diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 1560 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 2306 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1336 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9507 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 32455 |
5 files changed, 23580 insertions, 23584 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index d5474542..a3869037 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2280030 . 3486501423) +(2279924 . 3486517510) (-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)) +((-4462 . T) (-4461 . 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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4459 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4455 . T) (-4460 . T) (-4454 . T)) +((-4458 . T) (-4456 . T) (-4455 . T) ((-4463 "*") . T) (-4454 . T) (-4459 . T) (-4453 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -2221) +(-32 R -2060) ((|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))))) (-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 -4461))) (-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)) +((-4461 . T) (-4462 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,17 +82,17 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4455 . T) (-4456 . T) (-4458 . 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 -2221 UP UPUP -1567) +(-40 -2060 UP UPUP -3325) ((|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))) (-3765 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-3765 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3765 (-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)))) (-3765 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-3765 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-3765 (|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 (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) -(-41 R -2221) +((-4454 |has| (-419 |#2|) (-374)) (-4459 |has| (-419 |#2|) (-374)) (-4453 |has| (-419 |#2|) (-374)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2835 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2835 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2835 (-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)))) (-2835 (-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))))) (-2835 (-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)))) (-2835 (|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 -2060) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-317)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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)) +((-4458 |has| |#1| (-568)) (-4456 . T) (-4455 . 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)) -((-3765 (-12 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2900) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2900) (|devaluate| |#2|))))))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2900) (|devaluate| |#2|))))))) +((-4461 . T) (-4462 . T)) +((-2835 (-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4353) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4353) (|devaluate| |#2|))))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4353) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) ((|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (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|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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)) +((-4458 . 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 -2221) +(-54 |Base| R -2060) ((|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)) +((-4461 . T) (-4462 . 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)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|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))) (-3765 (-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))))) -(-61 -4124) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) +(-61 -2706) ((|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 -4124) +(-62 -2706) ((|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 -4124) +(-63 -2706) ((|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 -4124) +(-64 -2706) ((|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 -4124) +(-65 -2706) ((|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 -4124) +(-66 -2706) ((|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 -4124) +(-67 -2706) ((|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 -4124) +(-68 -2706) ((|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 -4124) +(-69 -2706) ((|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 -4124) +(-70 -2706) ((|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 -4124) +(-71 -2706) ((|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 -4124) +(-72 -2706) ((|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 -4124) +(-73 -2706) ((|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 -4124) +(-74 -2706) ((|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 -4124) +(-77 -2706) ((|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 -4124) +(-78 -2706) ((|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 -4124) +(-79 -2706) ((|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 -4124) +(-80 -2706) ((|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 -4124) +(-81 -2706) ((|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 -4124) +(-82 -2706) ((|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 -4124) +(-83 -2706) ((|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 -4124) +(-84 -2706) ((|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 -4124) +(-85 -2706) ((|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 -4124) +(-86 -2706) ((|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 -4124) +(-87 -2706) ((|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 -4124) +(-88 -2706) ((|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 -4124) +(-89 -2706) ((|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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-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)) +((-4461 . 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)) +((-4461 . T) ((-4463 "*") . T) (-4462 . T) (-4458 . T) (-4456 . T) (-4455 . T) (-4454 . T) (-4459 . T) (-4453 . T) (-4452 . T) (-4451 . T) (-4450 . T) (-4449 . T) (-4457 . T) (-4460 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4448 . 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)) +((-4458 . 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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-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 (-4463 "*")))) (-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)) +((-4461 . 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)) +((-4462 . 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 (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-3765 (|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 (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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))) (-2835 (|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)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|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)) +((-4462 . T) (-4461 . 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))))) (-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)) +((-4456 . T) (-4455 . 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 -2221 UP) +(-116 -2060 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)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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 (-1196)))) (|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))) (-3765 (|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 (-1196)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1196)) (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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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))) (-2835 (|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)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (|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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4463))) +((|HasAttribute| |#1| (QUOTE -4462))) (-120 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-124) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4463 . T) (-4462 . T)) +((-4462 . T) (-4461 . T)) NIL (-125 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#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| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4462 . T) (-4463 . T)) +((-4461 . T) (-4462 . T)) NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-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)) -((-3765 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4464 "*") . T)) +(((-4463 "*") . T)) NIL -(-136 |minix| -1937 S T$) +(-136 |minix| -2722 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -1937 R) +(-137 |minix| -2722 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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)) -((-3765 (-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)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-4461 . T) (-4451 . T) (-4462 . T)) +((-2835 (-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)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|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)) +((-4458 . 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)) +((-4458 . T)) NIL -(-149 -2221 UP UPUP) +(-149 -2060 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 (-1119))) (|HasAttribute| |#1| (QUOTE -4461))) (-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)) +((-4456 . T) (-4455 . T) (-4458 . 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 -2221) +(-159 R -2060) ((|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 (-1222))) (|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 (-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 -4457)) (|HasAttribute| |#2| (QUOTE -4460)) (|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 -3765 (|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)) (-2738 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4454 -2835 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-926)))) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4457 |has| |#1| (-6 -4457)) (-4460 |has| |#1| (-6 -4460)) (-4136 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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 -3765 (|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)) (-2738 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-3765 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-3765 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-360)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-3765 (|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)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-926))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-926)))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-926))))) (-3765 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1222)))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3765 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-568)))) (-3765 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (|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 (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-1222)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasAttribute| |#1| (QUOTE -4461)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196))))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-360))))) +((-4454 -2835 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-926)))) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4457 |has| |#1| (-6 -4457)) (-4460 |has| |#1| (-6 -4460)) (-4136 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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(|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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)) +(((-4463 "*") . T) (-4454 . T) (-4459 . T) (-4453 . T) (-4455 . T) (-4456 . T) (-4458 . 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}."))) @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -2221) +(-190 R -2060) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -2221 UP UPUP R) +(-217 -2060 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 -2221 FP) +(-218 -2060 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 (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-3765 (|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 (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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))) (-2835 (|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)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -2221) +(-221 R -2060) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -826,19 +826,19 @@ NIL NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-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)) +((-4458 . T)) NIL -(-226 R -2221) +(-226 R -2060) ((|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}."))) -((-2728 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4125 . T) (-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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 (-4463 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (-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)) +((-4462 . 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)) +((-4458 . 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| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -870,7 +870,7 @@ NIL NIL (-235 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-4457 . T) (-4456 . T)) +((-4456 . T) (-4455 . T)) NIL (-236 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|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)) +((-4458 . 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 -4461))) (-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)) +((-4462 . 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 -1937 R) +(-242 S -2722 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 -1937 R) +((|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (QUOTE (-862))) (|HasAttribute| |#3| (QUOTE -4458)) (|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 -2722 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)) +((-4455 |has| |#2| (-1068)) (-4456 |has| |#2| (-1068)) (-4458 |has| |#2| (-6 -4458)) (-4461 . T)) NIL -(-244 -1937 A B) +(-244 -2722 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 -1937 R) +(-245 -2722 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)) -((-3765 (-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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(((|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)) +((-4454 . T) (-4455 . T) (-4456 . T) (-4458 . 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)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|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)) +((-4456 . T) (-4455 . 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))) (-3765 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3765 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3765 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3765 (|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)))) (-3765 (|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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4463 "*") |has| |#2| (-174)) (-4454 |has| |#2| (-568)) (-4459 |has| |#2| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#2| (QUOTE (-926))) (-2835 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2835 (|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)))) (-2835 (|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 -4459)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|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 -3765 (-2445 (|has| |#4| (-1068)) (|has| |#4| (-238))) (|has| |#4| (-6 -4459)) (-2445 (|has| |#4| (-1068)) (|has| |#4| (-915 (-1196))))) (-4456 |has| |#4| (-1068)) (-4457 |has| |#4| (-1068)) (-4462 . T)) -((-3765 (-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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(LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1119)))) (-2835 (|HasAttribute| |#3| (QUOTE -4458)) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (QUOTE (-1068)))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1195)))))) (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1068)))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -917) (QUOTE (-1195))))) (|HasCategory| |#3| (QUOTE (-862))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (-259 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-238)))) (-260 R S V E) ((|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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . 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)) +((-4461 . T) (-4462 . 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 (-1196)))) (|HasCategory| |#2| (QUOTE (-237)))) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3765 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3765 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|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)))) (-3765 (|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 (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-926))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|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)))) (-2835 (|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 -4459)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) (-274 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -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 -2221) +(-285 R -2060) ((|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 -2221) +(-286 R -2060) ((|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 @@ -1098,7 +1098,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119)))) (-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)) +((-4462 . 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 -4462))) (-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| -1597 -3257 |exactQuo|) +(-299 S R |Mod| -2314 -1854 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-300) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4455 . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4454 . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-301) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2900) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4353) (|devaluate| |#2|)))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) (-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 -2221 S) +(-307 -2060 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 -2221) +(-308 E -2060) ((|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 @@ -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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-318 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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 -2221) +(-320 -2060) ((|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}.")) 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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 -3765 (-12 (|has| |#1| (-568)) (-3765 (|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))) -((-3765 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) 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(|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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3765 (|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 -4092) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|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 -3597) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1541) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|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))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2835 (|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 -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2835 (-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 -3848) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1991) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|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)) +((-4456 . T) (-4455 . 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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . 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)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-338 S -2221) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-338 S -2060) ((|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 -2221) +(-339 -2060) ((|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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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 -2221 UP UPUP R) +(-345 S -2060 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 -2221 UP UPUP R) +(-346 -2060 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 -2221 UP UPUP R) +(-347 -2060 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|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|)))) (-349 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|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)) +((-4455 . T) (-4456 . T) (-4458 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-390)))) (|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (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 -2221 UP UPUP) +(-352 S -2060 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 -2221 UP UPUP) +(-353 -2060 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)) +((-4454 |has| (-419 |#2|) (-374)) (-4459 |has| (-419 |#2|) (-374)) (-4453 |has| (-419 |#2|) (-374)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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)) -((-3765 (|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)))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-2835 (|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)))) (-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)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-2835 (|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)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-2835 (|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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-361 R UP -2221) +(-361 R UP -2060) ((|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)) -((-3765 (|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)))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-2835 (|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)))) (-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)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-2835 (|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)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-2835 (|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)) -((-3765 (|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)))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-2835 (|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)))) (-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)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) -(-367 -2221 GF) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-2835 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +(-367 -2060 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 -2221 FP FPP) +(-369 -2060 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)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-2835 (|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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4459 . T)) +((-4458 . T)) NIL (-373 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1426,7 +1426,7 @@ NIL NIL (-374) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4459 |has| |#1| (-568)) (-4457 . T) (-4456 . T)) +((-4458 |has| |#1| (-568)) (-4456 . T) (-4455 . T)) NIL (-379) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4455 . T) (-4456 . T) (-4458 . T)) NIL (-382 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119)))) +((|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119)))) (-384 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4462 . T)) +((-4461 . T)) NIL (-385 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4456 . T) (-4455 . 