ((-1083 . -234) 121702) ((-869 . -25) T) ((-254 . -1238) T) ((-44 . -378) 121686) ((-869 . -21) T) ((-743 . -464) 121637) ((-1311 . -625) 121619) ((-722 . -1238) T) ((-711 . -1238) T) ((-1300 . -1072) 121589) ((-1075 . -319) 121527) ((-683 . -1104) T) ((-618 . -1104) T) ((-402 . -1121) T) ((-583 . -25) T) ((-583 . -21) T) ((-182 . -1104) T) ((-162 . -1104) T) ((-157 . -1104) T) ((-155 . -1104) T) ((-1300 . -652) 121497) ((-633 . -1121) T) ((-711 . -901) 121479) ((-1288 . -1238) T) ((-229 . -319) 121417) ((-145 . -379) T) ((-1211 . -1238) T) ((-1067 . -626) 121359) ((-1067 . -625) 121302) ((-323 . -928) NIL) ((-1246 . -856) T) ((-1134 . -919) 121171) ((-711 . -1059) 121116) ((-723 . -939) T) ((-486 . -1242) 121095) ((-1194 . -464) 121074) ((-1188 . -464) 121053) ((-340 . -102) T) ((-886 . -1133) T) ((-329 . -658) 120935) ((-326 . -660) 120664) ((-323 . -660) 120593) ((-486 . -568) 120544) ((-350 . -526) 120510) ((-562 . -152) 120460) ((-40 . -317) T) ((-855 . -625) 120442) ((-713 . -300) T) ((-886 . -23) T) ((-390 . -505) T) ((-1101 . -272) 120412) ((-1101 . -232) 120382) ((-524 . -102) T) ((-419 . -626) 120189) ((-419 . -625) 120171) ((-270 . -625) 120153) ((-117 . -300) T) ((-1274 . -738) T) ((-635 . -1238) T) ((-1313 . -1121) T) ((-1272 . -374) 120132) ((-1251 . -374) 120111) ((-1301 . -34) T) ((-1246 . -1121) T) ((-118 . -1238) T) ((-108 . -272) 120093) ((-108 . -232) 120075) ((-1199 . -102) T) ((-489 . -1121) T) ((-535 . -501) 120059) ((-749 . -34) T) ((-665 . -1072) 120043) ((-665 . -652) 120013) ((-885 . -234) NIL) ((-142 . -34) T) ((-118 . -899) 119990) ((-118 . -901) NIL) ((-635 . -1059) 119873) ((-1300 . -102) T) ((-1280 . -237) 119832) ((-656 . -862) 119811) ((-1273 . -237) 119763) ((-1252 . -237) 119586) ((-305 . -102) T) ((-724 . -379) 119565) ((-118 . -1059) 119542) ((-402 . -729) 119526) ((-607 . -237) 119485) ((-633 . -729) 119469) ((-1126 . -1238) T) ((-45 . -319) 119273) ((-828 . -146) 119252) ((-828 . -148) 119231) ((-299 . -658) 119203) ((-1311 . -393) 119182) ((-831 . -862) T) ((-1290 . -1121) T) ((-1180 . -231) 119129) ((-398 . -862) 119108) ((-1280 . -35) 119074) ((-1280 . -1226) 119040) ((-1280 . -1223) 119006) ((-1273 . -1223) 118972) ((-527 . -132) T) ((-1273 . -1226) 118938) ((-1252 . -1223) 118904) ((-1252 . -1226) 118870) ((-1280 . -95) 118836) ((-1273 . -95) 118802) ((-430 . -911) 118723) ((-647 . -625) 118692) ((-619 . -625) 118661) ((-227 . -862) T) ((-1273 . -35) 118627) ((-1272 . -1133) T) ((-1252 . -95) 118593) ((-1141 . -660) 118565) ((-1252 . -35) 118531) ((-1251 . -1133) T) ((-605 . -152) 118513) ((-1101 . -360) 118492) ((-176 . -300) T) ((-118 . -388) 118469) ((-118 . -349) 118446) ((-171 . -234) 118371) ((-884 . -317) T) ((-323 . -806) NIL) ((-323 . -803) NIL) ((-326 . -738) 118220) ((-323 . -738) T) ((-486 . -374) 118199) ((-370 . -360) 118178) ((-364 . -360) 118157) ((-356 . -360) 118136) ((-326 . -485) 118115) ((-1272 . -23) T) ((-1251 . -23) T) ((-730 . -1133) T) ((-726 . -132) T) ((-665 . -102) T) ((-489 . -729) 118080) ((-45 . -292) 118030) ((-105 . -1121) T) ((-68 . -625) 118012) ((-991 . -102) T) ((-878 . -102) T) ((-635 . -917) 117971) ((-1312 . -1121) T) ((-392 . -1121) T) ((-1261 . -234) 117958) ((-1237 . -1121) T) ((-82 . -1238) T) ((-1134 . -272) 117927) ((-1083 . -862) T) ((-118 . -917) NIL) ((-794 . -939) 117906) ((-725 . -862) T) ((-543 . -1121) T) ((-512 . -1121) T) ((-366 . -1242) T) ((-363 . -1242) T) ((-355 . -1242) T) ((-273 . -1242) 117885) ((-253 . -1242) 117864) ((-545 . -874) T) ((-1134 . -232) 117833) ((-1179 . -840) T) ((-1163 . -1077) 117817) ((-402 . -773) T) ((-706 . -1238) T) ((-703 . -1059) 117801) ((-366 . -568) T) ((-363 . -568) T) ((-355 . -568) T) ((-273 . -568) 117732) ((-253 . -568) 117663) ((-537 . -1104) T) ((-1163 . -111) 117642) ((-465 . -756) 117612) ((-880 . -1077) 117582) ((-829 . -38) 117524) ((-706 . -899) 117506) ((-706 . -901) 117488) ((-305 . -319) 117292) ((-1178 . -298) 117269) ((-929 . -1242) T) ((-1101 . -658) 117164) ((-1025 . -464) T) ((-682 . -423) 117148) ((-880 . -111) 117113) ((-933 . -464) T) ((-706 . -1059) 117058) ((-929 . -568) T) ((-545 . -625) 117040) ((-593 . -939) T) ((-499 . -1072) 116990) ((-486 . -1133) T) ((-530 . -939) T) ((-494 . -919) 116859) ((-65 . -625) 116841) ((-219 . -1072) 116791) ((-499 . -652) 116741) ((-370 . -658) 116678) ((-364 . -658) 116615) ((-356 . -658) 116552) ((-644 . -231) 116498) ((-219 . -652) 116448) ((-108 . -658) 116398) ((-486 . -23) T) ((-1141 . -806) T) ((-886 . -132) T) ((-1141 . -803) T) ((-1303 . -1305) 116377) ((-1141 . -738) T) ((-666 . -660) 116351) ((-304 . -625) 116092) ((-1163 . -628) 116010) ((-1056 . -34) T) ((-828 . -237) 115961) ((-592 . -317) T) ((-576 . -317) T) ((-507 . -317) T) ((-1312 . -729) 115931) ((-706 . -388) 115913) ((-706 . -349) 115895) 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T) ((-1188 . -994) 115002) ((-48 . -1238) T) ((-76 . -625) 114984) ((-1147 . -994) 114951) ((-711 . -317) T) ((-130 . -856) T) ((-929 . -374) T) ((-390 . -25) T) ((-390 . -21) T) ((-929 . -339) 114938) ((-86 . -625) 114920) ((-711 . -1043) T) ((-689 . -862) T) ((-400 . -1238) T) ((-1272 . -132) T) ((-1251 . -132) T) ((-920 . -1031) 114904) ((-848 . -21) T) ((-48 . -1059) 114847) ((-848 . -25) T) ((-839 . -25) T) ((-839 . -21) T) ((-1134 . -658) 114626) ((-1310 . -1079) T) ((-561 . -102) T) ((-1308 . -1079) T) ((-666 . -738) T) ((-1125 . -630) 114529) ((-1024 . -628) 114459) ((-1311 . -1077) 114443) ((-923 . -1238) T) ((-827 . -423) 114412) ((-103 . -120) 114396) ((-130 . -1121) T) ((-52 . -1121) T) ((-945 . -625) 114378) ((-885 . -1013) 114355) ((-835 . -102) T) ((-1311 . -111) 114334) ((-743 . -911) 114309) ((-665 . -38) 114279) ((-583 . -862) T) ((-366 . -1133) T) ((-363 . -1133) T) ((-355 . -1133) T) ((-273 . -1133) T) ((-253 . -1133) T) ((-1171 . -319) 114083) ((-1109 . -234) 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112679) ((-1243 . -102) T) ((-1084 . -102) T) ((-855 . -628) 112547) ((-512 . -526) NIL) ((-494 . -243) 112526) ((-419 . -628) 112424) ((-982 . -1072) 112307) ((-747 . -1072) 112277) ((-982 . -652) 112174) ((-1193 . -146) 112153) ((-747 . -652) 112123) ((-465 . -1072) 112093) ((-1193 . -148) 112072) ((-1146 . -148) 112051) ((-1146 . -146) 112030) ((-647 . -1077) 112014) ((-619 . -1077) 111998) ((-465 . -652) 111968) ((-1195 . -1279) 111952) ((-1195 . -1266) 111929) ((-1194 . -1271) 111890) ((-682 . -1121) T) ((-682 . -1074) 111830) ((-1194 . -1266) 111800) ((-560 . -1121) T) ((-499 . -1173) T) ((-1194 . -1269) 111784) ((-1188 . -1250) 111745) ((-830 . -275) 111729) ((-219 . -1173) T) ((-354 . -939) T) ((-99 . -1238) T) ((-647 . -111) 111708) ((-619 . -111) 111687) ((-1188 . -1266) 111664) ((-855 . -1070) 111643) ((-1188 . -1248) 111627) ((-527 . -25) T) ((-507 . -312) T) ((-523 . -23) T) ((-522 . -25) T) ((-520 . -25) T) ((-519 . -23) T) ((-430 . -1072) 111601) ((-419 . -1070) T) 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-1121) T) ((-45 . -231) 110509) ((-1025 . -911) NIL) ((-811 . -1072) 110493) ((-977 . -862) 110472) ((-1020 . -660) 110374) ((-811 . -652) 110358) ((-245 . -1295) 110328) ((-1045 . -317) T) ((-304 . -1077) 110249) ((-929 . -132) T) ((-40 . -939) T) ((-499 . -412) 110231) ((-365 . -317) T) ((-219 . -412) 110213) ((-1101 . -423) 110197) ((-304 . -111) 110113) ((-1204 . -862) T) ((-1203 . -862) T) ((-886 . -25) T) ((-886 . -21) T) ((-1274 . -47) 110057) ((-350 . -625) 110039) ((-1193 . -237) T) ((-227 . -148) T) ((-176 . -625) 110021) ((-786 . -625) 110003) ((-129 . -862) T) ((-620 . -240) 109950) ((-487 . -240) 109900) ((-1310 . -729) 109870) ((-48 . -317) T) ((-1308 . -729) 109840) ((-65 . -628) 109769) ((-983 . -1121) T) ((-827 . -1121) 109521) ((-322 . -102) T) ((-920 . -1238) T) ((-48 . -1043) T) ((-1251 . -651) 109429) ((-701 . -102) 109379) ((-44 . -729) 109363) ((-562 . -102) T) ((-304 . -628) 109294) ((-67 . -394) T) ((-499 . -919) NIL) ((-67 . -407) T) ((-219 . -919) NIL) ((-674 . -23) T) ((-829 . -658) 109230) ((-682 . -773) T) ((-1235 . -1121) 109208) ((-362 . -1077) 109153) ((-687 . -1121) 109131) ((-1083 . -148) T) ((-971 . -148) 109110) ((-971 . -146) 109089) ((-811 . -102) T) ((-153 . -729) 109073) ((-493 . -148) 109052) ((-493 . -146) 109031) ((-362 . -111) 108960) ((-1101 . -1079) T) ((-332 . -862) 108939) ((-1280 . -994) 108908) ((-1274 . -1238) T) ((-639 . -1121) T) ((-1273 . -994) 108870) ((-523 . -132) T) ((-519 . -132) T) ((-305 . -231) 108820) ((-370 . -1079) T) ((-364 . -1079) T) ((-356 . -1079) T) ((-304 . -1070) 108762) ((-1252 . -994) 108731) ((-390 . -862) T) ((-108 . -1079) T) ((-1020 . -738) T) ((-884 . -939) T) ((-855 . -807) 108710) ((-855 . -804) 108689) ((-430 . -319) 108628) ((-480 . -102) T) ((-607 . -994) 108597) ((-329 . -1121) T) ((-419 . -807) 108576) ((-419 . -804) 108555) ((-512 . -501) 108537) ((-1274 . -1059) 108503) ((-1272 . -21) T) ((-1272 . -25) T) ((-1251 . -21) T) ((-1251 . -25) T) ((-827 . -729) 108445) ((-362 . -628) 108375) ((-711 . -416) T) ((-1301 . -1238) T) ((-1134 . -423) 108344) ((-1098 . -1238) T) ((-618 . -102) T) ((-1024 . -379) NIL) ((-1008 . -1238) T) ((-683 . -102) T) ((-182 . -102) T) ((-162 . -102) T) ((-157 . -102) T) ((-155 . -102) T) ((-103 . -34) T) ((-1199 . -658) 108254) ((-749 . -1238) T) ((-743 . -1072) 108097) ((-44 . -773) T) ((-743 . -652) 107946) ((-605 . -102) T) ((-665 . -668) 107930) ((-77 . -408) T) ((-77 . -407) T) ((-142 . -1238) T) ((-885 . -148) T) ((-885 . -146) NIL) ((-1300 . -658) 107875) ((-1280 . -911) 107763) ((-1273 . -911) 107644) ((-1237 . -93) T) ((-362 . -1070) T) ((-227 . -237) T) ((-70 . -394) T) ((-70 . -407) T) ((-1186 . -102) T) ((-682 . -526) 107577) ((-1252 . -911) 107313) ((-1232 . -568) 107292) ((-701 . -319) 107230) ((-982 . -38) 107127) ((-1201 . -625) 107109) ((-747 . -38) 107079) ((-562 . -319) 106883) ((-1195 . -1072) 106766) ((-326 . -1238) T) ((-362 . -238) T) ((-362 . -248) T) ((-323 . -1238) T) ((-299 . -1121) T) ((-1194 . -1072) 106601) ((-1188 . -1072) 106391) ((-1147 . -1072) 106274) ((-1195 . -652) 106171) ((-1194 . -652) 106012) ((-723 . -1242) T) ((-1188 . -652) 105808) ((-1178 . -663) 105792) ((-1147 . -652) 105689) ((-831 . -397) 105673) ((-723 . -568) T) ((-607 . -911) 105584) ((-326 . -899) 105568) ((-326 . -901) 105493) ((-323 . -899) 105454) ((-140 . -1238) T) ((-137 . -1238) T) ((-115 . -1238) T) ((-323 . -901) NIL) ((-811 . -319) 105419) ((-329 . -729) 105260) ((-398 . -397) 105244) ((-334 . -333) 105221) ((-497 . -102) T) ((-486 . -25) T) ((-486 . -21) T) ((-430 . -38) 105195) ((-326 . -1059) 104858) ((-227 . -1223) T) ((-227 . -1226) T) ((-3 . -625) 104840) ((-323 . -1059) 104770) ((-886 . -234) 104715) ((-2 . -1121) T) ((-2 . |RecordCategory|) T) ((-1134 . -1079) 104693) ((-845 . -625) 104675) ((-1083 . -237) T) ((-592 . -939) T) ((-576 . -832) T) ((-576 . -939) T) ((-507 . -939) T) ((-137 . -1059) 104659) ((-227 . -95) T) ((-171 . -148) 104638) ((-75 . -453) T) ((0 . -625) 104620) ((-75 . -407) T) ((-171 . -146) 104571) ((-227 . -35) T) ((-49 . -625) 104553) ((-489 . -1079) T) ((-499 . -272) 104535) ((-499 . -232) 104517) ((-496 . -989) 104501) ((-219 . -272) 104483) ((-219 . -232) 104465) ((-81 . -453) T) ((-81 . -407) T) ((-1167 . -34) T) ((-743 . -102) T) ((-665 . -658) 104424) ((-1047 . -625) 104391) ((-512 . -296) 104341) ((-326 . -388) 104310) ((-323 . -388) 104271) ((-323 . -349) 104232) ((-1106 . -625) 104214) ((-828 . -968) 104161) ((-674 . -132) T) ((-1261 . -146) 104140) ((-1261 . -148) 104119) ((-1195 . -102) T) ((-1194 . -102) T) ((-1188 . -102) T) ((-1180 . -1121) T) ((-1147 . -102) T) ((-1096 . -1238) T) ((-224 . -34) T) ((-299 . -729) 104106) ((-1180 . -622) 104082) ((-605 . -319) NIL) ((-1280 . -1279) 104066) ((-1171 . -231) 104016) ((-496 . -1121) 103994) ((-450 . -1238) T) ((-402 . -625) 103976) ((-522 . -862) T) ((-1141 . -1238) T) ((-1280 . -1266) 103953) ((-1273 . -1271) 103914) ((-1273 . -1266) 103884) ((-1273 . -1269) 103868) ((-1252 . -1250) 103829) ((-1252 . -1266) 103806) ((-1252 . -1248) 103790) ((-633 . -625) 103772) ((-1195 . -294) 103738) ((-711 . -939) T) ((-1194 . -294) 103704) ((-1188 . -294) 103670) ((-1147 . -294) 103636) ((-1101 . -1121) T) ((-1082 . -1121) T) ((-48 . -312) T) ((-326 . -917) 103602) ((-323 . -917) NIL) ((-1082 . -1089) 103581) ((-1141 . -901) 103563) ((-811 . -38) 103547) ((-273 . -651) 103495) ((-253 . -651) 103443) ((-713 . -1077) 103430) ((-607 . -1266) 103407) ((-1141 . -1059) 103389) ((-329 . -174) 103320) ((-370 . -1121) T) ((-364 . -1121) T) ((-356 . -1121) T) ((-512 . -19) 103302) ((-1123 . -152) 103286) ((-885 . -237) NIL) ((-108 . -1121) T) ((-117 . -1077) 103273) ((-723 . -374) T) ((-512 . -616) 103248) ((-713 . -111) 103233) ((-1313 . -625) 103200) ((-1313 . -502) 103182) ((-1272 . -234) 103128) ((-1251 . -234) 102981) ((-448 . -102) T) ((-890 . -1283) T) ((-256 . -102) T) ((-45 . -1170) 102931) ((-117 . -111) 102916) ((-1290 . -625) 102898) ((-1261 . -237) T) ((-1246 . -625) 102880) ((-1244 . -862) T) ((-647 . -732) T) ((-619 . -732) T) ((-1232 . -1133) T) ((-1232 . -23) T) ((-1193 . -464) 102811) ((-1188 . -319) 102696) ((-1187 . -1121) T) ((-827 . -526) 102629) ((-1056 . -1238) T) ((-245 . -1072) 102530) ((-1179 . -1121) T) ((-1163 . -660) 102468) ((-962 . -152) 102452) ((-1147 . -319) 102439) ((-1146 . -464) 102390) ((-245 . -652) 102312) ((-1108 . -568) 102243) ((-1108 . -1242) 102222) ((-1101 . -729) 102090) ((-537 . -102) T) ((-532 . -102) 102020) ((-1025 . -1072) 101970) ((-1015 . -1121) T) ((-828 . -911) 101866) ((-794 . -1242) 101845) ((-792 . -1242) 101824) ((-62 . -1238) T) ((-489 . -625) 101776) ((-489 . -626) 101698) ((-794 . -568) 101609) ((-792 . -568) 101540) ((-743 . -319) 101527) ((-713 . -628) 101499) ((-494 . -423) 101468) ((-635 . -939) 101447) ((-466 . -1242) 101426) ((-687 . -526) 101359) ((-676 . -25) T) ((-410 . -625) 101341) ((-676 . -21) T) ((-466 . -568) 101272) ((-430 . -919) 101195) ((-366 . -25) T) ((-366 . -21) T) ((-363 . -25) T) ((-118 . -939) T) ((-118 . -832) NIL) ((-363 . -21) T) ((-355 . -25) T) ((-355 . -21) T) ((-273 . -25) T) ((-273 . -21) T) ((-253 . -25) T) ((-253 . -21) T) ((-171 . -237) 101126) ((-83 . -395) T) ((-83 . -407) T) ((-135 . -628) 101108) ((-117 . -628) 101080) ((-1025 . -652) 101030) ((-962 . -1001) 101014) ((-933 . -652) 100966) ((-933 . -1072) 100918) ((-929 . -21) T) ((-929 . -25) T) ((-886 . -862) 100869) ((-880 . -660) 100829) ((-723 . -1133) T) ((-723 . -23) T) ((-713 . -1070) T) ((-713 . -238) T) ((-299 . -174) T) ((-666 . -1238) T) ((-321 . -93) T) ((-659 . -1121) 100807) ((-644 . -622) 100782) ((-644 . -1121) T) ((-593 . -1242) T) ((-593 . -568) T) ((-530 . -1242) T) ((-530 . -568) T) ((-499 . -658) 100732) ((-486 . -234) 100678) ((-439 . -1072) 100662) ((-439 . -652) 100646) ((-370 . -729) 100598) ((-364 . -729) 100550) ((-350 . -1077) 100534) ((-356 . -729) 100486) ((-350 . -111) 100465) ((-176 . -1077) 100397) ((-176 . -111) 100308) ((-108 . -729) 100258) ((-219 . -658) 100208) ((-283 . -1121) T) ((-282 . -1121) T) ((-281 . -1121) T) ((-280 . -1121) T) ((-279 . -1121) T) ((-278 . -1121) T) ((-277 . -1121) T) ((-214 . -1121) T) ((-213 . -1121) T) ((-171 . -1226) 100186) ((-171 . -1223) 100164) ((-211 . -1121) T) ((-210 . -1121) T) ((-117 . -1070) T) ((-209 . -1121) T) ((-208 . -1121) T) ((-205 . -1121) T) ((-204 . -1121) T) ((-203 . -1121) T) ((-202 . -1121) T) ((-201 . -1121) T) ((-200 . -1121) T) ((-199 . -1121) T) ((-198 . -1121) T) ((-197 . -1121) T) ((-196 . -1121) T) ((-195 . -1121) T) ((-245 . -102) 99896) ((-171 . -35) 99874) ((-171 . -95) 99852) ((-666 . -1059) 99748) ((-494 . -1079) 99726) ((-1134 . -1121) 99478) ((-1163 . -34) T) ((-682 . -501) 99462) ((-73 . -1238) T) ((-105 . -625) 99444) ((-908 . -1238) T) ((-1312 . -625) 99426) ((-392 . -625) 99408) ((-350 . -628) 99360) ((-176 . -628) 99277) ((-1237 . -502) 99258) ((-743 . -38) 99107) ((-583 . -1226) T) ((-583 . -1223) T) ((-543 . -625) 99089) ((-532 . -319) 99027) ((-512 . -625) 99009) ((-512 . -626) 98991) ((-1237 . -625) 98957) ((-1188 . -1173) NIL) ((-215 . -1238) T) ((-1048 . -1092) 98926) ((-1048 . -1121) T) ((-1025 . -102) T) ((-992 . -102) T) ((-933 . -102) T) ((-908 . -1059) 98903) ((-1163 . -738) T) ((-1024 . -660) 98810) ((-488 . -1121) T) ((-475 . -1121) T) ((-598 . -23) T) ((-583 . -35) T) ((-583 . -95) T) ((-439 . -102) T) ((-1084 . -231) 98756) ((-1195 . -38) 98653) ((-1194 . -38) 98494) ((-880 . -738) T) ((-706 . -939) T) ((-523 . -25) T) ((-519 . -21) T) ((-519 . -25) T) ((-1188 . -38) 98290) ((-350 . -1070) T) ((-145 . -1238) T) ((-1101 . -174) T) ((-176 . -1070) T) ((-1147 . -38) 98187) ((-724 . -47) 98164) ((-370 . -174) T) ((-364 . -174) T) ((-531 . -57) 98138) ((-509 . -57) 98088) ((-362 . -1307) 98065) ((-227 . -464) T) ((-329 . -300) 98016) ((-356 . -174) T) ((-176 . -248) T) ((-1251 . -862) 97915) ((-108 . -174) T) ((-886 . -1013) 97899) ((-670 . -1133) T) ((-593 . -374) T) ((-593 . -339) 97886) ((-530 . -339) 97863) ((-530 . -374) T) 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-866) 89763) ((-1199 . -1121) T) ((-103 . -1238) T) ((-971 . -968) 89724) ((-829 . -729) 89666) ((-1252 . -1173) NIL) ((-493 . -968) 89611) ((-1083 . -144) T) ((-60 . -102) 89561) ((-44 . -625) 89543) ((-78 . -625) 89525) ((-362 . -660) 89470) ((-1300 . -1121) T) ((-523 . -862) T) ((-299 . -296) 89449) ((-354 . -1133) T) ((-305 . -1121) T) ((-1020 . -917) 89408) ((-305 . -622) 89387) ((-1312 . -628) 89336) ((-1280 . -38) 89233) ((-1273 . -38) 89074) ((-1252 . -38) 88870) ((-499 . -1079) T) ((-392 . -628) 88854) ((-219 . -1079) T) ((-354 . -23) T) ((-153 . -625) 88836) ((-845 . -807) 88815) ((-845 . -804) 88794) ((-1237 . -628) 88775) ((-608 . -38) 88748) ((-607 . -38) 88645) ((-884 . -568) T) ((-225 . -132) T) ((-329 . -1023) 88611) ((-79 . -625) 88593) ((-724 . -317) 88572) ((-304 . -738) 88474) ((-836 . -102) T) ((-878 . -856) T) ((-304 . -485) 88453) ((-1303 . -102) T) ((-40 . -374) T) ((-886 . -148) 88432) ((-497 . -658) 88414) ((-886 . -146) 88393) ((-1179 . -501) 88375) ((-1312 . -1070) T) ((-494 . -526) 88308) ((-1167 . -1238) T) ((-983 . -625) 88290) ((-659 . -501) 88274) ((-644 . -501) 88205) ((-827 . -625) 87898) ((-48 . -27) T) ((-1199 . -729) 87795) ((-971 . -911) 87774) ((-665 . -1121) T) ((-875 . -874) T) ((-448 . -375) 87748) ((-743 . -658) 87658) ((-493 . -911) 87633) ((-1123 . -102) T) ((-991 . -1121) T) ((-878 . -1121) T) ((-828 . -319) 87620) ((-545 . -539) T) ((-545 . -588) T) ((-1308 . -393) 87592) ((-1075 . -526) 87525) ((-1180 . -296) 87501) ((-245 . -272) 87470) ((-245 . -232) 87439) ((-258 . -1072) 87340) ((-257 . -1072) 87241) ((-1300 . -729) 87211) ((-1187 . -93) T) ((-1015 . -93) T) ((-829 . -174) 87190) ((-258 . -652) 87112) ((-257 . -652) 87034) ((-1235 . -502) 87011) ((-590 . -1238) T) ((-229 . -526) 86944) ((-633 . -807) 86923) ((-633 . -804) 86902) ((-1235 . -625) 86814) ((-224 . -1238) T) ((-687 . -625) 86746) ((-1195 . -658) 86656) ((-1178 . -1031) 86640) ((-962 . -102) 86570) ((-362 . -738) T) ((-875 . -625) 86552) ((-1194 . -658) 86434) ((-1188 . -658) 86271) ((-1147 . -658) 86181) ((-1252 . -412) 86133) ((-1134 . -501) 86117) ((-60 . -319) 86055) ((-341 . -102) T) ((-1232 . -21) T) ((-1232 . -25) T) ((-40 . -1133) T) ((-723 . -21) T) ((-639 . -625) 86037) ((-527 . -333) 86016) ((-723 . -25) T) ((-451 . -102) T) ((-108 . -296) NIL) ((-940 . -1133) T) ((-40 . -23) T) ((-783 . -1133) T) ((-576 . -1242) T) ((-507 . -1242) T) ((-1025 . -272) 85998) ((-329 . -625) 85980) ((-1025 . -232) 85962) ((-171 . -167) 85946) ((-592 . -568) T) ((-576 . -568) T) ((-507 . -568) T) ((-783 . -23) T) ((-1272 . -148) 85925) ((-1272 . -146) 85904) ((-1180 . -616) 85880) ((-1251 . -146) 85805) ((-1048 . -501) 85789) ((-1245 . -1238) T) ((-1251 . -148) 85714) ((-1303 . -1309) 85693) ((-885 . -911) NIL) ((-488 . -501) 85677) ((-475 . -501) 85661) ((-535 . -34) T) ((-665 . -729) 85631) ((-1280 . -919) 85544) ((-1273 . -919) 85450) ((-1252 . -919) 85211) ((-112 . -988) T) ((-1199 . -174) 85162) ((-674 . -862) 85141) ((-376 . -102) T) 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-625) 83801) ((-188 . -102) T) ((-1179 . -19) 83783) ((-1179 . -616) 83758) ((-670 . -21) T) ((-670 . -25) T) ((-605 . -1165) T) ((-1134 . -296) 83735) ((-347 . -25) T) ((-347 . -21) T) ((-904 . -1238) T) ((-900 . -1238) T) ((-1310 . -1077) 83719) ((-245 . -658) 83498) ((-507 . -374) T) ((-1308 . -1077) 83482) ((-1303 . -38) 83452) ((-1272 . -1223) 83418) ((-1272 . -1226) 83384) ((-1261 . -911) 83287) ((-1193 . -1072) 83110) ((-1163 . -1238) T) ((-1146 . -1072) 82953) ((-868 . -1072) 82937) ((-644 . -616) 82912) ((-1272 . -95) 82878) ((-1272 . -237) 82830) ((-1255 . -102) 82808) ((-1193 . -652) 82637) ((-1146 . -652) 82486) ((-868 . -652) 82456) ((-1252 . -232) 82408) ((-1108 . -25) T) ((-561 . -1121) T) ((-1108 . -21) T) ((-982 . -1079) T) ((-543 . -804) T) ((-543 . -807) T) ((-118 . -1242) T) ((-880 . -1238) T) ((-635 . -568) T) ((-794 . -25) T) ((-794 . -21) T) ((-792 . -21) T) ((-792 . -25) T) ((-747 . -1079) T) ((-727 . -1079) T) ((-682 . -1077) 82392) ((-529 . -1104) T) ((-473 . -25) T) ((-118 . -568) T) ((-473 . -21) T) ((-466 . -25) T) ((-466 . -21) T) ((-1252 . -272) 82344) ((-1172 . -93) T) ((-1163 . -1059) 82240) ((-829 . -300) 82219) ((-1251 . -1223) 82185) ((-835 . -1121) T) ((-985 . -988) T) ((-682 . -111) 82164) ((-629 . -1238) T) ((-305 . -526) 81956) ((-1251 . -1226) 81922) ((-1251 . -237) 81781) ((-1246 . -379) T) ((-258 . -319) 81719) ((-257 . -319) 81657) ((-1243 . -856) T) ((-1180 . -626) NIL) ((-1180 . -625) 81639) ((-1163 . -388) 81623) ((-1141 . -832) T) ((-1141 . -939) T) ((-96 . -93) T) ((-1134 . -616) 81600) ((-1101 . -626) 81584) ((-1101 . -625) 81566) ((-1025 . -658) 81516) ((-933 . -658) 81453) ((-827 . -298) 81430) ((-496 . -625) 81362) ((-620 . -152) 81309) ((-499 . -729) 81259) ((-430 . -1079) T) ((-494 . -501) 81243) ((-439 . -658) 81202) ((-337 . -862) 81181) ((-350 . -660) 81155) ((-50 . -21) T) ((-50 . -25) T) ((-219 . -729) 81105) ((-171 . -736) 81076) ((-176 . -660) 81008) ((-593 . -21) T) ((-593 . -25) T) ((-530 . -25) T) 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80174) ((-1199 . -300) 80153) ((-1125 . -1238) T) ((-110 . -296) 80103) ((-1024 . -1238) T) ((-129 . -152) 80085) ((-1163 . -917) 80044) ((-44 . -111) 80023) ((-1243 . -1121) T) ((-1202 . -1283) T) ((-1188 . -860) NIL) ((-1187 . -502) 80004) ((-682 . -1070) T) ((-1187 . -625) 79970) ((-1179 . -625) 79952) ((-486 . -237) 79904) ((-1084 . -622) 79879) ((-1015 . -502) 79860) ((-74 . -453) T) ((-74 . -407) T) ((-1084 . -1121) T) ((-153 . -1077) 79844) ((-1015 . -625) 79810) ((-682 . -238) 79789) ((-583 . -566) 79773) ((-366 . -148) 79752) ((-366 . -146) 79703) ((-363 . -148) 79682) ((-363 . -146) 79633) ((-355 . -148) 79612) ((-355 . -146) 79563) ((-273 . -146) 79542) ((-273 . -148) 79521) ((-253 . -148) 79500) ((-118 . -374) T) ((-253 . -146) 79479) ((-1179 . -626) NIL) ((-153 . -111) 79458) ((-1024 . -1059) 79346) ((-1178 . -1238) T) ((-706 . -1242) T) ((-811 . -1079) T) ((-711 . -1133) T) ((-1024 . -388) 79323) ((-518 . -1238) T) ((-514 . -1238) T) ((-929 . -146) T) ((-929 . -148) 79305) ((-884 . -132) T) ((-827 . -1077) 79226) ((-711 . -23) T) ((-706 . -568) T) ((-227 . -1072) 79191) ((-659 . -625) 79123) ((-659 . -626) 79084) ((-644 . -626) NIL) ((-644 . -625) 79066) ((-499 . -174) T) ((-227 . -652) 79031) ((-219 . -174) T) ((-225 . -21) T) ((-225 . -25) T) ((-486 . -1226) 78997) ((-486 . -1223) 78963) ((-283 . -625) 78945) ((-282 . -625) 78927) ((-281 . -625) 78909) ((-280 . -625) 78891) ((-279 . -625) 78873) ((-512 . -663) 78855) ((-278 . -625) 78837) ((-350 . -738) T) ((-277 . -625) 78819) ((-110 . -19) 78801) ((-176 . -738) T) ((-512 . -384) 78783) ((-214 . -625) 78765) ((-532 . -1170) 78749) ((-512 . -124) T) ((-110 . -616) 78724) ((-213 . -625) 78706) ((-486 . -35) 78672) ((-486 . -95) 78638) ((-211 . -625) 78620) ((-210 . -625) 78602) ((-209 . -625) 78584) ((-208 . -625) 78566) ((-205 . -625) 78548) ((-204 . -625) 78530) ((-203 . -625) 78512) ((-202 . -625) 78494) ((-201 . -625) 78476) ((-200 . -625) 78458) ((-199 . -625) 78440) ((-548 . -1124) 78392) 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. -658) 51767) ((-828 . -729) 51616) ((-1290 . -1238) T) ((-589 . -874) T) ((-583 . -658) 51588) ((-118 . -862) NIL) ((-1193 . -423) 51572) ((-1146 . -423) 51556) ((-868 . -423) 51540) ((-887 . -102) 51491) ((-1272 . -102) T) ((-1252 . -526) 51260) ((-1251 . -102) T) ((-1224 . -319) 51198) ((-1195 . -296) 51163) ((-1194 . -296) 51121) ((-537 . -93) T) ((-1188 . -296) 50949) ((-322 . -625) 50931) ((-1123 . -1121) T) ((-1101 . -660) 50805) ((-723 . -464) T) ((-701 . -625) 50737) ((-299 . -738) T) ((-108 . -928) NIL) ((-701 . -626) 50698) ((-613 . -625) 50680) ((-589 . -625) 50662) ((-562 . -626) NIL) ((-562 . -625) 50644) ((-541 . -625) 50626) ((-523 . -521) 50605) ((-499 . -1077) 50555) ((-486 . -1072) 50390) ((-519 . -521) 50369) ((-486 . -652) 50210) ((-219 . -1077) 50160) ((-370 . -660) 50112) ((-364 . -660) 50064) ((-227 . -860) T) ((-356 . -660) 50016) ((-614 . -102) 49946) ((-499 . -111) 49880) ((-494 . -379) 49859) ((-108 . -660) 49809) ((-365 . -234) 49796) ((-245 . -501) 49780) 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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 4f3f1d36..e876b75f 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3486772023) -(4465 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3486783783) +(4467 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -313,8 +313,8 @@ |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem| |OrderedCompletionFunctions2| |OrderedCompletion| |OrderedFinite| |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| - |OrderedSet&| |OrderedSet| |UnivariateSkewPolynomialCategory&| - |UnivariateSkewPolynomialCategory| + |OrderedSet&| |OrderedSet| |OrderedType&| |OrderedType| + |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| |OrderedSemiGroup| |OrdSetInts| |OutputByteConduit&| @@ -488,665 +488,666 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |space| |deleteRoutine!| |readInt16!| - |identification| |arg2| |makeCos| |pile| |string| |addPoint2| - |intermediateResultsIF| |basisOfCentroid| |startPolynomial| |tablePow| - |psolve| |diagonal| |computeCycleLength| |horizConcat| - |fortranLinkerArgs| |say| |OMunhandledSymbol| |upperCase?| - |multiEuclideanTree| |mainValue| |f01maf| |setEmpty!| |conditions| - |lfextlimint| |infix| |isList| |dfRange| |reopen!| |numberOfFactors| - |cAsinh| |zero?| |drawStyle| |title| |match| |bezoutDiscriminant| - 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|OMlistSymbols| - |factorFraction| |continue| |setScreenResolution3D| |mainVariable| - |inverse| |complexRoots| |duplicates?| |innerEigenvectors| |child?| - |antisymmetricTensors| |nextSublist| |fixPredicate| - |degreeSubResultantEuclidean| |mpsode| |createNormalElement| - |difference| |removeCoshSq| |countRealRootsMultiple| |prinb| - |listOfLists| |part?| ** |hash| |copy!| |middle| |inputBinaryFile| - |minPol| |branchIfCan| |isOp| |complexEigenvalues| |resultantReduit| - |returnTypeOf| |count| |e04jaf| |f01brf| |kroneckerDelta| |cAsech| - |presub| |open?| |splitLinear| |SturmHabicht| |LazardQuotient2| - |imagJ| |basicSet| |headReduced?| |leadingTerm| |initTable!| - |oblateSpheroidal| |univariatePolynomialsGcds| |rationalPower| - |numberOfPrimitivePoly| |dmp2rfi| |constant| |nullSpace| |s13aaf| - |showTheIFTable| |e04naf| |f04faf| |twoFactor| |leftMinimalPolynomial| - |screenResolution3D| |dequeue| |generalizedInverse| - |initializeGroupForWordProblem| |mantissa| |imagj| |outputMeasure| - |compactFraction| |dihedralGroup| |minColIndex| |aQuadratic| - |copyInto!| |LiePoly| |minimalPolynomial| |virtualDegree| |bat| - |zeroSquareMatrix| |triangulate| |scalarTypeOf| |property| |subCase?| - |denominator| |ScanFloatIgnoreSpacesIfCan| |edf2efi| - |tryFunctionalDecomposition?| |factorAndSplit| |extensionDegree| - |OMputEndObject| |stiffnessAndStabilityOfODEIF| |complex?| |Ci| - |setTopPredicate| |tanh2coth| |branchPoint?| |lfunc| |equiv| - |removeIrreducibleRedundantFactors| |iteratedInitials| |paren| - |s19acf| |subresultantVector| |cCos| - |zeroSetSplitIntoTriangularSystems| |basisOfNucleus| |factorList| - |c06eaf| |addiag| |completeEval| |exprToUPS| |moduleSum| - |discriminantEuclidean| |f01qef| |monomials| |f02wef| |before?| - |genericRightMinimalPolynomial| |check| |laurentRep| |mainVariables| - |nthRootIfCan| |findBinding| |iisec| |explimitedint| - |selectIntegrationRoutines| |blankSeparate| |iisech| |fill!| - |clearTheIFTable| |noLinearFactor?| |associative?| |separateFactors| - |stFunc1| |setScreenResolution| |purelyAlgebraicLeadingMonomial?| - |plenaryPower| |df2mf| |mapDown!| |categories| |f04axf| |groebner| - |f07aef| |deriv| |numer| |curryRight| |retractIfCan| |readable?| - |mainPrimitivePart| |eulerPhi| |iiasinh| |linears| |insertBottom!| - |e04dgf| |deref| |denom| |superscript| |HenselLift| |mainVariable?| - |reflect| |representationType| |bumptab1| |s18adf| |midpoints| - |nextSubsetGray| |exptMod| |inRadical?| |stoseInvertibleSet| - |seriesToOutputForm| |stiffnessAndStabilityFactor| |prinshINFO| - |chebyshevT| |pToHdmp| GF2FG |pi| |paraboloidal| |curryLeft| - |standardBasisOfCyclicSubmodule| |fixedPoints| |vark| |dark| - |expintegrate| |internalLastSubResultant| |rombergo| |infinity| - |exteriorDifferential| |radix| |cycleSplit!| |userOrdered?| |concat| - |step| |explogs2trigs| |f04asf| |squareFreePrim| |rroot| - |getMultiplicationTable| |reduceBasisAtInfinity| |pdct| |eyeDistance| - |generalSqFr| |algintegrate| |doubleFloatFormat| |complexNormalize| - |intensity| |OMserve| |curry| |hessian| |s17ahf| |decreasePrecision| - |ratpart| |cSinh| |palgRDE0| |rightRemainder| |kernel| |adaptive?| - |bits| |removeDuplicates| |quasiComponent| |algebraicOf| |formula| - |d01ajf| |s18dcf| |list| |internalAugment| |lex| |ptree| |norm| - |iiasin| |limitedIntegrate| |mapGen| |normalElement| |lhs| |rotatey| - |unit?| |yellow| |rootRadius| |draw| |UpTriBddDenomInv| |close!| - |cAtan| |semiSubResultantGcdEuclidean2| |clearCache| - |strongGenerators| |rhs| |vedf2vef| |substitute| |linGenPos| - |OMencodingXML| |elaborate| |dominantTerm| |bezoutResultant| - |fortranCompilerName| |interval| |genericRightDiscriminant| - |antiCommutator| |radicalOfLeftTraceForm| |currentScope| |subTriSet?| - |cos2sec| |unparse| |viewDefaults| |relativeApprox| |currentEnv| - |nrows| |d02kef| |selectAndPolynomials| |isobaric?| |coefficients| - |OMgetEndError| |stoseInvertibleSetreg| |associatedSystem| |d01bbf| - |integerBound| |ncols| |indiceSubResultantEuclidean| |getOperands| - |anticoord| |setStatus!| |makeObject| |rightExtendedGcd| |nlde| - |mappingAst| |setOfMinN| |bounds| |df2fi| |subPolSet?| |iflist2Result| - |lazyPseudoQuotient| |df2ef| |coef| |prod| |computeInt| - |hypergeometric0F1| |f2st| |coefChoose| |poisson| |elRow1!| - |writeBytes!| |traceMatrix| |unitVector| |padicallyExpand| |lambert| - |signAround| |alternating| |palgint| |separateDegrees| - |mightHaveRoots| |boundOfCauchy| |hermite| |normal?| |s19aaf| - |OMgetBind| |build| |numFunEvals3D| |tubePoints| |expintfldpoly| - |exactQuotient!| |bfEntry| |indices| |rdHack1| |radicalSolve| |kind| - |OMconnectTCP| |contractSolve| |thetaCoord| |coefficient| |sincos| - |unprotectedRemoveRedundantFactors| |reverse!| |slex| |laguerre| |op| - |cAsec| |po| |reify| |curveColorPalette| |showTheFTable| |kernels| - |setvalue!| |se2rfi| |inGroundField?| |useSingleFactorBound?| - |powerAssociative?| |rightDivide| |semiLastSubResultantEuclidean| - |zeroDim?| |leftDivide| |cyclicSubmodule| |callForm?| - |rowEchelonLocal| |operator| |startTableInvSet!| |setAdaptive3D| - |numberOfVariables| |specialTrigs| |simplifyLog| |divisors| - |symmetricProduct| |monicModulo| SEGMENT |makeYoungTableau| |dn| - |totolex| |leftAlternative?| |fortranComplex| |axesColorDefault| - |hermiteH| |partitions| |contours| |sort| |simplifyPower| - |cycleLength| |double?| |univariate| |d01asf| |doubleRank| |digit?| - |mapCoef| |trueEqual| |scale| |cardinality| |dec| |checkRur| |symFunc| - |linearPart| |overbar| |lazyVariations| |nextPrimitiveNormalPoly| - |closeComponent| |setClipValue| |iExquo| |setnext!| |infieldint| - |companionBlocks| |union| |summation| |fortranCarriageReturn| |binary| - |getExplanations| |wordsForStrongGenerators| |belong?| |duplicates| - |rightScalarTimes!| |factor| |numberOfCycles| |sizeLess?| - |factorPolynomial| |charpol| |supRittWu?| |moreAlgebraic?| |random| - |littleEndian| |normalDenom| |f04arf| |sqrt| |mirror| |factors| - |monicRightFactorIfCan| |nthFactor| |lazyPremWithDefault| |comp| - |tube| |f2df| |shiftRight| |real| |simpson| |completeSmith| |e02dff| - |changeVar| |leftReducedSystem| |empty| |setLength!| |cAcsc| |ode1| - |imag| |bracket| |iiabs| |super| |properties| |root| |leastMonomial| - |ellipticCylindrical| |patternMatch| |nand| |copy| |solid?| - |directProduct| |symmetricGroup| |merge| |leftRecip| |groebnerIdeal| - |selectODEIVPRoutines| |translate| |Nul| |leftNorm| |iiacoth| - |makeResult| |bit?| |setMinPoints3D| |invertible?| |rangeIsFinite| - |depth| |fmecg| |iisin| |scanOneDimSubspaces| |ideal| |alphabetic| - |graeffe| |drawComplexVectorField| |brace| |getBadValues| |iibinom| - |fortranDoubleComplex| |laplace| |asecIfCan| |clipParametric| - |mapBivariate| |birth| |destruct| |removeZero| |smith| |determinant| - |curve| |cyclePartition| |viewWriteAvailable| |categoryFrame| - |semiSubResultantGcdEuclidean1| |numberOfComputedEntries| - |rowEchLocal| |getOrder| |match?| |writeByte!| |polyred| - |integralMatrix| |prologue| |autoCoerce| |argumentList!| |addMatch| - |nextColeman| |rewriteIdealWithQuasiMonicGenerators| |arguments| - |totalDegree| |toseLastSubResultant| |algSplitSimple| - |characteristicSet| |host| |truncate| |central?| |bigEndian| |minus!| - |iicot| |numberOfMonomials| |radicalSimplify| |expand| |twist| - |s21bbf| |monomial| |lowerPolynomial| |primintegrate| |maxdeg| - |jacobian| |OMencodingBinary| |routines| |filterWhile| |limit| - |e02bef| |multivariate| |uniform01| |close| |mat| |polCase| - |consnewpol| F |factorByRecursion| |invertIfCan| |filterUntil| - |variables| |monomRDEsys| |aCubic| |elementary| |rischNormalize| - |pushdown| |select| |degree| |solid| |quasiMonic?| |f02bjf| |display| - |applyRules| |updatD| |clipPointsDefault| |shallowCopy| - |exportedOperators| |repSq| |maxPoints3D| |shufflein| - |integralAtInfinity?| |stronglyReduced?| |mapUnivariate| |acosIfCan| - |OMParseError?| |leftUnits| |split!| |reducedForm| |sncndn| - |fillPascalTriangle| |resultant| |order| |dmpToP| |domainTemplate| - |predicate| |gradient| |epilogue| |pmintegrate| |cAcsch| |lintgcd| - |c06gsf| |reseed| |debug| |taylor| |escape| |modulus| - |createPrimitiveNormalPoly| |setPoly| |halfExtendedSubResultantGcd2| - |cycleTail| |cn| |completeHensel| |polynomialZeros| |atom?| D - |laurent| |input| |removeDuplicates!| |getRef| |coord| - |permutationRepresentation| |iilog| |lieAdmissible?| |lyndon| |opeval| - |reduceByQuasiMonic| |puiseux| |library| |continuedFraction| |c06ecf| - |push| |setUnion| EQ |antiAssociative?| |putProperty| |over| - |acoshIfCan| |intersect| |child| |cycleEntry| |outputSpacing| - |selectSumOfSquaresRoutines| |halfExtendedResultant2| |knownInfBasis| - |odd?| |inv| |coerceImages| |mathieu23| |weights| |pdf2ef| - |cyclicGroup| |setPrologue!| |Hausdorff| - |generalizedContinuumHypothesisAssumed| |lowerCase!| |ground?| - |pomopo!| |removeRedundantFactorsInPols| |polyRDE| - |rewriteSetWithReduction| |increase| |unit| - |functionIsFracPolynomial?| |monomialIntegrate| |frobenius| |ground| - |set| |column| |rightUnit| |genericRightTrace| |innerSolve1| - |transpose| |firstDenom| |OMbindTCP| |badNum| |leftLcm| - |leadingMonomial| |ord| |e01daf| |parametersOf| |GospersMethod| - |rename| |rotate!| |basisOfCommutingElements| |divideIfCan| - |computePowers| |leadingCoefficient| |parameters| |pastel| - |dictionary| |f02ajf| |ricDsolve| |integrate| |size| |modularFactor| - |OMgetApp| |presuper| |geometric| |primitiveMonomials| RF2UTS - |yCoordinates| |rightExactQuotient| |multiple?| |invertibleSet| - |matrixGcd| |symmetricSquare| |position!| |front| |print| |reductum| - |unary?| |complexEigenvectors| |slash| |substring?| |setleaves!| - |divisorCascade| |possiblyNewVariety?| |f07fef| |permanent| - |cosh2sech| |resolve| |pointSizeDefault| |atrapezoidal| |charClass| - |f01qdf| |exponent| |initiallyReduce| |zeroSetSplit| - |quasiMonicPolynomials| |partialDenominators| |wrregime| |lSpaceBasis| - |e01bgf| |setRow!| |irCtor| |sample| |suffix?| |true| |c06gcf| - |f04atf| |category| |iicsc| |mainMonomials| |bivariateSLPEBR| - |uniform| |content| |pop!| |domain| |distdfact| |shiftRoots| |hue| - |shuffle| |viewPhiDefault| |optional| |magnitude| |eigenvectors| - |setLabelValue| |collect| |adaptive| |LyndonWordsList| - |bandedJacobian| |prefix?| |nextItem| |equality| - |rightCharacteristicPolynomial| |package| |s21bcf| - |leftCharacteristicPolynomial| |safetyMargin| |tableau| |permutations| - |insert| |indicialEquationAtInfinity| |nsqfree| |factorSquareFree| - |sumOfSquares| |inf| |enterInCache| |curveColor| |const| - |readLineIfCan!| |expenseOfEvaluationIF| |show| |putColorInfo| |qPot| - |restorePrecision| |probablyZeroDim?| |unexpand| |overset?| - |enterPointData| |var1Steps| |OMgetVariable| |search| |normalise| - |removeSuperfluousQuasiComponents| |reduceLODE| |maxColIndex| - |genericPosition| |deepestTail| |makeEq| |node| - |tableForDiscreteLogarithm| |dimensionsOf| |coordinates| - |pseudoQuotient| |trace| |internalDecompose| |decimal| |vertConcat| - |voidMode| |OMmakeConn| |e04ucf| |OMputBind| |branchPointAtInfinity?| - |physicalLength!| |zeroOf| |iiGamma| |binomThmExpt| |product| - |parabolic| |sylvesterSequence| |findConstructor| |mapdiv| |irVar| - |polygamma| |ipow| |cyclotomicFactorization| |even?| |cAsin| |infix?| - |cCsch| |setlast!| |getCode| |iidprod| |reduction| |FormatRoman| - |positiveSolve| |drawComplex| |mask| |makeMulti| |exQuo| |e02def| - |supersub| |identity| |isExpt| |closed| |s01eaf| |groebgen| |flatten| - |viewport3D| |mainContent| |recip| |sin?| |dimension| |clikeUniv| - |e02bbf| |bernoulli| |listBranches| |s14abf| |iitan| |singularitiesOf| - |pushup| |hMonic| |mathieu12| |constantOperator| |whatInfinity| - |flagFactor| |roman| |printStatement| |isQuotient| |alternatingGroup| - |thenBranch| |round| |splitNodeOf!| |mainExpression| |capacity| - |write!| |conjunction| |randnum| |limitPlus| |writeLine!| - |resultantReduitEuclidean| |baseRDE| |balancedBinaryTree| |pol| |back| - |f01bsf| |style| |fi2df| |setValue!| |traverse| |e04mbf| - |symbolTableOf| |coth2tanh| |constant?| |find| |deepCopy| - |variationOfParameters| |tubePointsDefault| |evaluate| - |outputFloating| |fortranLiteral| |d02cjf| |OMgetEndAttr| |torsion?| - |directory| |any?| |factorSquareFreePolynomial| |redmat| |region| - |euler| |createZechTable| |transcendent?| |rangePascalTriangle| - |OMcloseConn| |OMgetEndBind| |Is| |critMonD1| |subQuasiComponent?| - |extractIfCan| |viewDeltaYDefault| |nextsousResultant2| |height| - |units| |rotatez| |log10| |leaf?| |hcrf| |evaluateInverse| |cCot| - |satisfy?| |pointColorPalette| |equation| |alternative?| |seriesSolve| - |lfextendedint| |spherical| |bitand| |nthFractionalTerm| |c05pbf| - |setClosed| |frst| |numberOfFractionalTerms| |critT| |readLine!| - |nullary| |RittWuCompare| |measure2Result| |leaves| |has?| - |outerProduct| |bitior| |max| |tab1| |linear| |showAll?| - |univariatePolynomial| |rightFactorCandidate| |operators| - |increasePrecision| |makeSin| |fortranReal| |power!| - |positiveRemainder| |meshPar1Var| |lfinfieldint| |permutationGroup| - |c06fpf| |s13adf| |gramschmidt| |showTheRoutinesTable| |macroExpand| - |e02aef| |stirling1| |mix| |upDateBranches| |clearTheSymbolTable| - |inverseColeman| |polynomial| |OMputObject| |divergence| - |lexTriangular| |nextsubResultant2| |indicialEquation| |comment| - |chebyshevU| |bandedHessian| |fixedDivisor| |rk4f| |OMgetEndApp| - |factorGroebnerBasis| |center| |quoted?| |tanhIfCan| |stopTable!| - |low| |validExponential| |airyBi| |noKaratsuba| |algint| |composite| - |elaborateFile| |readInt32!| |primaryDecomp| |factor1| |OMputSymbol| - |index?| |quotedOperators| |d01apf| |rule| |SturmHabichtCoefficients| - |weierstrass| |cycles| |bipolarCylindrical| |declare| |rightUnits| - |asinIfCan| |extendedSubResultantGcd| |cylindrical| - |particularSolution| |linearPolynomials| |startTableGcd!| |common| - |tan2trig| |iroot| |squareFreePolynomial| |makeSketch| - |doublyTransitive?| |powern| |expenseOfEvaluation| |areEquivalent?| - |nextPrimitivePoly| |length| |cup| |quasiRegular| |f01mcf| - |quotientByP| |homogeneous?| |iFTable| |algebraicVariables| |qfactor| - |d01alf| |scripts| |OMreadFile| |readUInt32!| |realEigenvectors| - |setDifference| |s20acf| |blue| |modTree| |OMgetEndAtp| |imagi| - |selectPDERoutines| |fullDisplay| |root?| |f04adf| |scan| |OMputBVar| - |colorFunction| |rename!| |less?| |outputAsTex| |matrix| |module| - |localReal?| |sinIfCan| |square?| |number?| |romberg| |pointPlot| - |getVariableOrder| |f04qaf| |integralLastSubResultant| |list?| - |monomRDE| |tracePowMod| |more?| |closedCurve?| |repeating| |mdeg| - |rischDEsys| |exactQuotient| |stoseInvertible?| |addmod| - |radicalEigenvectors| |rootProduct| |trapezoidalo| |approxNthRoot| - |minimumDegree| |f02xef| Y |discriminant| |tanQ| |c06fuf| - |viewPosDefault| |represents| |plot| |processTemplate| |polyRicDE| - |label| |isAtom| |unitNormal| |lastSubResultant| |packageCall| - |selectOptimizationRoutines| |OMUnknownSymbol?| |doubleResultant| - |rubiksGroup| |raisePolynomial| |phiCoord| |replace| |showArrayValues| - |createNormalPrimitivePoly| |linSolve| |zeroVector| |failed?| - |LiePolyIfCan| |palgLODE0| |rightQuotient| |useEisensteinCriterion?| - |primPartElseUnitCanonical| |outputArgs| |radicalRoots| |listLoops| - |recolor| |result| |axes| |d03edf| |delay| |accuracyIF| |external?| - |var2Steps| |ocf2ocdf| |nonSingularModel| |resetAttributeButtons| - |outputGeneral| |pureLex| |halfExtendedSubResultantGcd1| - |swapColumns!| |s17adf| |xCoord| |univariatePolynomials| - |linearMatrix| |sqfrFactor| |monomial?