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) (-2728 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4444 . T) (-4452 . T) (-4125 . T) (-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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)) +((-4456 . T) (-4455 . 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)) +((-4456 . T) (-4455 . 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)) +((-4456 . T) (-4455 . 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1526,7 +1526,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-862)))) (-399) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-400) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1538,13 +1538,13 @@ NIL NIL (-402 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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)) +((-4456 . T) (-4455 . 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 -2221 UP UPUP R) +(-404 -2060 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 -4124 |returnType| -3829 |symbols|) +(-410 -2706 |returnType| -1912 |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 -2221 UP) +(-411 -2060 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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-415 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4444)) (|HasAttribute| |#1| (QUOTE -4452))) (-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\"."))) -((-2728 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4125 . T) (-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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."))) @@ -1606,15 +1606,15 @@ 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 (-1196)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-832))) (-3765 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-862)))) (-3765 (-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)))) (-3765 (-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))))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-3765 (|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 (-1196)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (|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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +((-4448 -12 (|has| |#1| (-6 -4459)) (|has| |#1| (-464)) (|has| |#1| (-6 -4448))) (-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-832))) (-2835 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-862)))) (-2835 (-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)))) (-2835 (-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))))) (-2835 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-2835 (|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 -4459)) (|HasAttribute| |#1| (QUOTE -4448)) (|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)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4455 . T) (-4456 . T) (-4458 . T)) NIL (-422 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1628,11 +1628,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-425 R -2221 UP A) +(-425 R -2060 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)) +((-4458 . T)) NIL -(-426 R -2221 UP A |ibasis|) +(-426 R -2060 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1057) (|devaluate| |#2|)))) @@ -1646,12 +1646,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-429 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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)) +((-4458 |has| |#1| (-568)) (-4456 . T) (-4455 . 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 (-1196)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1241))) (-3765 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1241)))) (|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 (-1196)) (|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 (-1196)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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))) (-2835 (|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)))) (-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 @@ -1678,17 +1678,17 @@ 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4462 . T) (-4452 . T) (-4463 . T)) +((-4461 . T) (-4451 . T) (-4462 . T)) NIL -(-438 R -2221) +(-438 R -2060) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-439 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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 -2221) +((-4448 -12 (|has| |#1| (-6 -4448)) (|has| |#2| (-6 -4448))) (-4455 . T) (-4456 . T) (-4458 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4448)) (|HasAttribute| |#2| (QUOTE -4448)))) +(-440 R -2060) ((|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 @@ -1698,17 +1698,17 @@ 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))))) (-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 -3765 (|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))) +((-4458 -2835 (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) ((-4463 "*") |has| |#1| (-568)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-568)) (-4453 |has| |#1| (-568))) NIL -(-443 R -2221) +(-443 R -2060) ((|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 -2221) +(-444 R -2060) ((|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 -2221) +(-445 R -2060) ((|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 @@ -1716,7 +1716,7 @@ 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 -2221 UP) +(-447 R -2060 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))))) @@ -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 -2221) +(-455 R UP -2060) ((|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)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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)) +((-4458 |has| (-419 (-969 |#1|)) (-568)) (-4456 . T) (-4455 . T)) ((|HasCategory| (-419 (-969 |#1|)) (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-419 (-969 |#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))) (-3765 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3765 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3765 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3765 (|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)))) (-3765 (|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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4463 "*") |has| |#2| (-174)) (-4454 |has| |#2| (-568)) (-4459 |has| |#2| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#2| (QUOTE (-926))) (-2835 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2835 (|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)))) (-2835 (|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 -4459)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) (-467 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4457 . T) (-4456 . T)) +((-4456 . T) (-4455 . T)) NIL (-474 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1830,7 +1830,7 @@ NIL NIL (-475 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4463 . T) (-4462 . T)) +((-4462 . T) (-4461 . 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))))) (-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}."))) @@ -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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-483 |lv| -2221 R) +(-483 |lv| -2060 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1870,23 +1870,23 @@ NIL NIL (-485) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4459 . T)) +((-4458 . T)) NIL (-486 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3765 (|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 -4092) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|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 -3597) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1541) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|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))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2835 (|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 -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2835 (-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 -3848) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1991) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-487 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2900) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119)))) +((-4462 . T)) +((-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4353) (|devaluate| |#2|)))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119)))) (-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)) +((-4462 . T) (-4461 . 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))))) (-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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2900) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4353) (|devaluate| |#2|)))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) (-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.")) (|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 . 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(-1068))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-1068)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195))))) (-2835 (|HasCategory| |#2| (QUOTE (-1068))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasAttribute| |#2| (QUOTE -4458)) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-1068)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195))))) (|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 (-874)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))))) (-495) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-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))) (-3765 (-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))))) -(-497 -2221 UP UPUP R) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) +(-497 -2060 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 . T)) -((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-3765 (|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 (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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))) (-2835 (|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)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|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| (LIST (QUOTE -625) (QUOTE (-874))))) +((|HasAttribute| |#1| (QUOTE -4461)) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1952,33 +1952,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-506 -2221 UP |AlExt| |AlPol|) +(-506 -2060 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-507) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) ((|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (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)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-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 -2221) +(-511 R UP -2060) ((|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)) +((-4462 . T) (-4461 . 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))))) (-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)}."))) @@ -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 -2221 |Expon| |VarSet| |DPoly|) +(-516 -2060 |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 (-1196))))) +((|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-1195))))) (-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)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|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)) -((-3765 (|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)))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-2835 (|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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-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)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|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 -4462))) (-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 -4462))) (-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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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 (-4463 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (-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 -2221 |Par|) +(-544 K -2060 |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 -2221 |Par|) +(-550 K -2060 |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)) +((-4459 . T) (-4460 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2900) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) -(-563 R -2221) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4353) (|devaluate| |#2|)))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) +(-563 R -2060) ((|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 -2221 UP UPUP R) +(-564 R0 -2060 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."))) -((-2728 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4125 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-569 R -2221) +(-569 R -2060) ((|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 -2221 L) +(-572 R -2060 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 -2221 UP UPUP R) +(-574 -2060 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 -2221 UP) +(-575 -2060 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)) +((-4443 . T) (-4449 . T) (-4453 . T) (-4448 . T) (-4459 . T) (-4460 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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 -2221 L) +(-578 R -2060 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 -2221) +(-579 R -2060) ((|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 -2221 UP) +(-580 -2060 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 -2221) +(-582 -2060) ((|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."))) -((-2728 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4125 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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 -2221) +(-585 R -2060) ((|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 (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) -(-586 -2221 UP) +((-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 -2060 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 -2221) +(-587 R -2060) ((|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)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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 -2221) +(-595 R -2060) ((|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 -2221) +(-596 E -2060) ((|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 -2221) +(-598 -2060) ((|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 (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1196))))) +((-4456 . T) (-4455 . T)) +((|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1195))))) (-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)) -((-3765 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-3765 (|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)))) (-3765 (|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)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2835 (|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)))) (-2835 (|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)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|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))) (-3765 (|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 (-1196)))) (|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 -4092) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2835 (|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 -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4463 "*") |has| |#1| (-568)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-568)))) (-609) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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 -2221 FG) +(-612 R -2060 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)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|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 -4462)) (|HasCategory| |#2| (QUOTE (-862))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasCategory| |#3| (QUOTE (-1119)))) (-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 -3765 (-2445 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) -((-3765 (|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|)))) (-3765 (-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|)))) +((-4458 -2835 (-2758 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4456 . T) (-4455 . T)) +((-2835 (|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|)))) (-2835 (-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 (|:| -2371 (-1178)) (|:| -2900 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (QUOTE (-1178))) (LIST (QUOTE |:|) (QUOTE -2900) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| (-1178) (QUOTE (-862))) (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 |#1|)) (LIST (QUOTE -625) (QUOTE (-874))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4353) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#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 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (LIST (QUOTE -625) (QUOTE (-874))))) (-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)) +((-4462 . 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"))) @@ -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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-627 -2221 UP) +(-627 -2060 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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)) +((-4458 . 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)) +((-4455 . T) (-4456 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-860)))) -(-634 R -2221) +(-634 R -2060) ((|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 (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1196)))) (|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))))) +((-4456 . T) (-4455 . T) ((-4463 "*") . T) (-4454 . T) (-4458 . 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))))) (-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)) +((-4458 . 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 -2221) +(-642 R -2060) ((|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| -2221) +(-643 |lv| -2060) ((|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 (|:| -2371 (-1178)) (|:| -2900 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (QUOTE (-1178))) (LIST (QUOTE |:|) (QUOTE -2900) (QUOTE (-52))))))) (-3765 (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-3765 (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1178) (QUOTE (-862))) (-3765 (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 (-1178)) (|:| -2900 (-52))) (QUOTE (-1119)))) +((-4462 . T)) +((-12 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4353) (QUOTE (-52))))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1177) (QUOTE (-862))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 (-52))) (QUOTE (-1119)))) (-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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4457 . T) (-4456 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4456 . T) (-4455 . T)) NIL (-647 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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 -3765 (-2445 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) -((-3765 (|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|)))) (-3765 (-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|)))) +((-4458 -2835 (-2758 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4456 . T) (-4455 . T)) +((-2835 (|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|)))) (-2835 (-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 -((-2433 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) +((-2746 (|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}.") (((|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| $)) "\\spad{reducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} 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)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-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 @@ -2579,22 +2579,22 @@ 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 -4462))) (-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 -2221 L) +(-664 R -2060 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)) +((-4455 . T) (-4456 . T) (-4458 . 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)))) (-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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4455 . T) (-4456 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-667 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2602,15 +2602,15 @@ 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)) +((-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-669 -2221 UP) +(-669 -2060 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 -4102) +(-670 A -1965) ((|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)) +((-4455 . T) (-4456 . T) (-4458 . 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)))) (-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."))) @@ -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)) +((-4456 . T) (-4455 . 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) (-4456 . T) (-4455 . 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)) +((-4462 . T) (-4461 . T)) NIL -(-679 -2221) +(-679 -2060) ((|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 -2221 |Row| |Col| M) +(-680 -2060 |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 (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1196)))) (|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)))) (-3765 (-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 (-1196)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-3765 (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4458 . T) (-4461 . T) (-4455 . T) (-4456 . 