| |numeric| |mesh| |read!| - |commaSeparate| |OMputEndApp| |incrementKthElement| |critM| - |putProperties| |resultantEuclidean| |dot| |critMTonD1| |radical| - |monic?| |indicialEquations| |ldf2vmf| |taylorRep| |constructor| - |retractable?| |palglimint0| |symbol?| |addMatchRestricted| |meatAxe| - |trigs| |integralBasis| |setButtonValue| |null?| |compdegd| |bindings| - |option| |flexibleArray| |loopPoints| |clearDenominator| |writable?| - |symbolTable| |showSummary| |setAdaptive| |clearTable!| |orbit| - |figureUnits| |rquo| |brillhartIrreducible?| |lowerBound| - |subResultantGcdEuclidean| |removeSquaresIfCan| |mvar| |externalList| - |jacobiIdentity?| |qinterval| |cAcos| |multiplyCoefficients| |points| - |characteristic| |pushFortranOutputStack| |evenInfiniteProduct| - |showAttributes| |makeViewport2D| |shape| |bytes| |approxSqrt| - |lifting1| |localAbs| |noValueMode| |makeRecord| |showClipRegion| - |popFortranOutputStack| |saturate| |hasTopPredicate?| |btwFact| - |cyclicCopy| |completeHermite| |numberOfComposites| |acotIfCan| - |swap!| |outputAsFortran| |primitivePart| |autoReduced?| |setright!| - |trailingCoefficient| |OMopenString| |name| |parents| |e02agf| - |secIfCan| |rarrow| |green| |clipWithRanges| |tubePlot| |randomLC| - |rightTrim| |addBadValue| |cyclic?| |body| |pdf2df| |digamma| |maxrow| - |graphStates| |toScale| |orthonormalBasis| |leftTrim| - |viewSizeDefault| |integralMatrixAtInfinity| |rightFactorIfCan| |null| - |fractionFreeGauss!| |changeName| |s17def| |youngGroup| |stack| - |extractProperty| |prinpolINFO| |reduced?| |monicRightDivide| - |legendreP| |not| |wordInGenerators| |associatorDependence| |fTable| - |lowerCase| |rootOf| BY |factorOfDegree| |conditionsForIdempotents| - |cothIfCan| |sin2csc| |and| |nativeModuleExtension| |singRicDE| - |invmod| |An| |squareFreeLexTriangular| |outputList| |d03eef| - |setVariableOrder| |triangular?| |node?| |or| |selectsecond| |lexico| - |OMputAttr| |numerator| |leastAffineMultiple| |f01qcf| |superHeight| - |toseInvertibleSet| |xor| |lastSubResultantElseSplit| |stronglyReduce| - |isTimes| |isImplies| |rootPower| |getButtonValue| |multiEuclidean| - |linkToFortran| |c02aff| |fortranLogical| |signature| |dim| - |integralCoordinates| |case| |combineFeatureCompatibility| - |irreducible?| |polygon?| |assert| |pushdterm| |nthr| |port| - |dmpToHdmp| |transcendentalDecompose| - |dimensionOfIrreducibleRepresentation| |normal01| |pattern| |Zero| - |chiSquare1| |triangularSystems| |constantCoefficientRicDE| - |ratDsolve| |decrease| |balancedFactorisation| |testModulus| |listexp| - |shallowExpand| |denomRicDE| |One| |untab| |iiasec| |rightTrace| - |palgextint0| |putGraph| |alphanumeric?| |t| |arity| - |screenResolution| |PollardSmallFactor| |removeSinSq| |s17dgf| |shift| - NOT |numerators| |explicitlyFinite?| |ip4Address| |meshFun2Var| - |output| |oddInfiniteProduct| |ramifiedAtInfinity?| |safeCeiling| - |characteristicSerie| |log2| |dequeue!| |adaptive3D?| |leader| OR - |leftTraceMatrix| |vector| |constantRight| |SturmHabichtMultiple| - |rightDiscriminant| |changeThreshhold| |halfExtendedResultant1| - |initiallyReduced?| |iiacot| |digits| |message| |insert!| AND - |constantIfCan| |differentiate| |firstUncouplingMatrix| - |rationalIfCan| |goodnessOfFit| |infRittWu?| |numericIfCan| - |ListOfTerms| |fprindINFO| |e01sbf| |commutative?| |insertMatch| - |call| |predicates| |rightTraceMatrix| |real?| |fortran| |sign| - |atanh| |cCoth| |internal?| |outputBinaryFile| |hdmpToP| - |numberOfDivisors| |printStats!| |elt| |rur| - |unrankImproperPartitions0| |push!| |OMputEndError| |viewport2D| - |acoth| |critB| |inconsistent?| |rightMinimalPolynomial| - |setLegalFortranSourceExtensions| |ScanRoman| |extendIfCan| - |doubleComplex?| |unravel| |monicCompleteDecompose| |dihedral| - |linearlyDependentOverZ?| |asech| |level| |setfirst!| |sts2stst| - |edf2df| |decomposeFunc| |OMputApp| |OMputEndBind| |mapExpon| - |sizeMultiplication| |c06gbf| FG2F |sub| |printCode| |acothIfCan| - |complementaryBasis| |leftTrace| |nilFactor| LODO2FUN |collectUnder| - |showIntensityFunctions| |mesh?| |irreducibleFactor| - |removeRedundantFactorsInContents| |multiple| |cons| |top!| |f01rdf| - |minPoints3D| |direction| |complement| |compound?| |setTex!| - |integralRepresents| |charthRoot| |bag| |key?| |applyQuote| |cond| - |goto| |subSet| |intPatternMatch| |OMUnknownCD?| |iiacsc| |mindeg| - |retract| |transcendenceDegree| |realZeros| |SturmHabichtSequence| - |iicsch| |nextPartition| |stopMusserTrials| |merge!| |ptFunc| - |cycleRagits| |c06frf| |queue| |rootsOf| |unitNormalize| |oddlambert| - |basisOfRightNucleus| |tubeRadiusDefault| |setColumn!| - |subscriptedVariables| |dioSolve| |elem?| |quadraticNorm| - |zeroDimPrimary?| |d01fcf| |second| * |OMencodingSGML| - |factorSquareFreeByRecursion| |pushNewContour| |insertRoot!| - |element?| |ruleset| |basisOfLeftNucloid| |skewSFunction| - |numberOfNormalPoly| |prevPrime| |iisqrt3| |patternVariable| - |complexExpand| |third| |digit| |basisOfLeftNucleus| - |createThreeSpace| |identitySquareMatrix| |quadratic| |normalize| - |headReduce| |createLowComplexityNormalBasis| |hclf| |e01sef| - |mainMonomial| |c06ebf| |df2st| |d01aqf| |computeBasis| |tValues| - |source| |void| |primextendedint| |isOr| |tryFunctionalDecomposition| - |viewWriteDefault| |rightRecip| |OMgetAttr| = |string?| |d01gbf| - |buildSyntax| |leftZero| |cRationalPower| |suchThat| |pole?| - |lazyPseudoDivide| |jacobi| |car| |f02aef| |linearDependenceOverZ| - |ef2edf| |numberOfIrreduciblePoly| |ldf2lst| |divideExponents| - |measure| |script| |BasicMethod| |inputOutputBinaryFile| |varselect| - |ode| |iomode| |viewZoomDefault| < |listYoungTableaus| - |normalizeIfCan| |conjugate| |critBonD| F2FG |plusInfinity| |cycle| - |plotPolar| |mkIntegral| |differentialVariables| |Si| - |makeFloatFunction| |char| > |readIfCan!| |associatedEquations| UTS2UP - |e02baf| |setrest!| |bombieriNorm| |minusInfinity| |systemCommand| - |ridHack1| |ScanFloatIgnoreSpaces| |graphCurves| |zeroMatrix| |e02dcf| - |chvar| <= |invmultisect| |linearlyDependent?| |sinhIfCan| - |eigenvector| |tex| |target| |s15aef| |RemainderList| |rk4| |ref| - |roughBase?| |asinhIfCan| |compBound| >= |sayLength| |leftFactor| - |jokerMode| |ReduceOrder| |absolutelyIrreducible?| |moebiusMu| |lprop| - |leftMult| |enqueue!| |readInt8!| |coshIfCan| |expr| - |selectOrPolynomials| |getConstant| |singularAtInfinity?| |mkcomm| - |OMsetEncoding| |constantOpIfCan| |nextNormalPrimitivePoly| |contract| - |semiResultantEuclidean2| |gcdPrimitive| |normal| |nthExponent| - |splitDenominator| |OMgetAtp| |setleft!| |OMgetObject| |morphism| - |plus!| |acschIfCan| |compose| |leftRank| - |solveLinearPolynomialEquationByRecursion| |c05adf| |clipSurface| - |nodeOf?| + |f04mcf| |shiftLeft| |powerSum| |generalInfiniteProduct| - |type| |changeBase| |internalZeroSetSplit| |leftRemainder| - |stoseLastSubResultant| |solveLinearPolynomialEquationByFractions| - |shade| |tubeRadius| |point| - |float| |complexLimit| |fractRadix| - |iiperm| |cot2trig| |baseRDEsys| |closed?| |pleskenSplit| - |leftRankPolynomial| |mapmult| |variable| |mapMatrixIfCan| / - |polarCoordinates| |postfix| |leftRegularRepresentation| - |OMencodingUnknown| |sortConstraints| |infieldIntegrate| - |eisensteinIrreducible?| |maxint| |algDsolve| |iterators| - |constDsolve| |numberOfOperations| |squareMatrix| |isMult| |palgLODE| - |iitanh| |getlo| |normalizedDivide| |extendedEuclidean| |bernoulliB| - |positive?| |mainCoefficients| |series| |setIntersection| |qqq| - |safeFloor| |stFuncN| |alphanumeric| |signatureAst| |f04mbf| |atoms| - |logGamma| |rightZero| |maximumExponent| |resetBadValues| - |appendPoint| |cfirst| |deepExpand| |integer?| |iipow| |zeroDimPrime?| - |id| |laplacian| |generateIrredPoly| |setelt!| |lazyPquo| - |closedCurve| |e04fdf| |value| |sizePascalTriangle| |setFieldInfo| - |symbol| |finite?| |cosIfCan| |writeInt8!| |lo| |f02fjf| - |rootOfIrreduciblePoly| |cyclicParents| |nextNormalPoly| |regime| - |jordanAdmissible?| |definingPolynomial| |removeSuperfluousCases| - |expression| |semiDiscriminantEuclidean| |rotatex| |leadingExponent| - |min| |sumOfKthPowerDivisors| |ParCondList| |setFormula!| |bringDown| - |interactiveEnv| |corrPoly| |cyclicEqual?| |integer| |Lazard2| - |shanksDiscLogAlgorithm| |polygon| |kovacic| GE |drawToScale| |s17dlf| - |gcdprim| |cyclotomic| |ffactor| |reducedSystem| |cCsc| |OMclose| - |realElementary| |OMputEndAttr| |cyclicEntries| GT |d01anf| |s17dcf| - |rightNorm| |roughUnitIdeal?| |oneDimensionalArray| |s13acf| - |basisOfRightNucloid| |newReduc| |rightGcd| |optpair| LE |e02bcf| - |torsionIfCan| |getMultiplicationMatrix| |listOfMonoms| |iicos| - |bsolve| |extendedIntegrate| |intcompBasis| |OMputError| - |hyperelliptic| LT |expt| |argscript| |compiledFunction| - |purelyTranscendental?| |wreath| |e02ajf| |rootKerSimp| - |completeEchelonBasis| |mkAnswer| |lyndonIfCan| |subspace| - |idealSimplify| |laurentIfCan| |times!| |indiceSubResultant| - |internalIntegrate0| |prem| |zag| |lagrange| |extendedint| - |repeatUntilLoop| |topPredicate| |hasoln| |lineColorDefault| - |pointColorDefault| |recoverAfterFail| |nthFlag| |constantLeft| - |bivariatePolynomials| |keys| |quasiAlgebraicSet| |algebraic?| - |makeUnit| |edf2ef| |imports| |harmonic| |s17akf| |e04gcf| - |atanhIfCan| |exponential1| |componentUpperBound| |getCurve| |diag| - |e02bdf| |curve?| |lazyGintegrate| |whileLoop| |trapezoidal| - |toroidal| |exponents| |xn| |index| |augment| |changeMeasure| - |bumptab| |leftOne| |singleFactorBound| |composites| - |rationalFunction| |dflist| |reducedQPowers| |OMgetType| - |coerceListOfPairs| |fracPart| |prepareDecompose| |redPo| |c06fqf| - |noncommutativeJordanAlgebra?| |member?| |quickSort| |simplify| - |showTheSymbolTable| |iprint| |quotient| |gderiv| |ranges| |floor| - |symmetricRemainder| |e01bhf| |pair| |imagK| |fractionPart| |tree| - |open| |cAcot| |f02awf| |normalDeriv| |realSolve| - |linearAssociatedOrder| |bright| |wholeRagits| |f02abf| - |defineProperty| |monicDecomposeIfCan| |Vectorise| |monicLeftDivide| - |iterationVar| |returns| |wordInStrongGenerators| |inverseLaplace| - |asechIfCan| |numberOfHues| |distance| |lazyIrreducibleFactors| - |subHeight| |setAttributeButtonStep| |diophantineSystem| |eulerE| - |tanIfCan| |minIndex| |eval| |subresultantSequence| |myDegree| - |llprop| |character?| |iicoth| |primitivePart!| |stopTableGcd!| - |getStream| |bat1| |explicitEntries?| |fixedPoint| |high| - |basisOfCenter| |att2Result| |operations| |leftUnit| |groebner?| - |argument| |comparison| |implies| |lllip| |modifyPointData| |hex| - |generic| |quadratic?| |scalarMatrix| |interpret| |matrixConcat3D| - |redpps| |error| |e02ddf| |resetNew| |functionIsContinuousAtEndPoints| - |KrullNumber| |s18aef| |elaboration| |perfectNthPower?| |expandPower| - |jordanAlgebra?| |pade| |rectangularMatrix| |pointData| |s17acf| - |rationalPoints| |ramified?| |eigenMatrix| |universe| |power| - |optimize| |swap| |repeating?| |aspFilename| |imagI| |primitive?| - |fortranTypeOf| |precision| |e02gaf| |function| |besselK| - |basisOfLeftAnnihilator| |reducedContinuedFraction| |polyPart| - |midpoint| |outputFixed| |mainSquareFreePart| |solveid| - |principalAncestors| |convergents| |errorInfo| |firstSubsetGray| - |selectfirst| |iisqrt2| |moebius| |checkForZero| |FormatArabic| - |shrinkable| |width| |cartesian| |exprToGenUPS| |tab| |rootPoly| - |UP2ifCan| |mainCharacterization| |rules| |Gamma| |double| - |crushedSet| |associator| |rootSimp| |weakBiRank| |asimpson| - |minordet| |makeVariable| |tan2cot| |selectNonFiniteRoutines| - |outputForm| |divideIfCan!| |besselJ| |musserTrials| |henselFact| - |iicosh| |OMread| |cAcoth| UP2UTS |computeCycleEntry| |palgextint| - |symmetric?| |c06ekf| |removeSinhSq| |solveLinearlyOverQ| |lifting| - |minrank| |polar| |quote| |ignore?| |rightMult| |s15adf| - |clearFortranOutputStack| |directSum| |distribute| - |stoseInternalLastSubResultant| |checkPrecision| |mr| - |createNormalPoly| |Beta| |d02bhf| |getPickedPoints| |roughBasicSet| - |ksec| |updatF| |resultantnaif| |bitLength| |tanNa| |integral?| - |OMputVariable| |reciprocalPolynomial| |hasSolution?| - |LyndonWordsList1| |f07fdf| |cAtanh| |squareFree| |s21baf| - |generalLambert| |subst| |rem| |fibonacci| |ode2| |distFact| |parent| - |innerint| |integral| |useSingleFactorBound| |totalfract| - |listConjugateBases| |makingStats?| |attributeData| |quo| - |createMultiplicationMatrix| |setsubMatrix!| |symmetricPower| - |numericalIntegration| |declare!| |varList| |rowEch| |Ei| |badValues| - |principal?| |cPower| |rootSplit| |limitedint| |members| - |extractSplittingLeaf| |droot| |variable?| |radicalEigenvalues| |lcm| - |mainDefiningPolynomial| |OMlistCDs| |resultantEuclideannaif| - |shellSort| |div| |delete| |imagk| |complexZeros| |OMconnOutDevice| - |newLine| |trunc| |functionIsOscillatory| |var2StepsDefault| |elRow2!| - |partialFraction| |exquo| |squareTop| |extractPoint| |idealiser| - |remainder| |palginfieldint| |any| |stirling2| |exprex| |append| - |surface| |inHallBasis?| |status| ~= |mkPrim| |notelem| |conical| - |printTypes| |irreducibleRepresentation| |mapExponents| |finiteBasis| - |symbolIfCan| |gcd| |internalInfRittWu?| |mainKernel| |d01akf| - |objects| |#| |f02agf| |inR?| |nullary?| |binaryTournament| |rischDE| - |primPartElseUnitCanonical!| |false| |mainForm| |lazyPrem| |decompose| - |credPol| |resize| |base| ~ |someBasis| |remove!| |isConnected?| |cdr| - |enumerate| |f02adf| |transform| |wholePart| |idealiserMatrix| - |removeRoughlyRedundantFactorsInPol| |uncouplingMatrices| |ravel| - |diagonal?| |rightAlternative?| |lllp| |leftExactQuotient| |segment| - |s17ajf| |separant| |leastPower| |powmod| |ParCond| |init| - |complexIntegrate| |coerceS| |solveInField| |conjugates| |reshape| - |d01gaf| |discreteLog| |iiatanh| |nthExpon| |factorsOfCyclicGroupSize| - |makeViewport3D| |/\\| |brillhartTrials| |e02adf| |normalForm| - |removeZeroes| |solve| |cAcosh| |swapRows!| |definingInequation| - |ODESolve| |expint| |\\/| |makeTerm| |e01baf| |edf2fi| |readUInt8!| - |possiblyInfinite?| |apply| |coerce| |ran| |imaginary| - |solveLinearPolynomialEquation| |conjug| |hostByteOrder| |aromberg| - |OMgetString| |d02bbf| |move| |mapSolve| |first| |construct| - |structuralConstants| |eof?| |argumentListOf| |alphabetic?| - |taylorIfCan| |recur| |rightLcm| |LyndonBasis| |generalTwoFactor| - |genericLeftMinimalPolynomial| |rest| |matrixDimensions| - |regularRepresentation| |maxrank| |leadingSupport| |subset?| - |anfactor| |plus| |leftPower| |OMopenFile| |subNode?| |newSubProgram| - |update| |e02daf| |integerIfCan| |f02axf| |nor| |physicalLength| - |degreePartition| |sumSquares| |setErrorBound| |getGraph| |one?| - |besselI| |dual| |subResultantGcd| |fortranInteger| |in?| - |solveLinear| |cross| |debug3D| |maxRowIndex| |prepareSubResAlgo| - |viewpoint| |setprevious!| |removeRoughlyRedundantFactorsInContents| - |every?| |modifyPoint| |factorial| |setMaxPoints| |fortranDouble| - |stripCommentsAndBlanks| |yCoord| |times| |innerSolve| |infinityNorm| - |commutator| |identityMatrix| |stoseInvertibleSetsqfreg| |previous| - |delta| |diff| |LazardQuotient| |partialNumerators| |f01rcf| - |exprHasLogarithmicWeights| |typeForm| |rightPower| |choosemon| - |assign| |laguerreL| |minset| |hexDigit?| |mergeDifference| |box| - |bipolar| |isPlus| |pascalTriangle| |position| |e02ahf| |irForm| - |definingEquations| |lfintegrate| |bubbleSort!| |d01amf| - |numericalOptimization| |chineseRemainder| |negative?| |padecf| - |datalist| |lift| |exponentialOrder| |dimensions| |mapUp!| |quartic| - |multinomial| |OMReadError?| |cap| |interpretString| |Aleph| - |pointLists| |nary?| |monom| |reduce| |gcdcofact| |s17aff| |makeFR| - |collectQuasiMonic| |cSin| |hostPlatform| |euclideanGroebner| |tRange| - |vconcat| |rootDirectory| |genericLeftTraceForm| |loadNativeModule| - |f07adf| |cubic| |inverseIntegralMatrix| |expPot| |s19abf| |quoByVar| - |relationsIdeal| |setPredicates| |factorSFBRlcUnit| |categoryMode| - |csc2sin| |infiniteProduct| |errorKind| |hasPredicate?| |divide| - |Frobenius| |expextendedint| |s17dhf| |s18acf| |problemPoints| - |isPower| |constantToUnaryFunction| |qroot| |writeUInt8!| |reindex| - |primeFactor| |firstNumer| |just| |rowEchelon| |lambda| |removeCosSq| - |hasHi| |finiteBound| |getIdentifier| |initials| |rank| - |primextintfrac| |size?| |unknownEndian| - |semiIndiceSubResultantEuclidean| |countRealRoots| |component| - |UnVectorise| |pushucoef| |endOfFile?| |mathieu24| |log| - |irreducibleFactors| |perfectNthRoot| |extendedResultant| |complete| - |bumprow| |OMsend| |getDatabase| |setProperty| |binaryTree| - |socf2socdf| |setelt| |normDeriv2| |setMaxPoints3D| |viewThetaDefault| - |coordinate| |symmetricDifference| |sequences| |resetVariableOrder| - |expandLog| |unmakeSUP| |addPoint| |zerosOf| |f04jgf| |dualSignature| - |maxIndex| |functorData| |mindegTerm| |extractBottom!| - |explicitlyEmpty?| |coerceP| |fractRagits| |isEquiv| |antisymmetric?| - |setMinPoints| |selectPolynomials| |s21bdf| |sech2cosh| |makeCrit| - |endSubProgram| |linearDependence| |lighting| |oddintegers| - |encodingDirectory| |schwerpunkt| |tanAn| |iiatan| |triangSolve| - |generalizedEigenvectors| |preprocess| |multiset| - |rewriteIdealWithRemainder| |setImagSteps| - |rewriteIdealWithHeadRemainder| |is?| |linearAssociatedLog| - |patternMatchTimes| |OMgetBVar| |evenlambert| |singular?| |cSech| - |largest| |youngDiagram| |lexGroebner| |byte| |lists| - |stoseInvertible?sqfreg| |nullity| |genericLeftDiscriminant| - |factorset| |nonLinearPart| |reorder| |nthCoef| |replaceKthElement| - |rootNormalize| |simplifyExp| |fortranCharacter| |prindINFO| |minPoly| - |tensorProduct| |divisor| |showAllElements| |erf| |partialQuotients| - |groebnerFactorize| |stosePrepareSubResAlgo| |neglist| |zero| - |leadingIdeal| |exponential| |mulmod| |reverse| |simpleBounds?| - |makeGraphImage| |systemSizeIF| |medialSet| |printHeader| |zoom| - |generators| |commonDenominator| |primlimintfrac| |showRegion| |irDef| - |fglmIfCan| |li| |omError| |sup| |LowTriBddDenomInv| |iiacsch| |rk4qc| - |nonQsign| |showScalarValues| |And| |rightRank| |beauzamyBound| - |subResultantsChain| |setCondition!| |unknown| |insertionSort!| - |dilog| |binarySearchTree| |c02agf| |currentCategoryFrame| |infLex?| - |Or| |nthRoot| |cExp| |logIfCan| |rationalApproximation| - |LagrangeInterpolation| |pack!| |OMputEndBVar| |sin| - |euclideanNormalForm| |OMgetEndObject| |collectUpper| |typeLists| - |Not| |prolateSpheroidal| |latex| |leviCivitaSymbol| |solve1| - |getGoodPrime| |colorDef| |cos| |critpOrder| |certainlySubVariety?| - |setPosition| |subNodeOf?| |stoseSquareFreePart| |int| |karatsubaOnce| - |intChoose| |OMconnInDevice| |scopes| |elements| |tan| - |fortranLiteralLine| |split| |showFortranOutputStack| |lazy?| |weight| - |palgRDE| |extend| |concat!| |cot| |genericLeftNorm| |euclideanSize| - |doubleDisc| |expIfCan| |rotate| |lepol| |light| |radicalEigenvector| - |internalSubQuasiComponent?| |sec| |dAndcExp| |rightRankPolynomial| - |perfectSquare?| |elColumn2!| |linearAssociatedExp| |iCompose| - |vectorise| |row| |head| |csc| |simpsono| |parabolicCylindrical| - |insertTop!| |children| |s18def| |s17aef| |roughEqualIdeals?| |asin| - |hconcat| |test| |mapUnivariateIfCan| |randomR| |operation| - |outlineRender| |remove| |interpolate| |meshPar2Var| |OMsupportsCD?| - |isAbsolutelyIrreducible?| |stopTableInvSet!| |acos| - |antiCommutative?| |s17agf| |rk4a| |leftScalarTimes!| - |topFortranOutputStack| |range| |cotIfCan| |rdregime| |diagonals| - |atan| |B1solve| |sn| |pquo| |monicDivide| |parts| |terms| - |rightRegularRepresentation| |last| |exprToXXP| |trigs2explogs| - |getOperator| |qualifier| |acot| |basisOfMiddleNucleus| |tanh2trigh| - |assoc| |upperBound| |e01bef| |leftQuotient| |sparsityIF| |froot| - |asec| |splitSquarefree| |wronskianMatrix| |powers| |condition| |eq?| - |tower| |getProperties| |localUnquote| |minPoints| |block| |gensym| - |acsc| |iiacosh| |s19adf| |prefixRagits| |overlabel| |lflimitedint| - |tanintegrate| |OMgetError| |OMgetSymbol| |prefix| - |localIntegralBasis| |sinh| |weighted| |cTan| |vspace| |bezoutMatrix| - |OMputAtp| |PDESolve| |fixedPointExquo| |cosh| |orbits| |e04ycf| - |hitherPlane| |numberOfChildren| |iifact| |elliptic?| - |listRepresentation| |ratPoly| |binomial| |obj| |tanh| |palglimint| - |eq| |imagE| |algebraicSort| |pow| |withPredicates| |biRank| - |viewDeltaXDefault| |extractTop!| |float?| |cache| |coth| |arrayStack| - |iter| |linear?| |pseudoRemainder| |pointColor| |complexNumeric| - |arbitrary| |ScanArabic| |eigenvalues| |lazyPseudoRemainder| - |leftExtendedGcd| |integers| |sech| |purelyAlgebraic?| - |deleteProperty!| |setStatus| |overlap| |optAttributes| - |OMsupportsSymbol?| |forLoop| |minimize| |infinite?| |lazyIntegrate| - |csch| |createPrimitiveElement| |rootBound| |outputAsScript| - |createGenericMatrix| |minRowIndex| |f01ref| |selectFiniteRoutines| - |relerror| |diagonalProduct| |asinh| |coerceL| |sdf2lst| |schema| - |inrootof| |bivariate?| |genus| |s20adf| |parametric?| |besselY| - |gcdcofactprim| |binaryFunction| |acosh| |realEigenvalues| |sort!| - |removeRoughlyRedundantFactorsInPols| |genericLeftTrace| |BumInSepFFE| - |coleman| |readBytes!| |semiResultantReduitEuclidean| |iiacos| - |s18aff| |leftGcd| |primlimitedint| |univcase| |internalSubPolSet?| - |f02akf| |gethi| |leftFactorIfCan| |conditionP| |nodes| |upperCase!| - |exp| |optional?| |components| |leftDiscriminant| - |useEisensteinCriterion| |OMreadStr| |sinhcosh| |getProperty| - |hdmpToDmp| |pToDmp| |rightOne| |f04maf| |scripted?| |map| - |factorsOfDegree| |palgint0| |mappingMode| |OMputEndAtp| |OMreceive| - |createPrimitivePoly| |unitsColorDefault| |makeSUP| |var1StepsDefault| - |allRootsOf| |table| |generator| |setRealSteps| |totalLex| - |toseInvertible?| |HermiteIntegrate| |getMatch| |nil| |lquo| - |reducedDiscriminant| |e02akf| |connect| |heap| |new| |bothWays| - |minimumExponent| |cscIfCan| |delete!| |subscript| |compile| - |fintegrate| |lyndon?| |supDimElseRittWu?| |headRemainder| - |OMputInteger| |lookupFunction| |tanSum| |removeConstantTerm| |janko2| - |lazyResidueClass| |factorials| |basis| |trivialIdeal?| |wholeRadix| - |messagePrint| |mathieu22| |primitiveElement| |extractIndex| - |approximate| |stop| |rationalPoint?| |connectTo| |algebraicDecompose| - |lazyEvaluate| |convert| |karatsuba| |heapSort| |quadraticForm| - |parseString| |e01saf| |complex| |algebraicCoefficients?| - |exprHasAlgebraicWeight| |pmComplexintegrate| |normalized?| - |complexForm| |ratDenom| |e02zaf| |cLog| |multisect| |submod| - |createIrreduciblePoly| |airyAi| |normFactors| - |generalizedEigenvector| |getZechTable| |zeroDimensional?| - |reverseLex| |sqfree| |failed| |d02ejf| |associates?| |f02aff| - |setEpilogue!| |disjunction| |internalIntegrate| |LyndonCoordinates| - |nextPrime| |sec2cos| |integralDerivationMatrix| |empty?| - |expandTrigProducts| |sinh2csch| |setProperties| |f02bbf| - |degreeSubResultant| |semiResultantEuclidean1| |startStats!| - |useNagFunctions| |cyclotomicDecomposition| |npcoef| |unaryFunction| - |incr| |derivationCoordinates| |inspect| |totalGroebner| |setref| - |perspective| |increment| |logical?| |octon| |maxPoints| |hi| - |stoseIntegralLastSubResultant| |sPol| |palgintegrate| - |integralBasisAtInfinity| |expressIdealMember| |controlPanel| |iidsum| - |genericRightNorm| |semiDegreeSubResultantEuclidean| |left| - |byteBuffer| |semicolonSeparate| |csch2sinh| |moduloP| |printingInfo?| - |trace2PowMod| |calcRanges| |seed| |color| |right| |zCoord| |gbasis| - |createRandomElement| |multMonom| |kmax| |c06gqf| - |invertibleElseSplit?| |multiplyExponents| |graphImage| |freeOf?| - |generic?| |aQuartic| |partition| |coth2trigh| |univariateSolve| - |generalizedContinuumHypothesisAssumed?| |quasiRegular?| - |constantKernel| |clearTheFTable| |nextLatticePermutation| - |splitConstant| |rspace| |d02gaf| |qelt| |semiResultantEuclideannaif| - |hexDigit| |complexSolve| |typeList| |qsetelt| |csubst| |entries| - |pseudoDivide| |prime| |setchildren!| |initial| |prime?| - |generalPosition| |makeprod| |normalizeAtInfinity| |cTanh| |sh| - |subMatrix| |ddFact| |xRange| |quatern| |exprHasWeightCosWXorSinWX| - |next| |testDim| |nil?| |legendre| |key| |subtractIfCan| - |modularGcdPrimitive| |s14aaf| |sturmSequence| |yRange| |create| - |revert| |lowerCase?| |OMgetEndBVar| |abs| |clipBoolean| |realRoots| - |d02gbf| |cschIfCan| |primes| |zRange| |binding| |bitCoef| |ceiling| - |makeop| |filename| |map!| |pr2dmp| |symmetricTensors| |coHeight| - |characteristicPolynomial| |pair?| |backOldPos| |exp1| |mathieu11| - |padicFraction| |qsetelt!| |OMputString| |toseSquareFreePart| - |findCycle| |f02aaf| |rational| |cosSinInfo| |clip| |isOpen?| |trim| - |parse| |numberOfComponents| |univariate?| |setOrder| |countable?| - |deepestInitial| |code| |createMultiplicationTable| |e01sff| - |squareFreeFactors| |e01bff| |generate| |numFunEvals| - |leadingCoefficientRicDE| |rCoord| |goodPoint| |leadingBasisTerm| - |refine| |SFunction| |OMwrite| |red| |iiexp| |cSec| |point?| - |nextIrreduciblePoly| |monomialIntPoly| |aLinear| |acscIfCan| - |stFunc2| |derivative| |incrementBy| |flexible?| |sorted?| - |extractClosed| |makeSeries| |returnType!| |create3Space| |logpart| - |changeWeightLevel| |lookup| |unitCanonical| |d02raf| |sumOfDivisors| - |support| |atanIfCan| |acsch| |sturmVariationsOf| |headAst| - |usingTable?| |cCosh| |mergeFactors| |minGbasis| |readByte!| - |printInfo| |select!| |crest| |getSyntaxFormsFromFile| |unvectorise| - |drawCurves| |isAnd| |unrankImproperPartitions1| |s14baf| - |complexNumericIfCan| |lieAlgebra?| |OMputFloat| |gcdPolynomial| - |changeNameToObjf| |normalizedAssociate| |entry?| |redPol| - |perfectSqrt| |htrigs| |interReduce| |numberOfImproperPartitions| - |iisinh| |lastSubResultantEuclidean| |genericRightTraceForm| |options| - |option?| |elliptic| |whitePoint| |denomLODE| |tail| |rational?| - |karatsubaDivide| |dom| |chainSubResultants| |separate| |graphs| - |chiSquare| |solveRetract| |highCommonTerms| |diagonalMatrix| - |abelianGroup| |updateStatus!| |arg1| |extract!| |entry| |bottom!| - |readUInt16!| |permutation| |basisOfRightAnnihilator| |sequence| |nil| - |infinite| |arbitraryExponent| |approximate| |complex| - |shallowMutable| |canonical| |noetherian| |central| + |Record| |Union| |fixedDivisor| |var2StepsDefault| |hdmpToDmp| + |leftTrim| |intcompBasis| |OMbindTCP| |encodingDirectory| + |fortranLogical| |elliptic| |roughSubIdeal?| |thetaCoord| |elRow2!| + |rk4f| |pToDmp| |OMputError| |badNum| |schwerpunkt| + |integralCoordinates| |whitePoint| |coefficient| |OMgetEndApp| + |partialFraction| |rightOne| |hyperelliptic| |leftLcm| + |combineFeatureCompatibility| |tanAn| |denomLODE| |sincos| + |factorGroebnerBasis| |squareTop| |f04maf| |ord| |expt| |irreducible?| + |iiatan| |rational?| |mantissa| |unprotectedRemoveRedundantFactors| + |quoted?| |extractPoint| |scripted?| |e01daf| |argscript| |polygon?| + |triangSolve| |karatsubaDivide| |idealiser| |reverse!| + |complexNumeric| |tanhIfCan| |factorsOfDegree| |compiledFunction| + |parametersOf| |generalizedEigenvectors| |pushdterm| + |chainSubResultants| |slex| |remainder| |stopTable!| |palgint0| + |GospersMethod| |purelyTranscendental?| |nthr| |preprocess| |separate| + |kernels| |laguerre| |palginfieldint| |low| |mappingMode| |wreath| + |rename| |multiset| |dmpToHdmp| |graphs| |stirling2| |cAsec| + |validExponential| |operator| |OMputEndAtp| |e02ajf| |rotate!| + |rewriteIdealWithRemainder| |transcendentalDecompose| |chiSquare| |po| + |exprex| |airyBi| |OMreceive| |rootKerSimp| |basisOfCommutingElements| + |setImagSteps| |dimensionOfIrreducibleRepresentation| |solveRetract| + |reify| |surface| |varList| |univariate| |noKaratsuba| + |createPrimitivePoly| |arg1| |completeEchelonBasis| |divideIfCan| + |rewriteIdealWithHeadRemainder| |normal01| |highCommonTerms| + |curveColorPalette| |inHallBasis?| |algint| |arg2| |unitsColorDefault| + |mkAnswer| |computePowers| |is?| |chiSquare1| |diagonalMatrix| Y + |showTheFTable| |status| |composite| |makeSUP| |lyndonIfCan| |pastel| + |linearAssociatedLog| |triangularSystems| |abelianGroup| + |elaborateFile| |setvalue!| |mkPrim| |factor| |conditions| + |var1StepsDefault| |dictionary| |subspace| |constantCoefficientRicDE| + |patternMatchTimes| |updateStatus!| |readInt32!| |se2rfi| |notelem| + |sqrt| |allRootsOf| |match| |f02ajf| |idealSimplify| |ratDsolve| + |OMgetBVar| |extract!| |conical| |inGroundField?| |primaryDecomp| + |real| |setRealSteps| |decrease| |ricDsolve| |laurentIfCan| |tree| + |evenlambert| |bottom!| |useSingleFactorBound?| |factor1| |printTypes| + |imag| |totalLex| |times!| |integrate| |balancedFactorisation| + |singular?| |readUInt16!| |directProduct| |powerAssociative?| + |irreducibleRepresentation| |OMputSymbol| |toseInvertible?| + |modularFactor| |indiceSubResultant| |testModulus| |cSech| + |permutation| |rightDivide| |options| |mapExponents| |index?| + |HermiteIntegrate| |internalIntegrate0| |OMgetApp| |listexp| |largest| + |basisOfRightAnnihilator| |finiteBasis| + |semiLastSubResultantEuclidean| |quotedOperators| |brace| |getMatch| + |presuper| |prem| |shallowExpand| |youngDiagram| |sequence| |zeroDim?| + |symbolIfCan| |d01apf| |destruct| |lquo| |zag| |geometric| + |denomRicDE| |lexGroebner| |leftDivide| |string| |internalInfRittWu?| + |SturmHabichtCoefficients| |reducedDiscriminant| |lagrange| RF2UTS + |stoseInvertible?sqfreg| |untab| |cyclicSubmodule| |mainKernel| + |weierstrass| |e02akf| |yCoordinates| |extendedint| |iiasec| |nullity| + |macroExpand| |callForm?| |plus| |d01akf| |cycles| |connect| |convert| + |repeatUntilLoop| |rightExactQuotient| |rightTrace| + |genericLeftDiscriminant| |bipolarCylindrical| |rowEchelonLocal| + |f02agf| |monomial| |heap| |topPredicate| |multiple?| |palgextint0| + |factorset| |rightUnits| |inR?| |startTableInvSet!| |ptree| + |multivariate| |bothWays| |nonLinearPart| |hasoln| |invertibleSet| + |flatten| |putGraph| |nullary?| |times| |setAdaptive3D| |asinIfCan| + |variables| |minimumExponent| |matrixGcd| |lineColorDefault| + |alphanumeric?| |reorder| |numberOfVariables| |binaryTournament| + |extendedSubResultantGcd| |cscIfCan| |symmetricSquare| |close| + |pointColorDefault| |nthCoef| |arity| |specialTrigs| |cylindrical| + |rischDE| |delete!| |position!| |recoverAfterFail| |screenResolution| + |replaceKthElement| |simplifyLog| |primPartElseUnitCanonical!| + |particularSolution| |subscript| |nthFlag| |front| |display| + |rootNormalize| |PollardSmallFactor| |expr| |divisors| |monom| + |linearPolynomials| |mainForm| |fintegrate| |unary?| |constantLeft| + |simplifyExp| |removeSinSq| |symmetricProduct| |lazyPrem| + |startTableGcd!| |taylor| |lyndon?| |complexEigenvectors| + |bivariatePolynomials| |fortranCharacter| |s17dgf| |decompose| + |monicModulo| |tan2trig| |laurent| |supDimElseRittWu?| |slash| + |quasiAlgebraicSet| |numerators| |prindINFO| |iroot| |common| + |credPol| |puiseux| |headRemainder| |setleaves!| |algebraic?| + |minPoly| |explicitlyFinite?| |variable| |rootRadius| + |squareFreePolynomial| |resize| |OMputInteger| |divisorCascade| + |showSummary| |input| |ip4Address| |makeUnit| |tensorProduct| + |outerProduct| |iterators| |UpTriBddDenomInv| |makeSketch| |someBasis| + |inv| |lookupFunction| |edf2ef| |library| |possiblyNewVariety?| + |divisor| |meshFun2Var| |close!| |doublyTransitive?| |ground?| + |remove!| |tanSum| |oddInfiniteProduct| |showAllElements| |cAtan| |id| + |ground| |isConnected?| |powern| |removeConstantTerm| |value| + |optimize| |acosIfCan| |stFuncN| |partialQuotients| + |ramifiedAtInfinity?| |semiSubResultantGcdEuclidean2| |lo| + |expenseOfEvaluation| |leadingMonomial| |cdr| |janko2| |alphanumeric| + |OMParseError?| |safeCeiling| |groebnerFactorize| |showAttributes| + |strongGenerators| |mainVariable| |areEquivalent?| + |leadingCoefficient| |enumerate| |lazyResidueClass| |leftUnits| + |signatureAst| |stosePrepareSubResAlgo| |characteristicSerie| + |vedf2vef| |assert| |inverse| |factorials| |f04mbf| |split!| |neglist| + |log2| |substitute| |d02cjf| |symmetric?| |basis| |reducedForm| + |atoms| |leadingIdeal| |dequeue!| |linGenPos| |c06ekf| |OMgetEndAttr| + |trivialIdeal?| |logGamma| |sncndn| |adaptive3D?| |exponential| + |OMencodingXML| |torsion?| |removeSinhSq| |wholeRadix| |rightZero| + |fillPascalTriangle| |elaborate| |any?| |solveLinearlyOverQ| + |messagePrint| |expextendedint| |maximumExponent| |resultant| + |acotIfCan| |first| |dominantTerm| |lifting| + |factorSquareFreePolynomial| |mathieu22| |swap!| |resetBadValues| + |order| |s17dhf| |rest| |bezoutResultant| |minrank| |redmat| + |primitiveElement| |appendPoint| |dmpToP| |s18acf| |primitivePart| + |polar| |fortranCompilerName| |lhs| |region| |domainTemplate| |cfirst| + |problemPoints| |autoReduced?| |interval| |quote| |euler| |rhs| + |pseudoRemainder| |constructor| |deepExpand| |gradient| |setright!| + |isPower| |ignore?| |genericRightDiscriminant| |pointColor| + |createZechTable| |subst| |minPol| |integer?| |epilogue| + |constantToUnaryFunction| |trailingCoefficient| |currentEnv| + |antiCommutator| |rightMult| |transcendent?| |arbitrary| |branchIfCan| + |iipow| |pmintegrate| |OMopenString| |qroot| |radicalOfLeftTraceForm| + |rangePascalTriangle| |s15adf| |ScanArabic| |isOp| |zeroDimPrime?| + |cAcsch| |e02agf| |writeUInt8!| |leadingCoefficientRicDE| + |currentScope| |clearFortranOutputStack| |OMcloseConn| |eigenvalues| + |complexEigenvalues| |lintgcd| |li| |laplacian| |reindex| |secIfCan| + |rCoord| |subTriSet?| |directSum| |OMgetEndBind| |lazyPseudoRemainder| + |resultantReduit| |generateIrredPoly| |c06gsf| |primeFactor| |rarrow| + |goodPoint| |cos2sec| |distribute| |Is| |leftExtendedGcd| + |returnTypeOf| |c05nbf| |setelt!| |reseed| |firstNumer| |green| + |leadingBasisTerm| |critMonD1| |unparse| |e04jaf| + |stoseInternalLastSubResultant| |objects| |integers| |rst| |escape| + |lazyPquo| |clipWithRanges| |just| |refine| |createNormalPoly| + |viewDefaults| |f01brf| |subQuasiComponent?| |base| |purelyAlgebraic?| + |modulus| |closedCurve| |tubePlot| |rowEchelon| |SFunction| + |relativeApprox| |Beta| |extractIfCan| |deleteProperty!| + |kroneckerDelta| |createPrimitiveNormalPoly| |e04fdf| |randomLC| + |removeCosSq| |OMwrite| |d02kef| |d02bhf| |viewDeltaYDefault| |cAsech| + |setStatus| |type| |sizePascalTriangle| |setPoly| |rem| |addBadValue| + |hasHi| |red| |map!| |selectAndPolynomials| |nextsousResultant2| + |getPickedPoints| |overlap| |presub| |finiteBound| |setFieldInfo| + |halfExtendedSubResultantGcd2| |quo| |cyclic?| |iiexp| |qsetelt!| + |rotatez| |isobaric?| |dim| |roughBasicSet| |optAttributes| |open?| + |finite?| |cycleTail| |getIdentifier| |pdf2df| |inc| |cSec| |test| + |width| |coefficients| |ksec| |leaf?| |splitLinear| + |OMsupportsSymbol?| |completeHensel| |div| |cosIfCan| |digamma| + |initials| |point?| |OMgetEndError| |hcrf| |updatF| |forLoop| + |SturmHabicht| |polynomialZeros| |numberOfFactors| |primextintfrac| + |writeInt8!| |exquo| |maxrow| |nextIrreduciblePoly| + |stoseInvertibleSetreg| |evaluateInverse| |resultantnaif| |minimize| + |LazardQuotient2| |size?| |cAsinh| |f02fjf| |atom?| ~= |graphStates| + |monomialIntPoly| |pattern| |associatedSystem| |bitLength| |cCot| + |infinite?| |imagJ| |unknownEndian| |rootOfIrreduciblePoly| + |removeDuplicates!| |toScale| |#| |aLinear| |acsch| |d01bbf| + |lazyIntegrate| |satisfy?| |tanNa| |table| |basicSet| |getRef| ~ + |cyclicParents| |semiIndiceSubResultantEuclidean| |orthonormalBasis| + |acscIfCan| |integerBound| |pointColorPalette| |integral?| + |createPrimitiveElement| |rules| |new| |headReduced?| |nextNormalPoly| + |delta| |coord| |prefix| |countRealRoots| |viewSizeDefault| |obj| + |stFunc2| |previous| |indiceSubResultantEuclidean| |alternative?| + |OMputVariable| |leadingTerm| |rootBound| |regime| + |permutationRepresentation| |integralMatrixAtInfinity| |component| + |derivative| |cache| |message| |optional| |getOperands| + |reciprocalPolynomial| |seriesSolve| |outputAsScript| |initTable!| + |iilog| |jordanAdmissible?| |/\\| |UnVectorise| |rightFactorIfCan| + |flexible?| |anticoord| |lfextendedint| |hasSolution?| + |oblateSpheroidal| |createGenericMatrix| |lieAdmissible?| |\\/| + |definingPolynomial| |fractionFreeGauss!| |pushucoef| |sorted?| + |setStatus!| |spherical| |LyndonWordsList1| |minRowIndex| + |univariatePolynomialsGcds| |lyndon| |removeSuperfluousCases| + |changeName| |endOfFile?| |extractClosed| |rightExtendedGcd| |f07fdf| + |nthFractionalTerm| |f01ref| |rationalPower| |search| |opeval| + |semiDiscriminantEuclidean| |s17def| |mathieu24| |makeSeries| |nlde| + |cAtanh| |c05pbf| |adjoint| |selectFiniteRoutines| |innerEigenvectors| + |rotatex| |reduceByQuasiMonic| |youngGroup| |irreducibleFactors| + |returnType!| |mappingAst| |setClosed| |squareFree| |bfKeys| + |relerror| |lambda| |leadingExponent| |continuedFraction| + |perfectNthRoot| |extractProperty| |create3Space| |setOfMinN| |frst| + |s21baf| |diagonalProduct| |sumOfKthPowerDivisors| |c06ecf| + |prinpolINFO| |extendedResultant| |logpart| |bounds| + |numberOfFractionalTerms| |generalLambert| |coerceL| |child?| |push| + |ParCondList| |complete| |reduced?| |changeWeightLevel| |df2fi| + |critT| |fibonacci| |sdf2lst| |left| |setFormula!| |setUnion| + |monicRightDivide| |level| |bumprow| |lookup| |subPolSet?| |readLine!| + |ode2| |schema| |right| |antiAssociative?| |bringDown| |OMsend| + |legendreP| |unitCanonical| F |iflist2Result| |distFact| |nullary| + |inrootof| |bright| |interactiveEnv| |putProperty| |getDatabase| + |wordInGenerators| |d02raf| |lazyPseudoQuotient| |RittWuCompare| + |parent| |bivariate?| |part?| |corrPoly| |over| |setProperty| + |associatorDependence| |sumOfDivisors| |df2ef| |innerint| + |measure2Result| |genus| |copy!| |eval| |acoshIfCan| |cyclicEqual?| + |binaryTree| |fTable| |support| |has?| |s20adf| |prod| |zero| + |integral| |exp| |middle| |Lazard2| |intersect| |socf2socdf| + |lowerCase| |atanIfCan| |computeInt| |useSingleFactorBound| |max| + |inputBinaryFile| |parametric?| |shanksDiscLogAlgorithm| |child| + |normDeriv2| |rootOf| |sturmVariationsOf| |hypergeometric0F1| + |totalfract| |tab1| |And| |besselY| |error| |polygon| |cycleEntry| + |factorOfDegree| |setMaxPoints3D| |headAst| |f2st| + |listConjugateBases| |showAll?| |gcdcofactprim| |Or| |outputSpacing| + |kovacic| |conditionsForIdempotents| |viewThetaDefault| |usingTable?| + |space| |coefChoose| |makingStats?| |univariatePolynomial| + |binaryFunction| |Not| |drawToScale| |selectSumOfSquaresRoutines| + |size| |coordinate| |cothIfCan| |cCosh| |deleteRoutine!| |poisson| + |attributeData| |rightFactorCandidate| |realEigenvalues| |s17dlf| + |halfExtendedResultant2| |symmetricDifference| |sin2csc| + |mergeFactors| |readInt16!| |elRow1!| |operators| + |createMultiplicationMatrix| |sort!| |symbol| |knownInfBasis| + |gcdprim| |sequences| |nativeModuleExtension| |minGbasis| + |identification| |writeBytes!| |increasePrecision| |setsubMatrix!| + |removeRoughlyRedundantFactorsInPols| |expression| |odd?| |cyclotomic| + |singRicDE| |substring?| |resetVariableOrder| |readByte!| + |traceMatrix| |makeCos| |systemCommand| |key| |makeSin| + |symmetricPower| |genericLeftTrace| |integer| |double| |ffactor| + |coerceImages| |invmod| |expandLog| |select!| |pile| |fortranReal| + |numericalIntegration| |BumInSepFFE| |reducedSystem| |An| |mathieu23| + |suffix?| |unmakeSUP| |crest| |prinshINFO| |addPoint2| |filename| + |power!| |rowEch| |coleman| |weights| |cCsc| |squareFreeLexTriangular| + |addPoint| |getSyntaxFormsFromFile| |intermediateResultsIF| + |chebyshevT| |positiveRemainder| |Ei| |readBytes!| |subResultantChain| + |zerosOf| |pdf2ef| |OMclose| |d03eef| |prefix?| |unvectorise| + |basisOfCentroid| |pToHdmp| |null| |parse| |meshPar1Var| |badValues| + |semiResultantReduitEuclidean| |cyclic| |f04jgf| |setVariableOrder| + |startPolynomial| |drawCurves| |initial| GF2FG |principal?| + |lfinfieldint| |not| |iiacos| |setleft!| |writeByte!| |node| + |dualSignature| |triangular?| |isAnd| |paraboloidal| |tablePow| + |cPower| |and| |permutationGroup| |s18aff| |OMgetObject| |polyred| + |maxIndex| |node?| |retract| |unrankImproperPartitions1| |curryLeft| + |psolve| |rootSplit| |c06fpf| |or| |leftGcd| |declare!| |morphism| + |integralMatrix| |functorData| |selectsecond| |s14baf| + |standardBasisOfCyclicSubmodule| |diagonal| |primlimitedint| |delete| + |plus!| |prologue| |lexico| |mindegTerm| |computeCycleLength| + |complexNumericIfCan| |ramified?| |fixedPoints| |isExpt| |box| + |univcase| |acschIfCan| |argumentList!| |extractBottom!| |OMputAttr| + |infix?| |lieAlgebra?| |keys| |vark| |horizConcat| |closed| + |eigenMatrix| |internalSubPolSet?| ** |addMatch| |compose| |mask| + |explicitlyEmpty?| |numerator| |OMputFloat| |fortranLinkerArgs| |dark| + |universe| |s01eaf| |f02akf| |predicate| |leftRank| |nextColeman| + |gcdPolynomial| |expintegrate| |OMunhandledSymbol| |groebgen| |power| + |gethi| |sort| |solveLinearPolynomialEquationByRecursion| + |rewriteIdealWithQuasiMonicGenerators| |assign| |incrementKthElement| + |changeNameToObjf| |upperCase?| |internalLastSubResultant| |swap| + |viewport3D| |leftFactorIfCan| |c05adf| |totalDegree| |critM| + |laguerreL| |multiEuclideanTree| |normalizedAssociate| + |inverseIntegralMatrixAtInfinity| |rombergo| |mainContent| + |repeating?| |conditionP| |segment| |toseLastSubResultant| + |clipSurface| |putProperties| |minset| |exteriorDifferential| |entry?| + |index| |OMgetInteger| |mainValue| |aspFilename| |recip| + |algSplitSimple| |nodeOf?| |hexDigit?| |resultantEuclidean| |sin?| + |redPol| |f01maf| |radix| |imagI| |map| |exprToXXP| |pushNewContour| + |f04mcf| |characteristicSet| |mergeDifference| |dot| |primitive?| + |perfectSqrt| |cycleSplit!| |setEmpty!| |void| |dimension| + |insertRoot!| |trigs2explogs| |bipolar| |host| |shiftLeft| + |critMTonD1| |equation| |lfextlimint| |htrigs| |fortranTypeOf| + |userOrdered?| |clikeUniv| |pair| |element?| |getOperator| |powerSum| + |truncate| |isPlus| |monic?| |explogs2trigs| |infix| |e02bbf| |e02gaf| + |basisOfLeftNucloid| |qualifier| |central?