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 (-4463 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2835 (-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))) (-2835 (|HasAttribute| |#2| (QUOTE (-4463 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|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 -((-3765 (-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))) (-3765 (-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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2835 (-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))) (-2835 (-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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|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| (($ (|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 (-4463 "*"))) (|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| (($ (|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)) +((-4461 . T) (-4462 . 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)) -((-3765 (-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))) (-3765 (-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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4461 . T) (-4462 . T)) +((-2835 (-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))) (-2835 (-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 (-4463 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|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 -2221 FLAF FLAS) +(-704 S -2060 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}.")) 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T) (-4459 |has| (-711) (-374)) (-4453 |has| (-711) (-374)) (-4136 . T) (-4460 |has| (-711) (-6 -4460)) (-4457 |has| (-711) (-6 -4457)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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))) (-2835 (|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))) (-2835 (-12 (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195))))) (-2835 (|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))))) (-2835 (|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)))) (-2835 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-926))))) (-2835 (-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))) (-2835 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374)))) (-2835 (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (QUOTE (-237)))) (-2835 (-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 -4460)) (|HasAttribute| (-711) (QUOTE -4457)) (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-146)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|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)) +((-4462 . 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 -2221 PG) +(-710 OV E -2060 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}"))) -((-2728 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4125 . T) (-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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)) +((-4460 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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 -4286 I) +(-718 S -2051 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)) +((-4455 . T) (-4456 . T) (-4458 . 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| -1597 -3257 |exactQuo|) +(-723 R |Mod| -2314 -1854 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-724 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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))) (-3765 (|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)))) (-3765 (|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))))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3765 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3765 (|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 (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4457 |has| |#1| (-374)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|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)))) (-2835 (|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))))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|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 -4459)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) +((-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-727 R |Mod| -1597 -3257 |exactQuo|) +(-727 R |Mod| -2314 -1854 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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)) +((-4458 . 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)) +((-4456 . T) (-4455 . T)) NIL -(-730 -2221) +(-730 -2060) ((|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)) +((-4458 . 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)) +((-4454 |has| |#1| (-374)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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 -2221 UP) +(-739 -2060 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))) (-3765 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3765 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3765 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3765 (|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)))) (-3765 (|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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4463 "*") |has| |#2| (-174)) (-4454 |has| |#2| (-568)) (-4459 |has| |#2| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#2| (QUOTE (-926))) (-2835 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2835 (|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)))) (-2835 (|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 -4459)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2918,15 +2918,15 @@ NIL NIL (-747 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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)) +((-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) (-4458 . 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)) +((-4451 . T) (-4462 . 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)) +((-4461 . T) (-4451 . T) (-4462 . 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))))) (-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."))) @@ -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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4456 . T) (-4455 . T) (-4458 . 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)) +((-4456 . T) (-4455 . 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 -2221) +(-777 -2060) ((|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 -2221) +(-778 P -2060) ((|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 -2221) +(-780 UP -2060) ((|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)) +(((-4463 "*") . T)) NIL -(-784 R -2221) +(-784 R -2060) ((|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 -2221 |ExtF| |SUEx| |ExtP| |n|) +(-789 -2060 |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 @@ -3098,23 +3098,23 @@ 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.")) 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(|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)) +((-4462 . T) (-4461 . 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}."))) @@ -3166,25 +3166,25 @@ 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)))) (-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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4456 . T) (-4457 . T) (-4459 . T)) +((-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-810 -3765 R OS S) +(-810 -2835 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-811 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|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 (-1196)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-3765 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3765 (|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))))) +((-4455 . T) (-4456 . T) (-4458 . 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|))) (-2835 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2835 (|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))))) (-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 -2221 L) +(-813 R -2060 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 -2221) +(-814 R -2060) ((|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 -2221) +(-816 R -2060) ((|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 -2221 UP UPUP R) +(-818 -2060 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 -2221 UP L LQ) +(-819 -2060 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 -2221 UP L LQ) +(-821 -2060 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 -2221 UP) +(-822 -2060 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 -2221 L UP A LO) +(-823 -2060 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 -2221 UP) +(-824 -2060 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 -2221 LO) +(-825 -2060 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-826 -2221 LODO) +(-826 -2060 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)) +(((-4463 "*") |has| |#2| (-374)) (-4454 |has| |#2| (-374)) (-4459 |has| |#2| (-374)) (-4453 |has| |#2| (-374)) (-4458 . T) (-4456 . T) (-4455 . 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)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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)) +((-4455 . T) (-4456 . T) (-4458 . 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)) +((-4461 . T) (-4451 . T) (-4462 . 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))) (-3765 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-3765 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4458 |has| |#1| (-860))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2835 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2835 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (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)) +((-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) (-4458 . 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4459 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-3765 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-3765 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4458 |has| |#1| (-860))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2835 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2835 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-856) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-857 -1937 S) +(-857 -2722 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3370,7 +3370,7 @@ NIL NIL (-860) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4459 . T)) +((-4458 . T)) NIL (-861 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3386,19 +3386,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) (-864 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)) +((-4455 . T) (-4456 . T) (-4458 . T)) NIL (-865 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| -1354) +(-866 R |sigma| -2843) ((|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)) +((-4455 . T) (-4456 . T) (-4458 . 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| -1354) +(-867 |x| R |sigma| -2843) ((|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)) +((-4455 . T) (-4456 . T) (-4458 . 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) ((|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..)}."))) @@ -3442,7 +3442,7 @@ NIL NIL (-878 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) +((-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) (-879 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3454,24 +3454,24 @@ NIL NIL (-881 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-882 |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)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-883 |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 (-1196)))) (|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))) (-3765 (|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 (-1196)))) (|HasCategory| (-882 |#1|) (QUOTE (-238))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -526) (QUOTE (-1196)) (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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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))) (-2835 (|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)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))))) (-884 |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 (-1196)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-832))) (-3765 (|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 (-1196)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1196)) (|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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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))) (-2835 (|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)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) (-885 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)))) (-3765 (-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)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (-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) ((|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 @@ -3531,7 +3531,7 @@ NIL (-900 |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 (-2433 (|HasCategory| |#2| (QUOTE (-1068)))) (-2433 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1196)))))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (-2433 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1196)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1196))))) +((-12 (-2746 (|HasCategory| |#2| (QUOTE (-1068)))) (-2746 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (-2746 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195))))) (-901 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 @@ -3540,7 +3540,7 @@ NIL ((|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 -4286) +(-903 R -2051) ((|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 @@ -3572,7 +3572,7 @@ NIL ((|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 -2221) +(-911 UP -2060) ((|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 @@ -3586,11 +3586,11 @@ NIL NIL (-914 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4457 . T) (-4456 . T)) +((-4456 . T) (-4455 . T)) NIL (-915 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4459 . T)) +((-4458 . T)) NIL (-916 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)}."))) @@ -3603,14 +3603,14 @@ NIL (-918 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))) (-3765 (-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))))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-919 |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) ((|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)) +((-4458 . T)) NIL (-921 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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3618,8 +3618,8 @@ NIL NIL (-922 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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)) -((-3765 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) +((-4458 . T)) +((-2835 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (-923 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 @@ -3634,13 +3634,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-146)))) (-926) ((|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)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-927 |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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) -(-928 R0 -2221 UP UPUP R) +(-928 R0 -2060 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 @@ -3654,7 +3654,7 @@ NIL NIL (-931 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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-932 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."))) @@ -3668,7 +3668,7 @@ NIL ((|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 -2221) +(-935 -2060) ((|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 @@ -3678,17 +3678,17 @@ NIL NIL (-937) ((|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| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-938) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4464 "*") . T)) +(((-4463 "*") . T)) NIL -(-939 -2221 P) +(-939 -2060 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-940 |xx| -2221) +(-940 |xx| -2060) ((|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 @@ -3712,7 +3712,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-946 R -2221) +(-946 R -2060) ((|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 @@ -3724,7 +3724,7 @@ NIL ((|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 -2221) +(-949 S R -2060) ((|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 @@ -3744,11 +3744,11 @@ NIL ((|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 -2221 -4286) +(-954 R -2060 -2051) ((|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 -4286) +(-955 -2051) ((|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 @@ -3770,8 +3770,8 @@ NIL NIL (-960 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4463 . T) (-4462 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-961 |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 @@ -3791,12 +3791,12 @@ NIL (-965 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))))) +((|HasCategory| |#2| (QUOTE (-926))) (|HasAttribute| |#2| (QUOTE -4459)) (|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|) ((|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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) NIL -(-967 E V R P -2221) +(-967 E V R P -2060) ((|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 @@ -3806,9 +3806,9 @@ NIL NIL (-969 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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3765 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3765 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1196) (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)))) (-3765 (|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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-970 E V R P -2221) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-926))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|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)))) (-2835 (|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 -4459)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-970 E V R P -2060) ((|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)))) @@ -3830,13 +3830,13 @@ NIL NIL (-975 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)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-976) ((|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 -2221) +(-977 -2060) ((|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 @@ -3850,12 +3850,12 @@ NIL NIL (-980 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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3765 (|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))) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2835 (|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 -4459))) (-981 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) -((-4459 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738))))) (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) +((-4458 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738))))) (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-982) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3878,7 +3878,7 @@ NIL NIL (-987 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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)) +((-4461 . T) (-4462 . T)) NIL (-988 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}}"))) @@ -3898,7 +3898,7 @@ NIL NIL (-992 |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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-993) ((|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}."))) @@ -3910,7 +3910,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-568)))) (-995 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)) +((-4461 . T)) NIL (-996 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."))) @@ -3926,7 +3926,7 @@ NIL NIL (-999 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)) +((-4462 . T) (-4461 . T)) NIL (-1000 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) @@ -3944,7 +3944,7 @@ NIL ((|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 -2221) +(-1004 K R UP -2060) ((|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 @@ -3971,10 +3971,10 @@ NIL (-1010 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 (-1196)))) (|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)))) +((|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) ((|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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-1012 |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}."))) @@ -3986,7 +3986,7 @@ NIL NIL (-1014 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)) +((-4461 . T) (-4462 . T)) NIL (-1015 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}."))) @@ -3994,7 +3994,7 @@ 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) ((|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)) +((-4454 |has| |#1| (-300)) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-1017 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}."))) @@ -4002,12 +4002,12 @@ NIL NIL (-1018 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))) (-3765 (|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 (-1196)) (|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 (-1196)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (-3765 (|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)))) +((-4454 |has| |#1| (-300)) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-2835 (|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)))) (-2835 (|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) ((|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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-1020 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4016,14 +4016,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -2221 UP UPUP |radicnd| |n|) +(-1022 -2060 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))) (-3765 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-3765 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3765 (-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)))) (-3765 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-3765 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-3765 (|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 (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +((-4454 |has| (-419 |#2|) (-374)) (-4459 |has| (-419 |#2|) (-374)) (-4453 |has| (-419 |#2|) (-374)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2835 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2835 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2835 (-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)))) (-2835 (-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))))) (-2835 (-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)))) (-2835 (|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|) ((|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 (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-3765 (|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 (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (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)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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))) (-2835 (|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)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) (-1024) ((|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 @@ -4043,7 +4043,7 @@ NIL (-1028 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)))) +((|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-1119)))) (-1029 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 @@ -4054,21 +4054,21 @@ NIL NIL (-1031) ((|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)) +((-4454 . T) (-4459 . T) (-4453 . T) (-4456 . T) (-4455 . T) ((-4463 "*") . T) (-4458 . T)) NIL -(-1032 R -2221) +(-1032 R -2060) ((|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 -2221) +(-1033 R -2060) ((|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 -2221 UP) +(-1034 -2060 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 -2221 UP) +(-1035 -2060 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 @@ -4102,9 +4102,9 @@ NIL NIL (-1043 |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)) -((-3765 (|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 -2221 L) +((-4454 . T) (-4459 . T) (-4453 . T) (-4456 . T) (-4455 . T) ((-4463 "*") . T) (-4458 . T)) +((-2835 (|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 -2060 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 @@ -4114,12 +4114,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1119)))) (-1046 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)) +((-4462 . T) (-4461 . 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))))) (-1047 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 "*")))) +((|HasAttribute| |#1| (QUOTE (-4463 "*")))) (-1048 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 @@ -4140,14 +4140,14 @@ NIL ((|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 -2221 |Expon| |VarSet| |FPol| |LFPol|) +(-1053 -2060 |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)) +(((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-1054) ((|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 (|:| -2371 (-1196)) (|:| -2900 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (QUOTE (-1196))) (LIST (QUOTE |:|) (QUOTE -2900) (QUOTE (-52))))))) (-3765 (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-3765 (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (QUOTE (-1119))) (|HasCategory| (-1196) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-3765 (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (LIST (QUOTE -625) (QUOTE (-874))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4353) (QUOTE (-52))))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (LIST (QUOTE -625) (QUOTE (-874))))) (-1055) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4190,7 +4190,7 @@ NIL NIL (-1065 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)) +((-4462 . T) (-4461 . 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))))) (-1066) ((|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"))) @@ -4202,9 +4202,9 @@ NIL NIL (-1068) ((|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)) +((-4458 . T)) NIL -(-1069 |xx| -2221) +(-1069 |xx| -2060) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4218,12 +4218,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-374))) (|HasCategory| |#4| (QUOTE (-568))) (|HasCategory| |#4| (QUOTE (-174)))) (-1072 |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)) +((-4461 . T) (-4456 . T) (-4455 . T)) NIL (-1073 |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))) (-3765 (-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)))) (-3765 (|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| (LIST (QUOTE -625) (QUOTE (-874))))) +((-4461 . T) (-4456 . T) (-4455 . T)) +((|HasCategory| |#3| (QUOTE (-174))) (-2835 (-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)))) (-2835 (|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| (LIST (QUOTE -625) (QUOTE (-874))))) (-1074 |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 @@ -4246,7 +4246,7 @@ NIL NIL (-1079) ((|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)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-1080 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4254,19 +4254,19 @@ NIL NIL (-1081) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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)) +((-4449 . T) (-4453 . T) (-4448 . T) (-4459 . T) (-4460 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-1082) ((|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 (|:| -2371 (-1196)) (|:| -2900 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (QUOTE (-1196))) (LIST (QUOTE |:|) (QUOTE -2900) (QUOTE (-52))))))) (-3765 (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-3765 (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (QUOTE (-1119))) (|HasCategory| (-1196) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-3765 (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (LIST (QUOTE -625) (QUOTE (-874))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4353) (QUOTE (-52))))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (LIST (QUOTE -625) (QUOTE (-874))))) (-1083 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-1196))))) +((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-1195))))) (-1084 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) NIL (-1085) ((|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'."))) @@ -4290,7 +4290,7 @@ NIL NIL (-1090 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)) +((-4462 . T) (-4461 . T)) NIL (-1091 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."))) @@ -4308,11 +4308,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1095 |Base| R -2221) +(-1095 |Base| R -2060) ((|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 -2221) +(-1096 |Base| R -2060) ((|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 @@ -4326,8 +4326,8 @@ NIL NIL (-1099 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))) (-3765 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-3765 (|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)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196))))) (-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 (-1196)))))) +((-4454 |has| |#1| (-374)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2835 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))))) (-2835 (-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)))) (-2835 (|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)))) (-2835 (-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) ((|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 @@ -4354,8 +4354,8 @@ NIL NIL (-1106 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 . 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T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-926))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|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)))) (-2835 (|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 -4459)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1107 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 @@ -4398,7 +4398,7 @@ NIL NIL (-1117 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)) +((-4451 . T)) NIL (-1118 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}."))) @@ -4414,8 +4414,8 @@ NIL NIL (-1121 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)) -((-3765 (-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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4461 . T) (-4451 . T) (-4462 . T)) +((-2835 (-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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-1122 |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 @@ -4442,7 +4442,7 @@ NIL NIL (-1128 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)) +((-4462 . T) (-4461 . T)) NIL (-1129) ((|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."))) @@ -4458,8 +4458,8 @@ NIL NIL (-1132 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4456 |has| |#3| (-1068)) (-4457 |has| |#3| (-1068)) (-4459 |has| |#3| (-6 -4459)) (-4462 . 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(-1068))) (|HasCategory| |#3| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1068)))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -917) (QUOTE (-1195))))) (-2835 (|HasCategory| |#3| (QUOTE (-1068))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576)))))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1119)))) (|HasAttribute| |#3| (QUOTE -4458)) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (QUOTE (-1068)))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1195))))) (|HasCategory| |#3| (QUOTE (-862))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (-1133 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4468,7 +4468,7 @@ NIL ((|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 -2221) +(-1135 R -2060) ((|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 @@ -4486,19 +4486,19 @@ NIL NIL (-1139) ((|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)) +((-4449 . T) (-4453 . T) (-4448 . T) (-4459 . T) (-4460 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-1140 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4462 . T) (-4463 . T)) +((-4461 . T) (-4462 . T)) NIL (-1141 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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)))) +((|HasCategory| |#3| (QUOTE (-374))) (|HasAttribute| |#3| (QUOTE (-4463 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) (-1142 |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)) +((-4461 . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL (-1143 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}."))) @@ -4506,17 +4506,17 @@ NIL NIL (-1144 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. 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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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4456 . T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) (-1146 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)) +((-4462 . T) (-4461 . T)) NIL -(-1147 UP -2221) +(-1147 UP -2060) ((|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 @@ -4570,19 +4570,19 @@ NIL NIL (-1160 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))) (-3765 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))))) (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))) (-2835 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))))) (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874))))) (-1161 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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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(|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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1163) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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)) +((-4462 . T) (-4461 . T)) NIL (-1164 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.}"))) @@ -4590,12 +4590,12 @@ NIL NIL (-1165 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)) +((-4462 . T) (-4461 . 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))))) (-1166 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))) (-3765 (-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))))) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-1167 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 @@ -4606,8 +4606,8 @@ NIL NIL (-1169 |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 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2900) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119)))) +((-4462 . T)) +((-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4353) (|devaluate| |#2|)))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119)))) (-1170) ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4634,567 +4634,563 @@ NIL NIL (-1176 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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))) (-3765 (-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))))) +((-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-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))))) (-1177) -((|constructor| (NIL "A category for string-like objects")) (|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)) -NIL -(-1178) -NIL -((-4463 . T) (-4462 . T)) -((-3765 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-3765 (|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)))) (-3765 (|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)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) -(-1179 |Entry|) +((|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"))) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2835 (|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)))) (-2835 (|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)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +(-1178 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4462 . T) (-4463 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4353) (|devaluate| |#1|)))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (QUOTE (-1119))) (|HasCategory| (-1177) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4353 |#1|)) (LIST (QUOTE -625) (QUOTE (-874))))) +(-1179 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)))))) -(-1181 |Coef|) +(-1180 |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 -(-1182 |Coef|) +(-1181 |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 -(-1183 R UP) +(-1182 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)))) -(-1184 |n| R) +(-1183 |n| R) ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented"))) NIL NIL -(-1185 S1 S2) +(-1184 S1 S2) ((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} makes a form \\spad{s:t}"))) NIL NIL -(-1186) +(-1185) ((|constructor| (NIL "This domain represents the filter iterator syntax.")) 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We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4464 "*") -3765 (-2445 (|has| |#1| (-374)) (|has| (-1194 |#1| |#2| |#3|) (-832))) (|has| |#1| (-174)) (-2445 (|has| |#1| (-374)) (|has| (-1194 |#1| |#2| |#3|) (-926)))) (-4455 -3765 (-2445 (|has| |#1| (-374)) (|has| (-1194 |#1| |#2| |#3|) (-832))) (|has| |#1| (-568)) (-2445 (|has| |#1| (-374)) (|has| (-1194 |#1| |#2| |#3|) (-926)))) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . 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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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3765 (|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 -4092) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|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 -3597) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1541) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) -(-1194 |Coef| |var| |cen|) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|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))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2835 (|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 -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2835 (-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 -3848) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1991) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +(-1193 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-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))) (-3765 (|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 (-1196)))) (|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 -4092) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|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 -3597) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1541) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) -(-1195) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2835 (|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 -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2835 (-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 -3848) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1991) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +(-1194) ((|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 -(-1196) +(-1195) ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([a1,{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) NIL NIL -(-1197 R) +(-1196 R) ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r, n)} returns the vector of the elementary symmetric functions in \\spad{[r,r,...,r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,...,rn])} returns the vector of the elementary symmetric functions in the \\spad{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) NIL NIL -(-1198 R) +(-1197 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3765 (|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))) -(-1199) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2835 (|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 -4459))) +(-1198) ((|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 -(-1200) +(-1199) ((|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 -(-1201) +(-1200) ((|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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1202 N) +(-1201 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1203 N) +(-1202 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 -(-1204) +(-1203) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1205 R) +(-1204 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 -(-1206) +(-1205) ((|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 -(-1207 S) +(-1206 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 -(-1208 S) +(-1207 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 -(-1209 |Key| |Entry|) +(-1208 |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 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2900) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-3765 (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) -(-1210 S) +((-4461 . T) (-4462 . T)) +((-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4353) (|devaluate| |#2|)))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) +(-1209 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 -(-1211 R) +(-1210 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 -(-1212 S |Key| |Entry|) +(-1211 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 -(-1213 |Key| |Entry|) +(-1212 |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)) +((-4462 . T)) NIL -(-1214 |Key| |Entry|) +(-1213 |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 -(-1215) +(-1214) ((|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 -(-1216 S) +(-1215 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 -(-1217) +(-1216) ((|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 -(-1218) +(-1217) ((|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 -(-1219 R) +(-1218 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 -(-1220) +(-1219) ((|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 -(-1221 S) +(-1220 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1222) +(-1221) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1223 S) +(-1222 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4463 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) -(-1224 S) +((-4462 . T) (-4461 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) +(-1223 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1225) +(-1224) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1226 R -2221) +(-1225 R -2060) ((|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 -(-1227 R |Row| |Col| M) +(-1226 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 -(-1228 R -2221) +(-1227 R -2060) ((|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|))))) -(-1229 S R E V P) +(-1228 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)))) -(-1230 R E V P) +(-1229 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4463 . T) (-4462 . T)) +((-4462 . T) (-4461 . T)) NIL -(-1231 |Coef|) +(-1230 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) -(-1232 |Curve|) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4456 . T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +(-1231 |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 -(-1233) +(-1232) ((|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 -(-1234 S) +(-1233 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))))) -(-1235 -2221) +(-1234 -2060) ((|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 -(-1236) +(-1235) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1237) +(-1236) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1238 S) +(-1237 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)))) -(-1239) +(-1238) ((|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 -(-1240 S) +(-1239 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 -(-1241) +(-1240) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-1242) +(-1241) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1243) +(-1242) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1244) +(-1243) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1245) +(-1244) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) NIL NIL -(-1246 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1245 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1247 |Coef|) +(-1246 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-1248 S |Coef| UTS) +(-1247 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)))) -(-1249 |Coef| UTS) +(-1248 |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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-1250 |Coef| UTS) +(-1249 |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)) -((-3765 (|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 (-1196)) (|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 (-1196)))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-3765 (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-146))))) (-3765 (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-148))))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) 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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 -(-1253 R S) +(-1252 