| |createLowComplexityTable| + |generalInfiniteProduct| |pascalTriangle| |indicialEquations| + |normalizeAtInfinity| |f04asf| |isList| |bernoulli| |besselK| + |basisOfMiddleNucleus| |skewSFunction| |bigEndian| |parameters| + |changeBase| |addPointLast| |ldf2vmf| |e02ahf| |cTanh| + |squareFreePrim| |basisOfLeftAnnihilator| |listBranches| + |numberOfNormalPoly| |tanh2trigh| |log10| |minus!| + |internalZeroSetSplit| |irForm| |taylorRep| |sh| + |reducedContinuedFraction| |rroot| |say| |s14abf| |prevPrime| + |upperBound| SEGMENT |iicot| |leftRemainder| |retractable?| + |definingEquations| |subMatrix| |getMultiplicationTable| |iitan| + |polyPart| |iisqrt3| |e01bef| |datalist| |numberOfMonomials| + |stoseLastSubResultant| |lfintegrate| |palglimint0| |ddFact| + |reduceBasisAtInfinity| |reset| |singularitiesOf| |midpoint| + |leftQuotient| |patternVariable| + |solveLinearPolynomialEquationByFractions| |radicalSimplify| |symbol?| + |bubbleSort!| |quatern| |pdct| |outputFixed| |pushup| |sparsityIF| + |complexExpand| |groebSolve| |twist| |failed| |shade| |d01amf| + |addMatchRestricted| |exprHasWeightCosWXorSinWX| |write| |eyeDistance| + |hMonic| |mainSquareFreePart| |digit| |froot| |totalDifferential| + |tubeRadius| |s21bbf| |numericalOptimization| |meatAxe| |testDim| + |generator| |save| |generalSqFr| |solveid| |mathieu12| + |basisOfLeftNucleus| |splitSquarefree| |lowerPolynomial| + |complexLimit| |chineseRemainder| |trigs| |nil?| |algintegrate| + |constantOperator| |principalAncestors| |wronskianMatrix| + |createThreeSpace| |primeFrobenius| |primintegrate| |fractRadix| + |negative?| |integralBasis| |legendre| |denominators| + |doubleFloatFormat| |convergents| |whatInfinity| + |identitySquareMatrix| |powers| |iiperm| |graphState| |maxdeg| + |setButtonValue| |padecf| |subtractIfCan| |complexNormalize| + |flagFactor| |errorInfo| |eq?| |quadratic| |jacobian| |cot2trig| + |exponentialOrder| |null?| |modularGcdPrimitive| |cycleElt| + |intensity| |firstSubsetGray| |roman| |getProperties| |normalize| + |nil| |OMencodingBinary| |upperCase| |baseRDEsys| |zero?| |compdegd| + |dimensions| |s14aaf| |log| |environment| |OMserve| |printStatement| + |selectfirst| |localUnquote| |headReduce| |routines| |newTypeLists| + |closed?| |drawStyle| |mapUp!| |flexibleArray| |sturmSequence| |curry| + |iisqrt2| |alternatingGroup| |createLowComplexityNormalBasis| + |minPoints| |pleskenSplit| |limit| |quartic| |loopPoints| |create| + |hessian| |float| |thenBranch| |moebius| |block| |hclf| |multinomial| + |leftRankPolynomial| |e02bef| |clearDenominator| |approximate| + |revert| |s17ahf| |checkForZero| |round| |gensym| |e01sef| |complex| + |writable?| |uniform01| |mapmult| |apply| |OMReadError?| |lowerCase?| + |incr| |decreasePrecision| |FormatArabic| |splitNodeOf!| |iiacosh| + |mainMonomial| |cap| |mat| |mapMatrixIfCan| |setAdaptive| |constant| + |OMgetEndBVar| |hi| |complexRoots| |ratpart| |shrinkable| + |mainExpression| |c06ebf| |s19adf| |polarCoordinates| |polCase| + |clearTable!| |interpretString| |abs| |capacity| |cSinh| |cartesian| + |df2st| |duplicates?| |prefixRagits| |consnewpol| |numer| |postfix| + |Aleph| |orbit| |clipBoolean| |palgRDE0| |write!| |exprToGenUPS| + |d01aqf| |overlabel| |leftRegularRepresentation| |denom| + |factorByRecursion| |figureUnits| |pointLists| |realRoots| + |rightRemainder| |conjunction| |tab| |lflimitedint| |computeBasis| + |formula| |lift| |invertIfCan| |OMencodingUnknown| |nary?| |rquo| + |d02gbf| |normInvertible?| |adaptive?| |rootPoly| |randnum| + |tanintegrate| |tValues| |sortConstraints| |reduce| |pi| |monomRDEsys| + |brillhartIrreducible?| |gcdcofact| |cschIfCan| |sylvesterMatrix| + |bits| GE |UP2ifCan| |limitPlus| |primextendedint| |OMgetError| + |infieldIntegrate| |infinity| |aCubic| |s17aff| |lowerBound| |primes| + |removeDuplicates| GT |mainCharacterization| |writeLine!| + |OMgetSymbol| |isOr| |elementary| |eisensteinIrreducible?| |makeFR| + |subResultantGcdEuclidean| |binding| |quasiComponent| LE + |resultantReduitEuclidean| |Gamma| |tryFunctionalDecomposition| + |localIntegralBasis| |rischNormalize| |nrows| |precision| |maxint| + |removeSquaresIfCan| |collectQuasiMonic| |bitCoef| |algebraicOf| LT + |concat| |crushedSet| |baseRDE| |weighted| |viewWriteDefault| |kernel| + |ncols| |algDsolve| |pushdown| |cSin| |mvar| |ceiling| |d01ajf| + |balancedBinaryTree| |associator| |cTan| |rightRecip| |list| + |constDsolve| |degree| |externalList| |hostPlatform| |makeop| |s18dcf| + |rootSimp| |pol| |OMgetAttr| |vspace| |solid| |draw| + |numberOfOperations| |jacobiIdentity?| |euclideanGroebner| |pr2dmp| + |internalAugment| |weakBiRank| |back| |bezoutMatrix| |string?| + |quasiMonic?| |squareMatrix| |qinterval| |tRange| |symmetricTensors| + |elseBranch| |d01gbf| |f01bsf| |lex| |asimpson| |fortran| |OMputAtp| + |polynomial| |isMult| |f02bjf| |point| |cAcos| |vconcat| |remove| + |coHeight| |leadingIndex| |style| |norm| |minordet| |PDESolve| |isNot| + |buildSyntax| |applyRules| |palgLODE| |rootDirectory| + |multiplyCoefficients| |characteristicPolynomial| + |commutativeEquality| |iiasin| |makeVariable| |fi2df| |leftZero| + |fixedPointExquo| |makeObject| |iitanh| |updatD| + |genericLeftTraceForm| |points| |pair?| |last| |limitedIntegrate| |lp| + |setValue!| |tan2cot| |cRationalPower| |orbits| |byte| |getlo| + |clipPointsDefault| |complexElementary| |series| |coef| |f07adf| + |characteristic| |assoc| |backOldPos| |mapGen| + |selectNonFiniteRoutines| |traverse| |e04ycf| |pole?| |pushuconst| + |normalizedDivide| |shallowCopy| |cubic| |evenInfiniteProduct| |exp1| + |normalElement| |e04mbf| |outputForm| |lazyPseudoDivide| |hitherPlane| + |exportedOperators| |extendedEuclidean| |inverseIntegralMatrix| + |makeViewport2D| |mathieu11| |rotatey| |divideIfCan!| |symbolTableOf| + |jacobi| |numberOfChildren| |repSq| |bernoulliB| |expPot| |shape| + |padicFraction| |unit?| |isQuotient| |besselJ| |coth2tanh| |iifact| + |car| |entry| |min| |maxPoints3D| |positive?| |bytes| |s19abf| + |OMputString| |yellow| |musserTrials| |constant?| |elliptic?| |f02aef| + |any| |shufflein| |mainCoefficients| |approxSqrt| |quoByVar| + |toseSquareFreePart| |find| |henselFact| |listRepresentation| + |linearDependenceOverZ| |integralAtInfinity?| |setIntersection| + |relationsIdeal| |lifting1| |findCycle| |exprToUPS| |iicosh| + |deepCopy| |ratPoly| |ef2edf| |stronglyReduced?| |qqq| |localAbs| + |setPredicates| |f02aaf| |moduleSum| |variationOfParameters| |OMread| + |numberOfIrreduciblePoly| |binomial| |safeFloor| |mapUnivariate| + |noValueMode| |factorSFBRlcUnit| |cAcoth| |rational| |function| + |discriminantEuclidean| |height| |fixPredicate| |script| + |tubePointsDefault| |ldf2lst| |palglimint| |categoryMode| + |showClipRegion| |directory| |cosSinInfo| |f01qef| |evaluate| UP2UTS + |imagE| |divideExponents| |simpson| |conjugate| |saturate| |csc2sin| + |clip| |monomials| |computeCycleEntry| |outputFloating| |measure| + |algebraicSort| |bezoutDiscriminant| |critBonD| |retractIfCan| + |completeSmith| |hasTopPredicate?| |infiniteProduct| |mpsode| + |isOpen?| |f02wef| |fortranLiteral| |palgextint| |tex| |BasicMethod| + |pow| |radPoly| F2FG |e02dff| |btwFact| |errorKind| + |createNormalElement| |trim| |before?| |inputOutputBinaryFile| + |numeric| |withPredicates| |changeVar| |cycle| |hasPredicate?| + |cyclicCopy| |numberOfComponents| |genericRightMinimalPolynomial| + |putColorInfo| |monicLeftDivide| |biRank| |radical| |varselect| + |leftReducedSystem| |top| |plotPolar| |divide| |completeHermite| + |univariate?| |label| |check| |qPot| |iterationVar| |ode| + |viewDeltaXDefault| |mkIntegral| |continue| |empty| |extension| + |numberOfComposites| |Frobenius| |setOrder| |laurentRep| |returns| + |restorePrecision| |extractTop!| |iomode| |setLength!| + |differentialVariables| |OMlistSymbols| |countable?| EQ + |mainVariables| |wordInStrongGenerators| |probablyZeroDim?| |float?| + |viewZoomDefault| |cAcsc| |unknown| |Si| |rightLcm| |discriminant| + |sn| |deepestInitial| |nthRootIfCan| |inverseLaplace| |unexpand| + |arrayStack| |listYoungTableaus| |makeFloatFunction| |ode1| |tanQ| + |LyndonBasis| |createMultiplicationTable| |findBinding| |overset?| + |asechIfCan| |normalizeIfCan| |linear?| |bracket| |readIfCan!| + |c06fuf| |generalTwoFactor| |e01sff| |numberOfHues| |iisec| |lcm| + |enterPointData| |associatedEquations| |iiabs| + |genericLeftMinimalPolynomial| |viewPosDefault| |squareFreeFactors| + |explimitedint| |printInfo| |var1Steps| |distance| + |fortranLiteralLine| |c06gbf| |root| UTS2UP |represents| + |matrixDimensions| |tail| |e01bff| |append| + |selectIntegrationRoutines| |OMgetVariable| |lazyIrreducibleFactors| + FG2F |split| |removeCoshSq| |regularRepresentation| |e02baf| + |leastMonomial| |plot| |length| |option| |showFortranOutputStack| + |numFunEvals| |blankSeparate| |subHeight| |normalise| |gcd| |sub| + |hash| |declare| |countRealRootsMultiple| |ellipticCylindrical| + |category| |processTemplate| |setrest!| |maxrank| |scripts| + |setAttributeButtonStep| |iisech| |printCode| + |removeSuperfluousQuasiComponents| |false| |count| |lazy?| |domain| + |bombieriNorm| |patternMatch| |leadingSupport| |polyRicDE| |logical?| + |weight| |fill!| |reduceLODE| |diophantineSystem| |debug| |acothIfCan| + |nand| |package| |ridHack1| |isAtom| |subset?| |octon| + |complementaryBasis| |eulerE| |clearTheIFTable| |maxColIndex| + |degreeSubResultantEuclidean| |palgRDE| D |solid?| + |ScanFloatIgnoreSpaces| |anfactor| |unitNormal| |maxPoints| + |noLinearFactor?| |bitTruth| |genericPosition| |tanIfCan| |leftTrace| + |extend| |symmetricGroup| |graphCurves| |leftPower| |lastSubResultant| + |stoseIntegralLastSubResultant| |associative?| |principalIdeal| + |minIndex| |deepestTail| |nilFactor| |concat!| |zeroMatrix| |merge| + |packageCall| |OMopenFile| |sPol| |makeEq| |separateFactors| + |subresultantSequence| |center| |genericLeftNorm| LODO2FUN |leftRecip| + |e02dcf| |selectOptimizationRoutines| |subNode?| |palgintegrate| + |stFunc1| |tableForDiscreteLogarithm| |myDegree| |euclideanSize| + |collectUnder| |chvar| |groebnerIdeal| |OMUnknownSymbol?| + |newSubProgram| |integralBasisAtInfinity| |difference| + |setScreenResolution| |dimensionsOf| |llprop| |showIntensityFunctions| + |doubleDisc| |selectODEIVPRoutines| |invmultisect| |doubleResultant| + |e02daf| |expressIdealMember| |purelyAlgebraicLeadingMonomial?| + |character?| |coordinates| |expIfCan| |mesh?| |bindings| |Nul| + |linearlyDependent?| |integerIfCan| |rubiksGroup| |controlPanel| + |plenaryPower| |iicoth| |pseudoQuotient| |irreducibleFactor| |rotate| + |leftNorm| |sinhIfCan| |raisePolynomial| |f02axf| |iidsum| |df2mf| + |primitivePart!| |internalDecompose| |lepol| + |removeRedundantFactorsInContents| |iiacoth| |eigenvector| |nor| + |phiCoord| |genericRightNorm| |mapDown!| |decimal| |top!| + |stopTableGcd!| |light| |print| |s15aef| |makeResult| |physicalLength| + |replace| |semiDegreeSubResultantEuclidean| |resolve| |f04axf| + |getStream| |vertConcat| |f01rdf| |radicalEigenvector| |bit?| + |RemainderList| |degreePartition| |showArrayValues| |byteBuffer| + |groebner| |condition| |voidMode| |bat1| |minPoints3D| + |internalSubQuasiComponent?| |createNormalPrimitivePoly| + |fullPartialFraction| |rk4| |setMinPoints3D| |scaleRoots| |sumSquares| + |semicolonSeparate| |f07aef| |explicitEntries?| |OMmakeConn| + |dAndcExp| |direction| |prinb| |setErrorBound| |primintfldpoly| |ref| + |invertible?| |linSolve| |Lazard| |csch2sinh| |deriv| + |primitiveMonomials| |fixedPoint| |e04ucf| |complement| + |rightRankPolynomial| |listOfLists| |rangeIsFinite| |roughBase?| + |zeroVector| |getGraph| |moduloP| |comment| |curryRight| |reductum| + |OMputBind| |high| |perfectSquare?| |compound?| |one?| |asinhIfCan| + |fmecg| |failed?| |linear| |printingInfo?| |basisOfCenter| |readable?| + |branchPointAtInfinity?| |elColumn2!| |step| |setTex!| |iisin| + |compBound| |besselI| |LiePolyIfCan| |trace2PowMod| + |mainPrimitivePart| |att2Result| |physicalLength!| + |linearAssociatedExp| |integralRepresents| |sayLength| + |scanOneDimSubspaces| |palgLODE0| |dual| |calcRanges| |eulerPhi| + |zeroOf| |leftUnit| |iCompose| |charthRoot| |ideal| |leftFactor| + |rightQuotient| |subResultantGcd| |seed| |sum| |iiasinh| |iiGamma| + |groebner?| |bag| |vectorise| |alphabetic| |jokerMode| + |fortranInteger| |useEisensteinCriterion?| |color| |erf| |linears| + |binomThmExpt| |argument| |key?| |row| |graeffe| |ReduceOrder| |in?| + |primPartElseUnitCanonical| |zCoord| |insertBottom!| |comparison| + |product| |goto| |head| |eq| |drawComplexVectorField| + |absolutelyIrreducible?| |solveLinear| |outputArgs| |gbasis| |shift| + |insert| |e04dgf| |parabolic| |implies| |simpsono| |subSet| |iter| + |moebiusMu| |getBadValues| |radicalRoots| |cross| + |createRandomElement| |ravel| |dilog| |deref| |output| + |sylvesterSequence| |lllip| |parabolicCylindrical| |intPatternMatch| + |iibinom| |debug3D| |lprop| |matrix| |listLoops| |multMonom| |sin| + |reshape| |superscript| |findConstructor| |modifyPointData| + |insertTop!| |OMUnknownCD?| |fortranDoubleComplex| |leftMult| + |recolor| |maxRowIndex| |kmax| |cos| |HenselLift| |hex| |mapdiv| + |iiacsc| |children| |laplace| |enqueue!| |prepareSubResAlgo| |axes| + |c06gqf| |tan| |mainVariable?| |generic| |irVar| |s18def| |mindeg| + |readInt8!| |asecIfCan| |second| |d03edf| |viewpoint| + |invertibleElseSplit?| |reflect| |cot| |cn| |compile| |quadratic?| + |polygamma| |s17aef| |transcendenceDegree| |clipParametric| + |coshIfCan| |third| |setprevious!| |delay| |multiplyExponents| |sec| + |representationType| |ipow| |scalarMatrix| |roughEqualIdeals?| + |realZeros| |mapBivariate| |selectOrPolynomials| |accuracyIF| + |removeRoughlyRedundantFactorsInContents| |dfRange| |graphImage| + |cyclotomicFactorization| |csc| |bumptab1| |update| |matrixConcat3D| + |hconcat| |SturmHabichtSequence| |units| |getConstant| |birth| + |external?| |every?| |freeOf?| |reopen!| |asin| |s18adf| |even?| + |redpps| |iicsch| |mapUnivariateIfCan| |singularAtInfinity?| + |removeZero| |var2Steps| |modifyPoint| |generic?| |acos| |midpoints| + |cAsin| |e02ddf| |randomR| |nextPartition| |mkcomm| |smith| + |factorial| |ocf2ocdf| |aQuartic| |antisymmetricTensors| |atan| + |nextSubsetGray| |cCsch| |signature| |resetNew| |stopMusserTrials| + |outlineRender| |OMsetEncoding| |determinant| |nonSingularModel| + |setMaxPoints| |partition| |nextSublist| |acot| + |functionIsContinuousAtEndPoints| |exptMod| |generate| |setlast!| + |merge!| |interpolate| |super| |constantOpIfCan| |curve| + |resetAttributeButtons| |fortranDouble| |coth2trigh| |getCode| |asec| + |inRadical?| |position| |code| |KrullNumber| |meshPar2Var| |ptFunc| + |nextNormalPrimitivePoly| |cyclePartition| |outputGeneral| + |stripCommentsAndBlanks| |operation| |univariateSolve| |acsc| + |iidprod| |stoseInvertibleSet| |incrementBy| |s18aef| |OMsupportsCD?| + |cycleRagits| |contract| |viewWriteAvailable| |pureLex| |yCoord| + |generalizedContinuumHypothesisAssumed?| |sinh| |elaboration| + |seriesToOutputForm| |reduction| |c06frf| |expand| + |isAbsolutelyIrreducible?| |categoryFrame| |semiResultantEuclidean2| + |innerSolve| |halfExtendedSubResultantGcd1| |quasiRegular?| |cosh| + |stiffnessAndStabilityFactor| |perfectNthPower?| |FormatRoman| + |filterWhile| |queue| |stopTableInvSet!| |gcdPrimitive| + |semiSubResultantGcdEuclidean1| |infinityNorm| |swapColumns!| + |constantKernel| |tanh| |rootsOf| |expandPower| |positiveSolve| + |antiCommutative?| |filterUntil| |nthExponent| + |numberOfComputedEntries| |s17adf| |commutator| |clearTheFTable| + |stoseInvertible?reg| |numberOfPrimitivePoly| |coth| |drawComplex| + |jordanAlgebra?| |unitNormalize| |s17agf| |select| |rowEchLocal| + |splitDenominator| |identityMatrix| |xCoord| |modularGcd| + |nextLatticePermutation| |dmp2rfi| |sech| |makeMulti| |pade| |rk4a| + |oddlambert| |OMgetAtp| |getOrder| |univariatePolynomials| + |stoseInvertibleSetsqfreg| |splitConstant| |nullSpace| |csch| |exQuo| + |rectangularMatrix| |basisOfRightNucleus| |leftScalarTimes!| + |linearMatrix| |diff| |rspace| |s13aaf| |asinh| |e02def| |pointData| + |topFortranOutputStack| |tubeRadiusDefault| |makeYoungTableau| + |sqfrFactor| |LazardQuotient| |d02gaf| |showTheIFTable| |acosh| + |s17acf| |supersub| |setColumn!| |range| |dn| |partialNumerators| + |monomial?| |semiResultantEuclideannaif| |init| |e04naf| |atanh| + |identity| |cond| |rationalPoints| |subscriptedVariables| |cotIfCan| + |totolex| |f01rcf| |mesh| |hexDigit| |f04faf| |acoth| |dioSolve| + |makeRecord| |rdregime| |leftAlternative?| |exprHasLogarithmicWeights| + |read!| |complexSolve| |twoFactor| |asech| |imports| |f07fef| |elem?| + |diagonals| |fortranComplex| |rightPower| |commaSeparate| |typeList| + |leftMinimalPolynomial| |harmonic| |permanent| |quadraticNorm| + |B1solve| |axesColorDefault| |choosemon| |OMputEndApp| |csubst| + |screenResolution3D| |multiple| |s17akf| |cosh2sech| |zeroDimPrimary?| + |pquo| |hermiteH| |dom| |dequeue| |entries| |applyQuote| |e04gcf| + |set| |pointSizeDefault| |d01fcf| |monicDivide| |partitions| + |nextPrimitivePoly| |f02adf| |pseudoDivide| |generalizedInverse| + |atrapezoidal| |atanhIfCan| |OMencodingSGML| BY |terms| |contours| + |cup| |transform| |prime| |qelt| |parts| + |initializeGroupForWordProblem| |charClass| |exponential1| + |rightRegularRepresentation| |nothing| |factorSquareFreeByRecursion| + |simplifyPower| |wholePart| |quasiRegular| |qsetelt| |setchildren!| + |imagj| |ruleset| |f01qdf| |componentUpperBound| |cycleLength| + |idealiserMatrix| |f01mcf| |xRange| |prime?| |outputMeasure| + |exponent| |getCurve| |leftTraceMatrix| |mulmod| |double?| + |quotientByP| |removeRoughlyRedundantFactorsInPol| |title| + |simpleBounds?| |generalPosition| |yRange| |dec| |compactFraction| + |diag| |initiallyReduce| |typeForm| |constantRight| |d01asf| + |uncouplingMatrices| |homogeneous?| |makeprod| |zRange| + |dihedralGroup| |suchThat| |e02bdf| |zeroSetSplit| |makeGraphImage| + |SturmHabichtMultiple| |doubleRank| |iFTable| |diagonal?| + |minColIndex| |quasiMonicPolynomials| |curve?| |systemSizeIF| + |rightDiscriminant| |digit?| |e| |rightAlternative?| + |algebraicVariables| |extractIndex| NOT |aQuadratic| + |partialDenominators| |lazyGintegrate| |changeThreshhold| |medialSet| + |mapCoef| |qfactor| |lllp| |rationalPoint?| OR |copyInto!| |whileLoop| + |wrregime| |halfExtendedResultant1| |printHeader| |trueEqual| |d01alf| + |leftExactQuotient| |connectTo| |properties| AND |lSpaceBasis| + |LiePoly| |trapezoidal| |show| |initiallyReduced?| |zoom| |scale| + |s17ajf| |OMreadFile| |algebraicDecompose| |minimalPolynomial| + |translate| |toroidal| |e01bgf| |iiacot| |generators| |open| + |cardinality| |separant| |readUInt32!| |lazyEvaluate| + |removeRedundantFactors| |setRow!| |exponents| |virtualDegree| |trace| + |digits| |currentSubProgram| |commonDenominator| |checkRur| + |leastPower| |realEigenvectors| |d03faf| |karatsuba| |xn| |bat| + |primlimintfrac| |irCtor| |sechIfCan| |insert!| |symFunc| |powmod| + |setDifference| |heapSort| |zeroSquareMatrix| |augment| |sample| + |constantIfCan| |showRegion| |linearPart| |s20acf| |ParCond| + |quadraticForm| |bitand| |char| |triangulate| |c06gcf| |changeMeasure| + |irDef| |firstUncouplingMatrix| |operations| |overbar| + |complexIntegrate| |blue| |parseString| |factorFraction| |bitior| + |scalarTypeOf| |f04atf| |bumptab| |fglmIfCan| |rationalIfCan| + |lazyVariations| |getMeasure| |modTree| |coerceS| |e01saf| + |setScreenResolution3D| |result| |property| |iicsc| |leftOne| + |omError| |goodnessOfFit| |nextPrimitiveNormalPoly| |taylorQuoByVar| + |solveInField| |OMgetEndAtp| |algebraicCoefficients?| |exists?| + |subCase?| |singleFactorBound| |mainMonomials| |sup| |infRittWu?| + |closeComponent| |imagi| |conjugates| |exprHasAlgebraicWeight| * + |numericIfCan| |denominator| |bivariateSLPEBR| |composites| + |rewriteSetByReducingWithParticularGenerators| |LowTriBddDenomInv| + |setClipValue| |d01gaf| |selectPDERoutines| |pmComplexintegrate| + |ScanFloatIgnoreSpacesIfCan| |uniform| |rationalFunction| |iiacsch| + |ListOfTerms| |iExquo| |discreteLog| |fullDisplay| |normalized?| + |symbolTable| |edf2efi| |dflist| |content| |fprindINFO| |rk4qc| + |setnext!| |iiatanh| |root?| |OMgetFloat| |complexForm| + |reducedQPowers| |tryFunctionalDecomposition?| = |interpret| |pop!| + |e01sbf| |nonQsign| |infieldint| |nthExpon| |f04adf| |ratDenom| + |iiasech| |pushFortranOutputStack| |kind| |factorAndSplit| |distdfact| + |OMgetType| |commutative?| |showScalarValues| |companionBlocks| + |factorsOfCyclicGroupSize| |scan| |e02zaf| |popFortranOutputStack| + |op| < |extensionDegree| |shiftRoots| |coerceListOfPairs| |rightRank| + |insertMatch| |loadNativeModule| |summation| |OMputBVar| + |makeViewport3D| |cLog| |outputAsFortran| |OMputEndObject| > + |fracPart| |hue| |call| |beauzamyBound| |fortranCarriageReturn| + |brillhartTrials| |colorFunction| |multisect| + |stiffnessAndStabilityOfODEIF| <= |shuffle| |prepareDecompose| + |subResultantsChain| |predicates| |binary| |e02adf| |rename!| |submod| + |complex?| >= |redPo| |viewPhiDefault| |rightTraceMatrix| + |setCondition!| |getExplanations| |normalForm| |less?| + |createIrreduciblePoly| |Ci| |clearCache| |c06fqf| |magnitude| + |insertionSort!| |real?| |wordsForStrongGenerators| |outputAsTex| + |removeZeroes| |airyAi| |setTopPredicate| |eigenvectors| + |noncommutativeJordanAlgebra?| |binarySearchTree| |sign| |mr| + |belong?| |module| |solve| |normFactors| |categories| |union| + |tanh2coth| + |setLabelValue| |member?| |cCoth| |c02agf| |duplicates| + |localReal?| |cAcosh| |generalizedEigenvector| |branchPoint?| - + |quickSort| |collect| |currentCategoryFrame| |internal?| + |rightScalarTimes!| |swapRows!| |sinIfCan| |getZechTable| |lfunc| / + |adaptive| |simplify| |outputBinaryFile| |infLex?| |parents| + |numberOfCycles| |definingInequation| |square?| |zeroDimensional?| + |hspace| |cons| |equiv| |LyndonWordsList| |showTheSymbolTable| + |hdmpToP| |nthRoot| |sizeLess?| |number?| |ODESolve| |reverseLex| + |squareFreePart| |removeIrreducibleRedundantFactors| |iprint| + |bandedJacobian| |numberOfDivisors| |cExp| |factorPolynomial| + |romberg| |expint| |sqfree| |iteratedInitials| |quotient| |nextItem| + |logIfCan| |printStats!| |charpol| |makeTerm| |pointPlot| |d02ejf| + |paren| |equality| |gderiv| |rationalApproximation| |rur| |supRittWu?| + |e01baf| |getVariableOrder| |associates?| |vector| |s19acf| + |rightCharacteristicPolynomial| |ranges| |LagrangeInterpolation| + |unrankImproperPartitions0| |edf2fi| |moreAlgebraic?| |comp| |f04qaf| + |f02aff| |differentiate| |subresultantVector| |s21bcf| |floor| |pack!| + |push!| |littleEndian| |coerce| |readUInt8!| + |integralLastSubResultant| |setEpilogue!| |cCos| |source| + |leftCharacteristicPolynomial| |symmetricRemainder| |OMputEndBVar| + |OMputEndError| |normalDenom| |construct| |list?| |possiblyInfinite?| + |disjunction| |safetyMargin| |zeroSetSplitIntoTriangularSystems| + |e01bhf| |stack| |euclideanNormalForm| |viewport2D| |f04arf| |rank| + |ran| |monomRDE| |internalIntegrate| |basisOfNucleus| |imagK| + |tableau| |critB| |OMgetEndObject| |mirror| |imaginary| |tracePowMod| + |LyndonCoordinates| |name| |factorList| |permutations| |fractionPart| + |inconsistent?| |collectUpper| |factors| + |solveLinearPolynomialEquation| |more?| |nextPrime| |body| |c06eaf| + |cAcot| |indicialEquationAtInfinity| |rightMinimalPolynomial| + |typeLists| |monicRightFactorIfCan| |conjug| |closedCurve?| |sec2cos| + |outputList| |target| |addiag| |nsqfree| |f02awf| |prolateSpheroidal| + |setLegalFortranSourceExtensions| |next| |nthFactor| |repeating| + |hostByteOrder| |integralDerivationMatrix| |completeEval| + |normalDeriv| |factorSquareFree| |ScanRoman| |latex| |leaves| + |lazyPremWithDefault| |aromberg| |mdeg| |empty?| |sumOfSquares| + |realSolve| |leviCivitaSymbol| |extendIfCan| |leader| |tube| + |OMgetString| |rischDEsys| |expandTrigProducts| + |linearAssociatedOrder| |inf| |doubleComplex?| |solve1| |reverse| + |f2df| |lists| |d02bbf| |exactQuotient| |sinh2csch| |wholeRagits| + |enterInCache| |unravel| |getGoodPrime| + |selectMultiDimensionalRoutines| |shiftRight| |stoseInvertible?| + |move| |setProperties| |checkPrecision| |curveColor| |f02abf| + |monicCompleteDecompose| |colorDef| |printInfo!| |addmod| |mapSolve| + |f02bbf| |port| |const| |defineProperty| |dihedral| |critpOrder| + |unitVector| |radicalEigenvectors| |structuralConstants| + |degreeSubResultant| |readLineIfCan!| |monicDecomposeIfCan| + |certainlySubVariety?| |linearlyDependentOverZ?| |padicallyExpand| + |rootProduct| |eof?| |semiResultantEuclidean1| |t| + |expenseOfEvaluationIF| |Vectorise| |setPosition| |setfirst!| |normal| + |lambert| |trapezoidalo| |argumentListOf| |startStats!| |startTable!| + |subNodeOf?| |sts2stst| |signAround| |alphabetic?| |approxNthRoot| + |useNagFunctions| |realElementary| |cyclicGroup| |approximants| + |edf2df| |stoseSquareFreePart| |alternating| |setelt| |minimumDegree| + |taylorIfCan| |cyclotomicDecomposition| |OMputEndAttr| |setPrologue!| + |decomposeFunc| |karatsubaOnce| |palgint| |recur| |f02xef| |rule| + |npcoef| |cyclicEntries| |Hausdorff| |intChoose| |OMputApp| + |arguments| |separateDegrees| |copy| |unaryFunction| + |generalizedContinuumHypothesisAssumed| |d01anf| |OMconnInDevice| + |OMputEndBind| |limitedint| |mightHaveRoots| |s13adf| |xor| + |derivationCoordinates| |s17dcf| |lowerCase!| |scopes| |mapExpon| + |members| |boundOfCauchy| |gramschmidt| |case| |inspect| |depth| + |pomopo!| |rightNorm| |sizeMultiplication| |elements| |Zero| |hermite| + |showTheRoutinesTable| |extractSplittingLeaf| |totalGroebner| + |roughUnitIdeal?| |removeRedundantFactorsInPols| |droot| |normal?| + |e02aef| |One| |setref| |oneDimensionalArray| |polyRDE| |true| + |match?| |coerceP| |leastAffineMultiple| |stirling1| |s19aaf| + |variable?| |autoCoerce| |perspective| |s13acf| + |rewriteSetWithReduction| |f01qcf| |fractRagits| |copies| |OMgetBind| + |mix| |radicalEigenvalues| |increment| |basisOfRightNucloid| + |increase| |superHeight| |isEquiv| |cot2tan| |build| + |mainDefiningPolynomial| |upDateBranches| |unit| |newReduc| + |antisymmetric?| |toseInvertibleSet| |plusInfinity| |numFunEvals3D| + |OMlistCDs| |clearTheSymbolTable| |nodes| |functionIsFracPolynomial?| + |rightGcd| |setMinPoints| |lastSubResultantElseSplit| |minusInfinity| + |tubePoints| |resultantEuclideannaif| |inverseColeman| |elt| |random| + |upperCase!| |monomialIntegrate| |optpair| |selectPolynomials| + |stronglyReduce| |expintfldpoly| |shellSort| |OMputObject| |optional?| + |frobenius| |e02bcf| |s21bdf| |isTimes| |exactQuotient!| |divergence| + |imagk| |components| |torsionIfCan| |column| |isImplies| |sech2cosh| + |interReduce| |bfEntry| |complexZeros| |lexTriangular| + |leftDiscriminant| |getMultiplicationMatrix| |rightUnit| |rootPower| + |makeCrit| |numberOfImproperPartitions| |indices| |OMconnOutDevice| + |nextsubResultant2| |useEisensteinCriterion| |int| |genericRightTrace| + |listOfMonoms| |getButtonValue| |endSubProgram| |iisinh| |rdHack1| + |newLine| |indicialEquation| |OMreadStr| |iicos| |innerSolve1| + |multiEuclidean| |linearDependence| |lastSubResultantEuclidean| + |radicalSolve| |chebyshevU| |trunc| |sinhcosh| |bsolve| |transpose| + |linkToFortran| |lighting| |genericRightTraceForm| |OMconnectTCP| + |functionIsOscillatory| |bandedHessian| |getProperty| + |coercePreimagesImages| |rightTrim| |extendedIntegrate| |firstDenom| + |c02aff| |oddintegers| |option?| |contains?| |tower| |stop| + |contractSolve| |nil| |infinite| |arbitraryExponent| |approximate| + |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 28fdbe06..051550ac 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5435 +1,5444 @@ -(3260701 . 3486772049) -((-4372 (((-112) (-1 (-112) |#2| |#2|) $) 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -3795 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -3795 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-35) |has| |#1| (-1223)) ((-95) |has| |#1| (-1223)) ((-102) . T) ((-111 #0# #0#) -3795 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -3795 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -3795 (|has| |#1| (-1059 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -3795 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-625 (-876)) . T) ((-174) . T) ((-626 (-171 (-227))) |has| |#1| (-1043)) ((-626 (-171 (-390))) |has| |#1| (-1043)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-907 (-390))) |has| |#1| (-626 (-907 (-390)))) ((-626 (-907 (-576))) |has| |#1| (-626 (-907 (-576)))) ((-626 #1=(-1193 |#1|)) . 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T) ((-464) -3795 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-505) |has| |#1| (-1223)) ((-526 (-1197) |#1|) |has| |#1| (-526 (-1197) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) -3795 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-658 #0#) -3795 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) -3795 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-660 #2=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) -3795 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-652 |#1|) . T) ((-652 $) -3795 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-651 #2#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) -3795 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-729 |#1|) . T) ((-729 $) -3795 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-736 |#1| #1#) . T) ((-738) . T) ((-911 $ #3=(-1197)) -3795 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-917 (-1197)) |has| |#1| (-917 (-1197))) ((-919 #3#) -3795 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-901 (-390)) |has| |#1| (-901 (-390))) ((-901 (-576)) |has| |#1| (-901 (-576))) ((-899 |#1|) . T) ((-928) -12 (|has| |#1| (-317)) (|has| |#1| (-928))) ((-939) -3795 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-1023) -12 (|has| |#1| (-1023)) (|has| |#1| (-1223))) ((-1059 (-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) ((-1059 (-576)) |has| |#1| (-1059 (-576))) ((-1059 |#1|) . T) ((-1072 #0#) -3795 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1072 |#1|) . T) ((-1072 $) . T) ((-1077 #0#) -3795 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1077 |#1|) . T) ((-1077 $) . T) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1173) |has| |#1| (-360)) ((-1223) |has| |#1| (-1223)) ((-1226) |has| |#1| (-1223)) ((-1238) . T) ((-1242) -3795 (|has| |#1| (-360)) (|has| |#1| (-374)) (-12 (|has| |#1| (-317)) (|has| |#1| (-928))))) +((-1452 (((-430 |#2|) |#2|) 67))) +(((-168 |#1| |#2|) (-10 -7 (-15 -1452 ((-430 |#2|) |#2|))) (-317) (-1264 (-171 |#1|))) (T -168)) +((-1452 (*1 *2 *3) (-12 (-4 *4 (-317)) (-5 *2 (-430 *3)) (-5 *1 (-168 *4 *3)) (-4 *3 (-1264 (-171 *4)))))) +(-10 -7 (-15 -1452 ((-430 |#2|) |#2|))) +((-1548 (((-1156) (-1156) (-301)) 8)) (-1449 (((-656 (-703 (-290))) (-1179)) 81)) (-1745 (((-703 (-290)) (-1156)) 76))) +(((-169) (-13 (-1238) (-10 -7 (-15 -1548 ((-1156) (-1156) (-301))) (-15 -1745 ((-703 (-290)) (-1156))) (-15 -1449 ((-656 (-703 (-290))) (-1179)))))) (T -169)) +((-1548 (*1 *2 *2 *3) (-12 (-5 *2 (-1156)) (-5 *3 (-301)) (-5 *1 (-169)))) (-1745 (*1 *2 *3) (-12 (-5 *3 (-1156)) (-5 *2 (-703 (-290))) (-5 *1 (-169)))) (-1449 (*1 *2 *3) (-12 (-5 *3 (-1179)) (-5 *2 (-656 (-703 (-290)))) (-5 *1 (-169))))) +(-13 (-1238) (-10 -7 (-15 -1548 ((-1156) (-1156) (-301))) (-15 -1745 ((-703 (-290)) 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T) ((-234 $) -2755 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-232 |#2|) |has| |#2| (-1068)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1068))) ((-237) -2755 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-272 |#2|) |has| |#2| (-1068)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1068)) ((-423 |#2|) |has| |#2| (-1119)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-658 (-576)) -2755 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -2755 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-658 $) |has| |#2| (-1068)) ((-660 #2=(-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068))) ((-660 |#2|) -2755 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1068)) ((-652 |#2|) -2755 (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-651 #2#) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068))) ((-651 |#2|) |has| |#2| (-1068)) ((-729 |#2|) -2755 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-738) |has| |#2| (-1068)) ((-804) |has| |#2| (-805)) ((-805) |has| |#2| (-805)) ((-806) |has| |#2| (-805)) ((-807) |has| |#2| (-805)) ((-862) -2755 (|has| |#2| (-862)) (|has| |#2| (-805))) ((-909 $ #3=(-1195)) -2755 (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) ((-915 (-1195)) -12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068))) ((-917 #3#) -2755 (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) ((-1057 #0#) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119))) ((-1057 (-576)) -12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119))) ((-1057 |#2|) |has| |#2| (-1119)) ((-1070 |#2|) -2755 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1075 |#2|) -2755 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1068) |has| |#2| (-1068)) ((-1077) |has| |#2| (-1068)) ((-1131) |has| |#2| (-1068)) ((-1119) -2755 (|has| |#2| (-1119)) (|has| |#2| (-1068)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1236) . T) ((-1293 |#2|) |has| |#2| (-374))) -((-2456 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-3683 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-4114 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) -(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -2456 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -3683 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -4114 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-783) (-1236) (-1236)) (T -244)) -((-4114 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1236)) (-4 *7 (-1236)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-3683 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1236)) (-4 *2 (-1236)) (-5 *1 (-244 *5 *6 *2)))) (-2456 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-783)) (-4 *7 (-1236)) (-4 *5 (-1236)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-23) . T) ((-25) . T) ((-102) . T) ((-132) . T) ((-628 (-576)) . T) ((-625 (-876)) . T) ((-234 $) . T) ((-237) . T) ((-658 (-576)) . T) ((-658 $) . T) ((-660 $) . T) ((-738) . T) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1238) . 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T) ((-234 $) -3795 (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1070)))) ((-232 |#2|) |has| |#2| (-1070)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1070))) ((-237) -3795 (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1070)))) ((-272 |#2|) |has| |#2| (-1070)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1070)) ((-423 |#2|) |has| |#2| (-1121)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((-658 (-576)) -3795 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -3795 (|has| |#2| (-1070)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-658 $) |has| |#2| (-1070)) ((-660 #2=(-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070))) ((-660 |#2|) -3795 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1070)) ((-652 |#2|) -3795 (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-651 #2#) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070))) ((-651 |#2|) |has| |#2| (-1070)) ((-729 |#2|) -3795 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-738) |has| |#2| (-1070)) ((-804) |has| |#2| (-805)) ((-805) |has| |#2| (-805)) ((-806) |has| |#2| (-805)) ((-807) |has| |#2| (-805)) ((-862) -3795 (|has| |#2| (-862)) (|has| |#2| (-805))) ((-911 $ #3=(-1197)) -3795 (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070)))) ((-917 (-1197)) -12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070))) ((-919 #3#) -3795 (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070)))) ((-1059 #0#) -12 (|has| |#2| (-1059 (-419 (-576)))) (|has| |#2| (-1121))) ((-1059 (-576)) -12 (|has| |#2| (-1059 (-576))) (|has| |#2| (-1121))) ((-1059 |#2|) |has| |#2| (-1121)) ((-1072 |#2|) -3795 (|has| |#2| (-1070)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1077 |#2|) -3795 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1070) |has| |#2| (-1070)) ((-1079) |has| |#2| (-1070)) ((-1133) |has| |#2| (-1070)) ((-1121) -3795 (|has| |#2| (-1121)) (|has| |#2| (-1070)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1238) . T) ((-1295 |#2|) |has| |#2| (-374))) +((-3958 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-2722 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-2423 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) +(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -3958 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2722 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2423 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-783) (-1238) (-1238)) (T -244)) +((-2423 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1238)) (-4 *7 (-1238)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-2722 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1238)) (-4 *2 (-1238)) (-5 *1 (-244 *5 *6 *2)))) (-3958 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-783)) (-4 *7 (-1238)) (-4 *5 (-1238)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) . T) ((-38 |#1|) . T) ((-38 $) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) . T) ((-628 (-576)) . T) ((-628 #1=(-1197)) |has| |#1| (-1059 (-1197))) ((-628 |#1|) . T) ((-628 $) . T) ((-625 (-876)) . T) ((-174) . T) ((-626 (-227)) |has| |#1| (-1043)) ((-626 (-390)) |has| |#1| (-1043)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-907 (-390))) |has| |#1| (-626 (-907 (-390)))) ((-626 (-907 (-576))) |has| |#1| (-626 (-907 (-576)))) ((-234 $) -3795 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -3795 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-248) . T) ((-296 |#1| $) |has| |#1| (-296 |#1| |#1|)) ((-300) . T) ((-317) . T) ((-319 |#1|) |has| |#1| (-319 |#1|)) ((-374) . T) ((-349 |#1|) . T) ((-388 |#1|) . T) ((-412 |#1|) . T) ((-464) . 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T) ((-625 (-874)) . T) ((-1119) . T) ((-1236) . 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T) ((-23) . T) ((-47 |#1| #0=(-576)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-374)) ((-38 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-374)) ((-111 $ $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-628 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1195)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1195)))) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . T) ((-628 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-227)) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-626 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-626 (-548)) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-905 (-576))))) ((-234 $) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-232 |#2|) |has| |#1| (-374)) ((-238) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-237) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-272 |#2|) |has| |#1| (-374)) ((-248) |has| |#1| (-374)) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . T) ((-296 |#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) ((-296 $ $) |has| (-576) (-1131)) ((-300) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-374) |has| |#1| (-374)) ((-349 |#2|) |has| |#1| (-374)) ((-388 |#2|) |has| |#1| (-374)) ((-412 |#2|) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-526 (-1195) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1195) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-658 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-374)) ((-658 $) . T) ((-660 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-660 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-660 |#1|) . T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . T) ((-803) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-804) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-806) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-807) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-832) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-860) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-862) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-862))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-909 $ #4=(-1195)) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-915 (-1195)) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-917 #4#) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-899 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-390)))) ((-899 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-576)))) ((-897 |#2|) |has| |#1| (-374)) ((-926) -12 (|has| |#1| (-374)) (|has| |#2| (-926))) ((-992 |#1| #0# (-1101)) . T) ((-937) |has| |#1| (-374)) ((-1011 |#2|) |has| |#1| (-374)) ((-1021) |has| |#1| (-38 (-419 (-576)))) ((-1041) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-1057 (-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 #2#) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1195)))) ((-1057 |#2|) . T) ((-1070 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1070 |#1|) . T) ((-1070 |#2|) |has| |#1| (-374)) ((-1070 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1075 |#1|) . T) ((-1075 |#2|) |has| |#1| (-374)) ((-1075 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) -12 (|has| |#1| (-374)) (|has| |#2| (-1171))) ((-1221) |has| |#1| (-38 (-419 (-576)))) ((-1224) |has| |#1| (-38 (-419 (-576)))) ((-1236) . T) ((-1240) |has| |#1| (-374)) ((-1246 |#1|) . T) ((-1264 |#1| #0#) . 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T) ((-1075 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1221) |has| |#1| (-38 (-419 (-576)))) ((-1224) |has| |#1| (-38 (-419 (-576)))) ((-1236) . T) ((-1240) |has| |#1| (-374)) ((-1264 |#1| #0#) . T) ((-1267 |#1|) . 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T) ((-1070 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1075 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1221) |has| |#1| (-38 (-419 (-576)))) ((-1224) |has| |#1| (-38 (-419 (-576)))) ((-1236) . T) ((-1264 |#1| #0#) . 