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)))) -(-1254 S) +(-1253 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)))) -(-1255 |x| R |y| S) +(-1254 |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 -(-1256 R Q UP) +(-1255 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 -(-1257 R UP) +(-1256 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 -(-1258 R UP) +(-1257 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 -(-1259 R U) +(-1258 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 -(-1260 |x| R) +(-1259 |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| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4458 |has| |#2| (-374)) (-4460 |has| |#2| (-6 -4460)) (-4457 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1262 S R) +(-1261 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\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)))) -(-1263 R) +(-1262 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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4457 |has| |#1| (-374)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) NIL -(-1264 S |Coef| |Expon|) +(-1263 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 (-1196)))) (|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 -4092) (LIST (|devaluate| |#2|) (QUOTE (-1196)))))) -(-1265 |Coef| |Expon|) +((|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 -3563) (LIST (|devaluate| |#2|) (QUOTE (-1195)))))) +(-1264 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-1266 RC P) +(-1265 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1267 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1266 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1268 |Coef|) +(-1267 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-1269 S |Coef| ULS) +(-1268 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 -(-1270 |Coef| ULS) +(-1269 |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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-1271 |Coef| ULS) +(-1270 |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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3765 (|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 -4092) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|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 -3597) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1541) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) -(-1272 |Coef| |var| |cen|) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|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))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2835 (|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 -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2835 (-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 -3848) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1991) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) +(-1271 |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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|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))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3765 (|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 -4092) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|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 -3597) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1541) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) -(-1273 R FE |var| |cen|) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|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))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2835 (|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 -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2835 (-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 -3848) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1991) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +(-1272 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| (-1272 |#2| |#3| |#4|) (-174)) (-4455 |has| (-1272 |#2| |#3| |#4|) (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-174))) (-3765 (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-568)))) -(-1274 A S) +(((-4463 "*") |has| (-1271 |#2| |#3| |#4|) (-174)) (-4454 |has| (-1271 |#2| |#3| |#4|) (-568)) (-4455 . T) (-4456 . T) (-4458 . 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))) (-2835 (|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) ((|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4463))) -(-1275 S) +((|HasAttribute| |#1| (QUOTE -4462))) +(-1274 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1276 |Coef1| |Coef2| UTS1 UTS2) +(-1275 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1277 S |Coef|) +(-1276 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-1222))) (|HasSignature| |#2| (LIST (QUOTE -1541) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3597) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1196))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) -(-1278 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-1221))) (|HasSignature| |#2| (LIST (QUOTE -1991) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3848) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1195))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) +(-1277 |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)) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-1279 |Coef| |var| |cen|) +(-1278 |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))) (-3765 (|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 (-1196)))) (|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 -4092) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|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 -3597) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1541) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) -(-1280 |Coef| UTS) +(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2835 (|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 -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2835 (-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 -3848) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1991) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +(-1279 |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 -(-1281 -2221 UP L UTS) +(-1280 -2060 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)))) -(-1282) +(-1281) ((|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 -(-1283 |sym|) +(-1282 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1284 S R) +(-1283 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)))) -(-1285 R) +(-1284 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4463 . T) (-4462 . T)) +((-4462 . T) (-4461 . T)) NIL -(-1286 A B) +(-1285 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1287 R) +(-1286 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4463 . T) (-4462 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3765 (-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)))) (-3765 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-1288) +((-4462 . T) (-4461 . T)) +((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-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)))) (-2835 (|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)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-1287) ((|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 -(-1289) +(-1288) ((|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 -(-1290) +(-1289) ((|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 -(-1291) +(-1290) ((|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 -(-1292) +(-1291) ((|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| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1293 A S) +(-1292 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1294 S) +(-1293 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)) +((-4456 . T) (-4455 . T)) NIL -(-1295 R) +(-1294 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 -(-1296 K R UP -2221) +(-1295 K R UP -2060) ((|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 -(-1297) +(-1296) ((|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 -(-1298) +(-1297) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1299 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1298 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)) +((-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) -(-1300 R E V P) +(-1299 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)) +((-4462 . T) (-4461 . 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))))) -(-1301 R) +(-1300 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)) +((-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-1302 |vl| R) +(-1301 |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))) -(-1303 R |VarSet| XPOLY) +((-4458 . T) (-4454 |has| |#2| (-6 -4454)) (-4456 . T) (-4455 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4454))) +(-1302 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 -(-1304 |vl| R) +(-1303 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) +((-4454 |has| |#2| (-6 -4454)) (-4456 . T) (-4455 . T) (-4458 . T)) NIL -(-1305 S -2221) +(-1304 S -2060) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1306 -2221) +(-1305 -2060) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL -(-1307 |VarSet| R) +(-1306 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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))) -(-1308 |vl| R) +((-4454 |has| |#2| (-6 -4454)) (-4456 . T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -729) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasAttribute| |#2| (QUOTE -4454))) +(-1307 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) +((-4454 |has| |#2| (-6 -4454)) (-4456 . T) (-4455 . T) (-4458 . T)) NIL -(-1309 R) +(-1308 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4455 |has| |#1| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4455))) -(-1310 R E) +((-4454 |has| |#1| (-6 -4454)) (-4456 . T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4454))) +(-1309 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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))) -(-1311 |VarSet| R) +((-4458 . T) (-4459 |has| |#1| (-6 -4459)) (-4454 |has| |#1| (-6 -4454)) (-4456 . T) (-4455 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasAttribute| |#1| (QUOTE -4459)) (|HasAttribute| |#1| (QUOTE -4454))) +(-1310 |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))) -(-1312) +((-4454 |has| |#2| (-6 -4454)) (-4456 . T) (-4455 . T) (-4458 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4454))) +(-1311) ((|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 -(-1313 A) +(-1312 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 -(-1314 R |ls| |ls2|) +(-1313 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 -(-1315 R) +(-1314 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 -(-1316 |p|) +(-1315 |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)) +(((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) NIL NIL NIL @@ -5212,4 +5208,4 @@ NIL NIL NIL NIL -((-3 NIL 2280010 2280015 2280020 2280025) (-2 NIL 2279990 2279995 2280000 2280005) (-1 NIL 2279970 2279975 2279980 2279985) (0 NIL 2279950 2279955 2279960 2279965) (-1316 "ZMOD.spad" 2279759 2279772 2279888 2279945) (-1315 "ZLINDEP.spad" 2278825 2278836 2279749 2279754) (-1314 "ZDSOLVE.spad" 2268770 2268792 2278815 2278820) (-1313 "YSTREAM.spad" 2268265 2268276 2268760 2268765) (-1312 "YDIAGRAM.spad" 2267899 2267908 2268255 2268260) (-1311 "XRPOLY.spad" 2267119 2267139 2267755 2267824) (-1310 "XPR.spad" 2264914 2264927 2266837 2266936) (-1309 "XPOLY.spad" 2264469 2264480 2264770 2264839) (-1308 "XPOLYC.spad" 2263788 2263804 2264395 2264464) (-1307 "XPBWPOLY.spad" 2262225 2262245 2263568 2263637) (-1306 "XF.spad" 2260688 2260703 2262127 2262220) (-1305 "XF.spad" 2259131 2259148 2260572 2260577) (-1304 "XFALG.spad" 2256179 2256195 2259057 2259126) (-1303 "XEXPPKG.spad" 2255430 2255456 2256169 2256174) (-1302 "XDPOLY.spad" 2255044 2255060 2255286 2255355) (-1301 "XALG.spad" 2254704 2254715 2255000 2255039) (-1300 "WUTSET.spad" 2250543 2250560 2254350 2254377) (-1299 "WP.spad" 2249742 2249786 2250401 2250468) (-1298 "WHILEAST.spad" 2249540 2249549 2249732 2249737) (-1297 "WHEREAST.spad" 2249211 2249220 2249530 2249535) (-1296 "WFFINTBS.spad" 2246874 2246896 2249201 2249206) (-1295 "WEIER.spad" 2245096 2245107 2246864 2246869) (-1294 "VSPACE.spad" 2244769 2244780 2245064 2245091) (-1293 "VSPACE.spad" 2244462 2244475 2244759 2244764) (-1292 "VOID.spad" 2244139 2244148 2244452 2244457) (-1291 "VIEW.spad" 2241819 2241828 2244129 2244134) (-1290 "VIEWDEF.spad" 2237020 2237029 2241809 2241814) (-1289 "VIEW3D.spad" 2220981 2220990 2237010 2237015) (-1288 "VIEW2D.spad" 2208872 2208881 2220971 2220976) (-1287 "VECTOR.spad" 2207546 2207557 2207797 2207824) (-1286 "VECTOR2.spad" 2206185 2206198 2207536 2207541) (-1285 "VECTCAT.spad" 2204089 2204100 2206153 2206180) (-1284 "VECTCAT.spad" 2201800 2201813 2203866 2203871) (-1283 "VARIABLE.spad" 2201580 2201595 2201790 2201795) (-1282 "UTYPE.spad" 2201224 2201233 2201570 2201575) (-1281 "UTSODETL.spad" 2200519 2200543 2201180 2201185) (-1280 "UTSODE.spad" 2198735 2198755 2200509 2200514) (-1279 "UTS.spad" 2193682 2193710 2197202 2197299) (-1278 "UTSCAT.spad" 2191161 2191177 2193580 2193677) (-1277 "UTSCAT.spad" 2188284 2188302 2190705 2190710) (-1276 "UTS2.spad" 2187879 2187914 2188274 2188279) (-1275 "URAGG.spad" 2182552 2182563 2187869 2187874) (-1274 "URAGG.spad" 2177189 2177202 2182508 2182513) (-1273 "UPXSSING.spad" 2174834 2174860 2176270 2176403) (-1272 "UPXS.spad" 2172130 2172158 2172966 2173115) (-1271 "UPXSCONS.spad" 2169889 2169909 2170262 2170411) (-1270 "UPXSCCA.spad" 2168460 2168480 2169735 2169884) (-1269 "UPXSCCA.spad" 2167173 2167195 2168450 2168455) (-1268 "UPXSCAT.spad" 2165762 2165778 2167019 2167168) (-1267 "UPXS2.spad" 2165305 2165358 2165752 2165757) (-1266 "UPSQFREE.spad" 2163719 2163733 2165295 2165300) (-1265 "UPSCAT.spad" 2161506 2161530 2163617 2163714) (-1264 "UPSCAT.spad" 2158999 2159025 2161112 2161117) (-1263 "UPOLYC.spad" 2154039 2154050 2158841 2158994) (-1262 "UPOLYC.spad" 2148971 2148984 2153775 2153780) (-1261 "UPOLYC2.spad" 2148442 2148461 2148961 2148966) (-1260 "UP.spad" 2145548 2145563 2145935 2146088) (-1259 "UPMP.spad" 2144448 2144461 2145538 2145543) (-1258 "UPDIVP.spad" 2144013 2144027 2144438 2144443) (-1257 "UPDECOMP.spad" 2142258 2142272 2144003 2144008) (-1256 "UPCDEN.spad" 2141467 2141483 2142248 2142253) (-1255 "UP2.spad" 2140831 2140852 2141457 2141462) (-1254 "UNISEG.spad" 2140184 2140195 2140750 2140755) (-1253 "UNISEG2.spad" 2139681 2139694 2140140 2140145) (-1252 "UNIFACT.spad" 2138784 2138796 2139671 2139676) (-1251 "ULS.spad" 2128568 2128596 2129513 2129942) (-1250 "ULSCONS.spad" 2119702 2119722 2120072 2120221) (-1249 "ULSCCAT.spad" 2117439 2117459 2119548 2119697) (-1248 "ULSCCAT.spad" 2115284 2115306 2117395 2117400) (-1247 "ULSCAT.spad" 2113516 2113532 2115130 2115279) (-1246 "ULS2.spad" 2113030 2113083 2113506 2113511) (-1245 "UINT8.spad" 2112907 2112916 2113020 2113025) (-1244 "UINT64.spad" 2112783 2112792 2112897 2112902) (-1243 "UINT32.spad" 2112659 2112668 2112773 2112778) (-1242 "UINT16.spad" 2112535 2112544 2112649 2112654) (-1241 "UFD.spad" 2111600 2111609 2112461 2112530) (-1240 "UFD.spad" 2110727 2110738 2111590 2111595) (-1239 "UDVO.spad" 2109608 2109617 2110717 2110722) (-1238 "UDPO.spad" 2107101 2107112 2109564 2109569) (-1237 "TYPE.spad" 2107033 2107042 2107091 2107096) (-1236 "TYPEAST.spad" 2106952 2106961 2107023 2107028) (-1235 "TWOFACT.spad" 2105604 2105619 2106942 2106947) (-1234 "TUPLE.spad" 2105090 2105101 2105503 2105508) (-1233 "TUBETOOL.spad" 2101957 2101966 2105080 2105085) (-1232 "TUBE.spad" 2100604 2100621 2101947 2101952) (-1231 "TS.spad" 2099203 2099219 2100169 2100266) (-1230 "TSETCAT.spad" 2086330 2086347 2099171 2099198) (-1229 "TSETCAT.spad" 2073443 2073462 2086286 2086291) (-1228 "TRMANIP.spad" 2067809 2067826 2073149 2073154) (-1227 "TRIMAT.spad" 2066772 2066797 2067799 2067804) (-1226 "TRIGMNIP.spad" 2065299 2065316 2066762 2066767) (-1225 "TRIGCAT.spad" 2064811 2064820 2065289 2065294) (-1224 "TRIGCAT.spad" 2064321 2064332 2064801 2064806) (-1223 "TREE.spad" 2062896 2062907 2063928 2063955) (-1222 "TRANFUN.spad" 2062735 2062744 2062886 2062891) (-1221 "TRANFUN.spad" 2062572 2062583 2062725 2062730) (-1220 "TOPSP.spad" 2062246 2062255 2062562 2062567) (-1219 "TOOLSIGN.spad" 2061909 2061920 2062236 2062241) (-1218 "TEXTFILE.spad" 2060470 2060479 2061899 2061904) (-1217 "TEX.spad" 2057616 2057625 2060460 2060465) (-1216 "TEX1.spad" 2057172 2057183 2057606 2057611) (-1215 "TEMUTL.spad" 2056727 2056736 2057162 2057167) (-1214 "TBCMPPK.spad" 2054820 2054843 2056717 2056722) (-1213 "TBAGG.spad" 2053870 2053893 2054800 2054815) (-1212 "TBAGG.spad" 2052928 2052953 2053860 2053865) (-1211 "TANEXP.spad" 2052336 2052347 2052918 2052923) (-1210 "TALGOP.spad" 2052060 2052071 2052326 2052331) (-1209 "TABLE.spad" 2050471 2050494 2050741 2050768) (-1208 "TABLEAU.spad" 2049952 2049963 2050461 2050466) (-1207 "TABLBUMP.spad" 2046755 2046766 2049942 2049947) (-1206 "SYSTEM.spad" 2045983 2045992 2046745 2046750) (-1205 "SYSSOLP.spad" 2043466 2043477 2045973 2045978) (-1204 "SYSPTR.spad" 2043365 2043374 2043456 2043461) (-1203 "SYSNNI.spad" 2042547 2042558 2043355 2043360) (-1202 "SYSINT.spad" 2041951 2041962 2042537 2042542) (-1201 "SYNTAX.spad" 2038157 2038166 2041941 2041946) (-1200 "SYMTAB.spad" 2036225 2036234 2038147 2038152) (-1199 "SYMS.spad" 2032248 2032257 2036215 2036220) (-1198 "SYMPOLY.spad" 2031255 2031266 2031337 2031464) (-1197 "SYMFUNC.spad" 2030756 2030767 2031245 2031250) (-1196 "SYMBOL.spad" 2028259 2028268 2030746 2030751) (-1195 "SWITCH.spad" 2025030 2025039 2028249 2028254) (-1194 "SUTS.spad" 2022078 2022106 2023497 2023594) (-1193 "SUPXS.spad" 2019361 2019389 2020210 2020359) (-1192 "SUP.spad" 2016081 2016092 2016854 2017007) (-1191 "SUPFRACF.spad" 2015186 2015204 2016071 2016076) (-1190 "SUP2.spad" 2014578 2014591 2015176 2015181) (-1189 "SUMRF.spad" 2013552 2013563 2014568 2014573) (-1188 "SUMFS.spad" 2013189 2013206 2013542 2013547) (-1187 "SULS.spad" 2002960 2002988 2003918 2004347) (-1186 "SUCHTAST.spad" 2002729 2002738 2002950 2002955) (-1185 "SUCH.spad" 2002411 2002426 2002719 2002724) (-1184 "SUBSPACE.spad" 1994526 1994541 2002401 2002406) (-1183 "SUBRESP.spad" 1993696 1993710 1994482 1994487) (-1182 "STTF.spad" 1989795 1989811 1993686 1993691) (-1181 "STTFNC.spad" 1986263 1986279 1989785 1989790) (-1180 "STTAYLOR.spad" 1978898 1978909 1986144 1986149) (-1179 "STRTBL.spad" 1977403 1977420 1977552 1977579) (-1178 "STRING.spad" 1976558 1976567 1976572 1976599) (-1177 "STRICAT.spad" 1976245 1976254 1976526 1976553) (-1176 "STREAM.spad" 1973163 1973174 1975770 1975785) (-1175 "STREAM3.spad" 1972736 1972751 1973153 1973158) (-1174 "STREAM2.spad" 1971864 1971877 1972726 1972731) (-1173 "STREAM1.spad" 1971570 1971581 1971854 1971859) (-1172 "STINPROD.spad" 1970506 1970522 1971560 1971565) (-1171 "STEP.spad" 1969707 1969716 1970496 1970501) (-1170 "STEPAST.spad" 1968941 1968950 1969697 1969702) (-1169 "STBL.spad" 1967467 1967495 1967634 1967649) (-1168 "STAGG.spad" 1966542 1966553 1967457 1967462) (-1167 "STAGG.spad" 1965615 1965628 1966532 1966537) (-1166 "STACK.spad" 1964972 1964983 1965222 1965249) (-1165 "SREGSET.spad" 1962676 1962693 1964618 1964645) (-1164 "SRDCMPK.spad" 1961237 1961257 1962666 1962671) (-1163 "SRAGG.spad" 1956380 1956389 1961205 1961232) (-1162 "SRAGG.spad" 1951543 1951554 1956370 1956375) (-1161 "SQMATRIX.spad" 1949122 1949140 1950038 1950125) (-1160 "SPLTREE.spad" 1943674 1943687 1948558 1948585) (-1159 "SPLNODE.spad" 1940262 1940275 1943664 1943669) (-1158 "SPFCAT.spad" 1939071 1939080 1940252 1940257) (-1157 "SPECOUT.spad" 1937623 1937632 1939061 1939066) (-1156 "SPADXPT.spad" 1929218 1929227 1937613 1937618) (-1155 "spad-parser.spad" 1928683 1928692 1929208 1929213) (-1154 "SPADAST.spad" 1928384 1928393 1928673 1928678) (-1153 "SPACEC.spad" 1912583 1912594 1928374 1928379) (-1152 "SPACE3.spad" 1912359 1912370 1912573 1912578) (-1151 "SORTPAK.spad" 1911908 1911921 1912315 1912320) (-1150 "SOLVETRA.spad" 1909671 1909682 1911898 1911903) (-1149 "SOLVESER.spad" 1908199 1908210 1909661 1909666) (-1148 "SOLVERAD.spad" 1904225 1904236 1908189 1908194) (-1147 "SOLVEFOR.spad" 1902687 1902705 1904215 1904220) (-1146 "SNTSCAT.spad" 1902287 1902304 1902655 1902682) (-1145 "SMTS.spad" 1900559 1900585 1901852 1901949) (-1144 "SMP.spad" 1898034 1898054 1898424 1898551) (-1143 "SMITH.spad" 1896879 1896904 1898024 1898029) (-1142 "SMATCAT.spad" 1894989 1895019 1896823 1896874) (-1141 "SMATCAT.spad" 1893031 1893063 1894867 1894872) (-1140 "SKAGG.spad" 1891994 1892005 1892999 1893026) (-1139 "SINT.spad" 1890934 1890943 1891860 1891989) (-1138 "SIMPAN.spad" 1890662 1890671 1890924 1890929) (-1137 "SIG.spad" 1889992 1890001 1890652 1890657) (-1136 "SIGNRF.spad" 1889110 1889121 1889982 1889987) (-1135 "SIGNEF.spad" 1888389 1888406 1889100 1889105) (-1134 "SIGAST.spad" 1887774 1887783 1888379 1888384) (-1133 "SHP.spad" 1885702 1885717 1887730 1887735) (-1132 "SHDP.spad" 1873984 1874011 1874493 1874592) (-1131 "SGROUP.spad" 1873592 1873601 1873974 1873979) (-1130 "SGROUP.spad" 1873198 1873209 1873582 1873587) (-1129 "SGCF.spad" 1866337 1866346 1873188 1873193) (-1128 "SFRTCAT.spad" 1865267 1865284 1866305 1866332) (-1127 "SFRGCD.spad" 1864330 1864350 1865257 1865262) (-1126 "SFQCMPK.spad" 1858967 1858987 1864320 1864325) (-1125 "SFORT.spad" 1858406 1858420 1858957 1858962) (-1124 "SEXOF.spad" 1858249 1858289 1858396 1858401) (-1123 "SEX.spad" 1858141 1858150 1858239 1858244) (-1122 "SEXCAT.spad" 1855913 1855953 1858131 1858136) (-1121 "SET.spad" 1854237 1854248 1855334 1855373) (-1120 "SETMN.spad" 1852687 1852704 1854227 1854232) (-1119 "SETCAT.spad" 1852009 1852018 1852677 1852682) (-1118 "SETCAT.spad" 1851329 1851340 1851999 1852004) (-1117 "SETAGG.spad" 1847878 1847889 1851309 1851324) (-1116 "SETAGG.spad" 1844435 1844448 1847868 1847873) (-1115 "SEQAST.spad" 1844138 1844147 1844425 1844430) (-1114 "SEGXCAT.spad" 1843294 1843307 1844128 1844133) (-1113 "SEG.spad" 1843107 1843118 1843213 1843218) (-1112 "SEGCAT.spad" 1842032 1842043 1843097 1843102) (-1111 "SEGBIND.spad" 1841790 1841801 1841979 1841984) (-1110 "SEGBIND2.spad" 1841488 1841501 1841780 1841785) (-1109 "SEGAST.spad" 1841202 1841211 1841478 1841483) (-1108 "SEG2.spad" 1840637 1840650 1841158 1841163) (-1107 "SDVAR.spad" 1839913 1839924 1840627 1840632) (-1106 "SDPOL.spad" 1837246 1837257 1837537 1837664) (-1105 "SCPKG.spad" 1835335 1835346 1837236 1837241) (-1104 "SCOPE.spad" 1834488 1834497 1835325 1835330) (-1103 "SCACHE.spad" 1833184 1833195 1834478 1834483) (-1102 "SASTCAT.spad" 1833093 1833102 1833174 1833179) (-1101 "SAOS.spad" 1832965 1832974 1833083 1833088) (-1100 "SAERFFC.spad" 1832678 1832698 1832955 1832960) (-1099 "SAE.spad" 1830148 1830164 1830759 1830894) (-1098 "SAEFACT.spad" 1829849 1829869 1830138 1830143) (-1097 "RURPK.spad" 1827508 1827524 1829839 1829844) (-1096 "RULESET.spad" 1826961 