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NIL) (-1247 2994945 2995190 2995578 "ULSCCAT-" 2995583 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1246 2984009 2990492 2990535 "ULSCAT" 2991398 NIL ULSCAT (NIL T) -9 NIL 2992129 NIL) (-1245 2983439 2983518 2983697 "ULS2" 2983924 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1244 2982558 2983068 2983175 "UINT8" 2983286 T UINT8 (NIL) -8 NIL NIL 2983371) (-1243 2981676 2982186 2982293 "UINT64" 2982404 T UINT64 (NIL) -8 NIL NIL 2982489) (-1242 2980794 2981304 2981411 "UINT32" 2981522 T UINT32 (NIL) -8 NIL NIL 2981607) (-1241 2979912 2980422 2980529 "UINT16" 2980640 T UINT16 (NIL) -8 NIL NIL 2980725) (-1240 2978201 2979158 2979188 "UFD" 2979400 T UFD (NIL) -9 NIL 2979514 NIL) (-1239 2977995 2978041 2978136 "UFD-" 2978141 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1238 2977077 2977260 2977476 "UDVO" 2977801 T UDVO (NIL) -7 NIL NIL NIL) (-1237 2974893 2975302 2975773 "UDPO" 2976641 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1236 2974826 2974831 2974861 "TYPE" 2974866 T TYPE (NIL) -9 NIL NIL NIL) (-1235 2974586 2974781 2974812 "TYPEAST" 2974817 T TYPEAST (NIL) -8 NIL NIL NIL) (-1234 2973557 2973759 2973999 "TWOFACT" 2974380 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1233 2972580 2972966 2973201 "TUPLE" 2973357 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1232 2970271 2970790 2971329 "TUBETOOL" 2972063 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1231 2969120 2969325 2969566 "TUBE" 2970064 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1230 2963849 2968092 2968375 "TS" 2968872 NIL TS (NIL T) -8 NIL NIL NIL) (-1229 2952489 2956608 2956705 "TSETCAT" 2961974 NIL TSETCAT (NIL T T T T) -9 NIL 2963505 NIL) (-1228 2947221 2948821 2950712 "TSETCAT-" 2950717 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1227 2941860 2942707 2943636 "TRMANIP" 2946357 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1226 2941301 2941364 2941527 "TRIMAT" 2941792 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1225 2939167 2939404 2939761 "TRIGMNIP" 2941050 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1224 2938687 2938800 2938830 "TRIGCAT" 2939043 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1223 2938356 2938435 2938576 "TRIGCAT-" 2938581 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1222 2935203 2937214 2937495 "TREE" 2938110 NIL TREE (NIL T) -8 NIL NIL NIL) (-1221 2934477 2935005 2935035 "TRANFUN" 2935070 T TRANFUN (NIL) -9 NIL 2935136 NIL) (-1220 2933756 2933947 2934227 "TRANFUN-" 2934232 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1219 2933560 2933592 2933653 "TOPSP" 2933717 T TOPSP (NIL) -7 NIL NIL NIL) (-1218 2932908 2933023 2933177 "TOOLSIGN" 2933441 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1217 2931542 2932085 2932324 "TEXTFILE" 2932691 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1216 2929454 2929995 2930424 "TEX" 2931135 T TEX (NIL) -8 NIL NIL NIL) (-1215 2929235 2929266 2929338 "TEX1" 2929417 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1214 2928883 2928946 2929036 "TEMUTL" 2929167 T TEMUTL (NIL) -7 NIL NIL NIL) (-1213 2927037 2927317 2927642 "TBCMPPK" 2928606 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1212 2918744 2925123 2925179 "TBAGG" 2925579 NIL TBAGG (NIL T T) -9 NIL 2925790 NIL) (-1211 2913814 2915302 2917056 "TBAGG-" 2917061 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1210 2913198 2913305 2913450 "TANEXP" 2913703 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1209 2912709 2912973 2913063 "TALGOP" 2913143 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1208 2906103 2912566 2912659 "TABLE" 2912664 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1207 2905515 2905614 2905752 "TABLEAU" 2906000 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1206 2900123 2901343 2902591 "TABLBUMP" 2904301 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1205 2899345 2899492 2899673 "SYSTEM" 2899964 T SYSTEM (NIL) -8 NIL NIL NIL) (-1204 2895804 2896503 2897286 "SYSSOLP" 2898596 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1203 2895602 2895759 2895790 "SYSPTR" 2895795 T SYSPTR (NIL) -8 NIL NIL NIL) (-1202 2894638 2895143 2895262 "SYSNNI" 2895448 NIL SYSNNI (NIL NIL) -8 NIL NIL 2895533) (-1201 2893937 2894396 2894475 "SYSINT" 2894535 NIL SYSINT (NIL NIL) -8 NIL NIL 2894580) (-1200 2890269 2891215 2891925 "SYNTAX" 2893249 T SYNTAX (NIL) -8 NIL NIL NIL) (-1199 2887427 2888029 2888661 "SYMTAB" 2889659 T SYMTAB (NIL) -8 NIL NIL NIL) (-1198 2882676 2883578 2884561 "SYMS" 2886466 T SYMS (NIL) -8 NIL NIL NIL) (-1197 2879911 2882134 2882364 "SYMPOLY" 2882481 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1196 2879428 2879503 2879626 "SYMFUNC" 2879823 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1195 2875448 2876740 2877553 "SYMBOL" 2878637 T SYMBOL (NIL) -8 NIL NIL NIL) (-1194 2868987 2870676 2872396 "SWITCH" 2873750 T SWITCH (NIL) -8 NIL NIL NIL) (-1193 2862331 2867943 2868237 "SUTS" 2868751 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1192 2854507 2861713 2861977 "SUPXS" 2862125 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2845990 2854125 2854251 "SUP" 2854416 NIL SUP (NIL T) -8 NIL NIL NIL) (-1190 2845149 2845276 2845493 "SUPFRACF" 2845858 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1189 2844770 2844829 2844942 "SUP2" 2845084 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1188 2843218 2843492 2843848 "SUMRF" 2844469 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1187 2842553 2842619 2842811 "SUMFS" 2843139 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1186 2825340 2841865 2842107 "SULS" 2842369 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1185 2824942 2825162 2825232 "SUCHTAST" 2825292 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1184 2824237 2824467 2824607 "SUCH" 2824850 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1183 2818104 2819143 2820102 "SUBSPACE" 2823325 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1182 2817534 2817624 2817788 "SUBRESP" 2817992 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1181 2810902 2812199 2813510 "STTF" 2816270 NIL STTF (NIL T) -7 NIL NIL NIL) (-1180 2805075 2806195 2807342 "STTFNC" 2809802 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1179 2796388 2798257 2800051 "STTAYLOR" 2803316 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1178 2789522 2796252 2796335 "STRTBL" 2796340 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1177 2784482 2789231 2789330 "STRING" 2789445 T STRING (NIL) -8 NIL NIL NIL) (-1176 2777237 2782101 2782712 "STREAM" 2783906 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1175 2776747 2776824 2776968 "STREAM3" 2777154 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1174 2775729 2775912 2776147 "STREAM2" 2776560 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1173 2775417 2775469 2775562 "STREAM1" 2775671 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1172 2774433 2774614 2774845 "STINPROD" 2775233 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1171 2773971 2774181 2774211 "STEP" 2774291 T STEP (NIL) -9 NIL 2774369 NIL) (-1170 2773158 2773460 2773608 "STEPAST" 2773845 T STEPAST (NIL) -8 NIL NIL NIL) (-1169 2766594 2773057 2773134 "STBL" 2773139 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1168 2761663 2765757 2765800 "STAGG" 2765953 NIL STAGG (NIL T) -9 NIL 2766042 NIL) (-1167 2759365 2759967 2760839 "STAGG-" 2760844 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1166 2757514 2759135 2759227 "STACK" 2759308 NIL STACK (NIL T) -8 NIL NIL NIL) (-1165 2750209 2755655 2756111 "SREGSET" 2757144 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1164 2742634 2744003 2745516 "SRDCMPK" 2748815 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1163 2735499 2740022 2740052 "SRAGG" 2741355 T SRAGG (NIL) -9 NIL 2741963 NIL) (-1162 2734516 2734771 2735150 "SRAGG-" 2735155 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1161 2728700 2733463 2733884 "SQMATRIX" 2734142 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1160 2722387 2725418 2726145 "SPLTREE" 2728045 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1159 2718350 2719043 2719689 "SPLNODE" 2721813 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1158 2717397 2717630 2717660 "SPFCAT" 2718104 T SPFCAT (NIL) -9 NIL NIL NIL) (-1157 2716134 2716344 2716608 "SPECOUT" 2717155 T SPECOUT (NIL) -7 NIL NIL NIL) (-1156 2707230 2709102 2709132 "SPADXPT" 2713808 T SPADXPT (NIL) -9 NIL 2715972 NIL) (-1155 2706991 2707031 2707100 "SPADPRSR" 2707183 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1154 2705040 2706946 2706977 "SPADAST" 2706982 T SPADAST (NIL) -8 NIL NIL NIL) (-1153 2696971 2698744 2698787 "SPACEC" 2703160 NIL SPACEC (NIL T) -9 NIL 2704976 NIL) (-1152 2695101 2696903 2696952 "SPACE3" 2696957 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1151 2693853 2694024 2694315 "SORTPAK" 2694906 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1150 2691945 2692248 2692660 "SOLVETRA" 2693517 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1149 2690995 2691217 2691478 "SOLVESER" 2691718 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1148 2686299 2687187 2688182 "SOLVERAD" 2690047 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1147 2682114 2682723 2683452 "SOLVEFOR" 2685666 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1146 2676384 2681463 2681560 "SNTSCAT" 2681565 NIL SNTSCAT (NIL T T T T) -9 NIL 2681635 NIL) (-1145 2670490 2674707 2675098 "SMTS" 2676074 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1144 2664899 2670378 2670455 "SMP" 2670460 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1143 2663058 2663359 2663757 "SMITH" 2664596 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1142 2655162 2659637 2659740 "SMATCAT" 2661091 NIL SMATCAT (NIL NIL T T T) -9 NIL 2661641 NIL) (-1141 2652102 2652925 2654103 "SMATCAT-" 2654108 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1140 2649742 2651310 2651353 "SKAGG" 2651614 NIL SKAGG (NIL T) -9 NIL 2651749 NIL) (-1139 2645932 2649215 2649399 "SINT" 2649551 T SINT (NIL) -8 NIL NIL 2649713) (-1138 2645704 2645742 2645808 "SIMPAN" 2645888 T SIMPAN (NIL) -7 NIL NIL NIL) (-1137 2644983 2645239 2645379 "SIG" 2645586 T SIG (NIL) -8 NIL NIL NIL) (-1136 2643821 2644042 2644317 "SIGNRF" 2644742 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1135 2642654 2642805 2643089 "SIGNEF" 2643650 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1134 2641960 2642237 2642361 "SIGAST" 2642552 T SIGAST (NIL) -8 NIL NIL NIL) (-1133 2639650 2640104 2640610 "SHP" 2641501 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1132 2633478 2639551 2639627 "SHDP" 2639632 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1131 2633037 2633229 2633259 "SGROUP" 2633352 T SGROUP (NIL) -9 NIL 2633414 NIL) (-1130 2632895 2632921 2632994 "SGROUP-" 2632999 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1129 2629686 2630384 2631107 "SGCF" 2632194 T SGCF (NIL) -7 NIL NIL NIL) (-1128 2624054 2629133 2629230 "SFRTCAT" 2629235 NIL SFRTCAT (NIL T T T T) -9 NIL 2629274 NIL) (-1127 2617475 2618493 2619629 "SFRGCD" 2623037 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1126 2610601 2611674 2612860 "SFQCMPK" 2616408 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1125 2610221 2610310 2610421 "SFORT" 2610542 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1124 2609339 2610061 2610182 "SEXOF" 2610187 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1123 2608446 2609220 2609288 "SEX" 2609293 T SEX (NIL) -8 NIL NIL NIL) (-1122 2604227 2604942 2605037 "SEXCAT" 2607659 NIL SEXCAT (NIL T T T T T) -9 NIL 2608219 NIL) (-1121 2601380 2604161 2604209 "SET" 2604214 NIL SET (NIL T) -8 NIL NIL NIL) (-1120 2599604 2600093 2600398 "SETMN" 2601121 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1119 2599086 2599238 2599268 "SETCAT" 2599444 T SETCAT (NIL) -9 NIL 2599554 NIL) (-1118 2598778 2598856 2598986 "SETCAT-" 2598991 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1117 2595139 2597239 2597282 "SETAGG" 2598152 NIL SETAGG (NIL T) -9 NIL 2598492 NIL) (-1116 2594597 2594713 2594950 "SETAGG-" 2594955 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1115 2594040 2594293 2594394 "SEQAST" 2594518 T SEQAST (NIL) -8 NIL NIL NIL) (-1114 2593239 2593533 2593594 "SEGXCAT" 2593880 NIL SEGXCAT (NIL T T) -9 NIL 2594000 NIL) (-1113 2592245 2592905 2593087 "SEG" 2593092 NIL SEG (NIL T) -8 NIL NIL NIL) (-1112 2591224 2591438 2591481 "SEGCAT" 2592003 NIL SEGCAT (NIL T) -9 NIL 2592224 NIL) (-1111 2590156 2590587 2590795 "SEGBIND" 2591051 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1110 2589777 2589836 2589949 "SEGBIND2" 2590091 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1109 2589350 2589578 2589655 "SEGAST" 2589722 T SEGAST (NIL) -8 NIL NIL NIL) (-1108 2588569 2588695 2588899 "SEG2" 2589194 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1107 2587940 2588504 2588551 "SDVAR" 2588556 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1106 2580191 2587710 2587840 "SDPOL" 2587845 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1105 2578784 2579050 2579369 "SCPKG" 2579906 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1104 2577948 2578120 2578312 "SCOPE" 2578614 T SCOPE (NIL) -8 NIL NIL NIL) (-1103 2577168 2577302 2577481 "SCACHE" 2577803 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1102 2576800 2576986 2577016 "SASTCAT" 2577021 T SASTCAT (NIL) -9 NIL 2577034 NIL) (-1101 2576287 2576635 2576711 "SAOS" 2576746 T SAOS (NIL) -8 NIL NIL NIL) (-1100 2575852 2575887 2576060 "SAERFFC" 2576246 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1099 2569515 2575749 2575829 "SAE" 2575834 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1098 2569108 2569143 2569302 "SAEFACT" 2569474 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1097 2567429 2567743 2568144 "RURPK" 2568774 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1096 2566066 2566372 2566677 "RULESET" 2567263 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1095 2563289 2563819 2564277 "RULE" 2565747 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1094 2562901 2563083 2563166 "RULECOLD" 2563241 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1093 2562691 2562719 2562790 "RTVALUE" 2562852 T RTVALUE (NIL) -8 NIL NIL NIL) (-1092 2562162 2562408 2562502 "RSTRCAST" 2562619 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1091 2557010 2557805 2558725 "RSETGCD" 2561361 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1090 2546240 2551319 2551416 "RSETCAT" 2555535 NIL RSETCAT (NIL T T T T) -9 NIL 2556632 NIL) (-1089 2544167 2544706 2545530 "RSETCAT-" 2545535 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1088 2536553 2537929 2539449 "RSDCMPK" 2542766 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1087 2534518 2534985 2535059 "RRCC" 2536145 NIL RRCC (NIL T T) -9 NIL 2536489 NIL) (-1086 2533869 2534043 2534322 "RRCC-" 2534327 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1085 2533312 2533565 2533666 "RPTAST" 2533790 T RPTAST (NIL) -8 NIL NIL NIL) (-1084 2506788 2516424 2516491 "RPOLCAT" 2527157 NIL RPOLCAT (NIL T T T) -9 NIL 2530317 NIL) (-1083 2498286 2500626 2503748 "RPOLCAT-" 2503753 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1082 2489221 2496497 2496979 "ROUTINE" 2497826 T ROUTINE (NIL) -8 NIL NIL NIL) (-1081 2485882 2488847 2488987 "ROMAN" 2489103 T ROMAN (NIL) -8 NIL NIL NIL) (-1080 2484126 2484742 2485002 "ROIRC" 2485687 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1079 2480344 2482628 2482658 "RNS" 2482962 T RNS (NIL) -9 NIL 2483236 NIL) (-1078 2478853 2479236 2479770 "RNS-" 2479845 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1077 2478242 2478650 2478680 "RNG" 2478685 T RNG (NIL) -9 NIL 2478706 NIL) (-1076 2477245 2477607 2477809 "RNGBIND" 2478093 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1075 2476630 2477018 2477061 "RMODULE" 2477066 NIL RMODULE (NIL T) -9 NIL 2477093 NIL) (-1074 2475466 2475560 2475896 "RMCAT2" 2476531 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1073 2472316 2474812 2475109 "RMATRIX" 2475228 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1072 2465143 2467403 2467518 "RMATCAT" 2470877 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2471859 NIL) (-1071 2464518 2464665 2464972 "RMATCAT-" 2464977 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1070 2464133 2464305 2464348 "RLINSET" 2464410 NIL RLINSET (NIL T) -9 NIL 2464454 NIL) (-1069 2463700 2463775 2463903 "RINTERP" 2464052 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1068 2462744 2463298 2463328 "RING" 2463384 T RING (NIL) -9 NIL 2463476 NIL) (-1067 2462536 2462580 2462677 "RING-" 2462682 NIL RING- (NIL T) -8 NIL NIL NIL) (-1066 2461377 2461614 2461872 "RIDIST" 2462300 T RIDIST (NIL) -7 NIL NIL NIL) (-1065 2452666 2460845 2461051 "RGCHAIN" 2461225 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1064 2452002 2452408 2452449 "RGBCSPC" 2452507 NIL RGBCSPC (NIL T) -9 NIL 2452559 NIL) (-1063 2451146 2451527 2451568 "RGBCMDL" 2451800 NIL RGBCMDL (NIL T) -9 NIL 2451914 NIL) (-1062 2448140 2448754 2449424 "RF" 2450510 NIL RF (NIL T) -7 NIL NIL NIL) (-1061 2447786 2447849 2447952 "RFFACTOR" 2448071 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1060 2447511 2447546 2447643 "RFFACT" 2447745 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1059 2445628 2445992 2446374 "RFDIST" 2447151 T RFDIST (NIL) -7 NIL NIL NIL) (-1058 2445081 2445173 2445336 "RETSOL" 2445530 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1057 2444717 2444797 2444840 "RETRACT" 2444973 NIL RETRACT (NIL T) -9 NIL 2445060 NIL) (-1056 2444566 2444591 2444678 "RETRACT-" 2444683 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1055 2444168 2444388 2444458 "RETAST" 2444518 T RETAST (NIL) -8 NIL NIL NIL) (-1054 2436910 2443821 2443948 "RESULT" 2444063 T RESULT (NIL) -8 NIL NIL NIL) (-1053 2435501 2436179 2436378 "RESRING" 2436813 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1052 2435137 2435186 2435284 "RESLATC" 2435438 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1051 2434842 2434877 2434984 "REPSQ" 2435096 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1050 2432264 2432844 2433446 "REP" 2434262 T REP (NIL) -7 NIL NIL NIL) (-1049 2431961 2431996 2432107 "REPDB" 2432223 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1048 2425861 2427250 2428473 "REP2" 2430773 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1047 2422238 2422919 2423727 "REP1" 2425088 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1046 2414934 2420379 2420835 "REGSET" 2421868 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1045 2413699 2414082 2414332 "REF" 2414719 NIL REF (NIL T) -8 NIL NIL NIL) (-1044 2413076 2413179 2413346 "REDORDER" 2413583 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1043 2409044 2412289 2412516 "RECLOS" 2412904 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1042 2408096 2408277 2408492 "REALSOLV" 2408851 T REALSOLV (NIL) -7 NIL NIL NIL) (-1041 2407942 2407983 2408013 "REAL" 2408018 T REAL (NIL) -9 NIL 2408053 NIL) (-1040 2404425 2405227 2406111 "REAL0Q" 2407107 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1039 2400026 2401014 2402075 "REAL0" 2403406 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1038 2399497 2399743 2399837 "RDUCEAST" 2399954 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1037 2398902 2398974 2399181 "RDIV" 2399419 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1036 2397970 2398144 2398357 "RDIST" 2398724 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1035 2396567 2396854 2397226 "RDETRS" 2397678 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1034 2394379 2394833 2395371 "RDETR" 2396109 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1033 2393004 2393282 2393679 "RDEEFS" 2394095 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1032 2391513 2391819 2392244 "RDEEF" 2392692 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1031 2385560 2388480 2388510 "RCFIELD" 2389805 T RCFIELD (NIL) -9 NIL 2390536 NIL) (-1030 2383624 2384128 2384824 "RCFIELD-" 2384899 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1029 2379867 2381697 2381740 "RCAGG" 2382824 NIL RCAGG (NIL T) -9 NIL 2383289 NIL) (-1028 2379495 2379589 2379752 "RCAGG-" 2379757 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1027 2378830 2378942 2379107 "RATRET" 2379379 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1026 2378383 2378450 2378571 "RATFACT" 2378758 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1025 2377691 2377811 2377963 "RANDSRC" 2378253 T RANDSRC (NIL) -7 NIL NIL NIL) (-1024 2377425 2377469 2377542 "RADUTIL" 2377640 T RADUTIL (NIL) -7 NIL NIL NIL) (-1023 2370253 2376256 2376567 "RADIX" 2377148 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1022 2360713 2370095 2370225 "RADFF" 2370230 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1021 2360360 2360435 2360465 "RADCAT" 2360625 T RADCAT (NIL) -9 NIL NIL NIL) (-1020 2360142 2360190 2360290 "RADCAT-" 2360295 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1019 2358242 2359912 2360004 "QUEUE" 2360085 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1018 2354503 2358175 2358223 "QUAT" 2358228 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1017 2354134 2354177 2354308 "QUATCT2" 2354454 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1016 2346960 2350584 2350626 "QUATCAT" 2351417 NIL QUATCAT (NIL T) -9 NIL 2352183 NIL) (-1015 2343099 2344136 2345526 "QUATCAT-" 2345622 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1014 2340538 2342147 2342190 "QUAGG" 2342571 NIL QUAGG (NIL T) -9 NIL 2342746 NIL) (-1013 2340140 2340360 2340430 "QQUTAST" 2340490 T QQUTAST (NIL) -8 NIL NIL NIL) (-1012 2339153 2339653 2339818 "QFORM" 2340021 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1011 2329540 2335055 2335097 "QFCAT" 2335765 NIL QFCAT (NIL T) -9 NIL 2336766 NIL) (-1010 2325107 2326308 2327902 "QFCAT-" 2327998 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1009 2324738 2324781 2324912 "QFCAT2" 2325058 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1008 2324193 2324303 2324435 "QEQUAT" 2324628 T QEQUAT (NIL) -8 NIL NIL NIL) (-1007 2317319 2318392 2319578 "QCMPACK" 2323126 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1006 2314857 2315305 2315735 "QALGSET" 2316974 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1005 2314092 2314268 2314504 "QALGSET2" 2314675 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1004 2312777 2313001 2313320 "PWFFINTB" 2313865 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1003 2310952 2311120 2311476 "PUSHVAR" 2312591 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1002 2306841 2307895 2307938 "PTRANFN" 2309849 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1001 2305232 2305523 2305847 "PTPACK" 2306552 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1000 2304861 2304918 2305029 "PTFUNC2" 2305169 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-999 2299288 2303683 2303724 "PTCAT" 2304020 NIL PTCAT (NIL T) -9 NIL 2304173 NIL) (-998 2298946 2298981 2299105 "PSQFR" 2299247 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-997 2297541 2297839 2298173 "PSEUDLIN" 2298644 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-996 2284304 2286675 2288999 "PSETPK" 2295301 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-995 2277322 2280062 2280158 "PSETCAT" 2283179 NIL PSETCAT (NIL T T T T) -9 NIL 2283993 NIL) (-994 2275158 2275792 2276613 "PSETCAT-" 2276618 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-993 2274507 2274672 2274700 "PSCURVE" 2274968 T PSCURVE (NIL) -9 NIL 2275135 NIL) (-992 2270491 2272007 2272072 "PSCAT" 2272916 NIL PSCAT (NIL T T T) -9 NIL 2273156 NIL) (-991 2269554 2269770 2270170 "PSCAT-" 2270175 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-990 2267913 2268623 2268886 "PRTITION" 2269311 T PRTITION (NIL) -8 NIL NIL NIL) (-989 2267388 2267634 2267726 "PRTDAST" 2267841 T PRTDAST (NIL) -8 NIL NIL NIL) (-988 2256478 2258692 2260880 "PRS" 2265250 NIL PRS (NIL T T) -7 NIL NIL NIL) (-987 2254263 2255800 2255840 "PRQAGG" 2256023 NIL PRQAGG (NIL T) -9 NIL 2256125 NIL) (-986 2253599 2253904 2253932 "PROPLOG" 2254071 T PROPLOG (NIL) -9 NIL 2254186 NIL) (-985 2253203 2253260 2253383 "PROPFUN2" 2253522 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-984 2252518 2252639 2252811 "PROPFUN1" 2253064 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-983 2250699 2251265 2251562 "PROPFRML" 2252254 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-982 2250168 2250275 2250403 "PROPERTY" 2250591 T PROPERTY (NIL) -8 NIL NIL NIL) (-981 2244226 2248334 2249154 "PRODUCT" 2249394 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-980 2241504 2243684 2243918 "PR" 2244037 NIL PR (NIL T T) -8 NIL NIL NIL) (-979 2241300 2241332 2241391 "PRINT" 2241465 T PRINT (NIL) -7 NIL NIL NIL) (-978 2240640 2240757 2240909 "PRIMES" 2241180 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-977 2238705 2239106 2239572 "PRIMELT" 2240219 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-976 2238434 2238483 2238511 "PRIMCAT" 2238635 T PRIMCAT (NIL) -9 NIL NIL NIL) (-975 2234551 2238372 2238417 "PRIMARR" 2238422 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-974 2233558 2233736 2233964 "PRIMARR2" 2234369 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-973 2233201 2233257 2233368 "PREASSOC" 2233496 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-972 2232676 2232809 2232837 "PPCURVE" 2233042 T PPCURVE (NIL) -9 NIL 2233178 NIL) (-971 2232271 2232471 2232554 "PORTNUM" 2232613 T PORTNUM (NIL) -8 NIL NIL NIL) (-970 2229630 2230029 2230621 "POLYROOT" 2231852 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-969 2223536 2229234 2229394 "POLY" 2229503 NIL POLY (NIL T) -8 NIL NIL NIL) (-968 2222919 2222977 2223211 "POLYLIFT" 2223472 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-967 2219194 2219643 2220272 "POLYCATQ" 2222464 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-966 2205536 2210941 2211006 "POLYCAT" 2214520 NIL POLYCAT (NIL T T T) -9 NIL 2216398 NIL) (-965 2198985 2200847 2203231 "POLYCAT-" 2203236 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-964 2198572 2198640 2198760 "POLY2UP" 2198911 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-963 2198204 2198261 2198370 "POLY2" 2198509 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-962 2196889 2197128 2197404 "POLUTIL" 2197978 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-961 2195244 2195521 2195852 "POLTOPOL" 2196611 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-960 2190711 2195180 2195226 "POINT" 2195231 NIL POINT (NIL T) -8 NIL NIL NIL) (-959 2188898 2189255 2189630 "PNTHEORY" 2190356 T PNTHEORY (NIL) -7 NIL NIL NIL) (-958 2187356 2187653 2188052 "PMTOOLS" 2188596 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-957 2186949 2187027 2187144 "PMSYM" 2187272 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-956 2186457 2186526 2186701 "PMQFCAT" 2186874 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-955 2185812 2185922 2186078 "PMPRED" 2186334 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-954 2185205 2185291 2185453 "PMPREDFS" 2185713 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-953 2183869 2184077 2184455 "PMPLCAT" 2184967 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-952 2183401 2183480 2183632 "PMLSAGG" 2183784 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-951 2182874 2182950 2183132 "PMKERNEL" 2183319 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-950 2182491 2182566 2182679 "PMINS" 2182793 NIL PMINS (NIL T) -7 NIL NIL NIL) (-949 2181933 2182002 2182211 "PMFS" 2182416 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-948 2181161 2181279 2181484 "PMDOWN" 2181810 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-947 2180328 2180486 2180667 "PMASS" 2181000 T PMASS (NIL) -7 NIL NIL NIL) (-946 2179601 2179711 2179874 "PMASSFS" 2180215 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-945 2179256 2179324 2179418 "PLOTTOOL" 2179527 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-944 2173863 2175067 2176215 "PLOT" 2178128 T PLOT (NIL) -8 NIL NIL NIL) (-943 2169667 2170711 2171632 "PLOT3D" 2172962 T PLOT3D (NIL) -8 NIL NIL NIL) (-942 2168579 2168756 2168991 "PLOT1" 2169471 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-941 2143970 2148645 2153496 "PLEQN" 2163845 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-940 2143288 2143410 2143590 "PINTERP" 2143835 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-939 2142981 2143028 2143131 "PINTERPA" 2143235 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-938 2142197 2142745 2142832 "PI" 2142872 T PI (NIL) -8 NIL NIL 2142939) (-937 2140480 2141455 2141483 "PID" 2141665 T PID (NIL) -9 NIL 2141799 NIL) (-936 2140231 2140268 2140343 "PICOERCE" 2140437 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-935 2139551 2139690 2139866 "PGROEB" 2140087 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-934 2135138 2135952 2136857 "PGE" 2138666 T PGE (NIL) -7 NIL NIL NIL) (-933 2133261 2133508 2133874 "PGCD" 2134855 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-932 2132599 2132702 2132863 "PFRPAC" 2133145 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-931 2129239 2131147 2131500 "PFR" 2132278 NIL PFR (NIL T) -8 NIL NIL NIL) (-930 2127628 2127872 2128197 "PFOTOOLS" 2128986 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-929 2126161 2126400 2126751 "PFOQ" 2127385 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-928 2124662 2124874 2125230 "PFO" 2125945 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-927 2121215 2124551 2124620 "PF" 2124625 NIL PF (NIL NIL) -8 NIL NIL NIL) (-926 2118535 2119806 2119834 "PFECAT" 2120419 T PFECAT (NIL) -9 NIL 2120803 NIL) (-925 2117980 2118134 2118348 "PFECAT-" 2118353 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-924 2116583 2116835 2117136 "PFBRU" 2117729 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-923 2114449 2114801 2115233 "PFBR" 2116234 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-922 2110495 2111961 2112608 "PERM" 2113835 NIL PERM (NIL T) -8 NIL NIL NIL) (-921 2105729 2106702 2107572 "PERMGRP" 2109658 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-920 2103848 2104808 2104849 "PERMCAT" 2105249 NIL PERMCAT (NIL T) -9 NIL 2105547 NIL) (-919 2103501 2103542 2103666 "PERMAN" 2103801 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-918 2100991 2103166 2103288 "PENDTREE" 2103412 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-917 2099920 2100135 2100176 "PDSPC" 2100709 NIL PDSPC (NIL T) -9 NIL 2100954 NIL) (-916 2099023 2099241 2099603 "PDSPC-" 2099608 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-915 2097905 2098673 2098714 "PDRING" 2098719 NIL PDRING (NIL T) -9 NIL 2098747 NIL) (-914 2096792 2097410 2097464 "PDMOD" 2097469 NIL PDMOD (NIL T T) -9 NIL 2097573 NIL) (-913 2094007 2094785 2095453 "PDEPROB" 2096144 T PDEPROB (NIL) -8 NIL NIL NIL) (-912 2091552 2092056 2092611 "PDEPACK" 2093472 T PDEPACK (NIL) -7 NIL NIL NIL) (-911 2090464 2090654 2090905 "PDECOMP" 2091351 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-910 2088029 2088872 2088900 "PDECAT" 2089687 T PDECAT (NIL) -9 NIL 2090400 NIL) (-909 2087658 2087713 2087767 "PDDOM" 2087932 NIL PDDOM (NIL T T) -9 NIL 2088012 NIL) (-908 2087477 2087507 2087614 "PDDOM-" 2087619 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-907 2087228 2087261 2087351 "PCOMP" 2087438 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-906 2085406 2086029 2086326 "PBWLB" 2086957 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-905 2077879 2079479 2080817 "PATTERN" 2084089 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-904 2077511 2077568 2077677 "PATTERN2" 2077816 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-903 2075268 2075656 2076113 "PATTERN1" 2077100 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-902 2072636 2073217 2073698 "PATRES" 2074833 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-901 2072200 2072267 2072399 "PATRES2" 2072563 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-900 2070083 2070488 2070895 "PATMATCH" 2071867 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-899 2069579 2069788 2069829 "PATMAB" 2069936 NIL PATMAB (NIL T) -9 NIL 2070019 NIL) (-898 2068097 2068433 2068691 "PATLRES" 2069384 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-897 2067643 2067766 2067807 "PATAB" 2067812 NIL PATAB (NIL T) -9 NIL 2067984 NIL) (-896 2065825 2066220 2066643 "PARTPERM" 2067240 T PARTPERM (NIL) -7 NIL NIL NIL) (-895 2065446 2065509 2065611 "PARSURF" 2065756 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-894 2065078 2065135 2065244 "PARSU2" 2065383 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-893 2064842 2064882 2064949 "PARSER" 2065031 T PARSER (NIL) -7 NIL NIL NIL) (-892 2064463 2064526 2064628 "PARSCURV" 2064773 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-891 2064095 2064152 2064261 "PARSC2" 2064400 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-890 2063734 2063792 2063889 "PARPCURV" 2064031 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-889 2063366 2063423 2063532 "PARPC2" 2063671 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-888 2062427 2062739 2062921 "PARAMAST" 2063204 T PARAMAST (NIL) -8 NIL NIL NIL) (-887 2061947 2062033 2062152 "PAN2EXPR" 2062328 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-886 2060724 2061068 2061296 "PALETTE" 2061739 T PALETTE (NIL) -8 NIL NIL NIL) (-885 2059117 2059729 2060089 "PAIR" 2060410 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-884 2052709 2058374 2058569 "PADICRC" 2058971 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-883 2045625 2052053 2052238 "PADICRAT" 2052556 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-882 2043940 2045562 2045607 "PADIC" 2045612 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-881 2041036 2042600 2042640 "PADICCT" 2043221 NIL PADICCT (NIL NIL) -9 NIL 2043503 NIL) (-880 2039993 2040193 2040461 "PADEPAC" 2040823 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-879 2039205 2039338 2039544 "PADE" 2039855 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-878 2037592 2038413 2038693 "OWP" 2039009 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-877 2037085 2037298 2037395 "OVERSET" 2037515 T OVERSET (NIL) -8 NIL NIL NIL) (-876 2036131 2036690 2036862 "OVAR" 2036953 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-875 2035395 2035516 2035677 "OUT" 2035990 T OUT (NIL) -7 NIL NIL NIL) (-874 2024267 2026504 2028704 "OUTFORM" 2033215 T OUTFORM (NIL) -8 NIL NIL NIL) (-873 2023603 2023864 2023991 "OUTBFILE" 2024160 T OUTBFILE (NIL) -8 NIL NIL NIL) (-872 2022910 2023075 2023103 "OUTBCON" 2023421 T OUTBCON (NIL) -9 NIL 2023587 NIL) (-871 2022511 2022623 2022780 "OUTBCON-" 2022785 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-870 2021891 2022240 2022329 "OSI" 2022442 T OSI (NIL) -8 NIL NIL NIL) (-869 2021407 2021745 2021773 "OSGROUP" 2021778 T OSGROUP (NIL) -9 NIL 2021800 NIL) (-868 2020152 2020379 2020664 "ORTHPOL" 2021154 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-867 2017703 2019987 2020108 "OREUP" 2020113 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-866 2015106 2017394 2017521 "ORESUP" 2017645 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-865 2012634 2013134 2013695 "OREPCTO" 2014595 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-864 2006306 2008507 2008548 "OREPCAT" 2010896 NIL OREPCAT (NIL T) -9 NIL 2012000 NIL) (-863 2003453 2004235 2005293 "OREPCAT-" 2005298 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-862 2002590 2002888 2002916 "ORDSET" 2003225 T ORDSET (NIL) -9 NIL 2003389 NIL) (-861 2002021 2002169 2002393 "ORDSET-" 2002398 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-860 2000572 2001363 2001391 "ORDRING" 2001593 T ORDRING (NIL) -9 NIL 2001718 NIL) (-859 2000217 2000311 2000455 "ORDRING-" 2000460 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 1999583 2000046 2000074 "ORDMON" 2000079 T ORDMON (NIL) -9 NIL 2000100 NIL) (-857 1998745 1998892 1999087 "ORDFUNS" 1999432 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1998069 1998488 1998516 "ORDFIN" 1998581 T ORDFIN (NIL) -9 NIL 1998655 NIL) (-855 1994628 1996655 1997064 "ORDCOMP" 1997693 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1993894 1994021 1994207 "ORDCOMP2" 1994488 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1990475 1991385 1992199 "OPTPROB" 1993100 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1987277 1987916 1988620 "OPTPACK" 1989791 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1984950 1985716 1985744 "OPTCAT" 1986563 T OPTCAT (NIL) -9 NIL 1987213 NIL) (-850 1984334 1984627 1984732 "OPSIG" 1984865 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1984102 1984141 1984207 "OPQUERY" 1984288 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1981233 1982413 1982917 "OP" 1983631 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1980593 1980819 1980860 "OPERCAT" 1981072 NIL OPERCAT (NIL T) -9 NIL 1981169 NIL) (-846 1980348 1980404 1980521 "OPERCAT-" 1980526 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1977161 1979145 1979514 "ONECOMP" 1980012 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1976466 1976581 1976755 "ONECOMP2" 1977033 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1975885 1975991 1976121 "OMSERVER" 1976356 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1972747 1975325 1975365 "OMSAGG" 1975426 NIL OMSAGG (NIL T) -9 NIL 1975490 NIL) (-841 1971370 1971633 1971915 "OMPKG" 1972485 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1970800 1970903 1970931 "OM" 1971230 T OM (NIL) -9 NIL NIL NIL) (-839 1969347 1970349 1970518 "OMLO" 1970681 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1968307 1968454 1968674 "OMEXPR" 1969173 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1967598 1967853 1967989 "OMERR" 1968191 T OMERR (NIL) -8 NIL NIL NIL) (-836 1966749 1967019 1967179 "OMERRK" 1967458 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1966200 1966426 1966534 "OMENC" 1966661 T OMENC (NIL) -8 NIL NIL NIL) (-834 1960095 1961280 1962451 "OMDEV" 1965049 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1959164 1959335 1959529 "OMCONN" 1959921 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1957671 1958647 1958675 "OINTDOM" 1958680 T OINTDOM (NIL) -9 NIL 1958701 NIL) (-831 1955009 1956359 1956696 "OFMONOID" 1957366 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1954381 1954946 1954991 "ODVAR" 1954996 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1951804 1954126 1954281 "ODR" 1954286 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1944109 1951580 1951706 "ODPOL" 1951711 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1937907 1943981 1944086 "ODP" 1944091 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1936673 1936888 1937163 "ODETOOLS" 1937681 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1933640 1934298 1935014 "ODESYS" 1936006 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1928522 1929430 1930455 "ODERTRIC" 1932715 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1927948 1928030 1928224 "ODERED" 1928434 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1924836 1925384 1926061 "ODERAT" 1927371 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1921795 1922260 1922857 "ODEPRRIC" 1924365 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1919738 1920334 1920820 "ODEPROB" 1921329 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1916258 1916743 1917390 "ODEPRIM" 1919217 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1915507 1915609 1915869 "ODEPAL" 1916150 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1911669 1912460 1913324 "ODEPACK" 1914663 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1910730 1910837 1911059 "ODEINT" 1911558 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1904831 1906256 1907703 "ODEIFTBL" 1909303 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1900229 1901015 1901967 "ODEEF" 1903990 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1899578 1899667 1899890 "ODECONST" 1900134 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1897689 1898350 1898378 "ODECAT" 1898983 T ODECAT (NIL) -9 NIL 1899514 NIL) (-811 1894544 1897394 1897516 "OCT" 1897599 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1894182 1894225 1894352 "OCTCT2" 1894495 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1888817 1891252 1891292 "OC" 1892389 NIL OC (NIL T) -9 NIL 1893247 NIL) (-808 1886044 1886792 1887782 "OC-" 1887876 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1885382 1885850 1885878 "OCAMON" 1885883 T OCAMON (NIL) -9 NIL 1885904 NIL) (-806 1884899 1885240 1885268 "OASGP" 1885273 T OASGP (NIL) -9 NIL 1885293 NIL) (-805 1884146 1884635 1884663 "OAMONS" 1884703 T OAMONS (NIL) -9 NIL 1884746 NIL) (-804 1883546 1883979 1884007 "OAMON" 1884012 T OAMON (NIL) -9 NIL 1884032 NIL) (-803 1882790 1883308 1883336 "OAGROUP" 1883341 T OAGROUP (NIL) -9 NIL 1883361 NIL) (-802 1882480 1882530 1882618 "NUMTUBE" 1882734 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1876053 1877571 1879107 "NUMQUAD" 1880964 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1871809 1872797 1873822 "NUMODE" 1875048 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1869150 1870030 1870058 "NUMINT" 1870981 T NUMINT (NIL) -9 NIL 1871745 NIL) (-798 1868098 1868295 1868513 "NUMFMT" 1868952 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1854457 1857402 1859934 "NUMERIC" 1865605 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1848827 1853906 1854001 "NTSCAT" 1854006 NIL NTSCAT (NIL T T T T) -9 NIL 1854045 NIL) (-795 1848021 1848186 1848379 "NTPOLFN" 1848666 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1835822 1844846 1845658 "NSUP" 1847242 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1835454 1835511 1835620 "NSUP2" 1835759 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1825404 1835228 1835361 "NSMP" 1835366 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1823836 1824137 1824494 "NREP" 1825092 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1822427 1822679 1823037 "NPCOEF" 1823579 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1821493 1821608 1821824 "NORMRETR" 1822308 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1819534 1819824 1820233 "NORMPK" 1821201 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1819219 1819247 1819371 "NORMMA" 1819500 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1819019 1819176 1819205 "NONE" 1819210 T NONE (NIL) -8 NIL NIL NIL) (-785 1818808 1818837 1818906 "NONE1" 1818983 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1818305 1818367 1818546 "NODE1" 1818740 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1816586 1817437 1817692 "NNI" 1818039 T NNI (NIL) -8 NIL NIL 1818274) (-782 1815006 1815319 1815683 "NLINSOL" 1816254 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1811247 1812242 1813141 "NIPROB" 1814127 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1810004 1810238 1810540 "NFINTBAS" 1811009 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1809178 1809654 1809695 "NETCLT" 1809867 NIL NETCLT (NIL T) -9 NIL 1809949 NIL) (-778 1807886 1808117 1808398 "NCODIV" 1808946 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1807648 1807685 1807760 "NCNTFRAC" 1807843 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1805828 1806192 1806612 "NCEP" 1807273 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1804665 1805438 1805466 "NASRING" 1805576 T NASRING (NIL) -9 NIL 1805656 NIL) (-774 1804460 1804504 1804598 "NASRING-" 1804603 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1803553 1804078 1804106 "NARNG" 1804223 T NARNG (NIL) -9 NIL 1804314 NIL) (-772 1803245 1803312 1803446 "NARNG-" 1803451 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1802124 1802331 1802566 "NAGSP" 1803030 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1793396 1795080 1796753 "NAGS" 1800471 T NAGS (NIL) -7 NIL NIL NIL) (-769 1791944 1792252 1792583 "NAGF07" 1793085 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1786482 1787773 1789080 "NAGF04" 1790657 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1779450 1781064 1782697 "NAGF02" 1784869 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1774674 1775774 1776891 "NAGF01" 1778353 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1768302 1769868 1771453 "NAGE04" 1773109 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1759471 1761592 1763722 "NAGE02" 1766192 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1755424 1756371 1757335 "NAGE01" 1758527 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1753219 1753753 1754311 "NAGD03" 1754886 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1744969 1746897 1748851 "NAGD02" 1751285 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1738780 1740205 1741645 "NAGD01" 1743549 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1734989 1735811 1736648 "NAGC06" 1737963 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1733454 1733786 1734142 "NAGC05" 1734653 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1732830 1732949 1733093 "NAGC02" 1733330 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1731775 1732358 1732398 "NAALG" 1732477 NIL NAALG (NIL T) -9 NIL 1732538 NIL) (-755 1731610 1731639 1731729 "NAALG-" 1731734 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1725560 1726668 1727855 "MULTSQFR" 1730506 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1724879 1724954 1725138 "MULTFACT" 1725472 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1717550 1721464 1721517 "MTSCAT" 1722587 NIL MTSCAT (NIL T T) -9 NIL 1723102 NIL) (-751 1717262 1717316 1717408 "MTHING" 1717490 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1717054 1717087 1717147 "MSYSCMD" 1717222 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1713136 1715809 1716129 "MSET" 1716767 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1710205 1712697 1712738 "MSETAGG" 1712743 NIL MSETAGG (NIL T) -9 NIL 1712777 NIL) (-747 1706047 1707584 1708329 "MRING" 1709505 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1705613 1705680 1705811 "MRF2" 1705974 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1705231 1705266 1705410 "MRATFAC" 1705572 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1702843 1703138 1703569 "MPRFF" 1704936 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1696864 1702697 1702794 "MPOLY" 1702799 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1696354 1696389 1696597 "MPCPF" 1696823 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1695868 1695911 1696095 "MPC3" 1696305 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1695063 1695144 1695365 "MPC2" 1695783 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1693364 1693701 1694091 "MONOTOOL" 1694723 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1692575 1692892 1692920 "MONOID" 1693139 T MONOID (NIL) -9 NIL 1693286 NIL) (-737 1692121 1692240 1692421 "MONOID-" 1692426 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1681711 1687941 1688000 "MONOGEN" 1688674 NIL MONOGEN (NIL T T) -9 NIL 1689130 NIL) (-735 1678929 1679664 1680664 "MONOGEN-" 1680783 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1677748 1678194 1678222 "MONADWU" 1678614 T MONADWU (NIL) -9 NIL 1678852 NIL) (-733 1677120 1677279 1677527 "MONADWU-" 1677532 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1676465 1676709 1676737 "MONAD" 1676944 T MONAD (NIL) -9 NIL 1677056 NIL) (-731 1676150 1676228 1676360 "MONAD-" 1676365 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1674439 1675063 1675342 "MOEBIUS" 1675903 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1673703 1674107 1674147 "MODULE" 1674152 NIL MODULE (NIL T) -9 NIL 1674191 NIL) (-728 1673271 1673367 1673557 "MODULE-" 1673562 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1670951 1671635 1671962 "MODRING" 1673095 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1667895 1669056 1669577 "MODOP" 1670480 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1666483 1666962 1667239 "MODMONOM" 1667758 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1656251 1664774 1665188 "MODMON" 1666120 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1653407 1655095 1655371 "MODFIELD" 1656126 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1652384 1652688 1652878 "MMLFORM" 1653237 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1651910 1651953 1652132 "MMAP" 1652335 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1649975 1650742 1650783 "MLO" 1651206 NIL MLO (NIL T) -9 NIL 1651448 NIL) (-719 1647341 1647857 1648459 "MLIFT" 1649456 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1646732 1646816 1646970 "MKUCFUNC" 1647252 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1646331 1646401 1646524 "MKRECORD" 1646655 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1645378 1645540 1645768 "MKFUNC" 1646142 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1644766 1644870 1645026 "MKFLCFN" 1645261 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1644043 1644145 1644330 "MKBCFUNC" 1644659 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1640632 1643597 1643733 "MINT" 1643927 T MINT (NIL) -8 NIL NIL NIL) (-712 1639444 1639687 1639964 "MHROWRED" 1640387 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1634824 1637979 1638384 "MFLOAT" 1639059 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1634181 1634257 1634428 "MFINFACT" 1634736 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1630496 1631344 1632228 "MESH" 1633317 T MESH (NIL) -7 NIL NIL NIL) (-708 1628886 1629198 1629551 "MDDFACT" 1630183 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1625655 1628017 1628058 "MDAGG" 1628313 NIL MDAGG (NIL T) -9 NIL 1628456 NIL) (-706 1614349 1624948 1625155 "MCMPLX" 1625468 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1613486 1613632 1613833 "MCDEN" 1614198 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1611376 1611646 1612026 "MCALCFN" 1613216 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1610301 1610541 1610774 "MAYBE" 1611182 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1607913 1608436 1608998 "MATSTOR" 1609772 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1603824 1607285 1607533 "MATRIX" 1607698 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1599590 1600297 1601033 "MATLIN" 1603181 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1589415 1592647 1592724 "MATCAT" 1597756 NIL MATCAT (NIL T T T) -9 NIL 1599228 NIL) (-698 1585608 1586678 1588091 "MATCAT-" 1588096 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1584202 1584355 1584688 "MATCAT2" 1585443 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1582314 1582638 1583022 "MAPPKG3" 1583877 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1581295 1581468 1581690 "MAPPKG2" 1582138 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1579794 1580078 1580405 "MAPPKG1" 1581001 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1578873 1579200 1579377 "MAPPAST" 1579637 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1578484 1578542 1578665 "MAPHACK3" 1578809 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1578076 1578137 1578251 "MAPHACK2" 1578416 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1577514 1577617 1577759 "MAPHACK1" 1577967 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1575593 1576214 1576518 "MAGMA" 1577242 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1575072 1575317 1575408 "MACROAST" 1575522 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1571492 1573311 1573772 "M3D" 1574644 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1565541 1569803 1569844 "LZSTAGG" 1570626 NIL LZSTAGG (NIL T) -9 NIL 1570921 NIL) (-685 1561499 1562672 1564129 "LZSTAGG-" 1564134 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1558586 1559390 1559877 "LWORD" 1561044 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1558162 1558390 1558465 "LSTAST" 1558531 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1551052 1557933 1558067 "LSQM" 1558072 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1550276 1550415 1550643 "LSPP" 1550907 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1548088 1548389 1548845 "LSMP" 1549965 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1544867 1545541 1546271 "LSMP1" 1547390 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1538695 1543984 1544025 "LSAGG" 1544087 NIL LSAGG (NIL T) -9 NIL 1544165 NIL) (-677 1535390 1536314 1537527 "LSAGG-" 1537532 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1532989 1534534 1534783 "LPOLY" 1535185 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1532571 1532656 1532779 "LPEFRAC" 1532898 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1530892 1531665 1531918 "LO" 1532403 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1530530 1530642 1530670 "LOGIC" 1530781 T LOGIC (NIL) -9 NIL 1530862 NIL) (-672 1530392 1530415 1530486 "LOGIC-" 1530491 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1529585 1529725 1529918 "LODOOPS" 1530248 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1527008 1529501 1529567 "LODO" 1529572 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1525546 1525781 1526134 "LODOF" 1526755 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1521750 1524181 1524222 "LODOCAT" 1524660 NIL LODOCAT (NIL T) -9 NIL 1524871 NIL) (-667 1521483 1521541 1521668 "LODOCAT-" 1521673 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1518803 1521324 1521442 "LODO2" 1521447 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1516238 1518740 1518785 "LODO1" 1518790 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1515119 1515284 1515589 "LODEEF" 1516061 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1510396 1513285 1513326 "LNAGG" 1514188 NIL LNAGG (NIL T) -9 NIL 1514623 NIL) (-662 1509543 1509757 1510099 "LNAGG-" 1510104 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1505679 1506468 1507107 "LMOPS" 1508958 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1505068 1505456 1505497 "LMODULE" 1505502 NIL LMODULE (NIL T) -9 NIL 1505528 NIL) (-659 1502268 1504713 1504836 "LMDICT" 1504978 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1501886 1502058 1502099 "LLINSET" 1502160 NIL LLINSET (NIL T) -9 NIL 1502204 NIL) (-657 1501585 1501794 1501854 "LITERAL" 1501859 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1494750 1500519 1500823 "LIST" 1501314 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1494275 1494349 1494488 "LIST3" 1494670 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1493282 1493460 1493688 "LIST2" 1494093 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1491416 1491728 1492127 "LIST2MAP" 1492929 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1491047 1491235 1491276 "LINSET" 1491281 NIL LINSET (NIL T) -9 NIL 1491315 NIL) (-651 1489460 1490074 1490115 "LINEXP" 1490605 NIL LINEXP (NIL T) -9 NIL 1490878 NIL) (-650 1488037 1488297 1488608 "LINDEP" 1489212 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1484804 1485523 1486300 "LIMITRF" 1487292 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1483107 1483403 1483812 "LIMITPS" 1484499 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1477535 1482618 1482846 "LIE" 1482928 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1476469 1476938 1476978 "LIECAT" 1477118 NIL LIECAT (NIL T) -9 NIL 1477269 NIL) (-645 1476310 1476337 1476425 "LIECAT-" 1476430 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1468901 1475850 1476006 "LIB" 1476174 T LIB (NIL) -8 NIL NIL NIL) (-643 1464536 1465419 1466354 "LGROBP" 1468018 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1462534 1462808 1463158 "LF" 1464257 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1461374 1462066 1462094 "LFCAT" 1462301 T LFCAT (NIL) -9 NIL 1462440 NIL) (-640 1458276 1458906 1459594 "LEXTRIPK" 1460738 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1455020 1455846 1456349 "LEXP" 1457856 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1454496 1454741 1454833 "LETAST" 1454948 T LETAST (NIL) -8 NIL NIL NIL) (-637 1452894 1453207 1453608 "LEADCDET" 1454178 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1452084 1452158 1452387 "LAZM3PK" 1452815 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1447001 1450161 1450699 "LAUPOL" 1451596 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1446580 1446624 1446785 "LAPLACE" 1446951 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1444519 1445681 1445932 "LA" 1446413 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1443499 1444083 1444124 "LALG" 1444186 NIL LALG (NIL T) -9 NIL 1444245 NIL) (-631 1443213 1443272 1443408 "LALG-" 1443413 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1443048 1443072 1443113 "KVTFROM" 1443175 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1441971 1442415 1442600 "KTVLOGIC" 1442883 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1441806 1441830 1441871 "KRCFROM" 1441933 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1440710 1440897 1441196 "KOVACIC" 1441606 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1440545 1440569 1440610 "KONVERT" 1440672 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1440380 1440404 1440445 "KOERCE" 1440507 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1438211 1438973 1439350 "KERNEL" 1440036 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1437707 1437788 1437920 "KERNEL2" 1438125 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1431417 1436184 1436238 "KDAGG" 1436615 NIL KDAGG (NIL T T) -9 NIL 1436821 NIL) (-621 1430946 1431070 1431275 "KDAGG-" 1431280 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1424094 1430607 1430762 "KAFILE" 1430824 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1418522 1423605 1423833 "JORDAN" 1423915 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1417901 1418171 1418292 "JOINAST" 1418421 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1417747 1417806 1417861 "JAVACODE" 1417866 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1413973 1415924 1415978 "IXAGG" 1416907 NIL IXAGG (NIL T T) -9 NIL 1417366 NIL) (-615 1412892 1413198 1413617 "IXAGG-" 1413622 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1408424 1412814 1412873 "IVECTOR" 1412878 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1407190 1407427 1407693 "ITUPLE" 1408191 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1405692 1405869 1406164 "ITRIGMNP" 1407012 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1404437 1404641 1404924 "ITFUN3" 1405468 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1404069 1404126 1404235 "ITFUN2" 1404374 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1403228 1403549 1403723 "ITFORM" 1403915 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1401189 1402248 1402526 "ITAYLOR" 1402983 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1390134 1395326 1396489 "ISUPS" 1400059 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1389238 1389378 1389614 "ISUMP" 1389981 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1384615 1389183 1389224 "ISTRING" 1389229 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1384091 1384336 1384428 "ISAST" 1384543 T ISAST (NIL) -8 NIL NIL NIL) (-603 1383300 1383382 1383598 "IRURPK" 1384005 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1382236 1382437 1382677 "IRSN" 1383080 T IRSN (NIL) -7 NIL NIL NIL) (-601 1380307 1380662 1381091 "IRRF2F" 1381874 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1380054 1380092 1380168 "IRREDFFX" 1380263 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1378669 1378928 1379227 "IROOT" 1379787 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1375273 1376353 1377045 "IR" 1378009 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1374478 1374766 1374917 "IRFORM" 1375142 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1372091 1372586 1373152 "IR2" 1373956 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1371191 1371304 1371518 "IR2F" 1371974 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1370982 1371016 1371076 "IPRNTPK" 1371151 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1367563 1370871 1370940 "IPF" 1370945 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1365890 1367488 1367545 "IPADIC" 1367550 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1365202 1365450 1365580 "IP4ADDR" 1365780 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1364576 1364831 1364963 "IOMODE" 1365090 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1363649 1364173 1364300 "IOBFILE" 1364469 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1363137 1363553 1363581 "IOBCON" 1363586 T IOBCON (NIL) -9 NIL 1363607 NIL) (-587 1362648 1362706 1362889 "INVLAPLA" 1363073 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1352296 1354650 1357036 "INTTR" 1360312 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1348631 1349373 1350238 "INTTOOLS" 1351481 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1348217 1348308 1348425 "INTSLPE" 1348534 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1346170 1348140 1348199 "INTRVL" 1348204 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1343772 1344284 1344859 "INTRF" 1345655 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1343183 1343280 1343422 "INTRET" 1343670 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1341180 1341569 1342039 "INTRAT" 1342791 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1338443 1339026 1339645 "INTPM" 1340665 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1335188 1335787 1336525 "INTPAF" 1337829 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1330367 1331329 1332380 "INTPACK" 1334157 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1327179 1330164 1330273 "INT" 1330278 T INT (NIL) -8 NIL NIL NIL) (-575 1326431 1326583 1326791 "INTHERTR" 1327021 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1325870 1325950 1326138 "INTHERAL" 1326345 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1323716 1324159 1324616 "INTHEORY" 1325433 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1315122 1316743 1318515 "INTG0" 1322068 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1295695 1300485 1305295 "INTFTBL" 1310332 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1294944 1295082 1295255 "INTFACT" 1295554 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1292371 1292817 1293374 "INTEF" 1294498 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1290724 1291463 1291491 "INTDOM" 1291792 T INTDOM (NIL) -9 NIL 1291999 NIL) (-567 1290093 1290267 1290509 "INTDOM-" 1290514 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1286467 1288395 1288449 "INTCAT" 1289248 NIL INTCAT (NIL T) -9 NIL 1289569 NIL) (-565 1285939 1286042 1286170 "INTBIT" 1286359 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1284638 1284792 1285099 "INTALG" 1285784 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1284121 1284211 1284368 "INTAF" 1284542 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1277468 1283931 1284071 "INTABL" 1284076 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1276801 1277267 1277332 "INT8" 1277366 T INT8 (NIL) -8 NIL NIL 1277411) (-560 1276133 1276599 1276664 "INT64" 1276698 T INT64 (NIL) -8 NIL NIL 1276743) (-559 1275465 1275931 1275996 "INT32" 1276030 T INT32 (NIL) -8 NIL NIL 1276075) (-558 1274797 1275263 1275328 "INT16" 1275362 T INT16 (NIL) -8 NIL NIL 1275407) (-557 1269506 1272358 1272386 "INS" 1273320 T INS (NIL) -9 NIL 1273985 NIL) (-556 1266746 1267517 1268491 "INS-" 1268564 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1265521 1265748 1266046 "INPSIGN" 1266499 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1264639 1264756 1264953 "INPRODPF" 1265401 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1263533 1263650 1263887 "INPRODFF" 1264519 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1262533 1262685 1262945 "INNMFACT" 1263369 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1261730 1261827 1262015 "INMODGCD" 1262432 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1260238 1260483 1260807 "INFSP" 1261475 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1259422 1259539 1259722 "INFPROD0" 1260118 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1256277 1257487 1258002 "INFORM" 1258915 T INFORM (NIL) -8 NIL NIL NIL) (-547 1255887 1255947 1256045 "INFORM1" 1256212 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1255410 1255499 1255613 "INFINITY" 1255793 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1254586 1255130 1255231 "INETCLTS" 1255329 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1253202 1253452 1253773 "INEP" 1254334 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1252407 1253099 1253164 "INDE" 1253169 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1251971 1252039 1252156 "INCRMAPS" 1252334 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1250789 1251240 1251446 "INBFILE" 1251785 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1246088 1247025 1247969 "INBFF" 1249877 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1244996 1245265 1245293 "INBCON" 1245806 T INBCON (NIL) -9 NIL 1246072 NIL) (-538 1244248 1244471 1244747 "INBCON-" 1244752 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1243727 1243972 1244063 "INAST" 1244177 T INAST (NIL) -8 NIL NIL NIL) (-536 1243154 1243406 1243512 "IMPTAST" 1243641 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1239554 1242998 1243102 "IMATRIX" 1243107 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1238262 1238385 1238701 "IMATQF" 1239410 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1236482 1236709 1237046 "IMATLIN" 1238018 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1231062 1236406 1236464 "ILIST" 1236469 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1228969 1230922 1231035 "IIARRAY2" 1231040 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1224367 1228880 1228944 "IFF" 1228949 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1223714 1223984 1224100 "IFAST" 1224271 T IFAST (NIL) -8 NIL NIL NIL) (-528 1218711 1223006 1223194 "IFARRAY" 1223571 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1217891 1218615 1218688 "IFAMON" 1218693 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1217475 1217540 1217594 "IEVALAB" 1217801 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1217150 1217218 1217378 "IEVALAB-" 1217383 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1216740 1217064 1217127 "IDPO" 1217132 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1215948 1216629 1216704 "IDPOAMS" 1216709 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1215213 1215837 1215912 "IDPOAM" 1215917 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214070 1214387 1214440 "IDPC" 1214958 NIL IDPC (NIL T T) -9 NIL 1215149 NIL) (-520 1213497 1213962 1214035 "IDPAM" 1214040 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1212831 1213389 1213462 "IDPAG" 1213467 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212476 1212667 1212742 "IDENT" 1212776 T IDENT (NIL) -8 NIL NIL NIL) (-517 1208731 1209579 1210474 "IDECOMP" 1211633 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1201568 1202654 1203701 "IDEAL" 1207767 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1200728 1200840 1201040 "ICDEN" 1201452 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1199799 1200208 1200355 "ICARD" 1200601 T ICARD (NIL) -8 NIL NIL NIL) (-513 1197859 1198172 1198577 "IBPTOOLS" 1199476 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193466 1197479 1197592 "IBITS" 1197778 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190189 1190765 1191460 "IBATOOL" 1192883 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1187968 1188430 1188963 "IBACHIN" 1189724 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1185799 1187814 1187917 "IARRAY2" 1187922 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1181907 1185725 1185782 "IARRAY1" 1185787 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1175767 1180319 1180800 "IAN" 1181446 T IAN (NIL) -8 NIL NIL NIL) (-506 1175278 1175335 1175508 "IALGFACT" 1175704 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1174806 1174919 1174947 "HYPCAT" 1175154 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174344 1174461 1174647 "HYPCAT-" 1174652 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1173939 1174139 1174222 "HOSTNAME" 1174281 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1173784 1173821 1173862 "HOMOTOP" 1173867 NIL HOMOTOP (NIL T) -9 NIL 1173900 NIL) (-501 1170340 1171716 1171757 "HOAGG" 1172738 NIL HOAGG (NIL T) -9 NIL 1173467 NIL) (-500 1168934 1169333 1169859 "HOAGG-" 1169864 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1162650 1168527 1168677 "HEXADEC" 1168804 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161398 1161620 1161883 "HEUGCD" 1162427 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160474 1161235 1161365 "HELLFDIV" 1161370 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1158655 1160251 1160339 "HEAP" 1160418 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1157918 1158207 1158341 "HEADAST" 1158541 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1151760 1157833 1157895 "HDP" 1157900 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145472 1151395 1151547 "HDMP" 1151661 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1144796 1144936 1145100 "HB" 1145328 T HB (NIL) -7 NIL NIL NIL) (-491 1138186 1144642 1144746 "HASHTBL" 1144751 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1137662 1137907 1137999 "HASAST" 1138114 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135440 1137284 1137466 "HACKPI" 1137500 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131108 1135293 1135406 "GTSET" 1135411 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1124527 1130986 1131084 "GSTBL" 1131089 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1116914 1123692 1123948 "GSERIES" 1124327 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1116041 1116458 1116486 "GROUP" 1116689 T GROUP (NIL) -9 NIL 1116823 NIL) (-484 1115407 1115566 1115817 "GROUP-" 1115822 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1113774 1114095 1114482 "GROEBSOL" 1115084 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1112674 1112962 1113013 "GRMOD" 1113542 NIL GRMOD (NIL T T) -9 NIL 1113710 NIL) (-481 1112442 1112478 1112606 "GRMOD-" 1112611 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1107732 1108796 1109796 "GRIMAGE" 1111462 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106198 1106459 1106783 "GRDEF" 1107428 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1105642 1105758 1105899 "GRAY" 1106077 T GRAY (NIL) -7 NIL NIL NIL) (-477 1104815 1105221 1105272 "GRALG" 1105425 NIL GRALG (NIL T T) -9 NIL 1105518 NIL) (-476 1104476 1104549 1104712 "GRALG-" 1104717 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101253 1104061 1104239 "GPOLSET" 1104383 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1100607 1100664 1100922 "GOSPER" 1101190 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096339 1097045 1097571 "GMODPOL" 1100306 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095344 1095528 1095766 "GHENSEL" 1096151 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1089500 1090343 1091363 "GENUPS" 1094428 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089197 1089248 1089337 "GENUFACT" 1089443 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1088609 1088686 1088851 "GENPGCD" 1089115 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1088083 1088118 1088331 "GENMFACT" 1088568 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1086649 1086906 1087213 "GENEEZ" 1087826 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1080521 1086260 1086422 "GDMP" 1086572 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1069864 1074292 1075398 "GCNAALG" 1079504 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068177 1069039 1069067 "GCDDOM" 1069322 T GCDDOM (NIL) -9 NIL 1069479 NIL) (-463 1067647 1067774 1067989 "GCDDOM-" 1067994 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066319 1066504 1066808 "GB" 1067426 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1054935 1057265 1059657 "GBINTERN" 1064010 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1052772 1053064 1053485 "GBF" 1054610 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1051553 1051718 1051985 "GBEUCLID" 1052588 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1050902 1051027 1051176 "GAUSSFAC" 1051424 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049269 1049571 1049885 "GALUTIL" 1050621 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1047577 1047851 1048175 "GALPOLYU" 1048996 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1044942 1045232 1045639 "GALFACTU" 1047274 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1036748 1038247 1039855 "GALFACT" 1043374 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034136 1034794 1034822 "FVFUN" 1035978 T FVFUN (NIL) -9 NIL 1036698 NIL) (-452 1033402 1033584 1033612 "FVC" 1033903 T FVC (NIL) -9 NIL 1034086 NIL) (-451 1033045 1033227 1033295 "FUNDESC" 1033354 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1032660 1032842 1032923 "FUNCTION" 1032997 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030404 1030982 1031448 "FT" 1032214 T FT (NIL) -8 NIL NIL NIL) (-448 1029195 1029705 1029908 "FTEM" 1030221 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027486 1027775 1028172 "FSUPFACT" 1028886 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1025883 1026172 1026504 "FST" 1027174 T FST (NIL) -8 NIL NIL NIL) (-445 1025082 1025188 1025376 "FSRED" 1025765 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1023781 1024037 1024384 "FSPRMELT" 1024797 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1021087 1021525 1022011 "FSPECF" 1023344 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002152 1010861 1010902 "FS" 1014786 NIL FS (NIL T) -9 NIL 1017075 NIL) (-441 990795 993788 997845 "FS-" 998145 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990323 990377 990547 "FSINT" 990736 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 988615 989316 989619 "FSERIES" 990102 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 987657 987773 987997 "FSCINT" 988495 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 983865 986601 986642 "FSAGG" 987012 NIL FSAGG (NIL T) -9 NIL 987271 NIL) (-436 981627 982228 983024 "FSAGG-" 983119 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 980669 980812 981039 "FSAGG2" 981480 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978347 978627 979175 "FS2UPS" 980387 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 977981 978024 978153 "FS2" 978298 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 976859 977030 977332 "FS2EXPXP" 977806 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976285 976400 976552 "FRUTIL" 976739 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 967698 971780 973138 "FR" 974959 NIL FR (NIL T) -8 NIL NIL NIL) (-429 962712 965387 965427 "FRNAALG" 966747 NIL FRNAALG (NIL T) -9 NIL 967345 NIL) (-428 958385 959461 960736 "FRNAALG-" 961486 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 958023 958066 958193 "FRNAAF2" 958336 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956398 956872 957168 "FRMOD" 957835 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954141 954773 955091 "FRIDEAL" 956189 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953332 953419 953710 "FRIDEAL2" 954048 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952465 952879 952920 "FRETRCT" 952925 NIL FRETRCT (NIL T) -9 NIL 953101 NIL) (-422 951577 951808 952159 "FRETRCT-" 952164 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 948651 949861 949920 "FRAMALG" 950802 NIL FRAMALG (NIL T T) -9 NIL 951094 NIL) (-420 946785 947240 947870 "FRAMALG-" 948093 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940428 946258 946535 "FRAC" 946540 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 940064 940121 940228 "FRAC2" 940365 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 939700 939757 939864 "FR2" 940001 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934199 937092 937120 "FPS" 938239 T FPS (NIL) -9 NIL 938796 NIL) (-415 933648 933757 933921 "FPS-" 934067 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 930936 932605 932633 "FPC" 932858 T FPC (NIL) -9 NIL 933000 NIL) (-413 930729 930769 930866 "FPC-" 930871 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 929519 930217 930258 "FPATMAB" 930263 NIL FPATMAB (NIL T) -9 NIL 930415 NIL) (-411 927758 928261 928608 "FPARFRAC" 929235 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923152 923650 924332 "FORTRAN" 927190 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 920868 921368 921907 "FORT" 922633 T FORT (NIL) -7 NIL NIL NIL) (-408 918544 919106 919134 "FORTFN" 920194 T FORTFN (NIL) -9 NIL 920818 NIL) (-407 918308 918358 918386 "FORTCAT" 918445 T FORTCAT (NIL) -9 NIL 918507 NIL) (-406 916414 916924 917314 "FORMULA" 917938 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916202 916232 916301 "FORMULA1" 916378 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 915725 915777 915950 "FORDER" 916144 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 914821 914985 915178 "FOP" 915552 T FOP (NIL) -7 NIL NIL NIL) (-402 913402 914101 914275 "FNLA" 914703 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912117 912532 912560 "FNCAT" 913020 T FNCAT (NIL) -9 NIL 913280 NIL) (-400 911656 912076 912104 "FNAME" 912109 T FNAME (NIL) -8 NIL NIL NIL) (-399 910205 911168 911196 "FMTC" 911201 T FMTC (NIL) -9 NIL 911237 NIL) (-398 908951 910141 910187 "FMONOID" 910192 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 905765 906933 906974 "FMONCAT" 908191 NIL FMONCAT (NIL T) -9 NIL 908796 NIL) (-396 904915 905507 905656 "FM" 905661 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902339 902985 903013 "FMFUN" 904157 T FMFUN (NIL) -9 NIL 904865 NIL) (-394 901608 901789 901817 "FMC" 902107 T FMC (NIL) -9 NIL 902289 NIL) (-393 898673 899533 899587 "FMCAT" 900782 NIL FMCAT (NIL T T) -9 NIL 901277 NIL) (-392 897539 898439 898539 "FM1" 898618 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895313 895729 896223 "FLOATRP" 897090 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 888891 893042 893663 "FLOAT" 894712 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886329 886829 887407 "FLOATCP" 888358 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 884977 885921 885962 "FLINEXP" 885967 NIL FLINEXP (NIL T) -9 NIL 886060 NIL) (-387 884131 884366 884694 "FLINEXP-" 884699 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883207 883351 883575 "FLASORT" 883983 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880309 881177 881229 "FLALG" 882456 NIL FLALG (NIL T T) -9 NIL 882923 NIL) (-384 873995 877745 877786 "FLAGG" 879048 NIL FLAGG (NIL T) -9 NIL 879700 NIL) (-383 872721 873060 873550 "FLAGG-" 873555 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 871763 871906 872133 "FLAGG2" 872574 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 868600 869608 869667 "FINRALG" 870795 NIL FINRALG (NIL T T) -9 NIL 871303 NIL) (-380 867760 867989 868328 "FINRALG-" 868333 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867126 867365 867393 "FINITE" 867589 T FINITE (NIL) -9 NIL 867696 NIL) (-378 859469 861656 861696 "FINAALG" 865363 NIL FINAALG (NIL T) -9 NIL 866816 NIL) (-377 854801 855851 856995 "FINAALG-" 858374 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854169 854556 854659 "FILE" 854731 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 852813 853151 853205 "FILECAT" 853889 NIL FILECAT (NIL T T) -9 NIL 854105 NIL) (-374 850515 852043 852071 "FIELD" 852111 T FIELD (NIL) -9 NIL 852191 NIL) (-373 849135 849520 850031 "FIELD-" 850036 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 846985 847770 848117 "FGROUP" 848821 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846075 846239 846459 "FGLMICPK" 846817 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 841907 846000 846057 "FFX" 846062 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841508 841569 841704 "FFSLPE" 841840 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837498 838280 839076 "FFPOLY" 840744 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837002 837038 837247 "FFPOLY2" 837456 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 832848 836921 836984 "FFP" 836989 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828246 832759 832823 "FF" 832828 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823372 827589 827779 "FFNBX" 828100 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818300 822507 822765 "FFNBP" 823226 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 812933 817584 817795 "FFNB" 818133 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 811765 811963 812278 "FFINTBAS" 812730 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 807791 810012 810040 "FFIELDC" 810660 T FFIELDC (NIL) -9 NIL 811036 NIL) (-359 806453 806824 807321 "FFIELDC-" 807326 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806022 806068 806192 "FFHOM" 806395 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 803717 804204 804721 "FFF" 805537 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799335 803459 803560 "FFCGX" 803660 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 794957 799067 799174 "FFCGP" 799278 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790140 794684 794792 "FFCG" 794893 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 769669 779872 779958 "FFCAT" 785123 NIL FFCAT (NIL T T T) -9 NIL 786574 NIL) (-352 764866 765914 767228 "FFCAT-" 768458 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764277 764320 764555 "FFCAT2" 764817 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 753600 757249 758469 "FEXPR" 763129 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752562 752997 753038 "FEVALAB" 753122 NIL FEVALAB (NIL T) -9 NIL 753383 NIL) (-348 751721 751931 752269 "FEVALAB-" 752274 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750287 751104 751307 "FDIV" 751620 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747293 748034 748149 "FDIVCAT" 749717 NIL FDIVCAT (NIL T T T T) -9 NIL 750154 NIL) (-345 747055 747082 747252 "FDIVCAT-" 747257 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746275 746362 746639 "FDIV2" 746962 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745249 745570 745772 "FCTRDATA" 746093 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 743935 744194 744483 "FCPAK1" 744980 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743034 743435 743576 "FCOMP" 743826 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 726739 730184 733722 "FC" 739516 T FC (NIL) -8 NIL NIL NIL) (-339 719032 723060 723100 "FAXF" 724902 NIL FAXF (NIL T) -9 NIL 725594 NIL) (-338 716309 716966 717791 "FAXF-" 718256 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711363 715685 715861 "FARRAY" 716166 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706243 708310 708363 "FAMR" 709386 NIL FAMR (NIL T T) -9 NIL 709846 NIL) (-335 705133 705435 705870 "FAMR-" 705875 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704302 705055 705108 "FAMONOID" 705113 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702074 702784 702837 "FAMONC" 703778 NIL FAMONC (NIL T T) -9 NIL 704164 NIL) (-332 700738 701828 701965 "FAGROUP" 701970 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698533 698852 699255 "FACUTIL" 700419 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 697632 697817 698039 "FACTFUNC" 698343 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690054 696935 697134 "EXPUPXS" 697488 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687537 688077 688663 "EXPRTUBE" 689488 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 683808 684400 685130 "EXPRODE" 686876 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669292 682457 682886 "EXPR" 683412 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 