1826985 1827498 1827503) (-1095 "RULE.spad" 1825201 1825225 1826951 1826956) (-1094 "RULECOLD.spad" 1825053 1825066 1825191 1825196) (-1093 "RTVALUE.spad" 1824788 1824797 1825043 1825048) (-1092 "RSTRCAST.spad" 1824505 1824514 1824778 1824783) (-1091 "RSETGCD.spad" 1820883 1820903 1824495 1824500) (-1090 "RSETCAT.spad" 1810819 1810836 1820851 1820878) (-1089 "RSETCAT.spad" 1800775 1800794 1810809 1810814) (-1088 "RSDCMPK.spad" 1799227 1799247 1800765 1800770) (-1087 "RRCC.spad" 1797611 1797641 1799217 1799222) (-1086 "RRCC.spad" 1795993 1796025 1797601 1797606) (-1085 "RPTAST.spad" 1795695 1795704 1795983 1795988) (-1084 "RPOLCAT.spad" 1775055 1775070 1795563 1795690) (-1083 "RPOLCAT.spad" 1754128 1754145 1774638 1774643) (-1082 "ROUTINE.spad" 1750011 1750020 1752775 1752802) (-1081 "ROMAN.spad" 1749339 1749348 1749877 1750006) (-1080 "ROIRC.spad" 1748419 1748451 1749329 1749334) (-1079 "RNS.spad" 1747322 1747331 1748321 1748414) (-1078 "RNS.spad" 1746311 1746322 1747312 1747317) (-1077 "RNG.spad" 1746046 1746055 1746301 1746306) (-1076 "RNGBIND.spad" 1745206 1745220 1746001 1746006) (-1075 "RMODULE.spad" 1744971 1744982 1745196 1745201) (-1074 "RMCAT2.spad" 1744391 1744448 1744961 1744966) (-1073 "RMATRIX.spad" 1743215 1743234 1743558 1743597) (-1072 "RMATCAT.spad" 1738794 1738825 1743171 1743210) (-1071 "RMATCAT.spad" 1734263 1734296 1738642 1738647) (-1070 "RLINSET.spad" 1733967 1733978 1734253 1734258) (-1069 "RINTERP.spad" 1733855 1733875 1733957 1733962) (-1068 "RING.spad" 1733325 1733334 1733835 1733850) (-1067 "RING.spad" 1732803 1732814 1733315 1733320) (-1066 "RIDIST.spad" 1732195 1732204 1732793 1732798) (-1065 "RGCHAIN.spad" 1730778 1730794 1731680 1731707) (-1064 "RGBCSPC.spad" 1730559 1730571 1730768 1730773) (-1063 "RGBCMDL.spad" 1730089 1730101 1730549 1730554) (-1062 "RF.spad" 1727731 1727742 1730079 1730084) (-1061 "RFFACTOR.spad" 1727193 1727204 1727721 1727726) (-1060 "RFFACT.spad" 1726928 1726940 1727183 1727188) (-1059 "RFDIST.spad" 1725924 1725933 1726918 1726923) (-1058 "RETSOL.spad" 1725343 1725356 1725914 1725919) (-1057 "RETRACT.spad" 1724771 1724782 1725333 1725338) (-1056 "RETRACT.spad" 1724197 1724210 1724761 1724766) (-1055 "RETAST.spad" 1724009 1724018 1724187 1724192) (-1054 "RESULT.spad" 1722069 1722078 1722656 1722683) (-1053 "RESRING.spad" 1721416 1721463 1722007 1722064) (-1052 "RESLATC.spad" 1720740 1720751 1721406 1721411) (-1051 "REPSQ.spad" 1720471 1720482 1720730 1720735) (-1050 "REP.spad" 1718025 1718034 1720461 1720466) (-1049 "REPDB.spad" 1717732 1717743 1718015 1718020) (-1048 "REP2.spad" 1707390 1707401 1717574 1717579) (-1047 "REP1.spad" 1701586 1701597 1707340 1707345) (-1046 "REGSET.spad" 1699383 1699400 1701232 1701259) (-1045 "REF.spad" 1698718 1698729 1699338 1699343) (-1044 "REDORDER.spad" 1697924 1697941 1698708 1698713) (-1043 "RECLOS.spad" 1696707 1696727 1697411 1697504) (-1042 "REALSOLV.spad" 1695847 1695856 1696697 1696702) (-1041 "REAL.spad" 1695719 1695728 1695837 1695842) (-1040 "REAL0Q.spad" 1693017 1693032 1695709 1695714) (-1039 "REAL0.spad" 1689861 1689876 1693007 1693012) (-1038 "RDUCEAST.spad" 1689582 1689591 1689851 1689856) (-1037 "RDIV.spad" 1689237 1689262 1689572 1689577) (-1036 "RDIST.spad" 1688804 1688815 1689227 1689232) (-1035 "RDETRS.spad" 1687668 1687686 1688794 1688799) (-1034 "RDETR.spad" 1685807 1685825 1687658 1687663) (-1033 "RDEEFS.spad" 1684906 1684923 1685797 1685802) (-1032 "RDEEF.spad" 1683916 1683933 1684896 1684901) (-1031 "RCFIELD.spad" 1681102 1681111 1683818 1683911) (-1030 "RCFIELD.spad" 1678374 1678385 1681092 1681097) (-1029 "RCAGG.spad" 1676302 1676313 1678364 1678369) (-1028 "RCAGG.spad" 1674157 1674170 1676221 1676226) (-1027 "RATRET.spad" 1673517 1673528 1674147 1674152) (-1026 "RATFACT.spad" 1673209 1673221 1673507 1673512) (-1025 "RANDSRC.spad" 1672528 1672537 1673199 1673204) (-1024 "RADUTIL.spad" 1672284 1672293 1672518 1672523) (-1023 "RADIX.spad" 1669108 1669122 1670654 1670747) (-1022 "RADFF.spad" 1666847 1666884 1666966 1667122) (-1021 "RADCAT.spad" 1666442 1666451 1666837 1666842) (-1020 "RADCAT.spad" 1666035 1666046 1666432 1666437) (-1019 "QUEUE.spad" 1665383 1665394 1665642 1665669) (-1018 "QUAT.spad" 1663871 1663882 1664214 1664279) (-1017 "QUATCT2.spad" 1663491 1663510 1663861 1663866) (-1016 "QUATCAT.spad" 1661661 1661672 1663421 1663486) (-1015 "QUATCAT.spad" 1659582 1659595 1661344 1661349) (-1014 "QUAGG.spad" 1658409 1658420 1659550 1659577) (-1013 "QQUTAST.spad" 1658177 1658186 1658399 1658404) (-1012 "QFORM.spad" 1657795 1657810 1658167 1658172) (-1011 "QFCAT.spad" 1656497 1656508 1657697 1657790) (-1010 "QFCAT.spad" 1654790 1654803 1655992 1655997) (-1009 "QFCAT2.spad" 1654482 1654499 1654780 1654785) (-1008 "QEQUAT.spad" 1654040 1654049 1654472 1654477) (-1007 "QCMPACK.spad" 1648786 1648806 1654030 1654035) (-1006 "QALGSET.spad" 1644864 1644897 1648700 1648705) (-1005 "QALGSET2.spad" 1642859 1642878 1644854 1644859) (-1004 "PWFFINTB.spad" 1640274 1640296 1642849 1642854) (-1003 "PUSHVAR.spad" 1639612 1639632 1640264 1640269) (-1002 "PTRANFN.spad" 1635739 1635750 1639602 1639607) (-1001 "PTPACK.spad" 1632826 1632837 1635729 1635734) (-1000 "PTFUNC2.spad" 1632648 1632663 1632816 1632821) (-999 "PTCAT.spad" 1631903 1631913 1632616 1632643) (-998 "PSQFR.spad" 1631210 1631234 1631893 1631898) (-997 "PSEUDLIN.spad" 1630096 1630106 1631200 1631205) (-996 "PSETPK.spad" 1615529 1615545 1629974 1629979) (-995 "PSETCAT.spad" 1609449 1609472 1615509 1615524) (-994 "PSETCAT.spad" 1603343 1603368 1609405 1609410) (-993 "PSCURVE.spad" 1602326 1602334 1603333 1603338) (-992 "PSCAT.spad" 1601109 1601138 1602224 1602321) (-991 "PSCAT.spad" 1599982 1600013 1601099 1601104) (-990 "PRTITION.spad" 1598680 1598688 1599972 1599977) (-989 "PRTDAST.spad" 1598399 1598407 1598670 1598675) (-988 "PRS.spad" 1587961 1587978 1598355 1598360) (-987 "PRQAGG.spad" 1587396 1587406 1587929 1587956) (-986 "PROPLOG.spad" 1586968 1586976 1587386 1587391) (-985 "PROPFUN2.spad" 1586591 1586604 1586958 1586963) (-984 "PROPFUN1.spad" 1585989 1586000 1586581 1586586) (-983 "PROPFRML.spad" 1584557 1584568 1585979 1585984) (-982 "PROPERTY.spad" 1584045 1584053 1584547 1584552) (-981 "PRODUCT.spad" 1581727 1581739 1582011 1582066) (-980 "PR.spad" 1580119 1580131 1580818 1580945) (-979 "PRINT.spad" 1579871 1579879 1580109 1580114) (-978 "PRIMES.spad" 1578124 1578134 1579861 1579866) (-977 "PRIMELT.spad" 1576205 1576219 1578114 1578119) (-976 "PRIMCAT.spad" 1575832 1575840 1576195 1576200) (-975 "PRIMARR.spad" 1574837 1574847 1575015 1575042) (-974 "PRIMARR2.spad" 1573604 1573616 1574827 1574832) (-973 "PREASSOC.spad" 1572986 1572998 1573594 1573599) (-972 "PPCURVE.spad" 1572123 1572131 1572976 1572981) (-971 "PORTNUM.spad" 1571898 1571906 1572113 1572118) (-970 "POLYROOT.spad" 1570747 1570769 1571854 1571859) (-969 "POLY.spad" 1568082 1568092 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(-486 "GSERIES.spad" 794056 794083 794875 795024) (-485 "GROUP.spad" 793329 793337 794036 794051) (-484 "GROUP.spad" 792610 792620 793319 793324) (-483 "GROEBSOL.spad" 791104 791125 792600 792605) (-482 "GRMOD.spad" 789675 789687 791094 791099) (-481 "GRMOD.spad" 788244 788258 789665 789670) (-480 "GRIMAGE.spad" 781133 781141 788234 788239) (-479 "GRDEF.spad" 779512 779520 781123 781128) (-478 "GRAY.spad" 777975 777983 779502 779507) (-477 "GRALG.spad" 777052 777064 777965 777970) (-476 "GRALG.spad" 776127 776141 777042 777047) (-475 "GPOLSET.spad" 775581 775604 775809 775836) (-474 "GOSPER.spad" 774850 774868 775571 775576) (-473 "GMODPOL.spad" 773998 774025 774818 774845) (-472 "GHENSEL.spad" 773081 773095 773988 773993) (-471 "GENUPS.spad" 769374 769387 773071 773076) (-470 "GENUFACT.spad" 768951 768961 769364 769369) (-469 "GENPGCD.spad" 768537 768554 768941 768946) (-468 "GENMFACT.spad" 767989 768008 768527 768532) (-467 "GENEEZ.spad" 765940 765953 767979 767984) (-466 "GDMP.spad" 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517235 517240) (-342 "FCPAK1.spad" 514820 514828 516243 516248) (-341 "FCOMP.spad" 514199 514209 514810 514815) (-340 "FC.spad" 504206 504214 514189 514194) (-339 "FAXF.spad" 497177 497191 504108 504201) (-338 "FAXF.spad" 490200 490216 497133 497138) (-337 "FARRAY.spad" 488350 488360 489383 489410) (-336 "FAMR.spad" 486486 486498 488248 488345) (-335 "FAMR.spad" 484606 484620 486370 486375) (-334 "FAMONOID.spad" 484274 484284 484560 484565) (-333 "FAMONC.spad" 482570 482582 484264 484269) (-332 "FAGROUP.spad" 482194 482204 482466 482493) (-331 "FACUTIL.spad" 480398 480415 482184 482189) (-330 "FACTFUNC.spad" 479592 479602 480388 480393) (-329 "EXPUPXS.spad" 476425 476448 477724 477873) (-328 "EXPRTUBE.spad" 473713 473721 476415 476420) (-327 "EXPRODE.spad" 470873 470889 473703 473708) (-326 "EXPR.spad" 466048 466058 466762 467057) (-325 "EXPR2UPS.spad" 462170 462183 466038 466043) (-324 "EXPR2.spad" 461875 461887 462160 462165) (-323 "EXPEXPAN.spad" 458676 458701 459308 459401) (-322 "EXIT.spad" 458347 458355 458666 458671) (-321 "EXITAST.spad" 458083 458091 458337 458342) (-320 "EVALCYC.spad" 457543 457557 458073 458078) (-319 "EVALAB.spad" 457115 457125 457533 457538) (-318 "EVALAB.spad" 456685 456697 457105 457110) (-317 "EUCDOM.spad" 454259 454267 456611 456680) (-316 "EUCDOM.spad" 451895 451905 454249 454254) (-315 "ESTOOLS.spad" 443741 443749 451885 451890) (-314 "ESTOOLS2.spad" 443344 443358 443731 443736) (-313 "ESTOOLS1.spad" 443029 443040 443334 443339) (-312 "ES.spad" 435844 435852 443019 443024) (-311 "ES.spad" 428565 428575 435742 435747) (-310 "ESCONT.spad" 425358 425366 428555 428560) (-309 "ESCONT1.spad" 425107 425119 425348 425353) (-308 "ES2.spad" 424612 424628 425097 425102) (-307 "ES1.spad" 424182 424198 424602 424607) (-306 "ERROR.spad" 421509 421517 424172 424177) (-305 "EQTBL.spad" 419981 420003 420190 420217) (-304 "EQ.spad" 414786 414796 417573 417685) (-303 "EQ2.spad" 414504 414516 414776 414781) (-302 "EP.spad" 410830 410840 414494 414499) (-301 "ENV.spad" 409508 409516 410820 410825) (-300 "ENTIRER.spad" 409176 409184 409452 409503) (-299 "EMR.spad" 408464 408505 409102 409171) (-298 "ELTAGG.spad" 406718 406737 408454 408459) (-297 "ELTAGG.spad" 404936 404957 406674 406679) (-296 "ELTAB.spad" 404411 404424 404926 404931) (-295 "ELFUTS.spad" 403798 403817 404401 404406) (-294 "ELEMFUN.spad" 403487 403495 403788 403793) (-293 "ELEMFUN.spad" 403174 403184 403477 403482) (-292 "ELAGG.spad" 401145 401155 403154 403169) (-291 "ELAGG.spad" 399053 399065 401064 401069) (-290 "ELABOR.spad" 398399 398407 399043 399048) (-289 "ELABEXPR.spad" 397331 397339 398389 398394) (-288 "EFUPXS.spad" 394107 394137 397287 397292) (-287 "EFULS.spad" 390943 390966 394063 394068) (-286 "EFSTRUC.spad" 388958 388974 390933 390938) (-285 "EF.spad" 383734 383750 388948 388953) (-284 "EAB.spad" 382010 382018 383724 383729) (-283 "E04UCFA.spad" 381546 381554 382000 382005) (-282 "E04NAFA.spad" 381123 381131 381536 381541) (-281 "E04MBFA.spad" 380703 380711 381113 381118) (-280 "E04JAFA.spad" 380239 380247 380693 380698) (-279 "E04GCFA.spad" 379775 379783 380229 380234) (-278 "E04FDFA.spad" 379311 379319 379765 379770) (-277 "E04DGFA.spad" 378847 378855 379301 379306) (-276 "E04AGNT.spad" 374697 374705 378837 378842) (-275 "DVARCAT.spad" 371587 371597 374687 374692) (-274 "DVARCAT.spad" 368475 368487 371577 371582) (-273 "DSMP.spad" 365849 365863 366154 366281) (-272 "DSEXT.spad" 365151 365161 365839 365844) (-271 "DSEXT.spad" 364360 364372 365050 365055) (-270 "DROPT.spad" 358319 358327 364350 364355) (-269 "DROPT1.spad" 357984 357994 358309 358314) (-268 "DROPT0.spad" 352841 352849 357974 357979) (-267 "DRAWPT.spad" 351014 351022 352831 352836) (-266 "DRAW.spad" 343890 343903 351004 351009) (-265 "DRAWHACK.spad" 343198 343208 343880 343885) (-264 "DRAWCX.spad" 340668 340676 343188 343193) (-263 "DRAWCURV.spad" 340215 340230 340658 340663) (-262 "DRAWCFUN.spad" 329747 329755 340205 340210) (-261 "DQAGG.spad" 327925 327935 329715 329742) (-260 "DPOLCAT.spad" 323274 323290 327793 327920) (-259 "DPOLCAT.spad" 318709 318727 323230 323235) (-258 "DPMO.spad" 310505 310521 310643 310856) (-257 "DPMM.spad" 302314 302332 302439 302652) (-256 "DOMTMPLT.spad" 302085 302093 302304 302309) (-255 "DOMCTOR.spad" 301840 301848 302075 302080) (-254 "DOMAIN.spad" 300927 300935 301830 301835) (-253 "DMP.spad" 298187 298202 298757 298884) (-252 "DMEXT.spad" 298054 298064 298155 298182) (-251 "DLP.spad" 297406 297416 298044 298049) (-250 "DLIST.spad" 295985 295995 296589 296616) (-249 "DLAGG.spad" 294402 294412 295975 295980) (-248 "DIVRING.spad" 293944 293952 294346 294397) (-247 "DIVRING.spad" 293530 293540 293934 293939) (-246 "DISPLAY.spad" 291720 291728 293520 293525) (-245 "DIRPROD.spad" 279871 279887 280511 280610) (-244 "DIRPROD2.spad" 278689 278707 279861 279866) (-243 "DIRPCAT.spad" 277882 277898 278585 278684) (-242 "DIRPCAT.spad" 276702 276720 277407 277412) (-241 "DIOSP.spad" 275527 275535 276692 276697) (-240 "DIOPS.spad" 274523 274533 275507 275522) (-239 "DIOPS.spad" 273493 273505 274479 274484) (-238 "DIFRING.spad" 273331 273339 273473 273488) (-237 "DIFFSPC.spad" 272910 272918 273321 273326) (-236 "DIFFSPC.spad" 272487 272497 272900 272905) (-235 "DIFFMOD.spad" 271976 271986 272455 272482) (-234 "DIFFDOM.spad" 271141 271152 271966 271971) (-233 "DIFFDOM.spad" 270304 270317 271131 271136) (-232 "DIFEXT.spad" 270123 270133 270284 270299) (-231 "DIAGG.spad" 269753 269763 270103 270118) (-230 "DIAGG.spad" 269391 269403 269743 269748) (-229 "DHMATRIX.spad" 267703 267713 268848 268875) (-228 "DFSFUN.spad" 261343 261351 267693 267698) (-227 "DFLOAT.spad" 258074 258082 261233 261338) (-226 "DFINTTLS.spad" 256305 256321 258064 258069) (-225 "DERHAM.spad" 254219 254251 256285 256300) (-224 "DEQUEUE.spad" 253543 253553 253826 253853) (-223 "DEGRED.spad" 253160 253174 253533 253538) (-222 "DEFINTRF.spad" 250697 250707 253150 253155) (-221 "DEFINTEF.spad" 249207 249223 250687 250692) (-220 "DEFAST.spad" 248575 248583 249197 249202) (-219 "DECIMAL.spad" 246584 246592 246945 247038) (-218 "DDFACT.spad" 244397 244414 246574 246579) (-217 "DBLRESP.spad" 243997 244021 244387 244392) (-216 "DBASE.spad" 242661 242671 243987 243992) (-215 "DATAARY.spad" 242123 242136 242651 242656) (-214 "D03FAFA.spad" 241951 241959 242113 242118) (-213 "D03EEFA.spad" 241771 241779 241941 241946) (-212 "D03AGNT.spad" 240857 240865 241761 241766) (-211 "D02EJFA.spad" 240319 240327 240847 240852) (-210 "D02CJFA.spad" 239797 239805 240309 240314) (-209 "D02BHFA.spad" 239287 239295 239787 239792) (-208 "D02BBFA.spad" 238777 238785 239277 239282) (-207 "D02AGNT.spad" 233591 233599 238767 238772) (-206 "D01WGTS.spad" 231910 231918 233581 233586) (-205 "D01TRNS.spad" 231887 231895 231900 231905) (-204 "D01GBFA.spad" 231409 231417 231877 231882) (-203 "D01FCFA.spad" 230931 230939 231399 231404) (-202 "D01ASFA.spad" 230399 230407 230921 230926) (-201 "D01AQFA.spad" 229845 229853 230389 230394) (-200 "D01APFA.spad" 229269 229277 229835 229840) (-199 "D01ANFA.spad" 228763 228771 229259 229264) (-198 "D01AMFA.spad" 228273 228281 228753 228758) (-197 "D01ALFA.spad" 227813 227821 228263 228268) (-196 "D01AKFA.spad" 227339 227347 227803 227808) (-195 "D01AJFA.spad" 226862 226870 227329 227334) (-194 "D01AGNT.spad" 222929 222937 226852 226857) (-193 "CYCLOTOM.spad" 222435 222443 222919 222924) (-192 "CYCLES.spad" 219227 219235 222425 222430) (-191 "CVMP.spad" 218644 218654 219217 219222) (-190 "CTRIGMNP.spad" 217144 217160 218634 218639) (-189 "CTOR.spad" 216835 216843 217134 217139) (-188 "CTORKIND.spad" 216438 216446 216825 216830) (-187 "CTORCAT.spad" 215687 215695 216428 216433) (-186 "CTORCAT.spad" 214934 214944 215677 215682) (-185 "CTORCALL.spad" 214523 214533 214924 214929) (-184 "CSTTOOLS.spad" 213768 213781 214513 214518) (-183 "CRFP.spad" 207492 207505 213758 213763) (-182 "CRCEAST.spad" 207212 207220 207482 207487) (-181 "CRAPACK.spad" 206263 206273 207202 207207) (-180 "CPMATCH.spad" 205767 205782 206188 206193) (-179 "CPIMA.spad" 205472 205491 205757 205762) (-178 "COORDSYS.spad" 200481 200491 205462 205467) (-177 "CONTOUR.spad" 199892 199900 200471 200476) (-176 "CONTFRAC.spad" 195642 195652 199794 199887) (-175 "CONDUIT.spad" 195400 195408 195632 195637) (-174 "COMRING.spad" 195074 195082 195338 195395) (-173 "COMPPROP.spad" 194592 194600 195064 195069) (-172 "COMPLPAT.spad" 194359 194374 194582 194587) (-171 "COMPLEX.spad" 189736 189746 189980 190241) (-170 "COMPLEX2.spad" 189451 189463 189726 189731) (-169 "COMPILER.spad" 189000 189008 189441 189446) (-168 "COMPFACT.spad" 188602 188616 188990 188995) (-167 "COMPCAT.spad" 186674 186684 188336 188597) (-166 "COMPCAT.spad" 184474 184486 186138 186143) (-165 "COMMUPC.spad" 184222 184240 184464 184469) (-164 "COMMONOP.spad" 183755 183763 184212 184217) (-163 "COMM.spad" 183566 183574 183745 183750) (-162 "COMMAAST.spad" 183329 183337 183556 183561) (-161 "COMBOPC.spad" 182244 182252 183319 183324) (-160 "COMBINAT.spad" 181011 181021 182234 182239) (-159 "COMBF.spad" 178393 178409 181001 181006) (-158 "COLOR.spad" 177230 177238 178383 178388) (-157 "COLONAST.spad" 176896 176904 177220 177225) (-156 "CMPLXRT.spad" 176607 176624 176886 176891) (-155 "CLLCTAST.spad" 176269 176277 176597 176602) (-154 "CLIP.spad" 172377 172385 176259 176264) (-153 "CLIF.spad" 171032 171048 172333 172372) (-152 "CLAGG.spad" 167537 167547 171022 171027) (-151 "CLAGG.spad" 163913 163925 167400 167405) (-150 "CINTSLPE.spad" 163244 163257 163903 163908) (-149 "CHVAR.spad" 161382 161404 163234 163239) (-148 "CHARZ.spad" 161297 161305 161362 161377) (-147 "CHARPOL.spad" 160807 160817 161287 161292) (-146 "CHARNZ.spad" 160560 160568 160787 160802) (-145 "CHAR.spad" 158434 158442 160550 160555) (-144 "CFCAT.spad" 157762 157770 158424 158429) (-143 "CDEN.spad" 156958 156972 157752 157757) (-142 "CCLASS.spad" 155107 155115 156369 156408) (-141 "CATEGORY.spad" 154149 154157 155097 155102) (-140 "CATCTOR.spad" 154040 154048 154139 154144) (-139 "CATAST.spad" 153658 153666 154030 154035) (-138 "CASEAST.spad" 153372 153380 153648 153653) (-137 "CARTEN.spad" 148739 148763 153362 153367) (-136 "CARTEN2.spad" 148129 148156 148729 148734) (-135 "CARD.spad" 145424 145432 148103 148124) (-134 "CAPSLAST.spad" 145198 145206 145414 145419) (-133 "CACHSET.spad" 144822 144830 145188 145193) (-132 "CABMON.spad" 144377 144385 144812 144817) (-131 "BYTEORD.spad" 144052 144060 144367 144372) (-130 "BYTE.spad" 143479 143487 144042 144047) (-129 "BYTEBUF.spad" 141338 141346 142648 142675) (-128 "BTREE.spad" 140411 140421 140945 140972) (-127 "BTOURN.spad" 139416 139426 140018 140045) (-126 "BTCAT.spad" 138808 138818 139384 139411) (-125 "BTCAT.spad" 138220 138232 138798 138803) (-124 "BTAGG.spad" 137686 137694 138188 138215) (-123 "BTAGG.spad" 137172 137182 137676 137681) (-122 "BSTREE.spad" 135913 135923 136779 136806) (-121 "BRILL.spad" 134110 134121 135903 135908) (-120 "BRAGG.spad" 133050 133060 134100 134105) (-119 "BRAGG.spad" 131954 131966 133006 133011) (-118 "BPADICRT.spad" 129828 129840 130083 130176) (-117 "BPADIC.spad" 129492 129504 129754 129823) (-116 "BOUNDZRO.spad" 129148 129165 129482 129487) (-115 "BOP.spad" 124330 124338 129138 129143) (-114 "BOP1.spad" 121796 121806 124320 124325) (-113 "BOOLE.spad" 121446 121454 121786 121791) (-112 "BOOLEAN.spad" 120884 120892 121436 121441) (-111 "BMODULE.spad" 120596 120608 120852 120879) (-110 "BITS.spad" 120017 120025 120232 120259) (-109 "BINDING.spad" 119430 119438 120007 120012) (-108 "BINARY.spad" 117444 117452 117800 117893) (-107 "BGAGG.spad" 116649 116659 117424 117439) (-106 "BGAGG.spad" 115862 115874 116639 116644) (-105 "BFUNCT.spad" 115426 115434 115842 115857) (-104 "BEZOUT.spad" 114566 114593 115376 115381) (-103 "BBTREE.spad" 111411 111421 114173 114200) (-102 "BASTYPE.spad" 111083 111091 111401 111406) (-101 "BASTYPE.spad" 110753 110763 111073 111078) (-100 "BALFACT.spad" 110212 110225 110743 110748) (-99 "AUTOMOR.spad" 109663 109672 110192 110207) (-98 "ATTREG.spad" 106386 106393 109415 109658) (-97 "ATTRBUT.spad" 102409 102416 106366 106381) (-96 "ATTRAST.spad" 102126 102133 102399 102404) (-95 "ATRIG.spad" 101596 101603 102116 102121) (-94 "ATRIG.spad" 101064 101073 101586 101591) (-93 "ASTCAT.spad" 100968 100975 101054 101059) (-92 "ASTCAT.spad" 100870 100879 100958 100963) (-91 "ASTACK.spad" 100209 100218 100477 100504) (-90 "ASSOCEQ.spad" 99035 99046 100165 100170) (-89 "ASP9.spad" 98116 98129 99025 99030) (-88 "ASP8.spad" 97159 97172 98106 98111) (-87 "ASP80.spad" 96481 96494 97149 97154) (-86 "ASP7.spad" 95641 95654 96471 96476) (-85 "ASP78.spad" 95092 95105 95631 95636) (-84 "ASP77.spad" 94461 94474 95082 95087) (-83 "ASP74.spad" 93553 93566 94451 94456) (-82 "ASP73.spad" 92824 92837 93543 93548) (-81 "ASP6.spad" 91691 91704 92814 92819) (-80 "ASP55.spad" 90200 90213 91681 91686) (-79 "ASP50.spad" 88017 88030 90190 90195) (-78 "ASP4.spad" 87312 87325 88007 88012) (-77 "ASP49.spad" 86311 86324 87302 87307) (-76 "ASP42.spad" 84718 84757 86301 86306) (-75 "ASP41.spad" 83297 83336 84708 84713) (-74 "ASP35.spad" 82285 82298 83287 83292) (-73 "ASP34.spad" 81586 81599 82275 82280) (-72 "ASP33.spad" 81146 81159 81576 81581) (-71 "ASP31.spad" 80286 80299 81136 81141) (-70 "ASP30.spad" 79178 79191 80276 80281) (-69 "ASP29.spad" 78644 78657 79168 79173) (-68 "ASP28.spad" 69917 69930 78634 78639) (-67 "ASP27.spad" 68814 68827 69907 69912) (-66 "ASP24.spad" 67901 67914 68804 68809) (-65 "ASP20.spad" 67365 67378 67891 67896) (-64 "ASP1.spad" 66746 66759 67355 67360) (-63 "ASP19.spad" 61432 61445 66736 66741) (-62 "ASP12.spad" 60846 60859 61422 61427) (-61 "ASP10.spad" 60117 60130 60836 60841) (-60 "ARRAY2.spad" 59477 59486 59724 59751) (-59 "ARRAY1.spad" 58314 58323 58660 58687) (-58 "ARRAY12.spad" 57027 57038 58304 58309) (-57 "ARR2CAT.spad" 52801 52822 56995 57022) (-56 "ARR2CAT.spad" 48595 48618 52791 52796) (-55 "ARITY.spad" 47967 47974 48585 48590) (-54 "APPRULE.spad" 47227 47249 47957 47962) (-53 "APPLYORE.spad" 46846 46859 47217 47222) (-52 "ANY.spad" 45705 45712 46836 46841) (-51 "ANY1.spad" 44776 44785 45695 45700) (-50 "ANTISYM.spad" 43221 43237 44756 44771) (-49 "ANON.spad" 42914 42921 43211 43216) (-48 "AN.spad" 41223 41230 42730 42823) (-47 "AMR.spad" 39408 39419 41121 41218) (-46 "AMR.spad" 37430 37443 39145 39150) (-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 2279904 2279909 2279914 2279919) (-2 NIL 2279884 2279889 2279894 2279899) (-1 NIL 2279864 2279869 2279874 2279879) (0 NIL 2279844 2279849 2279854 2279859) (-1315 "ZMOD.spad" 2279653 2279666 2279782 2279839) (-1314 "ZLINDEP.spad" 2278719 2278730 2279643 2279648) (-1313 "ZDSOLVE.spad" 2268664 2268686 2278709 2278714) (-1312 "YSTREAM.spad" 2268159 2268170 2268654 2268659) (-1311 "YDIAGRAM.spad" 2267793 2267802 2268149 2268154) (-1310 "XRPOLY.spad" 2267013 2267033 2267649 2267718) (-1309 "XPR.spad" 2264808 2264821 2266731 2266830) (-1308 "XPOLY.spad" 2264363 2264374 2264664 2264733) (-1307 "XPOLYC.spad" 2263682 2263698 2264289 2264358) (-1306 "XPBWPOLY.spad" 2262119 2262139 2263462 2263531) (-1305 "XF.spad" 2260582 2260597 2262021 2262114) (-1304 "XF.spad" 2259025 