663846 664433 665239 "EXPR2UPS" 668590 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663478 663535 663644 "EXPR2" 663783 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654475 662629 662920 "EXPEXPAN" 663314 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654275 654432 654461 "EXIT" 654466 T EXIT (NIL) -8 NIL NIL NIL) (-321 653755 653999 654090 "EXITAST" 654204 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653382 653444 653557 "EVALCYC" 653687 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 652923 653041 653082 "EVALAB" 653252 NIL EVALAB (NIL T) -9 NIL 653356 NIL) (-318 652404 652526 652747 "EVALAB-" 652752 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 649758 651060 651088 "EUCDOM" 651643 T EUCDOM (NIL) -9 NIL 651993 NIL) (-316 648163 648605 649195 "EUCDOM-" 649200 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 635702 638461 641211 "ESTOOLS" 645433 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635334 635391 635500 "ESTOOLS2" 635639 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635085 635127 635207 "ESTOOLS1" 635286 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629108 630716 630744 "ES" 633512 T ES (NIL) -9 NIL 634922 NIL) (-311 624055 625342 627159 "ES-" 627323 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620429 621190 621970 "ESCONT" 623295 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620174 620206 620288 "ESCONT1" 620391 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 619849 619899 619999 "ES2" 620118 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619479 619537 619646 "ES1" 619785 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 618695 618824 619000 "ERROR" 619323 T ERROR (NIL) -7 NIL NIL NIL) (-305 612091 618554 618645 "EQTBL" 618650 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 604594 607405 608854 "EQ" 610675 NIL -2032 (NIL T) -8 NIL NIL NIL) (-303 604226 604283 604392 "EQ2" 604531 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599517 600564 601657 "EP" 603165 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598117 598408 598714 "ENV" 599231 T ENV (NIL) -8 NIL NIL NIL) (-300 597197 597751 597779 "ENTIRER" 597784 T ENTIRER (NIL) -9 NIL 597830 NIL) (-299 593891 595379 595740 "EMR" 597005 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593021 593206 593260 "ELTAGG" 593640 NIL ELTAGG (NIL T T) -9 NIL 593851 NIL) (-297 592740 592802 592943 "ELTAGG-" 592948 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592504 592533 592587 "ELTAB" 592671 NIL ELTAB (NIL T T) -9 NIL 592723 NIL) (-295 591630 591776 591975 "ELFUTS" 592355 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591372 591428 591456 "ELEMFUN" 591561 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591242 591263 591331 "ELEMFUN-" 591336 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586030 589284 589325 "ELAGG" 590265 NIL ELAGG (NIL T) -9 NIL 590728 NIL) (-291 584315 584749 585412 "ELAGG-" 585417 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 583627 583764 583920 "ELABOR" 584179 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582288 582567 582861 "ELABEXPR" 583353 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575122 576925 577754 "EFUPXS" 581563 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568570 570371 571182 "EFULS" 574397 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566055 566413 566885 "EFSTRUC" 568202 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 555846 557412 558960 "EF" 564570 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 554920 555331 555480 "EAB" 555717 T EAB (NIL) -8 NIL NIL NIL) (-283 554102 554879 554907 "E04UCFA" 554912 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553284 554061 554089 "E04NAFA" 554094 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552466 553243 553271 "E04MBFA" 553276 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 551648 552425 552453 "E04JAFA" 552458 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 550832 551607 551635 "E04GCFA" 551640 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550016 550791 550819 "E04FDFA" 550824 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549198 549975 550003 "E04DGFA" 550008 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543371 544723 546087 "E04AGNT" 547854 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542142 542685 542725 "DVARCAT" 543066 NIL DVARCAT (NIL T) -9 NIL 543229 NIL) (-274 541346 541558 541872 "DVARCAT-" 541877 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534207 541145 541274 "DSMP" 541279 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 532630 533349 533390 "DSEXT" 533753 NIL DSEXT (NIL T) -9 NIL 534047 NIL) (-271 530915 531343 532009 "DSEXT-" 532014 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 525696 526860 527928 "DROPT" 529867 T DROPT (NIL) -8 NIL NIL NIL) (-269 525361 525420 525518 "DROPT1" 525631 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520476 521602 522739 "DROPT0" 524244 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 518821 519146 519532 "DRAWPT" 520110 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513408 514331 515410 "DRAW" 517795 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513041 513094 513212 "DRAWHACK" 513349 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 511772 512041 512332 "DRAWCX" 512770 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511287 511356 511507 "DRAWCURV" 511698 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 501755 503717 505832 "DRAWCFUN" 509192 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498493 500420 500461 "DQAGG" 501090 NIL DQAGG (NIL T) -9 NIL 501364 NIL) (-260 485958 492704 492787 "DPOLCAT" 494639 NIL DPOLCAT (NIL T T T T) -9 NIL 495184 NIL) (-259 480795 482143 484101 "DPOLCAT-" 484106 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474142 480656 480754 "DPMO" 480759 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467392 473922 474089 "DPMM" 474094 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 466962 467176 467265 "DOMTMPLT" 467323 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466395 466764 466844 "DOMCTOR" 466902 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 465607 465875 466026 "DOMAIN" 466264 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459319 465242 465394 "DMP" 465508 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457264 458386 458427 "DMEXT" 458432 NIL DMEXT (NIL T) -9 NIL 458608 NIL) (-251 456864 456920 457064 "DLP" 457202 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 450688 456191 456381 "DLIST" 456706 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447459 449513 449554 "DLAGG" 450104 NIL DLAGG (NIL T) -9 NIL 450334 NIL) (-248 446121 446785 446813 "DIVRING" 446905 T DIVRING (NIL) -9 NIL 446988 NIL) (-247 445358 445548 445848 "DIVRING-" 445853 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443460 443817 444223 "DISPLAY" 444972 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437322 443374 443437 "DIRPROD" 443442 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436170 436373 436638 "DIRPROD2" 437115 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 424899 430936 430989 "DIRPCAT" 431247 NIL DIRPCAT (NIL NIL T) -9 NIL 432122 NIL) (-242 422225 422867 423748 "DIRPCAT-" 424085 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421512 421672 421858 "DIOSP" 422059 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418141 420396 420437 "DIOPS" 420871 NIL DIOPS (NIL T) -9 NIL 421100 NIL) (-239 417690 417804 417995 "DIOPS-" 418000 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 416741 417369 417397 "DIFRING" 417402 T DIFRING (NIL) -9 NIL 417424 NIL) (-237 416413 416487 416515 "DIFFSPC" 416634 T DIFFSPC (NIL) -9 NIL 416709 NIL) (-236 416058 416136 416288 "DIFFSPC-" 416293 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415114 415592 415633 "DIFFMOD" 415638 NIL DIFFMOD (NIL T) -9 NIL 415736 NIL) (-234 414822 414867 414908 "DIFFDOM" 415029 NIL DIFFDOM (NIL T) -9 NIL 415097 NIL) (-233 414675 414699 414783 "DIFFDOM-" 414788 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412607 413879 413920 "DIFEXT" 413925 NIL DIFEXT (NIL T) -9 NIL 414078 NIL) (-231 409856 412111 412152 "DIAGG" 412157 NIL DIAGG (NIL T) -9 NIL 412177 NIL) (-230 409240 409397 409649 "DIAGG-" 409654 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404611 408199 408476 "DHMATRIX" 409009 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400223 401132 402142 "DFSFUN" 403621 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395301 399154 399466 "DFLOAT" 399931 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393564 393845 394234 "DFINTTLS" 395009 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390593 391585 391985 "DERHAM" 393230 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388396 390368 390457 "DEQUEUE" 390537 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 387650 387783 387966 "DEGRED" 388258 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384080 384825 385671 "DEFINTRF" 386878 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 381635 382104 382696 "DEFINTEF" 383599 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 380985 381255 381370 "DEFAST" 381540 T DEFAST (NIL) -8 NIL NIL NIL) (-219 374701 380578 380728 "DECIMAL" 380855 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372213 372671 373177 "DDFACT" 374245 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 371809 371852 372003 "DBLRESP" 372164 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 369677 370039 370400 "DBASE" 371575 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 368919 369157 369303 "DATAARY" 369576 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368025 368878 368906 "D03FAFA" 368911 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367132 367984 368012 "D03EEFA" 368017 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365082 365548 366037 "D03AGNT" 366663 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364371 365041 365069 "D02EJFA" 365074 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 363660 364330 364358 "D02CJFA" 364363 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 362949 363619 363647 "D02BHFA" 363652 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362238 362908 362936 "D02BBFA" 362941 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355435 357024 358630 "D02AGNT" 360652 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353203 353726 354272 "D01WGTS" 354909 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352270 353162 353190 "D01TRNS" 353195 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351338 352229 352257 "D01GBFA" 352262 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350406 351297 351325 "D01FCFA" 351330 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349474 350365 350393 "D01ASFA" 350398 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348542 349433 349461 "D01AQFA" 349466 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347610 348501 348529 "D01APFA" 348534 T D01APFA (NIL) -8 NIL NIL NIL) (-199 346678 347569 347597 "D01ANFA" 347602 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 345746 346637 346665 "D01AMFA" 346670 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 344814 345705 345733 "D01ALFA" 345738 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 343882 344773 344801 "D01AKFA" 344806 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 342950 343841 343869 "D01AJFA" 343874 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336245 337798 339359 "D01AGNT" 341409 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335582 335710 335862 "CYCLOTOM" 336113 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332315 333030 333757 "CYCLES" 334875 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331627 331761 331932 "CVMP" 332176 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329468 329726 330095 "CTRIGMNP" 331355 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 328904 329262 329335 "CTOR" 329415 T CTOR (NIL) -8 NIL NIL NIL) (-188 328413 328635 328736 "CTORKIND" 328823 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 327690 328006 328034 "CTORCAT" 328216 T CTORCAT (NIL) -9 NIL 328329 NIL) (-186 327288 327399 327558 "CTORCAT-" 327563 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 326750 326962 327070 "CTORCALL" 327212 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326124 326223 326376 "CSTTOOLS" 326647 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 321923 322580 323338 "CRFP" 325436 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321398 321644 321736 "CRCEAST" 321851 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320445 320630 320858 "CRAPACK" 321202 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 319829 319930 320134 "CPMATCH" 320321 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319554 319582 319688 "CPIMA" 319795 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 315902 316574 317293 "COORDSYS" 318889 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315314 315435 315577 "CONTOUR" 315780 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311205 313317 313809 "CONTFRAC" 314854 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311085 311106 311134 "CONDUIT" 311171 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310159 310713 310741 "COMRING" 310746 T COMRING (NIL) -9 NIL 310798 NIL) (-173 309213 309517 309701 "COMPPROP" 309995 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 308874 308909 309037 "COMPLPAT" 309172 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298177 308683 308792 "COMPLEX" 308797 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 297813 297870 297977 "COMPLEX2" 298114 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297152 297273 297433 "COMPILER" 297673 T COMPILER (NIL) -8 NIL NIL NIL) (-168 296870 296905 297003 "COMPFACT" 297111 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279149 290574 290614 "COMPCAT" 291618 NIL COMPCAT (NIL T) -9 NIL 292966 NIL) (-166 268661 271588 275215 "COMPCAT-" 275571 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268390 268418 268521 "COMMUPC" 268627 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268184 268218 268277 "COMMONOP" 268351 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 267740 267935 268022 "COMM" 268117 T COMM (NIL) -8 NIL NIL NIL) (-162 267316 267544 267619 "COMMAAST" 267685 T COMMAAST (NIL) -8 NIL NIL NIL) 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T) ((-23) . T) ((-47 |#1| #0=(-576)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -3795 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-374)) ((-38 $) -3795 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -3795 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-374)) ((-111 $ $) -3795 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) -3795 (-12 (|has| |#1| (-374)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -3795 (-12 (|has| |#1| (-374)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-628 #1#) -3795 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1197)) -12 (|has| |#1| (-374)) (|has| |#2| (-1059 (-1197)))) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . 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T) ((-296 |#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) ((-296 $ $) |has| (-576) (-1133)) ((-300) -3795 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-374) |has| |#1| (-374)) ((-349 |#2|) |has| |#1| (-374)) ((-388 |#2|) |has| |#1| (-374)) ((-412 |#2|) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-526 (-1197) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1197) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -3795 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-658 #1#) -3795 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-374)) ((-658 $) . T) ((-660 #1#) -3795 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-660 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-660 |#1|) . T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -3795 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -3795 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -3795 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -3795 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . 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T) ((-1077 $) -3795 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1223) |has| |#1| (-38 (-419 (-576)))) ((-1226) |has| |#1| (-38 (-419 (-576)))) ((-1238) . T) ((-1242) |has| |#1| (-374)) ((-1266 |#1| #0#) . T) ((-1269 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) |has| |#1| (-568)) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3795 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) |has| |#1| (-38 (-419 (-576)))) ((-628 (-576)) . T) ((-628 |#1|) |has| |#1| (-174)) ((-628 $) |has| |#1| (-568)) ((-625 (-876)) . T) ((-174) -3795 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-234 $) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-238) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-237) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . 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T) ((-1072 $) -3795 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1077 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1077 |#1|) . T) ((-1077 $) -3795 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1223) |has| |#1| (-38 (-419 (-576)))) ((-1226) |has| |#1| (-38 (-419 (-576)))) ((-1238) . T) ((-1266 |#1| #0#) . 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NIL) (-1249 2996026 2996271 2996659 "ULSCCAT-" 2996664 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1248 2985090 2991573 2991616 "ULSCAT" 2992479 NIL ULSCAT (NIL T) -9 NIL 2993210 NIL) (-1247 2984520 2984599 2984778 "ULS2" 2985005 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1246 2983639 2984149 2984256 "UINT8" 2984367 T UINT8 (NIL) -8 NIL NIL 2984452) (-1245 2982757 2983267 2983374 "UINT64" 2983485 T UINT64 (NIL) -8 NIL NIL 2983570) (-1244 2981875 2982385 2982492 "UINT32" 2982603 T UINT32 (NIL) -8 NIL NIL 2982688) (-1243 2980993 2981503 2981610 "UINT16" 2981721 T UINT16 (NIL) -8 NIL NIL 2981806) (-1242 2979282 2980239 2980269 "UFD" 2980481 T UFD (NIL) -9 NIL 2980595 NIL) (-1241 2979076 2979122 2979217 "UFD-" 2979222 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1240 2978158 2978341 2978557 "UDVO" 2978882 T UDVO (NIL) -7 NIL NIL NIL) (-1239 2975974 2976383 2976854 "UDPO" 2977722 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1238 2975907 2975912 2975942 "TYPE" 2975947 T TYPE (NIL) -9 NIL NIL NIL) (-1237 2975667 2975862 2975893 "TYPEAST" 2975898 T TYPEAST (NIL) -8 NIL NIL NIL) (-1236 2974638 2974840 2975080 "TWOFACT" 2975461 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1235 2973661 2974047 2974282 "TUPLE" 2974438 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1234 2971352 2971871 2972410 "TUBETOOL" 2973144 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1233 2970201 2970406 2970647 "TUBE" 2971145 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1232 2964930 2969173 2969456 "TS" 2969953 NIL TS (NIL T) -8 NIL NIL NIL) (-1231 2953570 2957689 2957786 "TSETCAT" 2963055 NIL TSETCAT (NIL T T T T) -9 NIL 2964586 NIL) (-1230 2948302 2949902 2951793 "TSETCAT-" 2951798 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1229 2942941 2943788 2944717 "TRMANIP" 2947438 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1228 2942382 2942445 2942608 "TRIMAT" 2942873 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1227 2940248 2940485 2940842 "TRIGMNIP" 2942131 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1226 2939768 2939881 2939911 "TRIGCAT" 2940124 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1225 2939437 2939516 2939657 "TRIGCAT-" 2939662 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1224 2936284 2938295 2938576 "TREE" 2939191 NIL TREE (NIL T) -8 NIL NIL NIL) (-1223 2935558 2936086 2936116 "TRANFUN" 2936151 T TRANFUN (NIL) -9 NIL 2936217 NIL) (-1222 2934837 2935028 2935308 "TRANFUN-" 2935313 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1221 2934641 2934673 2934734 "TOPSP" 2934798 T TOPSP (NIL) -7 NIL NIL NIL) (-1220 2933989 2934104 2934258 "TOOLSIGN" 2934522 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1219 2932623 2933166 2933405 "TEXTFILE" 2933772 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1218 2930535 2931076 2931505 "TEX" 2932216 T TEX (NIL) -8 NIL NIL NIL) (-1217 2930316 2930347 2930419 "TEX1" 2930498 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1216 2929964 2930027 2930117 "TEMUTL" 2930248 T TEMUTL (NIL) -7 NIL NIL NIL) (-1215 2928118 2928398 2928723 "TBCMPPK" 2929687 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1214 2919825 2926204 2926260 "TBAGG" 2926660 NIL TBAGG (NIL T T) -9 NIL 2926871 NIL) (-1213 2914895 2916383 2918137 "TBAGG-" 2918142 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1212 2914279 2914386 2914531 "TANEXP" 2914784 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1211 2913790 2914054 2914144 "TALGOP" 2914224 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1210 2907184 2913647 2913740 "TABLE" 2913745 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1209 2906596 2906695 2906833 "TABLEAU" 2907081 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1208 2901204 2902424 2903672 "TABLBUMP" 2905382 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1207 2900426 2900573 2900754 "SYSTEM" 2901045 T SYSTEM (NIL) -8 NIL NIL NIL) (-1206 2896885 2897584 2898367 "SYSSOLP" 2899677 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1205 2896683 2896840 2896871 "SYSPTR" 2896876 T SYSPTR (NIL) -8 NIL NIL NIL) (-1204 2895719 2896224 2896343 "SYSNNI" 2896529 NIL SYSNNI (NIL NIL) -8 NIL NIL 2896614) (-1203 2895018 2895477 2895556 "SYSINT" 2895616 NIL SYSINT (NIL NIL) -8 NIL NIL 2895661) (-1202 2891350 2892296 2893006 "SYNTAX" 2894330 T SYNTAX (NIL) -8 NIL NIL NIL) (-1201 2888508 2889110 2889742 "SYMTAB" 2890740 T SYMTAB (NIL) -8 NIL NIL NIL) (-1200 2883757 2884659 2885642 "SYMS" 2887547 T SYMS (NIL) -8 NIL NIL NIL) (-1199 2880992 2883215 2883445 "SYMPOLY" 2883562 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1198 2880509 2880584 2880707 "SYMFUNC" 2880904 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1197 2876529 2877821 2878634 "SYMBOL" 2879718 T SYMBOL (NIL) -8 NIL NIL NIL) (-1196 2870068 2871757 2873477 "SWITCH" 2874831 T SWITCH (NIL) -8 NIL NIL NIL) (-1195 2863412 2869024 2869318 "SUTS" 2869832 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1194 2855588 2862794 2863058 "SUPXS" 2863206 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1193 2847071 2855206 2855332 "SUP" 2855497 NIL SUP (NIL T) -8 NIL NIL NIL) (-1192 2846230 2846357 2846574 "SUPFRACF" 2846939 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1191 2845851 2845910 2846023 "SUP2" 2846165 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1190 2844299 2844573 2844929 "SUMRF" 2845550 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1189 2843634 2843700 2843892 "SUMFS" 2844220 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1188 2826421 2842946 2843188 "SULS" 2843450 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1187 2826023 2826243 2826313 "SUCHTAST" 2826373 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1186 2825318 2825548 2825688 "SUCH" 2825931 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1185 2819185 2820224 2821183 "SUBSPACE" 2824406 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1184 2818615 2818705 2818869 "SUBRESP" 2819073 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1183 2811983 2813280 2814591 "STTF" 2817351 NIL STTF (NIL T) -7 NIL NIL NIL) (-1182 2806156 2807276 2808423 "STTFNC" 2810883 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1181 2797469 2799338 2801132 "STTAYLOR" 2804397 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1180 2790603 2797333 2797416 "STRTBL" 2797421 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1179 2785563 2790312 2790411 "STRING" 2790526 T STRING (NIL) -8 NIL NIL NIL) (-1178 2778318 2783182 2783793 "STREAM" 2784987 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1177 2777828 2777905 2778049 "STREAM3" 2778235 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1176 2776810 2776993 2777228 "STREAM2" 2777641 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1175 2776498 2776550 2776643 "STREAM1" 2776752 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1174 2775514 2775695 2775926 "STINPROD" 2776314 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1173 2775052 2775262 2775292 "STEP" 2775372 T STEP (NIL) -9 NIL 2775450 NIL) (-1172 2774239 2774541 2774689 "STEPAST" 2774926 T STEPAST (NIL) -8 NIL NIL NIL) (-1171 2767675 2774138 2774215 "STBL" 2774220 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1170 2762744 2766838 2766881 "STAGG" 2767034 NIL STAGG (NIL T) -9 NIL 2767123 NIL) (-1169 2760446 2761048 2761920 "STAGG-" 2761925 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1168 2758595 2760216 2760308 "STACK" 2760389 NIL STACK (NIL T) -8 NIL NIL NIL) (-1167 2751290 2756736 2757192 "SREGSET" 2758225 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1166 2743715 2745084 2746597 "SRDCMPK" 2749896 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1165 2736580 2741103 2741133 "SRAGG" 2742436 T SRAGG (NIL) -9 NIL 2743044 NIL) (-1164 2735597 2735852 2736231 "SRAGG-" 2736236 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1163 2729781 2734544 2734965 "SQMATRIX" 2735223 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1162 2723468 2726499 2727226 "SPLTREE" 2729126 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1161 2719431 2720124 2720770 "SPLNODE" 2722894 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1160 2718478 2718711 2718741 "SPFCAT" 2719185 T SPFCAT (NIL) -9 NIL NIL NIL) (-1159 2717215 2717425 2717689 "SPECOUT" 2718236 T SPECOUT (NIL) -7 NIL NIL NIL) (-1158 2708311 2710183 2710213 "SPADXPT" 2714889 T SPADXPT (NIL) -9 NIL 2717053 NIL) (-1157 2708072 2708112 2708181 "SPADPRSR" 2708264 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1156 2706121 2708027 2708058 "SPADAST" 2708063 T SPADAST (NIL) -8 NIL NIL NIL) (-1155 2698052 2699825 2699868 "SPACEC" 2704241 NIL SPACEC (NIL T) -9 NIL 2706057 NIL) (-1154 2696182 2697984 2698033 "SPACE3" 2698038 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1153 2694934 2695105 2695396 "SORTPAK" 2695987 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1152 2693026 2693329 2693741 "SOLVETRA" 2694598 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1151 2692076 2692298 2692559 "SOLVESER" 2692799 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1150 2687380 2688268 2689263 "SOLVERAD" 2691128 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1149 2683195 2683804 2684533 "SOLVEFOR" 2686747 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1148 2677465 2682544 2682641 "SNTSCAT" 2682646 NIL SNTSCAT (NIL T T T T) -9 NIL 2682716 NIL) (-1147 2671571 2675788 2676179 "SMTS" 2677155 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1146 2665980 2671459 2671536 "SMP" 2671541 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1145 2664139 2664440 2664838 "SMITH" 2665677 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1144 2656243 2660718 2660821 "SMATCAT" 2662172 NIL SMATCAT (NIL NIL T T T) -9 NIL 2662722 NIL) (-1143 2653183 2654006 2655184 "SMATCAT-" 2655189 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1142 2650823 2652391 2652434 "SKAGG" 2652695 NIL SKAGG (NIL T) -9 NIL 2652830 NIL) (-1141 2647013 2650296 2650480 "SINT" 2650632 T SINT (NIL) -8 NIL NIL 2650794) (-1140 2646785 2646823 2646889 "SIMPAN" 2646969 T SIMPAN (NIL) -7 NIL NIL NIL) (-1139 2646064 2646320 2646460 "SIG" 2646667 T SIG (NIL) -8 NIL NIL NIL) (-1138 2644902 2645123 2645398 "SIGNRF" 2645823 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1137 2643735 2643886 2644170 "SIGNEF" 2644731 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1136 2643041 2643318 2643442 "SIGAST" 2643633 T SIGAST (NIL) -8 NIL NIL NIL) (-1135 2640731 2641185 2641691 "SHP" 2642582 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1134 2634559 2640632 2640708 "SHDP" 2640713 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1133 2634118 2634310 2634340 "SGROUP" 2634433 T SGROUP (NIL) -9 NIL 2634495 NIL) (-1132 2633976 2634002 2634075 "SGROUP-" 2634080 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1131 2630767 2631465 2632188 "SGCF" 2633275 T SGCF (NIL) -7 NIL NIL NIL) (-1130 2625135 2630214 2630311 "SFRTCAT" 2630316 NIL SFRTCAT (NIL T T T T) -9 NIL 2630355 NIL) (-1129 2618556 2619574 2620710 "SFRGCD" 2624118 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1128 2611682 2612755 2613941 "SFQCMPK" 2617489 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1127 2611302 2611391 2611502 "SFORT" 2611623 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1126 2610420 2611142 2611263 "SEXOF" 2611268 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1125 2609527 2610301 2610369 "SEX" 2610374 T SEX (NIL) -8 NIL NIL NIL) (-1124 2605308 2606023 2606118 "SEXCAT" 2608740 NIL SEXCAT (NIL T T T T T) -9 NIL 2609300 NIL) (-1123 2602461 2605242 2605290 "SET" 2605295 NIL SET (NIL T) -8 NIL NIL NIL) (-1122 2600685 2601174 2601479 "SETMN" 2602202 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1121 2600167 2600319 2600349 "SETCAT" 2600525 T SETCAT (NIL) -9 NIL 2600635 NIL) (-1120 2599859 2599937 2600067 "SETCAT-" 2600072 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1119 2596220 2598320 2598363 "SETAGG" 2599233 NIL SETAGG (NIL T) -9 NIL 2599573 NIL) (-1118 2595678 2595794 2596031 "SETAGG-" 2596036 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1117 2595121 2595374 2595475 "SEQAST" 2595599 T SEQAST (NIL) -8 NIL NIL NIL) (-1116 2594320 2594614 2594675 "SEGXCAT" 2594961 NIL SEGXCAT (NIL T T) -9 NIL 2595081 NIL) (-1115 2593326 2593986 2594168 "SEG" 2594173 NIL SEG (NIL T) -8 NIL NIL NIL) (-1114 2592305 2592519 2592562 "SEGCAT" 2593084 NIL SEGCAT (NIL T) -9 NIL 2593305 NIL) (-1113 2591237 2591668 2591876 "SEGBIND" 2592132 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1112 2590858 2590917 2591030 "SEGBIND2" 2591172 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1111 2590431 2590659 2590736 "SEGAST" 2590803 T SEGAST (NIL) -8 NIL NIL NIL) (-1110 2589650 2589776 2589980 "SEG2" 2590275 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1109 2589021 2589585 2589632 "SDVAR" 2589637 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1108 2581272 2588791 2588921 "SDPOL" 2588926 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1107 2579865 2580131 2580450 "SCPKG" 2580987 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1106 2579029 2579201 2579393 "SCOPE" 2579695 T SCOPE (NIL) -8 NIL NIL NIL) (-1105 2578249 2578383 2578562 "SCACHE" 2578884 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1104 2577881 2578067 2578097 "SASTCAT" 2578102 T SASTCAT (NIL) -9 NIL 2578115 NIL) (-1103 2577368 2577716 2577792 "SAOS" 2577827 T SAOS (NIL) -8 NIL NIL NIL) (-1102 2576933 2576968 2577141 "SAERFFC" 2577327 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1101 2570596 2576830 2576910 "SAE" 2576915 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1100 2570189 2570224 2570383 "SAEFACT" 2570555 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1099 2568510 2568824 2569225 "RURPK" 2569855 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1098 2567147 2567453 2567758 "RULESET" 2568344 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1097 2564370 2564900 2565358 "RULE" 2566828 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1096 2563982 2564164 2564247 "RULECOLD" 2564322 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1095 2563772 2563800 2563871 "RTVALUE" 2563933 T RTVALUE (NIL) -8 NIL NIL NIL) (-1094 2563243 2563489 2563583 "RSTRCAST" 2563700 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1093 2558091 2558886 2559806 "RSETGCD" 2562442 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1092 2547321 2552400 2552497 "RSETCAT" 2556616 NIL RSETCAT (NIL T T T T) -9 NIL 2557713 NIL) (-1091 2545248 2545787 2546611 "RSETCAT-" 2546616 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1090 2537634 2539010 2540530 "RSDCMPK" 2543847 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1089 2535599 2536066 2536140 "RRCC" 2537226 NIL RRCC (NIL T T) -9 NIL 2537570 NIL) (-1088 2534950 2535124 2535403 "RRCC-" 2535408 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1087 2534393 2534646 2534747 "RPTAST" 2534871 T RPTAST (NIL) -8 NIL NIL NIL) (-1086 2507869 2517505 2517572 "RPOLCAT" 2528238 NIL RPOLCAT (NIL T T T) -9 NIL 2531398 NIL) (-1085 2499367 2501707 2504829 "RPOLCAT-" 2504834 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1084 2490302 2497578 2498060 "ROUTINE" 2498907 T ROUTINE (NIL) -8 NIL NIL NIL) (-1083 2486963 2489928 2490068 "ROMAN" 2490184 T ROMAN (NIL) -8 NIL NIL NIL) (-1082 2485207 2485823 2486083 "ROIRC" 2486768 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1081 2481425 2483709 2483739 "RNS" 2484043 T RNS (NIL) -9 NIL 2484317 NIL) (-1080 2479934 2480317 2480851 "RNS-" 2480926 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1079 2479323 2479731 2479761 "RNG" 2479766 T RNG (NIL) -9 NIL 2479787 NIL) (-1078 2478326 2478688 2478890 "RNGBIND" 2479174 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1077 2477711 2478099 2478142 "RMODULE" 2478147 NIL RMODULE (NIL T) -9 NIL 2478174 NIL) (-1076 2476547 2476641 2476977 "RMCAT2" 2477612 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1075 2473397 2475893 2476190 "RMATRIX" 2476309 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1074 2466224 2468484 2468599 "RMATCAT" 2471958 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2472940 NIL) (-1073 2465599 2465746 2466053 "RMATCAT-" 2466058 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1072 2465214 2465386 2465429 "RLINSET" 2465491 NIL RLINSET (NIL T) -9 NIL 2465535 NIL) (-1071 2464781 2464856 2464984 "RINTERP" 2465133 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1070 2463825 2464379 2464409 "RING" 2464465 T RING (NIL) -9 NIL 2464557 NIL) (-1069 2463617 2463661 2463758 "RING-" 2463763 NIL RING- (NIL T) -8 NIL NIL NIL) (-1068 2462458 2462695 2462953 "RIDIST" 2463381 T RIDIST (NIL) -7 NIL NIL NIL) (-1067 2453747 2461926 2462132 "RGCHAIN" 2462306 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1066 2453083 2453489 2453530 "RGBCSPC" 2453588 NIL RGBCSPC (NIL T) -9 NIL 2453640 NIL) (-1065 2452227 2452608 2452649 "RGBCMDL" 2452881 NIL RGBCMDL (NIL T) -9 NIL 2452995 NIL) (-1064 2449221 2449835 2450505 "RF" 2451591 NIL RF (NIL T) -7 NIL NIL NIL) (-1063 2448867 2448930 2449033 "RFFACTOR" 2449152 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1062 2448592 2448627 2448724 "RFFACT" 2448826 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1061 2446709 2447073 2447455 "RFDIST" 2448232 T RFDIST (NIL) -7 NIL NIL NIL) (-1060 2446162 2446254 2446417 "RETSOL" 2446611 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1059 2445798 2445878 2445921 "RETRACT" 2446054 NIL RETRACT (NIL T) -9 NIL 2446141 NIL) (-1058 2445647 2445672 2445759 "RETRACT-" 2445764 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1057 2445249 2445469 2445539 "RETAST" 2445599 T RETAST (NIL) -8 NIL NIL NIL) (-1056 2437991 2444902 2445029 "RESULT" 2445144 T RESULT (NIL) -8 NIL NIL NIL) (-1055 2436582 2437260 2437459 "RESRING" 2437894 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1054 2436218 2436267 2436365 "RESLATC" 2436519 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1053 2435923 2435958 2436065 "REPSQ" 2436177 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1052 2433345 2433925 2434527 "REP" 2435343 T REP (NIL) -7 NIL NIL NIL) (-1051 2433042 2433077 2433188 "REPDB" 2433304 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1050 2426942 2428331 2429554 "REP2" 2431854 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1049 2423319 2424000 2424808 "REP1" 2426169 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1048 2416015 2421460 2421916 "REGSET" 2422949 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1047 2414780 2415163 2415413 "REF" 2415800 NIL REF (NIL T) -8 NIL NIL NIL) (-1046 2414157 2414260 2414427 "REDORDER" 2414664 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1045 2410125 2413370 2413597 "RECLOS" 2413985 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1044 2409177 2409358 2409573 "REALSOLV" 2409932 T REALSOLV (NIL) -7 NIL NIL NIL) (-1043 2409023 2409064 2409094 "REAL" 2409099 T REAL (NIL) -9 NIL 2409134 NIL) (-1042 2405506 2406308 2407192 "REAL0Q" 2408188 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1041 2401107 2402095 2403156 "REAL0" 2404487 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1040 2400578 2400824 2400918 "RDUCEAST" 2401035 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1039 2399983 2400055 2400262 "RDIV" 2400500 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1038 2399051 2399225 2399438 "RDIST" 2399805 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1037 2397648 2397935 2398307 "RDETRS" 2398759 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1036 2395460 2395914 2396452 "RDETR" 2397190 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1035 2394085 2394363 2394760 "RDEEFS" 2395176 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1034 2392594 2392900 2393325 "RDEEF" 2393773 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1033 2386641 2389561 2389591 "RCFIELD" 2390886 T RCFIELD (NIL) -9 NIL 2391617 NIL) (-1032 2384705 2385209 2385905 "RCFIELD-" 2385980 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1031 2380948 2382778 2382821 "RCAGG" 2383905 NIL RCAGG (NIL T) -9 NIL 2384370 NIL) (-1030 2380576 2380670 2380833 "RCAGG-" 2380838 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1029 2379911 2380023 2380188 "RATRET" 2380460 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1028 2379464 2379531 2379652 "RATFACT" 2379839 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1027 2378772 2378892 2379044 "RANDSRC" 2379334 T RANDSRC (NIL) -7 NIL NIL NIL) (-1026 2378506 2378550 2378623 "RADUTIL" 2378721 T RADUTIL (NIL) -7 NIL NIL NIL) (-1025 2371334 2377337 2377648 "RADIX" 2378229 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1024 2361794 2371176 2371306 "RADFF" 2371311 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1023 2361441 2361516 2361546 "RADCAT" 2361706 T RADCAT (NIL) -9 NIL NIL NIL) (-1022 2361223 2361271 2361371 "RADCAT-" 2361376 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1021 2359323 2360993 2361085 "QUEUE" 2361166 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1020 2355584 2359256 2359304 "QUAT" 2359309 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1019 2355215 2355258 2355389 "QUATCT2" 2355535 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1018 2348041 2351665 2351707 "QUATCAT" 2352498 NIL QUATCAT (NIL T) -9 NIL 2353264 NIL) (-1017 2344180 2345217 2346607 "QUATCAT-" 2346703 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1016 2341619 2343228 2343271 "QUAGG" 2343652 NIL QUAGG (NIL T) -9 NIL 2343827 NIL) (-1015 2341221 2341441 2341511 "QQUTAST" 2341571 T QQUTAST (NIL) -8 NIL NIL NIL) (-1014 2340234 2340734 2340899 "QFORM" 2341102 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1013 2330621 2336136 2336178 "QFCAT" 2336846 NIL QFCAT (NIL T) -9 NIL 2337847 NIL) (-1012 2326188 2327389 2328983 "QFCAT-" 2329079 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1011 2325819 2325862 2325993 "QFCAT2" 2326139 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1010 2325274 2325384 2325516 "QEQUAT" 2325709 T QEQUAT (NIL) -8 NIL NIL NIL) (-1009 2318400 2319473 2320659 "QCMPACK" 2324207 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1008 2315938 2316386 2316816 "QALGSET" 2318055 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1007 2315173 2315349 2315585 "QALGSET2" 2315756 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1006 2313858 2314082 2314401 "PWFFINTB" 2314946 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1005 2312033 2312201 2312557 "PUSHVAR" 2313672 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1004 2307922 2308976 2309019 "PTRANFN" 2310930 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1003 2306313 2306604 2306928 "PTPACK" 2307633 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1002 2305942 2305999 2306110 "PTFUNC2" 2306250 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1001 2300363 2304758 2304801 "PTCAT" 2305101 NIL PTCAT (NIL T) -9 NIL 2305254 NIL) (-1000 2300018 2300053 2300179 "PSQFR" 2300322 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-999 2298613 2298911 2299245 "PSEUDLIN" 2299716 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-998 2285376 2287747 2290071 "PSETPK" 2296373 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-997 2278394 2281134 2281230 "PSETCAT" 2284251 NIL PSETCAT (NIL T T T T) -9 NIL 2285065 NIL) (-996 2276230 2276864 2277685 "PSETCAT-" 2277690 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-995 2275579 2275744 2275772 "PSCURVE" 2276040 T PSCURVE (NIL) -9 NIL 2276207 NIL) (-994 2271563 2273079 2273144 "PSCAT" 2273988 NIL PSCAT (NIL T T T) -9 NIL 2274228 NIL) (-993 2270626 2270842 2271242 "PSCAT-" 2271247 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-992 2268985 2269695 2269958 "PRTITION" 2270383 T PRTITION (NIL) -8 NIL NIL NIL) (-991 2268460 2268706 2268798 "PRTDAST" 2268913 T PRTDAST (NIL) -8 NIL NIL NIL) (-990 2257550 2259764 2261952 "PRS" 2266322 NIL PRS (NIL T T) -7 NIL NIL NIL) (-989 2255335 2256872 2256912 "PRQAGG" 2257095 NIL PRQAGG (NIL T) -9 NIL 2257197 NIL) (-988 2254671 2254976 2255004 "PROPLOG" 2255143 T PROPLOG (NIL) -9 NIL 2255258 NIL) (-987 2254275 2254332 2254455 "PROPFUN2" 2254594 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-986 2253590 2253711 2253883 "PROPFUN1" 2254136 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-985 2251771 2252337 2252634 "PROPFRML" 2253326 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-984 2251240 