2259042 2260466 2260471) (-1303 "XFALG.spad" 2256073 2256089 2258951 2259020) (-1302 "XEXPPKG.spad" 2255324 2255350 2256063 2256068) (-1301 "XDPOLY.spad" 2254938 2254954 2255180 2255249) (-1300 "XALG.spad" 2254598 2254609 2254894 2254933) (-1299 "WUTSET.spad" 2250437 2250454 2254244 2254271) (-1298 "WP.spad" 2249636 2249680 2250295 2250362) (-1297 "WHILEAST.spad" 2249434 2249443 2249626 2249631) (-1296 "WHEREAST.spad" 2249105 2249114 2249424 2249429) (-1295 "WFFINTBS.spad" 2246768 2246790 2249095 2249100) (-1294 "WEIER.spad" 2244990 2245001 2246758 2246763) (-1293 "VSPACE.spad" 2244663 2244674 2244958 2244985) (-1292 "VSPACE.spad" 2244356 2244369 2244653 2244658) (-1291 "VOID.spad" 2244033 2244042 2244346 2244351) (-1290 "VIEW.spad" 2241713 2241722 2244023 2244028) (-1289 "VIEWDEF.spad" 2236914 2236923 2241703 2241708) (-1288 "VIEW3D.spad" 2220875 2220884 2236904 2236909) (-1287 "VIEW2D.spad" 2208766 2208775 2220865 2220870) (-1286 "VECTOR.spad" 2207440 2207451 2207691 2207718) (-1285 "VECTOR2.spad" 2206079 2206092 2207430 2207435) (-1284 "VECTCAT.spad" 2203983 2203994 2206047 2206074) (-1283 "VECTCAT.spad" 2201694 2201707 2203760 2203765) (-1282 "VARIABLE.spad" 2201474 2201489 2201684 2201689) (-1281 "UTYPE.spad" 2201118 2201127 2201464 2201469) (-1280 "UTSODETL.spad" 2200413 2200437 2201074 2201079) (-1279 "UTSODE.spad" 2198629 2198649 2200403 2200408) (-1278 "UTS.spad" 2193576 2193604 2197096 2197193) (-1277 "UTSCAT.spad" 2191055 2191071 2193474 2193571) (-1276 "UTSCAT.spad" 2188178 2188196 2190599 2190604) (-1275 "UTS2.spad" 2187773 2187808 2188168 2188173) (-1274 "URAGG.spad" 2182446 2182457 2187763 2187768) (-1273 "URAGG.spad" 2177083 2177096 2182402 2182407) (-1272 "UPXSSING.spad" 2174728 2174754 2176164 2176297) (-1271 "UPXS.spad" 2172024 2172052 2172860 2173009) (-1270 "UPXSCONS.spad" 2169783 2169803 2170156 2170305) (-1269 "UPXSCCA.spad" 2168354 2168374 2169629 2169778) (-1268 "UPXSCCA.spad" 2167067 2167089 2168344 2168349) (-1267 "UPXSCAT.spad" 2165656 2165672 2166913 2167062) (-1266 "UPXS2.spad" 2165199 2165252 2165646 2165651) (-1265 "UPSQFREE.spad" 2163613 2163627 2165189 2165194) (-1264 "UPSCAT.spad" 2161400 2161424 2163511 2163608) (-1263 "UPSCAT.spad" 2158893 2158919 2161006 2161011) (-1262 "UPOLYC.spad" 2153933 2153944 2158735 2158888) (-1261 "UPOLYC.spad" 2148865 2148878 2153669 2153674) (-1260 "UPOLYC2.spad" 2148336 2148355 2148855 2148860) (-1259 "UP.spad" 2145442 2145457 2145829 2145982) (-1258 "UPMP.spad" 2144342 2144355 2145432 2145437) (-1257 "UPDIVP.spad" 2143907 2143921 2144332 2144337) (-1256 "UPDECOMP.spad" 2142152 2142166 2143897 2143902) (-1255 "UPCDEN.spad" 2141361 2141377 2142142 2142147) (-1254 "UP2.spad" 2140725 2140746 2141351 2141356) (-1253 "UNISEG.spad" 2140078 2140089 2140644 2140649) (-1252 "UNISEG2.spad" 2139575 2139588 2140034 2140039) (-1251 "UNIFACT.spad" 2138678 2138690 2139565 2139570) (-1250 "ULS.spad" 2128462 2128490 2129407 2129836) (-1249 "ULSCONS.spad" 2119596 2119616 2119966 2120115) (-1248 "ULSCCAT.spad" 2117333 2117353 2119442 2119591) (-1247 "ULSCCAT.spad" 2115178 2115200 2117289 2117294) (-1246 "ULSCAT.spad" 2113410 2113426 2115024 2115173) (-1245 "ULS2.spad" 2112924 2112977 2113400 2113405) (-1244 "UINT8.spad" 2112801 2112810 2112914 2112919) (-1243 "UINT64.spad" 2112677 2112686 2112791 2112796) (-1242 "UINT32.spad" 2112553 2112562 2112667 2112672) (-1241 "UINT16.spad" 2112429 2112438 2112543 2112548) (-1240 "UFD.spad" 2111494 2111503 2112355 2112424) (-1239 "UFD.spad" 2110621 2110632 2111484 2111489) (-1238 "UDVO.spad" 2109502 2109511 2110611 2110616) (-1237 "UDPO.spad" 2106995 2107006 2109458 2109463) (-1236 "TYPE.spad" 2106927 2106936 2106985 2106990) (-1235 "TYPEAST.spad" 2106846 2106855 2106917 2106922) (-1234 "TWOFACT.spad" 2105498 2105513 2106836 2106841) (-1233 "TUPLE.spad" 2104984 2104995 2105397 2105402) (-1232 "TUBETOOL.spad" 2101851 2101860 2104974 2104979) (-1231 "TUBE.spad" 2100498 2100515 2101841 2101846) (-1230 "TS.spad" 2099097 2099113 2100063 2100160) (-1229 "TSETCAT.spad" 2086224 2086241 2099065 2099092) (-1228 "TSETCAT.spad" 2073337 2073356 2086180 2086185) (-1227 "TRMANIP.spad" 2067703 2067720 2073043 2073048) (-1226 "TRIMAT.spad" 2066666 2066691 2067693 2067698) (-1225 "TRIGMNIP.spad" 2065193 2065210 2066656 2066661) (-1224 "TRIGCAT.spad" 2064705 2064714 2065183 2065188) (-1223 "TRIGCAT.spad" 2064215 2064226 2064695 2064700) (-1222 "TREE.spad" 2062790 2062801 2063822 2063849) (-1221 "TRANFUN.spad" 2062629 2062638 2062780 2062785) (-1220 "TRANFUN.spad" 2062466 2062477 2062619 2062624) (-1219 "TOPSP.spad" 2062140 2062149 2062456 2062461) (-1218 "TOOLSIGN.spad" 2061803 2061814 2062130 2062135) (-1217 "TEXTFILE.spad" 2060364 2060373 2061793 2061798) (-1216 "TEX.spad" 2057510 2057519 2060354 2060359) (-1215 "TEX1.spad" 2057066 2057077 2057500 2057505) (-1214 "TEMUTL.spad" 2056621 2056630 2057056 2057061) (-1213 "TBCMPPK.spad" 2054714 2054737 2056611 2056616) (-1212 "TBAGG.spad" 2053764 2053787 2054694 2054709) (-1211 "TBAGG.spad" 2052822 2052847 2053754 2053759) (-1210 "TANEXP.spad" 2052230 2052241 2052812 2052817) (-1209 "TALGOP.spad" 2051954 2051965 2052220 2052225) (-1208 "TABLE.spad" 2050365 2050388 2050635 2050662) (-1207 "TABLEAU.spad" 2049846 2049857 2050355 2050360) (-1206 "TABLBUMP.spad" 2046649 2046660 2049836 2049841) (-1205 "SYSTEM.spad" 2045877 2045886 2046639 2046644) (-1204 "SYSSOLP.spad" 2043360 2043371 2045867 2045872) (-1203 "SYSPTR.spad" 2043259 2043268 2043350 2043355) (-1202 "SYSNNI.spad" 2042441 2042452 2043249 2043254) (-1201 "SYSINT.spad" 2041845 2041856 2042431 2042436) (-1200 "SYNTAX.spad" 2038051 2038060 2041835 2041840) (-1199 "SYMTAB.spad" 2036119 2036128 2038041 2038046) (-1198 "SYMS.spad" 2032142 2032151 2036109 2036114) (-1197 "SYMPOLY.spad" 2031149 2031160 2031231 2031358) (-1196 "SYMFUNC.spad" 2030650 2030661 2031139 2031144) (-1195 "SYMBOL.spad" 2028153 2028162 2030640 2030645) (-1194 "SWITCH.spad" 2024924 2024933 2028143 2028148) (-1193 "SUTS.spad" 2021972 2022000 2023391 2023488) (-1192 "SUPXS.spad" 2019255 2019283 2020104 2020253) (-1191 "SUP.spad" 2015975 2015986 2016748 2016901) (-1190 "SUPFRACF.spad" 2015080 2015098 2015965 2015970) (-1189 "SUP2.spad" 2014472 2014485 2015070 2015075) (-1188 "SUMRF.spad" 2013446 2013457 2014462 2014467) (-1187 "SUMFS.spad" 2013083 2013100 2013436 2013441) (-1186 "SULS.spad" 2002854 2002882 2003812 2004241) (-1185 "SUCHTAST.spad" 2002623 2002632 2002844 2002849) (-1184 "SUCH.spad" 2002305 2002320 2002613 2002618) (-1183 "SUBSPACE.spad" 1994420 1994435 2002295 2002300) (-1182 "SUBRESP.spad" 1993590 1993604 1994376 1994381) (-1181 "STTF.spad" 1989689 1989705 1993580 1993585) (-1180 "STTFNC.spad" 1986157 1986173 1989679 1989684) (-1179 "STTAYLOR.spad" 1978792 1978803 1986038 1986043) (-1178 "STRTBL.spad" 1977297 1977314 1977446 1977473) (-1177 "STRING.spad" 1976245 1976254 1976466 1976493) (-1176 "STREAM.spad" 1973163 1973174 1975770 1975785) (-1175 "STREAM3.spad" 1972736 1972751 1973153 1973158) (-1174 "STREAM2.spad" 1971864 1971877 1972726 1972731) (-1173 "STREAM1.spad" 1971570 1971581 1971854 1971859) (-1172 "STINPROD.spad" 1970506 1970522 1971560 1971565) (-1171 "STEP.spad" 1969707 1969716 1970496 1970501) (-1170 "STEPAST.spad" 1968941 1968950 1969697 1969702) (-1169 "STBL.spad" 1967467 1967495 1967634 1967649) (-1168 "STAGG.spad" 1966542 1966553 1967457 1967462) (-1167 "STAGG.spad" 1965615 1965628 1966532 1966537) (-1166 "STACK.spad" 1964972 1964983 1965222 1965249) (-1165 "SREGSET.spad" 1962676 1962693 1964618 1964645) (-1164 "SRDCMPK.spad" 1961237 1961257 1962666 1962671) (-1163 "SRAGG.spad" 1956380 1956389 1961205 1961232) (-1162 "SRAGG.spad" 1951543 1951554 1956370 1956375) (-1161 "SQMATRIX.spad" 1949122 1949140 1950038 1950125) (-1160 "SPLTREE.spad" 1943674 1943687 1948558 1948585) (-1159 "SPLNODE.spad" 1940262 1940275 1943664 1943669) (-1158 "SPFCAT.spad" 1939071 1939080 1940252 1940257) (-1157 "SPECOUT.spad" 1937623 1937632 1939061 1939066) (-1156 "SPADXPT.spad" 1929218 1929227 1937613 1937618) (-1155 "spad-parser.spad" 1928683 1928692 1929208 1929213) (-1154 "SPADAST.spad" 1928384 1928393 1928673 1928678) (-1153 "SPACEC.spad" 1912583 1912594 1928374 1928379) (-1152 "SPACE3.spad" 1912359 1912370 1912573 1912578) (-1151 "SORTPAK.spad" 1911908 1911921 1912315 1912320) (-1150 "SOLVETRA.spad" 1909671 1909682 1911898 1911903) (-1149 "SOLVESER.spad" 1908199 1908210 1909661 1909666) (-1148 "SOLVERAD.spad" 1904225 1904236 1908189 1908194) (-1147 "SOLVEFOR.spad" 1902687 1902705 1904215 1904220) (-1146 "SNTSCAT.spad" 1902287 1902304 1902655 1902682) (-1145 "SMTS.spad" 1900559 1900585 1901852 1901949) (-1144 "SMP.spad" 1898034 1898054 1898424 1898551) (-1143 "SMITH.spad" 1896879 1896904 1898024 1898029) (-1142 "SMATCAT.spad" 1894989 1895019 1896823 1896874) (-1141 "SMATCAT.spad" 1893031 1893063 1894867 1894872) (-1140 "SKAGG.spad" 1891994 1892005 1892999 1893026) (-1139 "SINT.spad" 1890934 1890943 1891860 1891989) (-1138 "SIMPAN.spad" 1890662 1890671 1890924 1890929) (-1137 "SIG.spad" 1889992 1890001 1890652 1890657) (-1136 "SIGNRF.spad" 1889110 1889121 1889982 1889987) (-1135 "SIGNEF.spad" 1888389 1888406 1889100 1889105) (-1134 "SIGAST.spad" 1887774 1887783 1888379 1888384) (-1133 "SHP.spad" 1885702 1885717 1887730 1887735) (-1132 "SHDP.spad" 1873984 1874011 1874493 1874592) (-1131 "SGROUP.spad" 1873592 1873601 1873974 1873979) (-1130 "SGROUP.spad" 1873198 1873209 1873582 1873587) (-1129 "SGCF.spad" 1866337 1866346 1873188 1873193) (-1128 "SFRTCAT.spad" 1865267 1865284 1866305 1866332) (-1127 "SFRGCD.spad" 1864330 1864350 1865257 1865262) (-1126 "SFQCMPK.spad" 1858967 1858987 1864320 1864325) (-1125 "SFORT.spad" 1858406 1858420 1858957 1858962) (-1124 "SEXOF.spad" 1858249 1858289 1858396 1858401) (-1123 "SEX.spad" 1858141 1858150 1858239 1858244) (-1122 "SEXCAT.spad" 1855913 1855953 1858131 1858136) (-1121 "SET.spad" 1854237 1854248 1855334 1855373) (-1120 "SETMN.spad" 1852687 1852704 1854227 1854232) (-1119 "SETCAT.spad" 1852009 1852018 1852677 1852682) (-1118 "SETCAT.spad" 1851329 1851340 1851999 1852004) (-1117 "SETAGG.spad" 1847878 1847889 1851309 1851324) (-1116 "SETAGG.spad" 1844435 1844448 1847868 1847873) (-1115 "SEQAST.spad" 1844138 1844147 1844425 1844430) (-1114 "SEGXCAT.spad" 1843294 1843307 1844128 1844133) (-1113 "SEG.spad" 1843107 1843118 1843213 1843218) (-1112 "SEGCAT.spad" 1842032 1842043 1843097 1843102) (-1111 "SEGBIND.spad" 1841790 1841801 1841979 1841984) (-1110 "SEGBIND2.spad" 1841488 1841501 1841780 1841785) (-1109 "SEGAST.spad" 1841202 1841211 1841478 1841483) (-1108 "SEG2.spad" 1840637 1840650 1841158 1841163) (-1107 "SDVAR.spad" 1839913 1839924 1840627 1840632) (-1106 "SDPOL.spad" 1837246 1837257 1837537 1837664) (-1105 "SCPKG.spad" 1835335 1835346 1837236 1837241) (-1104 "SCOPE.spad" 1834488 1834497 1835325 1835330) (-1103 "SCACHE.spad" 1833184 1833195 1834478 1834483) (-1102 "SASTCAT.spad" 1833093 1833102 1833174 1833179) (-1101 "SAOS.spad" 1832965 1832974 1833083 1833088) (-1100 "SAERFFC.spad" 1832678 1832698 1832955 1832960) (-1099 "SAE.spad" 1830148 1830164 1830759 1830894) (-1098 "SAEFACT.spad" 1829849 1829869 1830138 1830143) (-1097 "RURPK.spad" 1827508 1827524 1829839 1829844) (-1096 "RULESET.spad" 1826961 1826985 1827498 1827503) (-1095 "RULE.spad" 1825201 1825225 1826951 1826956) (-1094 "RULECOLD.spad" 1825053 1825066 1825191 1825196) (-1093 "RTVALUE.spad" 1824788 1824797 1825043 1825048) (-1092 "RSTRCAST.spad" 1824505 1824514 1824778 1824783) (-1091 "RSETGCD.spad" 1820883 1820903 1824495 1824500) (-1090 "RSETCAT.spad" 1810819 1810836 1820851 1820878) (-1089 "RSETCAT.spad" 1800775 1800794 1810809 1810814) (-1088 "RSDCMPK.spad" 1799227 1799247 1800765 1800770) (-1087 "RRCC.spad" 1797611 1797641 1799217 1799222) (-1086 "RRCC.spad" 1795993 1796025 1797601 1797606) (-1085 "RPTAST.spad" 1795695 1795704 1795983 1795988) (-1084 "RPOLCAT.spad" 1775055 1775070 1795563 1795690) (-1083 "RPOLCAT.spad" 1754128 1754145 1774638 1774643) (-1082 "ROUTINE.spad" 1750011 1750020 1752775 1752802) (-1081 "ROMAN.spad" 1749339 1749348 1749877 1750006) (-1080 "ROIRC.spad" 1748419 1748451 1749329 1749334) (-1079 "RNS.spad" 1747322 1747331 1748321 1748414) (-1078 "RNS.spad" 1746311 1746322 1747312 1747317) (-1077 "RNG.spad" 1746046 1746055 1746301 1746306) (-1076 "RNGBIND.spad" 1745206 1745220 1746001 1746006) (-1075 "RMODULE.spad" 1744971 1744982 1745196 1745201) (-1074 "RMCAT2.spad" 1744391 1744448 1744961 1744966) (-1073 "RMATRIX.spad" 1743215 1743234 1743558 1743597) (-1072 "RMATCAT.spad" 1738794 1738825 1743171 1743210) (-1071 "RMATCAT.spad" 1734263 1734296 1738642 1738647) (-1070 "RLINSET.spad" 1733967 1733978 1734253 1734258) (-1069 "RINTERP.spad" 1733855 1733875 1733957 1733962) (-1068 "RING.spad" 1733325 1733334 1733835 1733850) (-1067 "RING.spad" 1732803 1732814 1733315 1733320) (-1066 "RIDIST.spad" 1732195 1732204 1732793 1732798) (-1065 "RGCHAIN.spad" 1730778 1730794 1731680 1731707) (-1064 "RGBCSPC.spad" 1730559 1730571 1730768 1730773) (-1063 "RGBCMDL.spad" 1730089 1730101 1730549 1730554) (-1062 "RF.spad" 1727731 1727742 1730079 1730084) (-1061 "RFFACTOR.spad" 1727193 1727204 1727721 1727726) (-1060 "RFFACT.spad" 1726928 1726940 1727183 1727188) (-1059 "RFDIST.spad" 1725924 1725933 1726918 1726923) (-1058 "RETSOL.spad" 1725343 1725356 1725914 1725919) (-1057 "RETRACT.spad" 1724771 1724782 1725333 1725338) (-1056 "RETRACT.spad" 1724197 1724210 1724761 1724766) (-1055 "RETAST.spad" 1724009 1724018 1724187 1724192) (-1054 "RESULT.spad" 1722069 1722078 1722656 1722683) (-1053 "RESRING.spad" 1721416 1721463 1722007 1722064) (-1052 "RESLATC.spad" 1720740 1720751 1721406 1721411) (-1051 "REPSQ.spad" 1720471 1720482 1720730 1720735) (-1050 "REP.spad" 1718025 1718034 1720461 1720466) (-1049 "REPDB.spad" 1717732 1717743 1718015 1718020) (-1048 "REP2.spad" 1707390 1707401 1717574 1717579) (-1047 "REP1.spad" 1701586 1701597 1707340 1707345) (-1046 "REGSET.spad" 1699383 1699400 1701232 1701259) (-1045 "REF.spad" 1698718 1698729 1699338 1699343) (-1044 "REDORDER.spad" 1697924 1697941 1698708 1698713) (-1043 "RECLOS.spad" 1696707 1696727 1697411 1697504) (-1042 "REALSOLV.spad" 1695847 1695856 1696697 1696702) (-1041 "REAL.spad" 1695719 1695728 1695837 1695842) (-1040 "REAL0Q.spad" 1693017 1693032 1695709 1695714) (-1039 "REAL0.spad" 1689861 1689876 1693007 1693012) (-1038 "RDUCEAST.spad" 1689582 1689591 1689851 1689856) (-1037 "RDIV.spad" 1689237 1689262 1689572 1689577) (-1036 "RDIST.spad" 1688804 1688815 1689227 1689232) (-1035 "RDETRS.spad" 1687668 1687686 1688794 1688799) (-1034 "RDETR.spad" 1685807 1685825 1687658 1687663) (-1033 "RDEEFS.spad" 1684906 1684923 1685797 1685802) (-1032 "RDEEF.spad" 1683916 1683933 1684896 1684901) (-1031 "RCFIELD.spad" 1681102 1681111 1683818 1683911) (-1030 "RCFIELD.spad" 1678374 1678385 1681092 1681097) (-1029 "RCAGG.spad" 1676302 1676313 1678364 1678369) (-1028 "RCAGG.spad" 1674157 1674170 1676221 1676226) (-1027 "RATRET.spad" 1673517 1673528 1674147 1674152) (-1026 "RATFACT.spad" 1673209 1673221 1673507 1673512) (-1025 "RANDSRC.spad" 1672528 1672537 1673199 1673204) (-1024 "RADUTIL.spad" 1672284 1672293 1672518 1672523) (-1023 "RADIX.spad" 1669108 1669122 1670654 1670747) (-1022 "RADFF.spad" 1666847 1666884 1666966 1667122) (-1021 "RADCAT.spad" 1666442 1666451 1666837 1666842) (-1020 "RADCAT.spad" 1666035 1666046 1666432 1666437) (-1019 "QUEUE.spad" 1665383 1665394 1665642 1665669) (-1018 "QUAT.spad" 1663871 1663882 1664214 1664279) (-1017 "QUATCT2.spad" 1663491 1663510 1663861 1663866) (-1016 "QUATCAT.spad" 1661661 1661672 1663421 1663486) (-1015 "QUATCAT.spad" 1659582 1659595 1661344 1661349) (-1014 "QUAGG.spad" 1658409 1658420 1659550 1659577) (-1013 "QQUTAST.spad" 1658177 1658186 1658399 1658404) (-1012 "QFORM.spad" 1657795 1657810 1658167 1658172) (-1011 "QFCAT.spad" 1656497 1656508 1657697 1657790) (-1010 "QFCAT.spad" 1654790 1654803 1655992 1655997) (-1009 "QFCAT2.spad" 1654482 1654499 1654780 1654785) (-1008 "QEQUAT.spad" 1654040 1654049 1654472 1654477) (-1007 "QCMPACK.spad" 1648786 1648806 1654030 1654035) (-1006 "QALGSET.spad" 1644864 1644897 1648700 1648705) (-1005 "QALGSET2.spad" 1642859 1642878 1644854 1644859) (-1004 "PWFFINTB.spad" 1640274 1640296 1642849 1642854) (-1003 "PUSHVAR.spad" 1639612 1639632 1640264 1640269) (-1002 "PTRANFN.spad" 1635739 1635750 1639602 1639607) (-1001 "PTPACK.spad" 1632826 1632837 1635729 1635734) (-1000 "PTFUNC2.spad" 1632648 1632663 1632816 1632821) (-999 "PTCAT.spad" 1631903 1631913 1632616 1632643) (-998 "PSQFR.spad" 1631210 1631234 1631893 1631898) (-997 "PSEUDLIN.spad" 1630096 1630106 1631200 1631205) (-996 "PSETPK.spad" 1615529 1615545 1629974 1629979) (-995 "PSETCAT.spad" 1609449 1609472 1615509 1615524) (-994 "PSETCAT.spad" 1603343 1603368 1609405 1609410) (-993 "PSCURVE.spad" 1602326 1602334 1603333 1603338) (-992 "PSCAT.spad" 1601109 1601138 1602224 1602321) (-991 "PSCAT.spad" 1599982 1600013 1601099 1601104) (-990 "PRTITION.spad" 1598680 1598688 1599972 1599977) (-989 "PRTDAST.spad" 1598399 1598407 1598670 1598675) (-988 "PRS.spad" 1587961 1587978 1598355 1598360) (-987 "PRQAGG.spad" 1587396 1587406 1587929 1587956) (-986 "PROPLOG.spad" 1586968 1586976 1587386 1587391) (-985 "PROPFUN2.spad" 1586591 1586604 1586958 1586963) (-984 "PROPFUN1.spad" 1585989 1586000 1586581 1586586) (-983 "PROPFRML.spad" 1584557 1584568 1585979 1585984) (-982 "PROPERTY.spad" 1584045 1584053 1584547 1584552) (-981 "PRODUCT.spad" 1581727 1581739 1582011 1582066) (-980 "PR.spad" 1580119 1580131 1580818 1580945) (-979 "PRINT.spad" 1579871 1579879 1580109 1580114) (-978 "PRIMES.spad" 1578124 1578134 1579861 1579866) (-977 "PRIMELT.spad" 1576205 1576219 1578114 1578119) (-976 "PRIMCAT.spad" 1575832 1575840 1576195 1576200) (-975 "PRIMARR.spad" 1574837 1574847 1575015 1575042) (-974 "PRIMARR2.spad" 1573604 1573616 1574827 1574832) (-973 "PREASSOC.spad" 1572986 1572998 1573594 1573599) (-972 "PPCURVE.spad" 1572123 1572131 1572976 1572981) (-971 "PORTNUM.spad" 1571898 1571906 1572113 1572118) (-970 "POLYROOT.spad" 1570747 1570769 1571854 1571859) (-969 "POLY.spad" 1568082 1568092 1568597 1568724) (-968 "POLYLIFT.spad" 1567347 1567370 1568072 1568077) (-967 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"FCOMP.spad" 514199 514209 514810 514815) (-340 "FC.spad" 504206 504214 514189 514194) (-339 "FAXF.spad" 497177 497191 504108 504201) (-338 "FAXF.spad" 490200 490216 497133 497138) (-337 "FARRAY.spad" 488350 488360 489383 489410) (-336 "FAMR.spad" 486486 486498 488248 488345) (-335 "FAMR.spad" 484606 484620 486370 486375) (-334 "FAMONOID.spad" 484274 484284 484560 484565) (-333 "FAMONC.spad" 482570 482582 484264 484269) (-332 "FAGROUP.spad" 482194 482204 482466 482493) (-331 "FACUTIL.spad" 480398 480415 482184 482189) (-330 "FACTFUNC.spad" 479592 479602 480388 480393) (-329 "EXPUPXS.spad" 476425 476448 477724 477873) (-328 "EXPRTUBE.spad" 473713 473721 476415 476420) (-327 "EXPRODE.spad" 470873 470889 473703 473708) (-326 "EXPR.spad" 466048 466058 466762 467057) (-325 "EXPR2UPS.spad" 462170 462183 466038 466043) (-324 "EXPR2.spad" 461875 461887 462160 462165) (-323 "EXPEXPAN.spad" 458676 458701 459308 459401) (-322 "EXIT.spad" 458347 458355 458666 458671) (-321 "EXITAST.spad" 458083 458091 458337 458342) (-320 "EVALCYC.spad" 457543 457557 458073 458078) (-319 "EVALAB.spad" 457115 457125 457533 457538) (-318 "EVALAB.spad" 456685 456697 457105 457110) (-317 "EUCDOM.spad" 454259 454267 456611 456680) (-316 "EUCDOM.spad" 451895 451905 454249 454254) (-315 "ESTOOLS.spad" 443741 443749 451885 451890) (-314 "ESTOOLS2.spad" 443344 443358 443731 443736) (-313 "ESTOOLS1.spad" 443029 443040 443334 443339) (-312 "ES.spad" 435844 435852 443019 443024) (-311 "ES.spad" 428565 428575 435742 435747) (-310 "ESCONT.spad" 425358 425366 428555 428560) (-309 "ESCONT1.spad" 425107 425119 425348 425353) (-308 "ES2.spad" 424612 424628 425097 425102) (-307 "ES1.spad" 424182 424198 424602 424607) (-306 "ERROR.spad" 421509 421517 424172 424177) (-305 "EQTBL.spad" 419981 420003 420190 420217) (-304 "EQ.spad" 414786 414796 417573 417685) (-303 "EQ2.spad" 414504 414516 414776 414781) (-302 "EP.spad" 410830 410840 414494 414499) (-301 "ENV.spad" 409508 409516 410820 410825) (-300 "ENTIRER.spad" 409176 409184 409452 409503) (-299 "EMR.spad" 408464 408505 409102 409171) (-298 "ELTAGG.spad" 406718 406737 408454 408459) (-297 "ELTAGG.spad" 404936 404957 406674 406679) (-296 "ELTAB.spad" 404411 404424 404926 404931) (-295 "ELFUTS.spad" 403798 403817 404401 404406) (-294 "ELEMFUN.spad" 403487 403495 403788 403793) (-293 "ELEMFUN.spad" 403174 403184 403477 403482) (-292 "ELAGG.spad" 401145 401155 403154 403169) (-291 "ELAGG.spad" 399053 399065 401064 401069) (-290 "ELABOR.spad" 398399 398407 399043 399048) (-289 "ELABEXPR.spad" 397331 397339 398389 398394) (-288 "EFUPXS.spad" 394107 394137 397287 397292) (-287 "EFULS.spad" 390943 390966 394063 394068) (-286 "EFSTRUC.spad" 388958 388974 390933 390938) (-285 "EF.spad" 383734 383750 388948 388953) (-284 "EAB.spad" 382010 382018 383724 383729) (-283 "E04UCFA.spad" 381546 381554 382000 382005) (-282 "E04NAFA.spad" 381123 381131 381536 381541) (-281 "E04MBFA.spad" 380703 380711 381113 381118) (-280 "E04JAFA.spad" 380239 380247 380693 380698) (-279 "E04GCFA.spad" 379775 379783 380229 380234) (-278 "E04FDFA.spad" 379311 379319 379765 379770) (-277 "E04DGFA.spad" 378847 378855 379301 379306) (-276 "E04AGNT.spad" 374697 374705 378837 378842) (-275 "DVARCAT.spad" 371587 371597 374687 374692) (-274 "DVARCAT.spad" 368475 368487 371577 371582) (-273 "DSMP.spad" 365849 365863 366154 366281) (-272 "DSEXT.spad" 365151 365161 365839 365844) (-271 "DSEXT.spad" 364360 364372 365050 365055) (-270 "DROPT.spad" 358319 358327 364350 364355) (-269 "DROPT1.spad" 357984 357994 358309 358314) (-268 "DROPT0.spad" 352841 352849 357974 357979) (-267 "DRAWPT.spad" 351014 351022 352831 352836) (-266 "DRAW.spad" 343890 343903 351004 351009) (-265 "DRAWHACK.spad" 343198 343208 343880 343885) (-264 "DRAWCX.spad" 340668 340676 343188 343193) (-263 "DRAWCURV.spad" 340215 340230 340658 340663) (-262 "DRAWCFUN.spad" 329747 329755 340205 340210) (-261 "DQAGG.spad" 327925 327935 329715 329742) (-260 "DPOLCAT.spad" 323274 323290 327793 327920) (-259 "DPOLCAT.spad" 318709 318727 323230 323235) (-258 "DPMO.spad" 310505 310521 310643 310856) (-257 "DPMM.spad" 302314 302332 302439 302652) (-256 "DOMTMPLT.spad" 302085 302093 302304 302309) (-255 "DOMCTOR.spad" 301840 301848 302075 302080) (-254 "DOMAIN.spad" 300927 300935 301830 301835) (-253 "DMP.spad" 298187 298202 298757 298884) (-252 "DMEXT.spad" 298054 298064 298155 298182) (-251 "DLP.spad" 297406 297416 298044 298049) (-250 "DLIST.spad" 295985 295995 296589 296616) (-249 "DLAGG.spad" 294402 294412 295975 295980) (-248 "DIVRING.spad" 293944 293952 294346 294397) (-247 "DIVRING.spad" 293530 293540 293934 293939) (-246 "DISPLAY.spad" 291720 291728 293520 293525) (-245 "DIRPROD.spad" 279871 279887 280511 280610) (-244 "DIRPROD2.spad" 278689 278707 279861 279866) (-243 "DIRPCAT.spad" 277882 277898 278585 278684) (-242 "DIRPCAT.spad" 276702 276720 277407 277412) (-241 "DIOSP.spad" 275527 275535 276692 276697) (-240 "DIOPS.spad" 