2251347 2251475 "PROPERTY" 2251663 T PROPERTY (NIL) -8 NIL NIL NIL) (-983 2245298 2249406 2250226 "PRODUCT" 2250466 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-982 2242576 2244756 2244990 "PR" 2245109 NIL PR (NIL T T) -8 NIL NIL NIL) (-981 2242372 2242404 2242463 "PRINT" 2242537 T PRINT (NIL) -7 NIL NIL NIL) (-980 2241712 2241829 2241981 "PRIMES" 2242252 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-979 2239777 2240178 2240644 "PRIMELT" 2241291 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-978 2239506 2239555 2239583 "PRIMCAT" 2239707 T PRIMCAT (NIL) -9 NIL NIL NIL) (-977 2235623 2239444 2239489 "PRIMARR" 2239494 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-976 2234630 2234808 2235036 "PRIMARR2" 2235441 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-975 2234273 2234329 2234440 "PREASSOC" 2234568 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-974 2233748 2233881 2233909 "PPCURVE" 2234114 T PPCURVE (NIL) -9 NIL 2234250 NIL) (-973 2233343 2233543 2233626 "PORTNUM" 2233685 T PORTNUM (NIL) -8 NIL NIL NIL) (-972 2230702 2231101 2231693 "POLYROOT" 2232924 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-971 2224608 2230306 2230466 "POLY" 2230575 NIL POLY (NIL T) -8 NIL NIL NIL) (-970 2223991 2224049 2224283 "POLYLIFT" 2224544 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-969 2220266 2220715 2221344 "POLYCATQ" 2223536 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-968 2206608 2212013 2212078 "POLYCAT" 2215592 NIL POLYCAT (NIL T T T) -9 NIL 2217470 NIL) (-967 2200057 2201919 2204303 "POLYCAT-" 2204308 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-966 2199644 2199712 2199832 "POLY2UP" 2199983 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-965 2199276 2199333 2199442 "POLY2" 2199581 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-964 2197961 2198200 2198476 "POLUTIL" 2199050 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-963 2196316 2196593 2196924 "POLTOPOL" 2197683 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-962 2191781 2196250 2196297 "POINT" 2196302 NIL POINT (NIL T) -8 NIL NIL NIL) (-961 2189968 2190325 2190700 "PNTHEORY" 2191426 T PNTHEORY (NIL) -7 NIL NIL NIL) (-960 2188426 2188723 2189122 "PMTOOLS" 2189666 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-959 2188019 2188097 2188214 "PMSYM" 2188342 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-958 2187527 2187596 2187771 "PMQFCAT" 2187944 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-957 2186882 2186992 2187148 "PMPRED" 2187404 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-956 2186275 2186361 2186523 "PMPREDFS" 2186783 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-955 2184939 2185147 2185525 "PMPLCAT" 2186037 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-954 2184471 2184550 2184702 "PMLSAGG" 2184854 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-953 2183944 2184020 2184202 "PMKERNEL" 2184389 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-952 2183561 2183636 2183749 "PMINS" 2183863 NIL PMINS (NIL T) -7 NIL NIL NIL) (-951 2183003 2183072 2183281 "PMFS" 2183486 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-950 2182231 2182349 2182554 "PMDOWN" 2182880 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-949 2181398 2181556 2181737 "PMASS" 2182070 T PMASS (NIL) -7 NIL NIL NIL) (-948 2180671 2180781 2180944 "PMASSFS" 2181285 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-947 2180326 2180394 2180488 "PLOTTOOL" 2180597 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-946 2174933 2176137 2177285 "PLOT" 2179198 T PLOT (NIL) -8 NIL NIL NIL) (-945 2170737 2171781 2172702 "PLOT3D" 2174032 T PLOT3D (NIL) -8 NIL NIL NIL) (-944 2169649 2169826 2170061 "PLOT1" 2170541 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-943 2145040 2149715 2154566 "PLEQN" 2164915 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-942 2144358 2144480 2144660 "PINTERP" 2144905 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-941 2144051 2144098 2144201 "PINTERPA" 2144305 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-940 2143267 2143815 2143902 "PI" 2143942 T PI (NIL) -8 NIL NIL 2144009) (-939 2141550 2142525 2142553 "PID" 2142735 T PID (NIL) -9 NIL 2142869 NIL) (-938 2141301 2141338 2141413 "PICOERCE" 2141507 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-937 2140621 2140760 2140936 "PGROEB" 2141157 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-936 2136208 2137022 2137927 "PGE" 2139736 T PGE (NIL) -7 NIL NIL NIL) (-935 2134331 2134578 2134944 "PGCD" 2135925 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-934 2133669 2133772 2133933 "PFRPAC" 2134215 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-933 2130309 2132217 2132570 "PFR" 2133348 NIL PFR (NIL T) -8 NIL NIL NIL) (-932 2128698 2128942 2129267 "PFOTOOLS" 2130056 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-931 2127231 2127470 2127821 "PFOQ" 2128455 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-930 2125732 2125944 2126300 "PFO" 2127015 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-929 2122285 2125621 2125690 "PF" 2125695 NIL PF (NIL NIL) -8 NIL NIL NIL) (-928 2119605 2120876 2120904 "PFECAT" 2121489 T PFECAT (NIL) -9 NIL 2121873 NIL) (-927 2119050 2119204 2119418 "PFECAT-" 2119423 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-926 2117653 2117905 2118206 "PFBRU" 2118799 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-925 2115519 2115871 2116303 "PFBR" 2117304 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-924 2111565 2113031 2113678 "PERM" 2114905 NIL PERM (NIL T) -8 NIL NIL NIL) (-923 2106799 2107772 2108642 "PERMGRP" 2110728 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-922 2104918 2105878 2105919 "PERMCAT" 2106319 NIL PERMCAT (NIL T) -9 NIL 2106617 NIL) (-921 2104571 2104612 2104736 "PERMAN" 2104871 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-920 2102061 2104236 2104358 "PENDTREE" 2104482 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-919 2100990 2101205 2101246 "PDSPC" 2101779 NIL PDSPC (NIL T) -9 NIL 2102024 NIL) (-918 2100093 2100311 2100673 "PDSPC-" 2100678 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-917 2098975 2099743 2099784 "PDRING" 2099789 NIL PDRING (NIL T) -9 NIL 2099817 NIL) (-916 2097862 2098480 2098534 "PDMOD" 2098539 NIL PDMOD (NIL T T) -9 NIL 2098643 NIL) (-915 2095077 2095855 2096523 "PDEPROB" 2097214 T PDEPROB (NIL) -8 NIL NIL NIL) (-914 2092622 2093126 2093681 "PDEPACK" 2094542 T PDEPACK (NIL) -7 NIL NIL NIL) (-913 2091534 2091724 2091975 "PDECOMP" 2092421 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-912 2089099 2089942 2089970 "PDECAT" 2090757 T PDECAT (NIL) -9 NIL 2091470 NIL) (-911 2088728 2088783 2088837 "PDDOM" 2089002 NIL PDDOM (NIL T T) -9 NIL 2089082 NIL) (-910 2088547 2088577 2088684 "PDDOM-" 2088689 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-909 2088298 2088331 2088421 "PCOMP" 2088508 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-908 2086476 2087099 2087396 "PBWLB" 2088027 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-907 2078949 2080549 2081887 "PATTERN" 2085159 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-906 2078581 2078638 2078747 "PATTERN2" 2078886 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-905 2076338 2076726 2077183 "PATTERN1" 2078170 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-904 2073706 2074287 2074768 "PATRES" 2075903 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-903 2073270 2073337 2073469 "PATRES2" 2073633 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-902 2071153 2071558 2071965 "PATMATCH" 2072937 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-901 2070649 2070858 2070899 "PATMAB" 2071006 NIL PATMAB (NIL T) -9 NIL 2071089 NIL) (-900 2069167 2069503 2069761 "PATLRES" 2070454 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-899 2068713 2068836 2068877 "PATAB" 2068882 NIL PATAB (NIL T) -9 NIL 2069054 NIL) (-898 2066895 2067290 2067713 "PARTPERM" 2068310 T PARTPERM (NIL) -7 NIL NIL NIL) (-897 2066516 2066579 2066681 "PARSURF" 2066826 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-896 2066148 2066205 2066314 "PARSU2" 2066453 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-895 2065912 2065952 2066019 "PARSER" 2066101 T PARSER (NIL) -7 NIL NIL NIL) (-894 2065533 2065596 2065698 "PARSCURV" 2065843 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-893 2065165 2065222 2065331 "PARSC2" 2065470 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-892 2064804 2064862 2064959 "PARPCURV" 2065101 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-891 2064436 2064493 2064602 "PARPC2" 2064741 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-890 2063497 2063809 2063991 "PARAMAST" 2064274 T PARAMAST (NIL) -8 NIL NIL NIL) (-889 2063017 2063103 2063222 "PAN2EXPR" 2063398 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-888 2061794 2062138 2062366 "PALETTE" 2062809 T PALETTE (NIL) -8 NIL NIL NIL) (-887 2060187 2060799 2061159 "PAIR" 2061480 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-886 2053779 2059444 2059639 "PADICRC" 2060041 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-885 2046695 2053123 2053308 "PADICRAT" 2053626 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-884 2045010 2046632 2046677 "PADIC" 2046682 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-883 2042106 2043670 2043710 "PADICCT" 2044291 NIL PADICCT (NIL NIL) -9 NIL 2044573 NIL) (-882 2041063 2041263 2041531 "PADEPAC" 2041893 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-881 2040275 2040408 2040614 "PADE" 2040925 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-880 2038662 2039483 2039763 "OWP" 2040079 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-879 2038155 2038368 2038465 "OVERSET" 2038585 T OVERSET (NIL) -8 NIL NIL NIL) (-878 2037201 2037760 2037932 "OVAR" 2038023 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-877 2036465 2036586 2036747 "OUT" 2037060 T OUT (NIL) -7 NIL NIL NIL) (-876 2025337 2027574 2029774 "OUTFORM" 2034285 T OUTFORM (NIL) -8 NIL NIL NIL) (-875 2024673 2024934 2025061 "OUTBFILE" 2025230 T OUTBFILE (NIL) -8 NIL NIL NIL) (-874 2023980 2024145 2024173 "OUTBCON" 2024491 T OUTBCON (NIL) -9 NIL 2024657 NIL) (-873 2023581 2023693 2023850 "OUTBCON-" 2023855 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-872 2022961 2023310 2023399 "OSI" 2023512 T OSI (NIL) -8 NIL NIL NIL) (-871 2022477 2022815 2022843 "OSGROUP" 2022848 T OSGROUP (NIL) -9 NIL 2022870 NIL) (-870 2021222 2021449 2021734 "ORTHPOL" 2022224 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-869 2018773 2021057 2021178 "OREUP" 2021183 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-868 2016176 2018464 2018591 "ORESUP" 2018715 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-867 2013704 2014204 2014765 "OREPCTO" 2015665 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-866 2007376 2009577 2009618 "OREPCAT" 2011966 NIL OREPCAT (NIL T) -9 NIL 2013070 NIL) (-865 2004523 2005305 2006363 "OREPCAT-" 2006368 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-864 2003952 2004107 2004135 "ORDTYPE" 2004370 T ORDTYPE (NIL) -9 NIL 2004493 NIL) (-863 2003453 2003585 2003782 "ORDTYPE-" 2003787 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-862 2002590 2002888 2002916 "ORDSET" 2003225 T ORDSET (NIL) -9 NIL 2003389 NIL) (-861 2002021 2002169 2002393 "ORDSET-" 2002398 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-860 2000572 2001363 2001391 "ORDRING" 2001593 T ORDRING (NIL) -9 NIL 2001718 NIL) (-859 2000217 2000311 2000455 "ORDRING-" 2000460 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 1999583 2000046 2000074 "ORDMON" 2000079 T ORDMON (NIL) -9 NIL 2000100 NIL) (-857 1998745 1998892 1999087 "ORDFUNS" 1999432 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1998069 1998488 1998516 "ORDFIN" 1998581 T ORDFIN (NIL) -9 NIL 1998655 NIL) (-855 1994628 1996655 1997064 "ORDCOMP" 1997693 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1993894 1994021 1994207 "ORDCOMP2" 1994488 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1990475 1991385 1992199 "OPTPROB" 1993100 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1987277 1987916 1988620 "OPTPACK" 1989791 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1984950 1985716 1985744 "OPTCAT" 1986563 T OPTCAT (NIL) -9 NIL 1987213 NIL) (-850 1984334 1984627 1984732 "OPSIG" 1984865 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1984102 1984141 1984207 "OPQUERY" 1984288 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1981233 1982413 1982917 "OP" 1983631 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1980593 1980819 1980860 "OPERCAT" 1981072 NIL OPERCAT (NIL T) -9 NIL 1981169 NIL) (-846 1980348 1980404 1980521 "OPERCAT-" 1980526 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1977161 1979145 1979514 "ONECOMP" 1980012 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1976466 1976581 1976755 "ONECOMP2" 1977033 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1975885 1975991 1976121 "OMSERVER" 1976356 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1972747 1975325 1975365 "OMSAGG" 1975426 NIL OMSAGG (NIL T) -9 NIL 1975490 NIL) (-841 1971370 1971633 1971915 "OMPKG" 1972485 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1970800 1970903 1970931 "OM" 1971230 T OM (NIL) -9 NIL NIL NIL) (-839 1969347 1970349 1970518 "OMLO" 1970681 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1968307 1968454 1968674 "OMEXPR" 1969173 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1967598 1967853 1967989 "OMERR" 1968191 T OMERR (NIL) -8 NIL NIL NIL) (-836 1966749 1967019 1967179 "OMERRK" 1967458 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1966200 1966426 1966534 "OMENC" 1966661 T OMENC (NIL) -8 NIL NIL NIL) (-834 1960095 1961280 1962451 "OMDEV" 1965049 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1959164 1959335 1959529 "OMCONN" 1959921 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1957671 1958647 1958675 "OINTDOM" 1958680 T OINTDOM (NIL) -9 NIL 1958701 NIL) (-831 1955009 1956359 1956696 "OFMONOID" 1957366 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1954381 1954946 1954991 "ODVAR" 1954996 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1951804 1954126 1954281 "ODR" 1954286 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1944109 1951580 1951706 "ODPOL" 1951711 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1937907 1943981 1944086 "ODP" 1944091 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1936673 1936888 1937163 "ODETOOLS" 1937681 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1933640 1934298 1935014 "ODESYS" 1936006 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1928522 1929430 1930455 "ODERTRIC" 1932715 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1927948 1928030 1928224 "ODERED" 1928434 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1924836 1925384 1926061 "ODERAT" 1927371 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1921795 1922260 1922857 "ODEPRRIC" 1924365 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1919738 1920334 1920820 "ODEPROB" 1921329 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1916258 1916743 1917390 "ODEPRIM" 1919217 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1915507 1915609 1915869 "ODEPAL" 1916150 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1911669 1912460 1913324 "ODEPACK" 1914663 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1910730 1910837 1911059 "ODEINT" 1911558 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1904831 1906256 1907703 "ODEIFTBL" 1909303 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1900229 1901015 1901967 "ODEEF" 1903990 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1899578 1899667 1899890 "ODECONST" 1900134 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1897689 1898350 1898378 "ODECAT" 1898983 T ODECAT (NIL) -9 NIL 1899514 NIL) (-811 1894544 1897394 1897516 "OCT" 1897599 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1894182 1894225 1894352 "OCTCT2" 1894495 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1888817 1891252 1891292 "OC" 1892389 NIL OC (NIL T) -9 NIL 1893247 NIL) (-808 1886044 1886792 1887782 "OC-" 1887876 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1885382 1885850 1885878 "OCAMON" 1885883 T OCAMON (NIL) -9 NIL 1885904 NIL) (-806 1884899 1885240 1885268 "OASGP" 1885273 T OASGP (NIL) -9 NIL 1885293 NIL) (-805 1884146 1884635 1884663 "OAMONS" 1884703 T OAMONS (NIL) -9 NIL 1884746 NIL) (-804 1883546 1883979 1884007 "OAMON" 1884012 T OAMON (NIL) -9 NIL 1884032 NIL) (-803 1882790 1883308 1883336 "OAGROUP" 1883341 T OAGROUP (NIL) -9 NIL 1883361 NIL) (-802 1882480 1882530 1882618 "NUMTUBE" 1882734 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1876053 1877571 1879107 "NUMQUAD" 1880964 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1871809 1872797 1873822 "NUMODE" 1875048 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1869150 1870030 1870058 "NUMINT" 1870981 T NUMINT (NIL) -9 NIL 1871745 NIL) (-798 1868098 1868295 1868513 "NUMFMT" 1868952 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1854457 1857402 1859934 "NUMERIC" 1865605 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1848827 1853906 1854001 "NTSCAT" 1854006 NIL NTSCAT (NIL T T T T) -9 NIL 1854045 NIL) (-795 1848021 1848186 1848379 "NTPOLFN" 1848666 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1835822 1844846 1845658 "NSUP" 1847242 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1835454 1835511 1835620 "NSUP2" 1835759 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1825404 1835228 1835361 "NSMP" 1835366 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1823836 1824137 1824494 "NREP" 1825092 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1822427 1822679 1823037 "NPCOEF" 1823579 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1821493 1821608 1821824 "NORMRETR" 1822308 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1819534 1819824 1820233 "NORMPK" 1821201 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1819219 1819247 1819371 "NORMMA" 1819500 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1819019 1819176 1819205 "NONE" 1819210 T NONE (NIL) -8 NIL NIL NIL) (-785 1818808 1818837 1818906 "NONE1" 1818983 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1818305 1818367 1818546 "NODE1" 1818740 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1816586 1817437 1817692 "NNI" 1818039 T NNI (NIL) -8 NIL NIL 1818274) (-782 1815006 1815319 1815683 "NLINSOL" 1816254 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1811247 1812242 1813141 "NIPROB" 1814127 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1810004 1810238 1810540 "NFINTBAS" 1811009 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1809178 1809654 1809695 "NETCLT" 1809867 NIL NETCLT (NIL T) -9 NIL 1809949 NIL) (-778 1807886 1808117 1808398 "NCODIV" 1808946 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1807648 1807685 1807760 "NCNTFRAC" 1807843 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1805828 1806192 1806612 "NCEP" 1807273 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1804665 1805438 1805466 "NASRING" 1805576 T NASRING (NIL) -9 NIL 1805656 NIL) (-774 1804460 1804504 1804598 "NASRING-" 1804603 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1803553 1804078 1804106 "NARNG" 1804223 T NARNG (NIL) -9 NIL 1804314 NIL) (-772 1803245 1803312 1803446 "NARNG-" 1803451 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1802124 1802331 1802566 "NAGSP" 1803030 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1793396 1795080 1796753 "NAGS" 1800471 T NAGS (NIL) -7 NIL NIL NIL) (-769 1791944 1792252 1792583 "NAGF07" 1793085 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1786482 1787773 1789080 "NAGF04" 1790657 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1779450 1781064 1782697 "NAGF02" 1784869 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1774674 1775774 1776891 "NAGF01" 1778353 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1768302 1769868 1771453 "NAGE04" 1773109 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1759471 1761592 1763722 "NAGE02" 1766192 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1755424 1756371 1757335 "NAGE01" 1758527 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1753219 1753753 1754311 "NAGD03" 1754886 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1744969 1746897 1748851 "NAGD02" 1751285 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1738780 1740205 1741645 "NAGD01" 1743549 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1734989 1735811 1736648 "NAGC06" 1737963 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1733454 1733786 1734142 "NAGC05" 1734653 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1732830 1732949 1733093 "NAGC02" 1733330 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1731775 1732358 1732398 "NAALG" 1732477 NIL NAALG (NIL T) -9 NIL 1732538 NIL) (-755 1731610 1731639 1731729 "NAALG-" 1731734 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1725560 1726668 1727855 "MULTSQFR" 1730506 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1724879 1724954 1725138 "MULTFACT" 1725472 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1717550 1721464 1721517 "MTSCAT" 1722587 NIL MTSCAT (NIL T T) -9 NIL 1723102 NIL) (-751 1717262 1717316 1717408 "MTHING" 1717490 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1717054 1717087 1717147 "MSYSCMD" 1717222 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1713136 1715809 1716129 "MSET" 1716767 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1710205 1712697 1712738 "MSETAGG" 1712743 NIL MSETAGG (NIL T) -9 NIL 1712777 NIL) (-747 1706047 1707584 1708329 "MRING" 1709505 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1705613 1705680 1705811 "MRF2" 1705974 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1705231 1705266 1705410 "MRATFAC" 1705572 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1702843 1703138 1703569 "MPRFF" 1704936 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1696864 1702697 1702794 "MPOLY" 1702799 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1696354 1696389 1696597 "MPCPF" 1696823 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1695868 1695911 1696095 "MPC3" 1696305 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1695063 1695144 1695365 "MPC2" 1695783 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1693364 1693701 1694091 "MONOTOOL" 1694723 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1692575 1692892 1692920 "MONOID" 1693139 T MONOID (NIL) -9 NIL 1693286 NIL) (-737 1692121 1692240 1692421 "MONOID-" 1692426 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1681711 1687941 1688000 "MONOGEN" 1688674 NIL MONOGEN (NIL T T) -9 NIL 1689130 NIL) (-735 1678929 1679664 1680664 "MONOGEN-" 1680783 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1677748 1678194 1678222 "MONADWU" 1678614 T MONADWU (NIL) -9 NIL 1678852 NIL) (-733 1677120 1677279 1677527 "MONADWU-" 1677532 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1676465 1676709 1676737 "MONAD" 1676944 T MONAD (NIL) -9 NIL 1677056 NIL) (-731 1676150 1676228 1676360 "MONAD-" 1676365 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1674439 1675063 1675342 "MOEBIUS" 1675903 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1673703 1674107 1674147 "MODULE" 1674152 NIL MODULE (NIL T) -9 NIL 1674191 NIL) (-728 1673271 1673367 1673557 "MODULE-" 1673562 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1670951 1671635 1671962 "MODRING" 1673095 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1667895 1669056 1669577 "MODOP" 1670480 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1666483 1666962 1667239 "MODMONOM" 1667758 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1656251 1664774 1665188 "MODMON" 1666120 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1653407 1655095 1655371 "MODFIELD" 1656126 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1652384 1652688 1652878 "MMLFORM" 1653237 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1651910 1651953 1652132 "MMAP" 1652335 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1649975 1650742 1650783 "MLO" 1651206 NIL MLO (NIL T) -9 NIL 1651448 NIL) (-719 1647341 1647857 1648459 "MLIFT" 1649456 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1646732 1646816 1646970 "MKUCFUNC" 1647252 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1646331 1646401 1646524 "MKRECORD" 1646655 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1645378 1645540 1645768 "MKFUNC" 1646142 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1644766 1644870 1645026 "MKFLCFN" 1645261 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1644043 1644145 1644330 "MKBCFUNC" 1644659 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1640632 1643597 1643733 "MINT" 1643927 T MINT (NIL) -8 NIL NIL NIL) (-712 1639444 1639687 1639964 "MHROWRED" 1640387 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1634824 1637979 1638384 "MFLOAT" 1639059 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1634181 1634257 1634428 "MFINFACT" 1634736 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1630496 1631344 1632228 "MESH" 1633317 T MESH (NIL) -7 NIL NIL NIL) (-708 1628886 1629198 1629551 "MDDFACT" 1630183 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1625655 1628017 1628058 "MDAGG" 1628313 NIL MDAGG (NIL T) -9 NIL 1628456 NIL) (-706 1614349 1624948 1625155 "MCMPLX" 1625468 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1613486 1613632 1613833 "MCDEN" 1614198 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1611376 1611646 1612026 "MCALCFN" 1613216 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1610301 1610541 1610774 "MAYBE" 1611182 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1607913 1608436 1608998 "MATSTOR" 1609772 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1603824 1607285 1607533 "MATRIX" 1607698 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1599590 1600297 1601033 "MATLIN" 1603181 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1589415 1592647 1592724 "MATCAT" 1597756 NIL MATCAT (NIL T T T) -9 NIL 1599228 NIL) (-698 1585608 1586678 1588091 "MATCAT-" 1588096 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1584202 1584355 1584688 "MATCAT2" 1585443 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1582314 1582638 1583022 "MAPPKG3" 1583877 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1581295 1581468 1581690 "MAPPKG2" 1582138 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1579794 1580078 1580405 "MAPPKG1" 1581001 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1578873 1579200 1579377 "MAPPAST" 1579637 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1578484 1578542 1578665 "MAPHACK3" 1578809 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1578076 1578137 1578251 "MAPHACK2" 1578416 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1577514 1577617 1577759 "MAPHACK1" 1577967 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1575593 1576214 1576518 "MAGMA" 1577242 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1575072 1575317 1575408 "MACROAST" 1575522 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1571492 1573311 1573772 "M3D" 1574644 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1565541 1569803 1569844 "LZSTAGG" 1570626 NIL LZSTAGG (NIL T) -9 NIL 1570921 NIL) (-685 1561499 1562672 1564129 "LZSTAGG-" 1564134 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1558586 1559390 1559877 "LWORD" 1561044 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1558162 1558390 1558465 "LSTAST" 1558531 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1551052 1557933 1558067 "LSQM" 1558072 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1550276 1550415 1550643 "LSPP" 1550907 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1548088 1548389 1548845 "LSMP" 1549965 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1544867 1545541 1546271 "LSMP1" 1547390 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1538695 1543984 1544025 "LSAGG" 1544087 NIL LSAGG (NIL T) -9 NIL 1544165 NIL) (-677 1535390 1536314 1537527 "LSAGG-" 1537532 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1532989 1534534 1534783 "LPOLY" 1535185 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1532571 1532656 1532779 "LPEFRAC" 1532898 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1530892 1531665 1531918 "LO" 1532403 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1530530 1530642 1530670 "LOGIC" 1530781 T LOGIC (NIL) -9 NIL 1530862 NIL) (-672 1530392 1530415 1530486 "LOGIC-" 1530491 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1529585 1529725 1529918 "LODOOPS" 1530248 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1527008 1529501 1529567 "LODO" 1529572 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1525546 1525781 1526134 "LODOF" 1526755 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1521750 1524181 1524222 "LODOCAT" 1524660 NIL LODOCAT (NIL T) -9 NIL 1524871 NIL) (-667 1521483 1521541 1521668 "LODOCAT-" 1521673 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1518803 1521324 1521442 "LODO2" 1521447 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1516238 1518740 1518785 "LODO1" 1518790 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1515119 1515284 1515589 "LODEEF" 1516061 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1510396 1513285 1513326 "LNAGG" 1514188 NIL LNAGG (NIL T) -9 NIL 1514623 NIL) (-662 1509543 1509757 1510099 "LNAGG-" 1510104 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1505679 1506468 1507107 "LMOPS" 1508958 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1505068 1505456 1505497 "LMODULE" 1505502 NIL LMODULE (NIL T) -9 NIL 1505528 NIL) (-659 1502268 1504713 1504836 "LMDICT" 1504978 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1501886 1502058 1502099 "LLINSET" 1502160 NIL LLINSET (NIL T) -9 NIL 1502204 NIL) (-657 1501585 1501794 1501854 "LITERAL" 1501859 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1494750 1500519 1500823 "LIST" 1501314 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1494275 1494349 1494488 "LIST3" 1494670 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1493282 1493460 1493688 "LIST2" 1494093 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1491416 1491728 1492127 "LIST2MAP" 1492929 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1491047 1491235 1491276 "LINSET" 1491281 NIL LINSET (NIL T) -9 NIL 1491315 NIL) (-651 1489460 1490074 1490115 "LINEXP" 1490605 NIL LINEXP (NIL T) -9 NIL 1490878 NIL) (-650 1488037 1488297 1488608 "LINDEP" 1489212 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1484804 1485523 1486300 "LIMITRF" 1487292 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1483107 1483403 1483812 "LIMITPS" 1484499 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1477535 1482618 1482846 "LIE" 1482928 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1476469 1476938 1476978 "LIECAT" 1477118 NIL LIECAT (NIL T) -9 NIL 1477269 NIL) (-645 1476310 1476337 1476425 "LIECAT-" 1476430 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1468901 1475850 1476006 "LIB" 1476174 T LIB (NIL) -8 NIL NIL NIL) (-643 1464536 1465419 1466354 "LGROBP" 1468018 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1462534 1462808 1463158 "LF" 1464257 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1461374 1462066 1462094 "LFCAT" 1462301 T LFCAT (NIL) -9 NIL 1462440 NIL) (-640 1458276 1458906 1459594 "LEXTRIPK" 1460738 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1455020 1455846 1456349 "LEXP" 1457856 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1454496 1454741 1454833 "LETAST" 1454948 T LETAST (NIL) -8 NIL NIL NIL) (-637 1452894 1453207 1453608 "LEADCDET" 1454178 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1452084 1452158 1452387 "LAZM3PK" 1452815 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1447001 1450161 1450699 "LAUPOL" 1451596 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1446580 1446624 1446785 "LAPLACE" 1446951 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1444519 1445681 1445932 "LA" 1446413 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1443499 1444083 1444124 "LALG" 1444186 NIL LALG (NIL T) -9 NIL 1444245 NIL) (-631 1443213 1443272 1443408 "LALG-" 1443413 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1443048 1443072 1443113 "KVTFROM" 1443175 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1441971 1442415 1442600 "KTVLOGIC" 1442883 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1441806 1441830 1441871 "KRCFROM" 1441933 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1440710 1440897 1441196 "KOVACIC" 1441606 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1440545 1440569 1440610 "KONVERT" 1440672 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1440380 1440404 1440445 "KOERCE" 1440507 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1438211 1438973 1439350 "KERNEL" 1440036 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1437707 1437788 1437920 "KERNEL2" 1438125 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1431417 1436184 1436238 "KDAGG" 1436615 NIL KDAGG (NIL T T) -9 NIL 1436821 NIL) (-621 1430946 1431070 1431275 "KDAGG-" 1431280 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1424094 1430607 1430762 "KAFILE" 1430824 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1418522 1423605 1423833 "JORDAN" 1423915 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1417901 1418171 1418292 "JOINAST" 1418421 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1417747 1417806 1417861 "JAVACODE" 1417866 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1413973 1415924 1415978 "IXAGG" 1416907 NIL IXAGG (NIL T T) -9 NIL 1417366 NIL) (-615 1412892 1413198 1413617 "IXAGG-" 1413622 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1408424 1412814 1412873 "IVECTOR" 1412878 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1407190 1407427 1407693 "ITUPLE" 1408191 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1405692 1405869 1406164 "ITRIGMNP" 1407012 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1404437 1404641 1404924 "ITFUN3" 1405468 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1404069 1404126 1404235 "ITFUN2" 1404374 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1403228 1403549 1403723 "ITFORM" 1403915 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1401189 1402248 1402526 "ITAYLOR" 1402983 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1390134 1395326 1396489 "ISUPS" 1400059 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1389238 1389378 1389614 "ISUMP" 1389981 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1384615 1389183 1389224 "ISTRING" 1389229 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1384091 1384336 1384428 "ISAST" 1384543 T ISAST (NIL) -8 NIL NIL NIL) (-603 1383300 1383382 1383598 "IRURPK" 1384005 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1382236 1382437 1382677 "IRSN" 1383080 T IRSN (NIL) -7 NIL NIL NIL) (-601 1380307 1380662 1381091 "IRRF2F" 1381874 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1380054 1380092 1380168 "IRREDFFX" 1380263 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1378669 1378928 1379227 "IROOT" 1379787 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1375273 1376353 1377045 "IR" 1378009 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1374478 1374766 1374917 "IRFORM" 1375142 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1372091 1372586 1373152 "IR2" 1373956 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1371191 1371304 1371518 "IR2F" 1371974 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1370982 1371016 1371076 "IPRNTPK" 1371151 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1367563 1370871 1370940 "IPF" 1370945 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1365890 1367488 1367545 "IPADIC" 1367550 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1365202 1365450 1365580 "IP4ADDR" 1365780 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1364576 1364831 1364963 "IOMODE" 1365090 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1363649 1364173 1364300 "IOBFILE" 1364469 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1363137 1363553 1363581 "IOBCON" 1363586 T IOBCON (NIL) -9 NIL 1363607 NIL) (-587 1362648 1362706 1362889 "INVLAPLA" 1363073 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1352296 1354650 1357036 "INTTR" 1360312 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1348631 1349373 1350238 "INTTOOLS" 1351481 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1348217 1348308 1348425 "INTSLPE" 1348534 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1346170 1348140 1348199 "INTRVL" 1348204 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1343772 1344284 1344859 "INTRF" 1345655 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1343183 1343280 1343422 "INTRET" 1343670 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1341180 1341569 1342039 "INTRAT" 1342791 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1338443 1339026 1339645 "INTPM" 1340665 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1335188 1335787 1336525 "INTPAF" 1337829 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1330367 1331329 1332380 "INTPACK" 1334157 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1327179 1330164 1330273 "INT" 1330278 T INT (NIL) -8 NIL NIL NIL) (-575 1326431 1326583 1326791 "INTHERTR" 1327021 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1325870 1325950 1326138 "INTHERAL" 1326345 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1323716 1324159 1324616 "INTHEORY" 1325433 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1315122 1316743 1318515 "INTG0" 1322068 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1295695 1300485 1305295 "INTFTBL" 1310332 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1294944 1295082 1295255 "INTFACT" 1295554 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1292371 1292817 1293374 "INTEF" 1294498 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1290724 1291463 1291491 "INTDOM" 1291792 T INTDOM (NIL) -9 NIL 1291999 NIL) (-567 1290093 1290267 1290509 "INTDOM-" 1290514 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1286467 1288395 1288449 "INTCAT" 1289248 NIL INTCAT (NIL T) -9 NIL 1289569 NIL) (-565 1285939 1286042 1286170 "INTBIT" 1286359 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1284638 1284792 1285099 "INTALG" 1285784 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1284121 1284211 1284368 "INTAF" 1284542 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1277468 1283931 1284071 "INTABL" 1284076 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1276801 1277267 1277332 "INT8" 1277366 T INT8 (NIL) -8 NIL NIL 1277411) (-560 1276133 1276599 1276664 "INT64" 1276698 T INT64 (NIL) -8 NIL NIL 1276743) (-559 1275465 1275931 1275996 "INT32" 1276030 T INT32 (NIL) -8 NIL NIL 1276075) (-558 1274797 1275263 1275328 "INT16" 1275362 T INT16 (NIL) -8 NIL NIL 1275407) (-557 1269506 1272358 1272386 "INS" 1273320 T INS (NIL) -9 NIL 1273985 NIL) (-556 1266746 1267517 1268491 "INS-" 1268564 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1265521 1265748 1266046 "INPSIGN" 1266499 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1264639 1264756 1264953 "INPRODPF" 1265401 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1263533 1263650 1263887 "INPRODFF" 1264519 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1262533 1262685 1262945 "INNMFACT" 1263369 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1261730 1261827 1262015 "INMODGCD" 1262432 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1260238 1260483 1260807 "INFSP" 1261475 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1259422 1259539 1259722 "INFPROD0" 1260118 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1256277 1257487 1258002 "INFORM" 1258915 T INFORM (NIL) -8 NIL NIL NIL) (-547 1255887 1255947 1256045 "INFORM1" 1256212 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1255410 1255499 1255613 "INFINITY" 1255793 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1254586 1255130 1255231 "INETCLTS" 1255329 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1253202 1253452 1253773 "INEP" 1254334 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1252407 1253099 1253164 "INDE" 1253169 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1251971 1252039 1252156 "INCRMAPS" 1252334 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1250789 1251240 1251446 "INBFILE" 1251785 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1246088 1247025 1247969 "INBFF" 1249877 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1244996 1245265 1245293 "INBCON" 1245806 T INBCON (NIL) -9 NIL 1246072 NIL) (-538 1244248 1244471 1244747 "INBCON-" 1244752 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1243727 1243972 1244063 "INAST" 1244177 T INAST (NIL) -8 NIL NIL NIL) (-536 1243154 1243406 1243512 "IMPTAST" 1243641 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1239554 1242998 1243102 "IMATRIX" 1243107 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1238262 1238385 1238701 "IMATQF" 1239410 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1236482 1236709 1237046 "IMATLIN" 1238018 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1231062 1236406 1236464 "ILIST" 1236469 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1228969 1230922 1231035 "IIARRAY2" 1231040 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1224367 1228880 1228944 "IFF" 1228949 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1223714 1223984 1224100 "IFAST" 1224271 T IFAST (NIL) -8 NIL NIL NIL) (-528 1218711 1223006 1223194 "IFARRAY" 1223571 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1217891 1218615 1218688 "IFAMON" 1218693 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1217475 1217540 1217594 "IEVALAB" 1217801 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1217150 1217218 1217378 "IEVALAB-" 1217383 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1216740 1217064 1217127 "IDPO" 1217132 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1215948 1216629 1216704 "IDPOAMS" 1216709 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1215213 1215837 1215912 "IDPOAM" 1215917 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214070 1214387 1214440 "IDPC" 1214958 NIL IDPC (NIL T T) -9 NIL 1215149 NIL) (-520 1213497 1213962 1214035 "IDPAM" 1214040 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1212831 1213389 1213462 "IDPAG" 1213467 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212476 1212667 1212742 "IDENT" 1212776 T IDENT (NIL) -8 NIL NIL NIL) (-517 1208731 1209579 1210474 "IDECOMP" 1211633 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1201568 1202654 1203701 "IDEAL" 1207767 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1200728 1200840 1201040 "ICDEN" 1201452 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1199799 1200208 1200355 "ICARD" 1200601 T ICARD (NIL) -8 NIL NIL NIL) (-513 1197859 1198172 1198577 "IBPTOOLS" 1199476 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193466 1197479 1197592 "IBITS" 1197778 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190189 1190765 1191460 "IBATOOL" 1192883 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1187968 1188430 1188963 "IBACHIN" 1189724 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1185799 1187814 1187917 "IARRAY2" 1187922 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1181907 1185725 1185782 "IARRAY1" 1185787 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1175767 1180319 1180800 "IAN" 1181446 T IAN (NIL) -8 NIL NIL NIL) (-506 1175278 1175335 1175508 "IALGFACT" 1175704 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1174806 1174919 1174947 "HYPCAT" 1175154 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174344 1174461 1174647 "HYPCAT-" 1174652 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1173939 1174139 1174222 "HOSTNAME" 1174281 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1173784 1173821 1173862 "HOMOTOP" 1173867 NIL HOMOTOP (NIL T) -9 NIL 1173900 NIL) (-501 1170340 1171716 1171757 "HOAGG" 1172738 NIL HOAGG (NIL T) -9 NIL 1173467 NIL) (-500 1168934 1169333 1169859 "HOAGG-" 1169864 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1162650 1168527 1168677 "HEXADEC" 1168804 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161398 1161620 1161883 "HEUGCD" 1162427 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160474 1161235 1161365 "HELLFDIV" 1161370 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1158655 1160251 1160339 "HEAP" 1160418 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1157918 1158207 1158341 "HEADAST" 1158541 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1151760 1157833 1157895 "HDP" 1157900 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145472 1151395 1151547 "HDMP" 1151661 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1144796 1144936 1145100 "HB" 1145328 T HB (NIL) -7 NIL NIL NIL) (-491 1138186 1144642 1144746 "HASHTBL" 1144751 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1137662 1137907 1137999 "HASAST" 1138114 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135440 1137284 1137466 "HACKPI" 1137500 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131108 1135293 1135406 "GTSET" 1135411 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1124527 1130986 1131084 "GSTBL" 1131089 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1116914 1123692 1123948 "GSERIES" 1124327 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1116041 1116458 1116486 "GROUP" 1116689 T GROUP (NIL) -9 NIL 1116823 NIL) (-484 1115407 1115566 1115817 "GROUP-" 1115822 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1113774 1114095 1114482 "GROEBSOL" 1115084 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1112674 1112962 1113013 "GRMOD" 1113542 NIL GRMOD (NIL T T) -9 NIL 1113710 NIL) (-481 1112442 1112478 1112606 "GRMOD-" 1112611 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1107732 1108796 1109796 "GRIMAGE" 1111462 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106198 1106459 1106783 "GRDEF" 1107428 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1105642 1105758 1105899 "GRAY" 1106077 T GRAY (NIL) -7 NIL NIL NIL) (-477 1104815 1105221 1105272 "GRALG" 1105425 NIL GRALG (NIL T T) -9 NIL 1105518 NIL) (-476 1104476 1104549 1104712 "GRALG-" 1104717 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101253 1104061 1104239 "GPOLSET" 1104383 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1100607 1100664 1100922 "GOSPER" 1101190 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096339 1097045 1097571 "GMODPOL" 1100306 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095344 1095528 1095766 "GHENSEL" 1096151 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1089500 1090343 1091363 "GENUPS" 1094428 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089197 1089248 1089337 "GENUFACT" 1089443 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1088609 1088686 1088851 "GENPGCD" 1089115 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1088083 1088118 1088331 "GENMFACT" 1088568 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1086649 1086906 1087213 "GENEEZ" 1087826 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1080521 1086260 1086422 "GDMP" 1086572 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1069864 1074292 1075398 "GCNAALG" 1079504 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068177 1069039 1069067 "GCDDOM" 1069322 T GCDDOM (NIL) -9 NIL 1069479 NIL) (-463 1067647 1067774 1067989 "GCDDOM-" 1067994 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066319 1066504 1066808 "GB" 1067426 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1054935 1057265 1059657 "GBINTERN" 1064010 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1052772 1053064 1053485 "GBF" 1054610 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1051553 1051718 1051985 "GBEUCLID" 1052588 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1050902 1051027 1051176 "GAUSSFAC" 1051424 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049269 1049571 1049885 "GALUTIL" 1050621 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1047577 1047851 1048175 "GALPOLYU" 1048996 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1044942 1045232 1045639 "GALFACTU" 1047274 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1036748 1038247 1039855 "GALFACT" 1043374 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034136 1034794 1034822 "FVFUN" 1035978 T FVFUN (NIL) -9 NIL 1036698 NIL) (-452 1033402 1033584 1033612 "FVC" 1033903 T FVC (NIL) -9 NIL 1034086 NIL) (-451 1033045 1033227 1033295 "FUNDESC" 1033354 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1032660 1032842 1032923 "FUNCTION" 1032997 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030404 1030982 1031448 "FT" 1032214 T FT (NIL) -8 NIL NIL NIL) (-448 1029195 1029705 1029908 "FTEM" 1030221 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027486 1027775 1028172 "FSUPFACT" 1028886 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1025883 1026172 1026504 "FST" 1027174 T FST (NIL) -8 NIL NIL NIL) (-445 1025082 1025188 1025376 "FSRED" 1025765 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1023781 1024037 1024384 "FSPRMELT" 1024797 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1021087 1021525 1022011 "FSPECF" 1023344 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002152 1010861 1010902 "FS" 1014786 NIL FS (NIL T) -9 NIL 1017075 NIL) (-441 990795 993788 997845 "FS-" 998145 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990323 990377 990547 "FSINT" 990736 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 988615 989316 989619 "FSERIES" 990102 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 987657 987773 987997 "FSCINT" 988495 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 983865 986601 986642 "FSAGG" 987012 NIL FSAGG (NIL T) -9 NIL 987271 NIL) (-436 981627 982228 983024 "FSAGG-" 983119 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 980669 980812 981039 "FSAGG2" 981480 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978347 978627 979175 "FS2UPS" 980387 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 977981 978024 978153 "FS2" 978298 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 976859 977030 977332 "FS2EXPXP" 977806 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976285 976400 976552 "FRUTIL" 976739 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 967698 971780 973138 "FR" 974959 NIL FR (NIL T) -8 NIL NIL NIL) (-429 962712 965387 965427 "FRNAALG" 966747 NIL FRNAALG (NIL T) -9 NIL 967345 NIL) (-428 958385 959461 960736 "FRNAALG-" 961486 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 958023 958066 958193 "FRNAAF2" 958336 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956398 956872 957168 "FRMOD" 957835 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954141 954773 955091 "FRIDEAL" 956189 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953332 953419 953710 "FRIDEAL2" 954048 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952465 952879 952920 "FRETRCT" 952925 NIL FRETRCT (NIL T) -9 NIL 953101 NIL) (-422 951577 951808 952159 "FRETRCT-" 952164 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 948651 949861 949920 "FRAMALG" 950802 NIL FRAMALG (NIL T T) -9 NIL 951094 NIL) (-420 946785 947240 947870 "FRAMALG-" 948093 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940428 946258 946535 "FRAC" 946540 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 940064 940121 940228 "FRAC2" 940365 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 939700 939757 939864 "FR2" 940001 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934199 937092 937120 "FPS" 938239 T FPS (NIL) -9 NIL 938796 NIL) (-415 933648 933757 933921 "FPS-" 934067 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 930936 932605 932633 "FPC" 932858 T FPC (NIL) -9 NIL 933000 NIL) (-413 930729 930769 930866 "FPC-" 930871 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 929519 930217 930258 "FPATMAB" 930263 NIL FPATMAB (NIL T) -9 NIL 930415 NIL) (-411 927758 928261 928608 "FPARFRAC" 929235 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923152 923650 924332 "FORTRAN" 927190 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 920868 921368 921907 "FORT" 922633 T FORT (NIL) -7 NIL NIL NIL) (-408 918544 919106 919134 "FORTFN" 920194 T FORTFN (NIL) -9 NIL 920818 NIL) (-407 918308 918358 918386 "FORTCAT" 918445 T FORTCAT (NIL) -9 NIL 918507 NIL) (-406 916414 916924 917314 "FORMULA" 917938 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916202 916232 916301 "FORMULA1" 916378 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 915725 915777 915950 "FORDER" 916144 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 914821 914985 915178 "FOP" 915552 T FOP (NIL) -7 NIL NIL NIL) (-402 913402 914101 914275 "FNLA" 914703 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912117 912532 912560 "FNCAT" 913020 T FNCAT (NIL) -9 NIL 913280 NIL) (-400 911656 912076 912104 "FNAME" 912109 T FNAME (NIL) -8 NIL NIL NIL) (-399 910205 911168 911196 "FMTC" 911201 T FMTC (NIL) -9 NIL 911237 NIL) (-398 908951 910141 910187 "FMONOID" 910192 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 905765 906933 906974 "FMONCAT" 908191 NIL FMONCAT (NIL T) -9 NIL 908796 NIL) (-396 904915 905507 905656 "FM" 905661 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902339 902985 903013 "FMFUN" 904157 T FMFUN (NIL) -9 NIL 904865 NIL) (-394 901608 901789 901817 "FMC" 902107 T FMC (NIL) -9 NIL 902289 NIL) (-393 898673 899533 899587 "FMCAT" 900782 NIL FMCAT (NIL T T) -9 NIL 901277 NIL) (-392 897539 898439 898539 "FM1" 898618 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895313 895729 896223 "FLOATRP" 897090 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 888891 893042 893663 "FLOAT" 894712 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886329 886829 887407 "FLOATCP" 888358 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 884977 885921 885962 "FLINEXP" 885967 NIL FLINEXP (NIL T) -9 NIL 886060 NIL) (-387 884131 884366 884694 "FLINEXP-" 884699 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883207 883351 883575 "FLASORT" 883983 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880309 881177 881229 "FLALG" 882456 NIL FLALG (NIL T T) -9 NIL 882923 NIL) (-384 873995 877745 877786 "FLAGG" 879048 NIL FLAGG (NIL T) -9 NIL 879700 NIL) (-383 872721 873060 873550 "FLAGG-" 873555 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 871763 871906 872133 "FLAGG2" 872574 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 868600 869608 869667 "FINRALG" 870795 NIL FINRALG (NIL T T) -9 NIL 871303 NIL) (-380 867760 867989 868328 "FINRALG-" 868333 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867126 867365 867393 "FINITE" 867589 T FINITE (NIL) -9 NIL 867696 NIL) (-378 859469 861656 861696 "FINAALG" 865363 NIL FINAALG (NIL T) -9 NIL 866816 NIL) (-377 854801 855851 856995 "FINAALG-" 858374 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854169 854556 854659 "FILE" 854731 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 852813 853151 853205 "FILECAT" 853889 NIL FILECAT (NIL T T) -9 NIL 854105 NIL) (-374 850515 852043 852071 "FIELD" 852111 T FIELD (NIL) -9 NIL 852191 NIL) (-373 849135 849520 850031 "FIELD-" 850036 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 846985 847770 848117 "FGROUP" 848821 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846075 846239 846459 "FGLMICPK" 846817 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 841907 846000 846057 "FFX" 846062 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841508 841569 841704 "FFSLPE" 841840 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837498 838280 839076 "FFPOLY" 840744 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837002 837038 837247 "FFPOLY2" 837456 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 832848 836921 836984 "FFP" 836989 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828246 832759 832823 "FF" 832828 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823372 827589 827779 "FFNBX" 828100 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818300 822507 822765 "FFNBP" 823226 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 812933 817584 817795 "FFNB" 818133 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 811765 811963 812278 "FFINTBAS" 812730 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 807791 810012 810040 "FFIELDC" 810660 T FFIELDC (NIL) -9 NIL 811036 NIL) (-359 806453 806824 807321 "FFIELDC-" 807326 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806022 806068 806192 "FFHOM" 806395 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 803717 804204 804721 "FFF" 805537 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799335 803459 803560 "FFCGX" 803660 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 794957 799067 799174 "FFCGP" 799278 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790140 794684 794792 "FFCG" 794893 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 769669 779872 779958 "FFCAT" 785123 NIL FFCAT (NIL T T T) -9 NIL 786574 NIL) (-352 764866 765914 767228 "FFCAT-" 768458 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764277 764320 764555 "FFCAT2" 764817 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 753600 757249 758469 "FEXPR" 763129 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752562 752997 753038 "FEVALAB" 753122 NIL FEVALAB (NIL T) -9 NIL 753383 NIL) (-348 751721 751931 752269 "FEVALAB-" 752274 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750287 751104 751307 "FDIV" 751620 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747293 748034 748149 "FDIVCAT" 749717 NIL FDIVCAT (NIL T T T T) -9 NIL 750154 NIL) (-345 747055 747082 747252 "FDIVCAT-" 747257 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746275 746362 746639 "FDIV2" 746962 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745249 745570 745772 "FCTRDATA" 746093 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 743935 744194 744483 "FCPAK1" 744980 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743034 743435 743576 "FCOMP" 743826 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 726739 730184 733722 "FC" 739516 T FC (NIL) -8 NIL NIL NIL) (-339 719032 723060 723100 "FAXF" 724902 NIL FAXF (NIL T) -9 NIL 725594 NIL) (-338 716309 716966 717791 "FAXF-" 718256 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711363 715685 715861 "FARRAY" 716166 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706243 708310 708363 "FAMR" 709386 NIL FAMR (NIL T T) -9 NIL 709846 NIL) (-335 705133 705435 705870 "FAMR-" 705875 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704302 705055 705108 "FAMONOID" 705113 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702074 702784 702837 "FAMONC" 703778 NIL FAMONC (NIL T T) -9 NIL 704164 NIL) (-332 700738 701828 701965 "FAGROUP" 701970 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698533 698852 699255 "FACUTIL" 700419 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 697632 697817 698039 "FACTFUNC" 698343 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690054 696935 697134 "EXPUPXS" 697488 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687537 688077 688663 "EXPRTUBE" 689488 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 683808 684400 685130 "EXPRODE" 686876 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669292 682457 682886 "EXPR" 683412 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 663846 664433 665239 "EXPR2UPS" 668590 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663478 663535 663644 "EXPR2" 663783 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654475 662629 662920 "EXPEXPAN" 663314 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654275 654432 654461 "EXIT" 654466 T EXIT (NIL) -8 NIL NIL NIL) (-321 653755 653999 654090 "EXITAST" 654204 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653382 653444 653557 "EVALCYC" 653687 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 652923 653041 653082 "EVALAB" 653252 NIL EVALAB (NIL T) -9 NIL 653356 NIL) (-318 652404 652526 652747 "EVALAB-" 652752 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 649758 651060 651088 "EUCDOM" 651643 T EUCDOM (NIL) -9 NIL 651993 NIL) (-316 648163 648605 649195 "EUCDOM-" 649200 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 635702 638461 641211 "ESTOOLS" 645433 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635334 635391 635500 "ESTOOLS2" 635639 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635085 635127 635207 "ESTOOLS1" 635286 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629108 630716 630744 "ES" 633512 T ES (NIL) -9 NIL 634922 NIL) (-311 624055 625342 627159 "ES-" 627323 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620429 621190 621970 "ESCONT" 623295 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620174 620206 620288 "ESCONT1" 620391 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 619849 619899 619999 "ES2" 620118 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619479 619537 619646 "ES1" 619785 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 618695 618824 619000 "ERROR" 619323 T ERROR (NIL) -7 NIL NIL NIL) (-305 612091 618554 618645 "EQTBL" 618650 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 604594 607405 608854 "EQ" 610675 NIL -3043 (NIL T) -8 NIL NIL NIL) (-303 604226 604283 604392 "EQ2" 604531 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599517 600564 601657 "EP" 603165 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598117 598408 598714 "ENV" 599231 T ENV (NIL) -8 NIL NIL NIL) (-300 597197 597751 597779 "ENTIRER" 597784 T ENTIRER (NIL) -9 NIL 597830 NIL) (-299 593891 595379 595740 "EMR" 597005 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593021 593206 593260 "ELTAGG" 593640 NIL ELTAGG (NIL T T) -9 NIL 593851 NIL) (-297 592740 592802 592943 "ELTAGG-" 592948 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592504 592533 592587 "ELTAB" 592671 NIL ELTAB (NIL T T) -9 NIL 592723 NIL) (-295 591630 591776 591975 "ELFUTS" 592355 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591372 591428 591456 "ELEMFUN" 591561 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591242 591263 591331 "ELEMFUN-" 591336 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586030 589284 589325 "ELAGG" 590265 NIL ELAGG (NIL T) -9 NIL 590728 NIL) (-291 584315 584749 585412 "ELAGG-" 585417 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 583627 583764 583920 "ELABOR" 584179 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582288 582567 582861 "ELABEXPR" 583353 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575122 576925 577754 "EFUPXS" 581563 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568570 570371 571182 "EFULS" 574397 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566055 566413 566885 "EFSTRUC" 568202 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 555846 557412 558960 "EF" 564570 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 554920 555331 555480 "EAB" 555717 T EAB (NIL) -8 NIL NIL NIL) (-283 554102 554879 554907 "E04UCFA" 554912 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553284 554061 554089 "E04NAFA" 554094 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552466 553243 553271 "E04MBFA" 553276 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 551648 552425 552453 "E04JAFA" 552458 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 550832 551607 551635 "E04GCFA" 551640 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550016 550791 550819 "E04FDFA" 550824 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549198 549975 550003 "E04DGFA" 550008 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543371 544723 546087 "E04AGNT" 547854 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542142 542685 542725 "DVARCAT" 543066 NIL DVARCAT (NIL T) -9 NIL 543229 NIL) (-274 541346 541558 541872 "DVARCAT-" 541877 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534207 541145 541274 "DSMP" 541279 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 532630 533349 533390 "DSEXT" 533753 NIL DSEXT (NIL T) -9 NIL 534047 NIL) (-271 530915 531343 532009 "DSEXT-" 532014 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 525696 526860 527928 "DROPT" 529867 T DROPT (NIL) -8 NIL NIL NIL) (-269 525361 525420 525518 "DROPT1" 525631 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520476 521602 522739 "DROPT0" 524244 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 518821 519146 519532 "DRAWPT" 520110 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513408 514331 515410 "DRAW" 517795 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513041 513094 513212 "DRAWHACK" 513349 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 511772 512041 512332 "DRAWCX" 512770 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511287 511356 511507 "DRAWCURV" 511698 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 501755 503717 505832 "DRAWCFUN" 509192 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498493 500420 500461 "DQAGG" 501090 NIL DQAGG (NIL T) -9 NIL 501364 NIL) (-260 485958 492704 492787 "DPOLCAT" 494639 NIL DPOLCAT (NIL T T T T) -9 NIL 495184 NIL) (-259 480795 482143 484101 "DPOLCAT-" 484106 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474142 480656 480754 "DPMO" 480759 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467392 473922 474089 "DPMM" 474094 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 466962 467176 467265 "DOMTMPLT" 467323 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466395 466764 466844 "DOMCTOR" 466902 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 465607 465875 466026 "DOMAIN" 466264 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459319 465242 465394 "DMP" 465508 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457264 458386 458427 "DMEXT" 458432 NIL DMEXT (NIL T) -9 NIL 458608 NIL) (-251 456864 456920 457064 "DLP" 457202 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 450688 456191 456381 "DLIST" 456706 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447459 449513 449554 "DLAGG" 450104 NIL DLAGG (NIL T) -9 NIL 450334 NIL) (-248 446121 446785 446813 "DIVRING" 446905 T DIVRING (NIL) -9 NIL 446988 NIL) (-247 445358 445548 445848 "DIVRING-" 445853 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443460 443817 444223 "DISPLAY" 444972 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437322 443374 443437 "DIRPROD" 443442 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436170 436373 436638 "DIRPROD2" 437115 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 424899 430936 430989 "DIRPCAT" 431247 NIL DIRPCAT (NIL NIL T) -9 NIL 432122 NIL) (-242 422225 422867 423748 "DIRPCAT-" 424085 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421512 421672 421858 "DIOSP" 422059 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418141 420396 420437 "DIOPS" 420871 NIL DIOPS (NIL T) -9 NIL 421100 NIL) (-239 417690 417804 417995 "DIOPS-" 418000 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 416741 417369 417397 "DIFRING" 417402 T DIFRING (NIL) -9 NIL 417424 NIL) (-237 416413 416487 416515 "DIFFSPC" 416634 T DIFFSPC (NIL) -9 NIL 416709 NIL) (-236 416058 416136 416288 "DIFFSPC-" 416293 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415114 415592 415633 "DIFFMOD" 415638 NIL DIFFMOD (NIL T) -9 NIL 415736 NIL) (-234 414822 414867 414908 "DIFFDOM" 415029 NIL DIFFDOM (NIL T) -9 NIL 415097 NIL) (-233 414675 414699 414783 "DIFFDOM-" 414788 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412607 413879 413920 "DIFEXT" 413925 NIL DIFEXT (NIL T) -9 NIL 414078 NIL) (-231 409856 412111 412152 "DIAGG" 412157 NIL DIAGG (NIL T) -9 NIL 412177 NIL) (-230 409240 409397 409649 "DIAGG-" 409654 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404611 408199 408476 "DHMATRIX" 409009 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400223 401132 402142 "DFSFUN" 403621 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395301 399154 399466 "DFLOAT" 399931 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393564 393845 394234 "DFINTTLS" 395009 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390593 391585 391985 "DERHAM" 393230 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388396 390368 390457 "DEQUEUE" 390537 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 387650 387783 387966 "DEGRED" 388258 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384080 384825 385671 "DEFINTRF" 386878 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 381635 382104 382696 "DEFINTEF" 383599 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 380985 381255 381370 "DEFAST" 381540 T DEFAST (NIL) -8 NIL NIL NIL) (-219 374701 380578 380728 "DECIMAL" 380855 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372213 372671 373177 "DDFACT" 374245 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 371809 371852 372003 "DBLRESP" 372164 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 369677 370039 370400 "DBASE" 371575 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 368919 369157 369303 "DATAARY" 369576 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368025 368878 368906 "D03FAFA" 368911 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367132 367984 368012 "D03EEFA" 368017 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365082 365548 366037 "D03AGNT" 366663 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364371 365041 365069 "D02EJFA" 365074 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 363660 364330 364358 "D02CJFA" 364363 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 362949 363619 363647 "D02BHFA" 363652 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362238 362908 362936 "D02BBFA" 362941 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355435 357024 358630 "D02AGNT" 360652 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353203 353726 354272 "D01WGTS" 354909 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352270 353162 353190 "D01TRNS" 353195 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351338 352229 352257 "D01GBFA" 352262 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350406 351297 351325 "D01FCFA" 351330 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349474 350365 350393 "D01ASFA" 350398 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348542 349433 349461 "D01AQFA" 349466 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347610 348501 348529 "D01APFA" 348534 T D01APFA (NIL) -8 NIL NIL NIL) (-199 346678 347569 347597 "D01ANFA" 347602 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 345746 346637 346665 "D01AMFA" 346670 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 344814 345705 345733 "D01ALFA" 345738 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 343882 344773 344801 "D01AKFA" 344806 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 342950 343841 343869 "D01AJFA" 343874 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336245 337798 339359 "D01AGNT" 341409 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335582 335710 335862 "CYCLOTOM" 336113 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332315 333030 333757 "CYCLES" 334875 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331627 331761 331932 "CVMP" 332176 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329468 329726 330095 "CTRIGMNP" 331355 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 328904 329262 329335 "CTOR" 329415 T CTOR (NIL) -8 NIL NIL NIL) (-188 328413 328635 328736 "CTORKIND" 328823 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 327690 328006 328034 "CTORCAT" 328216 T CTORCAT (NIL) -9 NIL 328329 NIL) (-186 327288 327399 327558 "CTORCAT-" 327563 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 326750 326962 327070 "CTORCALL" 327212 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326124 326223 326376 "CSTTOOLS" 326647 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 321923 322580 323338 "CRFP" 325436 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321398 321644 321736 "CRCEAST" 321851 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320445 320630 320858 "CRAPACK" 321202 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 319829 319930 320134 "CPMATCH" 320321 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319554 319582 319688 "CPIMA" 319795 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 315902 316574 317293 "COORDSYS" 318889 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315314 315435 315577 "CONTOUR" 315780 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311205 313317 313809 "CONTFRAC" 314854 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311085 311106 311134 "CONDUIT" 311171 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310159 310713 310741 "COMRING" 310746 T COMRING (NIL) -9 NIL 310798 NIL) (-173 309213 309517 309701 "COMPPROP" 309995 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 308874 308909 309037 "COMPLPAT" 309172 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298177 308683 308792 "COMPLEX" 308797 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 297813 297870 297977 "COMPLEX2" 298114 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297152 297273 297433 "COMPILER" 297673 T COMPILER (NIL) -8 NIL NIL NIL) (-168 296870 296905 297003 "COMPFACT" 297111 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279149 290574 290614 "COMPCAT" 291618 NIL COMPCAT (NIL T) -9 NIL 292966 NIL) (-166 268661 271588 275215 "COMPCAT-" 275571 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268390 268418 268521 "COMMUPC" 268627 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268184 268218 268277 "COMMONOP" 268351 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 267740 267935 268022 "COMM" 268117 T COMM (NIL) -8 NIL NIL NIL) (-162 267316 267544 267619 "COMMAAST" 267685 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266565 266759 266787 "COMBOPC" 267125 T COMBOPC (NIL) -9 NIL 267300 NIL) (-160 265461 265671 265913 "COMBINAT" 266355 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 261918 262492 263119 "COMBF" 264883 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 260676 261034 261269 "COLOR" 261703 T COLOR (NIL) -8 NIL NIL NIL) (-157 260152 260397 260489 "COLONAST" 260604 T COLONAST (NIL) -8 NIL NIL NIL) (-156 259792 259839 259964 "CMPLXRT" 260099 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 259240 259492 259591 "CLLCTAST" 259713 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 254742 255770 256850 "CLIP" 258180 T CLIP (NIL) -7 NIL NIL NIL) (-153 253083 253843 254083 "CLIF" 254569 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 249232 251201 251242 "CLAGG" 252171 NIL CLAGG (NIL T) -9 NIL 252707 NIL) (-151 247654 248111 248694 "CLAGG-" 248699 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 247198 247283 247423 "CINTSLPE" 247563 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 244699 245170 245718 "CHVAR" 246726 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 243859 244413 244441 "CHARZ" 244446 T CHARZ (NIL) -9 NIL 244461 NIL) (-147 243613 243653 243731 "CHARPOL" 243813 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 242657 243244 243272 "CHARNZ" 243319 T CHARNZ (NIL) -9 NIL 243375 NIL) (-145 240563 241311 241664 "CHAR" 242324 T CHAR (NIL) -8 NIL NIL NIL) (-144 240289 240350 240378 "CFCAT" 240489 T CFCAT (NIL) -9 NIL NIL NIL) (-143 239530 239641 239824 "CDEN" 240173 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 235495 238683 238963 "CCLASS" 239270 T CCLASS (NIL) -8 NIL NIL NIL) (-141 234746 234903 235080 "CATEGORY" 235338 T -10 (NIL) -8 NIL NIL NIL) (-140 234319 234665 234713 "CATCTOR" 234718 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 233770 234022 234120 "CATAST" 234241 T CATAST (NIL) -8 NIL NIL NIL) (-138 233246 233491 233583 "CASEAST" 233698 T CASEAST (NIL) -8 NIL NIL NIL) (-137 228384 229403 230147 "CARTEN" 232558 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227492 227640 227861 "CARTEN2" 228231 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 225808 226642 226899 "CARD" 227255 T CARD (NIL) -8 NIL NIL NIL) (-134 225384 225612 225687 "CAPSLAST" 225753 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 224874 225082 225110 "CACHSET" 225242 T CACHSET (NIL) -9 NIL 225320 NIL) (-132 224330 224652 224680 "CABMON" 224730 T CABMON (NIL) -9 NIL 224786 NIL) (-131 223803 224034 224144 "BYTEORD" 224240 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 222780 223332 223474 "BYTE" 223637 T BYTE (NIL) -8 NIL NIL 223759) (-129 218132 222285 222457 "BYTEBUF" 222628 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 215643 217824 217931 "BTREE" 218058 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 213094 215291 215413 "BTOURN" 215553 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210438 212536 212577 "BTCAT" 212645 NIL BTCAT (NIL T) -9 NIL 212722 NIL) (-125 210105 210185 210334 "BTCAT-" 210339 NIL BTCAT- 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125581 125672 "ARRAY2" 125677 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 119357 123238 123352 "ARRAY1" 123507 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 118389 118562 118783 "ARRAY12" 119180 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 112675 114591 114666 "ARR2CAT" 117296 NIL ARR2CAT (NIL T T T) -9 NIL 118054 NIL) (-56 110109 110853 111807 "ARR2CAT-" 111812 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 109426 109736 109861 "ARITY" 110002 T ARITY (NIL) -8 NIL NIL NIL) (-54 108202 108354 108653 "APPRULE" 109262 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107853 107901 108020 "APPLYORE" 108148 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 107207 107446 107566 "ANY" 107751 T ANY (NIL) -8 NIL NIL NIL) (-51 106485 106608 106765 "ANY1" 107081 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 104015 104922 105249 "ANTISYM" 106209 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 103507 103722 103818 "ANON" 103937 T ANON (NIL) -8 NIL NIL NIL) (-48 97507 102046 102500 "AN" 103071 T AN (NIL) -8 NIL NIL NIL) (-47 93391 94779 94830 "AMR" 95578 NIL AMR (NIL T T) -9 NIL 96178 NIL) (-46 92503 92724 93087 "AMR-" 93092 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 76946 92420 92481 "ALIST" 92486 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73751 76540 76709 "ALGSC" 76864 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70307 70861 71468 "ALGPKG" 73191 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69584 69685 69869 "ALGMFACT" 70193 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65619 66198 66792 "ALGMANIP" 69168 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55830 65245 65395 "ALGFF" 65552 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55026 55157 55336 "ALGFACT" 55688 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53953 54553 54591 "ALGEBRA" 54596 NIL ALGEBRA (NIL T) -9 NIL 54637 NIL) (-37 53671 53730 53862 "ALGEBRA-" 53867 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35666 51569 51621 "ALAGG" 51757 NIL ALAGG (NIL T T) -9 NIL 51918 NIL) (-35 35202 35315 35341 "AHYP" 35542 T AHYP (NIL) -9 NIL NIL NIL) (-34 34133 34381 34407 "AGG" 34906 T AGG (NIL) -9 NIL 35185 NIL) (-33 33567 33729 33943 "AGG-" 33948 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31373 31796 32201 "AF" 33209 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30853 31098 31188 "ADDAST" 31301 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30121 30380 30536 "ACPLOT" 30715 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18744 27053 27091 "ACFS" 27698 NIL ACFS (NIL T) -9 NIL 27937 NIL) (-28 16771 17261 18023 "ACFS-" 18028 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12875 14804 14830 "ACF" 15709 T ACF (NIL) -9 NIL 16122 NIL) (-26 11579 11913 12406 "ACF-" 12411 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11137 11332 11358 "ABELSG" 11450 T ABELSG (NIL) -9 NIL 11515 NIL) (-24 11004 11029 11095 "ABELSG-" 11100 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10333 10620 10646 "ABELMON" 10816 T ABELMON (NIL) -9 NIL 10928 NIL) (-22 9997 10081 10219 "ABELMON-" 10224 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9331 9703 9729 "ABELGRP" 9801 T ABELGRP (NIL) -9 NIL 9876 NIL) (-20 8794 8923 9139 "ABELGRP-" 9144 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index ad93fe13..a6dd7934 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,4798 +1,1609 @@ -(731535 . 3486772027) -(((*1 *2 *1) (-12 (-5 *2 (-1154)) (-5 *1 (-537))))) +(731754 . 3486783787) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-304 (-419 (-971 *5)))) (-5 *4 (-1197)) + (-4 *5 (-13 (-317) (-148))) + (-5 *2 (-1186 (-656 (-326 *5)) (-656 (-304 (-326 *5))))) + (-5 *1 (-1150 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-419 (-971 *5))) (-5 *4 (-1197)) + (-4 *5 (-13 (-317) (-148))) + (-5 *2 (-1186 (-656 (-326 *5)) (-656 (-304 (-326 *5))))) + (-5 *1 (-1150 *5))))) +(((*1 *1) (-5 *1 (-340)))) +(((*1 *2 *1) (-12 (-5 *2 (-656 (-624 *1))) (-4 *1 (-312))))) +(((*1 *2 *1 *3) + (-12 (-4 *1 (-566 *3)) (-4 *3 (-13 (-416) (-1223))) (-5 *2 (-112))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-656 (-270))) (-5 *4 (-1197)) (-5 *2 (-112)) + (-5 *1 (-270))))) (((*1 *2 *3) - 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(-5 *2 (-656 (-656 *3))) (-4 *3 (-1121)) (-5 *1 (-924 *3))))) +(((*1 *2 *3 *3 *1) + (-12 (-5 *3 (-518)) (-5 *2 (-703 (-1125))) (-5 *1 (-301))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-783)) (-4 *6 (-1121)) (-4 *3 (-917 *6)) + (-5 *2 (-701 *3)) (-5 *1 (-704 *6 *3 *7 *4)) (-4 *7 (-384 *3)) + (-4 *4 (-13 (-384 *6) (-10 -7 (-6 -4464))))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) - (|:| -3954 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (-2 (|:| |var| (-1197)) (|:| |fn| (-326 (-227))) + (|:| -3646 (-1115 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) - (-5 *2 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1176 (-227))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3954 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))) - (-5 *1 (-571))))) -(((*1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1236))))) -(((*1 *2 *2 *3) - (-12 (-5 *1 (-691 *2 *3)) (-4 *2 (-1119)) (-4 *3 (-1119))))) -(((*1 *1 *1) - (-12 (-5 *1 (-1160 *2 *3)) (-4 *2 (-13 (-1119) (-34))) - (-4 *3 (-13 (-1119) (-34)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-656 (-938))) (-5 *2 (-921 (-576))) (-5 *1 (-934))))) -(((*1 *1 *2) - (-12 (-5 *2 (-656 *1)) (-4 *3 (-1068)) (-4 *1 (-699 *3 *4 *5)) - (-4 *4 (-384 *3)) (-4 *5 (-384 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-656 *3)) (-4 *3 (-1068)) (-4 *1 (-699 *3 *4 *5)) - (-4 *4 (-384 *3)) (-4 *5 (-384 *3)))) - 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124233) (-3997 . 124132) + (-3998 . 123873) (-3999 . 123765) (-4000 . 123683) (-4001 . 123324) + (-4002 . 123063) (-4003 . 122969) (-4004 . 122837) (-4005 . 122768) + (-4006 . 122642) (-4007 . 122548) (-4008 . 122252) (-4009 . 121908) + (-4010 . 121821) (-4011 . 121676) (-4012 . 121080) (-4013 . 120865) + (-4014 . 120761) (-4015 . 120493) (-4016 . 120335) (-4017 . 120262) + (-4018 . 118919) (-4019 . 118682) (-4020 . 117840) (-4021 . 117477) + (-4022 . 108027) (-4023 . 107862) (-4024 . 107738) (-4025 . 107376) + (-4026 . 107280) (-4027 . 106094) (-4028 . 106041) (-4029 . 105725) + (-4030 . 105639) (-4031 . 105520) (-4032 . 105405) (-4033 . 105295) + (-4034 . 105209) (-4035 . 104724) (-4036 . 104472) (-4037 . 103290) + (-4038 . 103153) (-4039 . 103025) (-4040 . 102996) (-4041 . 102900) + (-4042 . 102818) (-4043 . 102694) (-4044 . 102627) (-4045 . 102329) + (-4046 . 102274) (-4047 . 100066) (-4048 . 99840) (-4049 . 99448) + (-4050 . 99345) (-4051 . 99161) (-4052 . 99095) (-4053 . 99024) + 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