274523 274533 275507 275522) (-239 "DIOPS.spad" 273493 273505 274479 274484) (-238 "DIFRING.spad" 273331 273339 273473 273488) (-237 "DIFFSPC.spad" 272910 272918 273321 273326) (-236 "DIFFSPC.spad" 272487 272497 272900 272905) (-235 "DIFFMOD.spad" 271976 271986 272455 272482) (-234 "DIFFDOM.spad" 271141 271152 271966 271971) (-233 "DIFFDOM.spad" 270304 270317 271131 271136) (-232 "DIFEXT.spad" 270123 270133 270284 270299) (-231 "DIAGG.spad" 269753 269763 270103 270118) (-230 "DIAGG.spad" 269391 269403 269743 269748) (-229 "DHMATRIX.spad" 267703 267713 268848 268875) (-228 "DFSFUN.spad" 261343 261351 267693 267698) (-227 "DFLOAT.spad" 258074 258082 261233 261338) (-226 "DFINTTLS.spad" 256305 256321 258064 258069) (-225 "DERHAM.spad" 254219 254251 256285 256300) (-224 "DEQUEUE.spad" 253543 253553 253826 253853) (-223 "DEGRED.spad" 253160 253174 253533 253538) (-222 "DEFINTRF.spad" 250697 250707 253150 253155) (-221 "DEFINTEF.spad" 249207 249223 250687 250692) (-220 "DEFAST.spad" 248575 248583 249197 249202) (-219 "DECIMAL.spad" 246584 246592 246945 247038) (-218 "DDFACT.spad" 244397 244414 246574 246579) (-217 "DBLRESP.spad" 243997 244021 244387 244392) (-216 "DBASE.spad" 242661 242671 243987 243992) (-215 "DATAARY.spad" 242123 242136 242651 242656) (-214 "D03FAFA.spad" 241951 241959 242113 242118) (-213 "D03EEFA.spad" 241771 241779 241941 241946) (-212 "D03AGNT.spad" 240857 240865 241761 241766) (-211 "D02EJFA.spad" 240319 240327 240847 240852) (-210 "D02CJFA.spad" 239797 239805 240309 240314) (-209 "D02BHFA.spad" 239287 239295 239787 239792) (-208 "D02BBFA.spad" 238777 238785 239277 239282) (-207 "D02AGNT.spad" 233591 233599 238767 238772) (-206 "D01WGTS.spad" 231910 231918 233581 233586) (-205 "D01TRNS.spad" 231887 231895 231900 231905) (-204 "D01GBFA.spad" 231409 231417 231877 231882) (-203 "D01FCFA.spad" 230931 230939 231399 231404) (-202 "D01ASFA.spad" 230399 230407 230921 230926) (-201 "D01AQFA.spad" 229845 229853 230389 230394) (-200 "D01APFA.spad" 229269 229277 229835 229840) (-199 "D01ANFA.spad" 228763 228771 229259 229264) (-198 "D01AMFA.spad" 228273 228281 228753 228758) (-197 "D01ALFA.spad" 227813 227821 228263 228268) (-196 "D01AKFA.spad" 227339 227347 227803 227808) (-195 "D01AJFA.spad" 226862 226870 227329 227334) (-194 "D01AGNT.spad" 222929 222937 226852 226857) (-193 "CYCLOTOM.spad" 222435 222443 222919 222924) (-192 "CYCLES.spad" 219227 219235 222425 222430) (-191 "CVMP.spad" 218644 218654 219217 219222) (-190 "CTRIGMNP.spad" 217144 217160 218634 218639) (-189 "CTOR.spad" 216835 216843 217134 217139) (-188 "CTORKIND.spad" 216438 216446 216825 216830) (-187 "CTORCAT.spad" 215687 215695 216428 216433) (-186 "CTORCAT.spad" 214934 214944 215677 215682) (-185 "CTORCALL.spad" 214523 214533 214924 214929) (-184 "CSTTOOLS.spad" 213768 213781 214513 214518) (-183 "CRFP.spad" 207492 207505 213758 213763) (-182 "CRCEAST.spad" 207212 207220 207482 207487) (-181 "CRAPACK.spad" 206263 206273 207202 207207) (-180 "CPMATCH.spad" 205767 205782 206188 206193) (-179 "CPIMA.spad" 205472 205491 205757 205762) (-178 "COORDSYS.spad" 200481 200491 205462 205467) (-177 "CONTOUR.spad" 199892 199900 200471 200476) (-176 "CONTFRAC.spad" 195642 195652 199794 199887) (-175 "CONDUIT.spad" 195400 195408 195632 195637) (-174 "COMRING.spad" 195074 195082 195338 195395) (-173 "COMPPROP.spad" 194592 194600 195064 195069) (-172 "COMPLPAT.spad" 194359 194374 194582 194587) (-171 "COMPLEX.spad" 189736 189746 189980 190241) (-170 "COMPLEX2.spad" 189451 189463 189726 189731) (-169 "COMPILER.spad" 189000 189008 189441 189446) (-168 "COMPFACT.spad" 188602 188616 188990 188995) (-167 "COMPCAT.spad" 186674 186684 188336 188597) (-166 "COMPCAT.spad" 184474 184486 186138 186143) (-165 "COMMUPC.spad" 184222 184240 184464 184469) (-164 "COMMONOP.spad" 183755 183763 184212 184217) (-163 "COMM.spad" 183566 183574 183745 183750) (-162 "COMMAAST.spad" 183329 183337 183556 183561) (-161 "COMBOPC.spad" 182244 182252 183319 183324) (-160 "COMBINAT.spad" 181011 181021 182234 182239) (-159 "COMBF.spad" 178393 178409 181001 181006) (-158 "COLOR.spad" 177230 177238 178383 178388) (-157 "COLONAST.spad" 176896 176904 177220 177225) (-156 "CMPLXRT.spad" 176607 176624 176886 176891) (-155 "CLLCTAST.spad" 176269 176277 176597 176602) (-154 "CLIP.spad" 172377 172385 176259 176264) (-153 "CLIF.spad" 171032 171048 172333 172372) (-152 "CLAGG.spad" 167537 167547 171022 171027) (-151 "CLAGG.spad" 163913 163925 167400 167405) (-150 "CINTSLPE.spad" 163244 163257 163903 163908) (-149 "CHVAR.spad" 161382 161404 163234 163239) (-148 "CHARZ.spad" 161297 161305 161362 161377) (-147 "CHARPOL.spad" 160807 160817 161287 161292) (-146 "CHARNZ.spad" 160560 160568 160787 160802) (-145 "CHAR.spad" 158434 158442 160550 160555) (-144 "CFCAT.spad" 157762 157770 158424 158429) (-143 "CDEN.spad" 156958 156972 157752 157757) (-142 "CCLASS.spad" 155107 155115 156369 156408) (-141 "CATEGORY.spad" 154149 154157 155097 155102) (-140 "CATCTOR.spad" 154040 154048 154139 154144) (-139 "CATAST.spad" 153658 153666 154030 154035) (-138 "CASEAST.spad" 153372 153380 153648 153653) (-137 "CARTEN.spad" 148739 148763 153362 153367) (-136 "CARTEN2.spad" 148129 148156 148729 148734) (-135 "CARD.spad" 145424 145432 148103 148124) (-134 "CAPSLAST.spad" 145198 145206 145414 145419) (-133 "CACHSET.spad" 144822 144830 145188 145193) (-132 "CABMON.spad" 144377 144385 144812 144817) (-131 "BYTEORD.spad" 144052 144060 144367 144372) (-130 "BYTE.spad" 143479 143487 144042 144047) (-129 "BYTEBUF.spad" 141338 141346 142648 142675) (-128 "BTREE.spad" 140411 140421 140945 140972) (-127 "BTOURN.spad" 139416 139426 140018 140045) (-126 "BTCAT.spad" 138808 138818 139384 139411) (-125 "BTCAT.spad" 138220 138232 138798 138803) (-124 "BTAGG.spad" 137686 137694 138188 138215) (-123 "BTAGG.spad" 137172 137182 137676 137681) (-122 "BSTREE.spad" 135913 135923 136779 136806) (-121 "BRILL.spad" 134110 134121 135903 135908) (-120 "BRAGG.spad" 133050 133060 134100 134105) (-119 "BRAGG.spad" 131954 131966 133006 133011) (-118 "BPADICRT.spad" 129828 129840 130083 130176) (-117 "BPADIC.spad" 129492 129504 129754 129823) (-116 "BOUNDZRO.spad" 129148 129165 129482 129487) (-115 "BOP.spad" 124330 124338 129138 129143) (-114 "BOP1.spad" 121796 121806 124320 124325) (-113 "BOOLE.spad" 121446 121454 121786 121791) (-112 "BOOLEAN.spad" 120884 120892 121436 121441) (-111 "BMODULE.spad" 120596 120608 120852 120879) (-110 "BITS.spad" 120017 120025 120232 120259) (-109 "BINDING.spad" 119430 119438 120007 120012) (-108 "BINARY.spad" 117444 117452 117800 117893) (-107 "BGAGG.spad" 116649 116659 117424 117439) (-106 "BGAGG.spad" 115862 115874 116639 116644) (-105 "BFUNCT.spad" 115426 115434 115842 115857) (-104 "BEZOUT.spad" 114566 114593 115376 115381) (-103 "BBTREE.spad" 111411 111421 114173 114200) (-102 "BASTYPE.spad" 111083 111091 111401 111406) (-101 "BASTYPE.spad" 110753 110763 111073 111078) (-100 "BALFACT.spad" 110212 110225 110743 110748) (-99 "AUTOMOR.spad" 109663 109672 110192 110207) (-98 "ATTREG.spad" 106386 106393 109415 109658) (-97 "ATTRBUT.spad" 102409 102416 106366 106381) (-96 "ATTRAST.spad" 102126 102133 102399 102404) (-95 "ATRIG.spad" 101596 101603 102116 102121) (-94 "ATRIG.spad" 101064 101073 101586 101591) (-93 "ASTCAT.spad" 100968 100975 101054 101059) (-92 "ASTCAT.spad" 100870 100879 100958 100963) (-91 "ASTACK.spad" 100209 100218 100477 100504) (-90 "ASSOCEQ.spad" 99035 99046 100165 100170) (-89 "ASP9.spad" 98116 98129 99025 99030) (-88 "ASP8.spad" 97159 97172 98106 98111) (-87 "ASP80.spad" 96481 96494 97149 97154) (-86 "ASP7.spad" 95641 95654 96471 96476) (-85 "ASP78.spad" 95092 95105 95631 95636) (-84 "ASP77.spad" 94461 94474 95082 95087) (-83 "ASP74.spad" 93553 93566 94451 94456) (-82 "ASP73.spad" 92824 92837 93543 93548) (-81 "ASP6.spad" 91691 91704 92814 92819) (-80 "ASP55.spad" 90200 90213 91681 91686) (-79 "ASP50.spad" 88017 88030 90190 90195) (-78 "ASP4.spad" 87312 87325 88007 88012) (-77 "ASP49.spad" 86311 86324 87302 87307) (-76 "ASP42.spad" 84718 84757 86301 86306) (-75 "ASP41.spad" 83297 83336 84708 84713) (-74 "ASP35.spad" 82285 82298 83287 83292) (-73 "ASP34.spad" 81586 81599 82275 82280) (-72 "ASP33.spad" 81146 81159 81576 81581) (-71 "ASP31.spad" 80286 80299 81136 81141) (-70 "ASP30.spad" 79178 79191 80276 80281) (-69 "ASP29.spad" 78644 78657 79168 79173) (-68 "ASP28.spad" 69917 69930 78634 78639) (-67 "ASP27.spad" 68814 68827 69907 69912) (-66 "ASP24.spad" 67901 67914 68804 68809) (-65 "ASP20.spad" 67365 67378 67891 67896) (-64 "ASP1.spad" 66746 66759 67355 67360) (-63 "ASP19.spad" 61432 61445 66736 66741) (-62 "ASP12.spad" 60846 60859 61422 61427) (-61 "ASP10.spad" 60117 60130 60836 60841) (-60 "ARRAY2.spad" 59477 59486 59724 59751) (-59 "ARRAY1.spad" 58314 58323 58660 58687) (-58 "ARRAY12.spad" 57027 57038 58304 58309) (-57 "ARR2CAT.spad" 52801 52822 56995 57022) (-56 "ARR2CAT.spad" 48595 48618 52791 52796) (-55 "ARITY.spad" 47967 47974 48585 48590) (-54 "APPRULE.spad" 47227 47249 47957 47962) (-53 "APPLYORE.spad" 46846 46859 47217 47222) (-52 "ANY.spad" 45705 45712 46836 46841) (-51 "ANY1.spad" 44776 44785 45695 45700) (-50 "ANTISYM.spad" 43221 43237 44756 44771) (-49 "ANON.spad" 42914 42921 43211 43216) (-48 "AN.spad" 41223 41230 42730 42823) (-47 "AMR.spad" 39408 39419 41121 41218) (-46 "AMR.spad" 37430 37443 39145 39150) (-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 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 50d8f5c8..9b6edeb6 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(203171 . 3486501429) -(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((#0=(-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) #0#) |has| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (-319 (-2 (|:| -2371 |#1|) (|:| -2900 |#2|))))) -((((-576)) . T) (($) -3765 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -3765 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1057 (-419 (-576))))) ((|#1|) . T)) +(203171 . 3486517519) +(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((#0=(-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) #0#) |has| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (-319 (-2 (|:| -4282 |#1|) (|:| -4353 |#2|))))) +((((-576)) . 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T)) -((($ (-1196)) -3765 (-12 (|has| |#1| (-374)) (|has| |#1| (-915 (-1196)))) (-12 (|has| |#1| (-374)) (|has| |#1| (-917 (-1196)))))) +((($ (-1195)) -2835 (-12 (|has| |#1| (-374)) (|has| |#1| (-915 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#1| (-917 (-1195)))))) ((((-874)) . T)) -(((|#1| (-543 (-1196))) . T)) +(((|#1| (-543 (-1195))) . T)) ((($ $) . T)) (((|#1|) |has| |#1| (-174))) ((($) . T)) @@ -2809,29 +2809,29 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1119)))) (((|#2|) . 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T) (((-227)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-576)) . T)) -((((-2 (|:| -2371 (-1178)) (|:| -2900 (-52)))) . T)) +((((-2 (|:| -4282 (-1177)) (|:| -4353 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2371 |#1|) (|:| -2900 |#2|))) . T)) +((((-2 (|:| -4282 |#1|) (|:| -4353 |#2|))) . T)) ((((-874)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-576)) . T)) (((|#1| (-419 (-576))) . T)) (((|#1|) . T)) -(-3765 (|has| |#1| (-300)) (|has| |#1| (-374))) +(-2835 (|has| |#1| (-300)) (|has| |#1| (-374))) ((((-145)) . T)) ((((-576)) |has| #0=(-419 |#2|) (-651 (-576))) ((#0#) . T) (((-419 (-576))) . T) (($) . T)) (|has| |#1| (-860)) @@ -2847,25 +2847,25 @@ ((((-874)) . T)) ((((-874)) . T)) ((((-189)) . T) (((-874)) . T)) -((((-2 (|:| -2371 |#1|) (|:| -2900 |#2|))) . T)) +((((-2 (|:| -4282 |#1|) (|:| -4353 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-874)) . T)) ((((-874)) . 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T)) ((((-548)) |has| |#1| (-626 (-548)))) -((($) -3765 (-12 (|has| (-1194 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (-12 (|has| (-1194 |#1| |#2| |#3|) (-237)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|))))) +((($) -2835 (-12 (|has| (-1193 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (-12 (|has| (-1193 |#1| |#2| |#3|) (-237)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|))))) ((($) |has| |#1| (-15 * (|#1| (-419 (-576)) |#1|)))) ((((-874)) . T)) (((|#2|) |has| |#2| (-374))) @@ -2878,14 +2878,14 @@ ((($) . T) (((-576)) . T) (((-419 (-576))) . T) (((-624 $)) . T)) (|has| |#4| (-1068)) (|has| |#3| (-1068)) -((((-1196) (-52)) . T)) -(-3765 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) -(-3765 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +((((-1195) (-52)) . T)) +(-2835 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +(-2835 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3765 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068))) -(-3765 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) +(-2835 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068))) +(-2835 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) (|has| |#1| (-926)) ((((-927 |#1|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) (|has| |#1| (-926)) @@ -2894,7 +2894,7 @@ (((|#1|) . T)) ((((-874)) . T)) ((((-576)) . T)) -((($ (-1196)) -3765 (-12 (|has| |#2| (-915 (-1196))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-917 (-1196))) (|has| |#2| (-1068))))) +((($ (-1195)) -2835 (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))))) (((#0=(-419 (-576)) #0#) . T) (($ $) . T)) ((((-419 (-576))) . T) (($) . T)) (((|#1| (-419 (-576)) (-1101)) . T)) @@ -2903,12 +2903,12 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-3765 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +(-2835 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) (|has| |#1| (-832)) (((#0=(-927 |#1|) #0#) . T) (($ $) . T) ((#1=(-419 (-576)) #1#) . T)) ((((-419 |#2|)) . T)) (|has| |#1| (-860)) -((((-1223 |#1|)) . T) (((-874)) -3765 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-1222 |#1|)) . T) (((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) (((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) . T) ((#1=(-576) #1#) . T) (($ $) . T)) ((((-927 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#2|) |has| |#2| (-1068)) (((-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068)))) @@ -2919,48 +2919,48 @@ (|has| |#1| (-146)) (((|#2|) . T)) ((((-874)) . T)) -((((-1196)) . T)) +((((-1195)) . T)) ((((-419 (-576))) . T) (((-711)) . T) (($) . T) (((-576)) . T)) (((|#1|) |has| |#1| (-174))) (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-379))) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-379))) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-379))) -((((-2 (|:| -2371 (-1196)) (|:| -2900 (-52)))) . T)) +(-2835 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2835 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2835 (|has| |#1| (-146)) (|has| |#1| (-379))) +((((-2 (|:| -4282 (-1195)) (|:| -4353 (-52)))) . T)) ((((-576) |#3|) . 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T) ((|#1|) . T) ((|#2|) . T) ((|#3|) . T) ((|#4|) . T) ((|#5|) . T)) (-12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((((-419 (-576))) . T) (($) . T)) -((((-1194 |#1| |#2| |#3|)) |has| |#1| (-374))) +((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) ((($) . T) (((-419 (-576))) . T)) ((((-874)) . T)) (|has| |#1| (-374)) @@ -2972,10 +2972,10 @@ (|has| |#1| (-1119)) (((|#2|) . T)) (((|#1|) . T)) -((($) -3765 (|has| |#1| (-238)) (|has| |#1| (-237)))) +((($) -2835 (|has| |#1| (-238)) (|has| |#1| (-237)))) ((((-576)) . T)) (((|#2|) . T) (((-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((|#1|) . T) (($) . T) (((-576)) . T)) -(-3765 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +(-2835 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) (((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2985,7 +2985,7 @@ (((|#1|) . T) (($) . T)) (((|#1|) . T) (((-576)) . T)) (((|#1|) . T) (((-576)) . T)) -(((|#1| (-1287 |#1|) (-1287 |#1|)) . T)) +(((|#1| (-1286 |#1|) (-1286 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#2|) . T)) ((((-874)) . T)) @@ -3022,7 +3022,7 @@ (|has| |#2| (-1041)) ((($) . T)) (|has| |#1| (-926)) -((((-2 (|:| -2371 |#1|) (|:| -2900 |#2|))) . T)) +((((-2 (|:| -4282 |#1|) (|:| -4353 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -3031,32 +3031,32 @@ (|has| |#1| (-374)) ((((-927 |#1|)) . T)) ((($) . T) (((-576)) . T) ((|#1|) . T) (((-419 (-576))) . 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T)) -(((#0=(-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) #0#) |has| (-2 (|:| -2371 (-1196)) (|:| -2900 (-52))) (-319 (-2 (|:| -2371 (-1196)) (|:| -2900 (-52)))))) -((((-1178)) . T)) +(-2835 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +((((-1177)) . T) (((-874)) . T)) +(((#0=(-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) #0#) |has| (-2 (|:| -4282 (-1195)) (|:| -4353 (-52))) (-319 (-2 (|:| -4282 (-1195)) (|:| -4353 (-52)))))) +((((-1177)) . T)) (|has| |#1| (-926)) (|has| |#2| (-374)) (((|#1|) . T) (($) . T) (((-576)) . T)) -(-3765 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) +(-2835 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) ((((-171 (-390))) . T) (((-227)) . T) (((-390)) . T)) ((((-874)) . T)) (((|#1|) . T)) @@ -3073,13 +3073,13 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-3765 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2835 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-38 (-419 (-576)))) (-12 (|has| |#1| (-557)) (|has| |#1| (-840))) ((((-874)) . T)) -((((-1196)) -3765 (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1196)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1196)))))) +((((-1195)) -2835 (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))))) (|has| |#1| (-374)) -((((-1196)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1196))))) +((((-1195)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195))))) (|has| |#1| (-374)) ((((-419 (-576))) . T) (($) . T)) ((((-419 |#2|)) . T) (((-419 (-576))) . T) (((-576)) . T) (($) . T)) @@ -3088,25 +3088,25 @@ (|has| |#1| (-379)) (|has| |#1| (-379)) ((((-576) |#1|) . T)) -((((-1196)) |has| |#1| (-915 (-1196)))) +((((-1195)) |has| |#1| (-915 (-1195)))) (((|#1|) . T)) -(-3765 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360))) +(-2835 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360))) (((|#2|) |has| |#1| (-374))) (((|#2|) |has| |#1| (-374))) ((((-576)) . T) (($) . T)) -((((-2 (|:| -2371 |#1|) (|:| -2900 |#2|))) . T)) +((((-2 (|:| -4282 |#1|) (|:| -4353 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) ((($) . T)) (((|#1|) . T)) -(((|#2|) . T) (((-1196)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1196)))) (((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) (((-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576))))) +(((|#2|) . T) (((-1195)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1195)))) (((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) (((-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576))))) (((|#2|) . T)) ((($) . T)) -((((-1196) #0=(-1273 |#1| |#2| |#3| |#4|)) |has| #0# (-526 (-1196) #0#)) ((#0# #0#) |has| #0# (-319 #0#))) +((((-1195) #0=(-1272 |#1| |#2| |#3| |#4|)) |has| #0# (-526 (-1195) #0#)) ((#0# #0#) |has| #0# (-319 #0#))) ((((-419 (-576))) . T) (($) . T) (((-419 |#1|)) . T) ((|#1|) . T)) ((((-624 $) $) . T) (($ $) . T)) -((((-171 (-227))) . T) (((-171 (-390))) . T) (((-1192 (-711))) . T) (((-905 (-390))) . T)) +((((-171 (-227))) . T) (((-171 (-390))) . T) (((-1191 (-711))) . T) (((-905 (-390))) . T)) (((|#3|) . T)) (|has| |#1| (-568)) (|has| (-419 |#2|) (-238)) @@ -3118,7 +3118,7 @@ ((($ $) . T)) ((($) . T)) ((((-874)) . T)) -((((-1196)) |has| |#2| (-915 (-1196)))) +((((-1195)) |has| |#2| (-915 (-1195)))) ((((-419 (-576))) . T) (($) . T)) (((|#1|) |has| |#1| (-174)) (($) . T) (((-576)) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) @@ -3126,35 +3126,35 @@ (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#2|) |has| |#1| (-374))) ((((-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-390)))) (((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-576))))) -(-3765 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-374)) (((|#1|) . T)) ((($) . T) (((-576)) . T) ((|#2|) . T)) -(-3765 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) (((|#3|) . T)) -((((-1178)) . T) (((-518)) . T) (((-227)) . T) (((-576)) . T)) +((((-1177)) . T) (((-518)) . T) (((-227)) . T) (((-576)) . T)) (((|#1|) . T)) (|has| |#1| (-374)) (|has| |#1| (-568)) (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1119)))) ((((-419 |#2|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . 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T)) (|has| |#1| (-148)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2835 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2835 (|has| |#1| (-146)) (|has| |#1| (-379))) ((($) . T)) (|has| |#1| (-148)) ((((-593 |#1|)) . T)) @@ -3166,10 +3166,10 @@ ((($) . T)) ((((-419 |#2|)) . T)) ((((-419 |#2|)) . T)) -((((-419 (-576))) |has| |#2| (-1057 (-576))) (((-576)) |has| |#2| (-1057 (-576))) (((-1196)) |has| |#2| (-1057 (-1196))) ((|#2|) . T)) +((((-419 (-576))) |has| |#2| (-1057 (-576))) (((-576)) |has| |#2| (-1057 (-576))) (((-1195)) |has| |#2| (-1057 (-1195))) ((|#2|) . T)) (((#0=(-419 |#2|) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-360))) +(-2835 (|has| |#1| (-146)) (|has| |#1| (-360))) (|has| |#1| (-148)) ((((-874)) . T)) ((($) . T)) @@ -3185,11 +3185,11 @@ ((((-874)) . T)) (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) -((((-1196) (-52)) . T)) +((((-1195) (-52)) . T)) ((((-419 |#2|)) . T)) ((((-874)) . T)) (((|#1|) . T)) -((((-1196)) -3765 (|has| |#1| (-915 (-1196))) (|has| |#1| (-917 (-1196))))) +((((-1195)) -2835 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) (|has| |#1| (-1119)) (|has| |#1| (-803)) (|has| |#1| (-803)) @@ -3197,16 +3197,16 @@ ((((-927 |#1|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) ((((-874)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-874)) -3765 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) +((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-227)) . T) (((-390)) . T) (((-905 (-390))) . T)) ((((-874)) . T)) -((((-1273 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-419 (-576))) . T)) +((((-1272 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568)) (((-419 (-576))) |has| |#1| (-568))) ((((-874)) . T)) -(-3765 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068)))) +(-2835 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068)))) ((((-874)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -3219,25 +3219,25 @@ ((((-874)) . T)) (((|#2|) . T)) ((((-576)) . T)) -((((-1196)) -3765 (|has| (-419 |#2|) (-915 (-1196))) (|has| (-419 |#2|) (-917 (-1196))))) +((((-1195)) -2835 (|has| (-419 |#2|) (-915 (-1195))) (|has| (-419 |#2|) (-917 (-1195))))) ((((-874)) . T)) ((((-576)) . T)) -(-3765 (|has| |#2| (-805)) (|has| |#2| (-862))) +(-2835 (|has| |#2| (-805)) (|has| |#2| (-862))) ((((-171 (-390))) . T) (((-227)) . T) (((-390)) . T)) ((((-874)) . T)) ((((-874)) . T)) -((((-1178)) . T) (((-548)) . T) (((-576)) . T) (((-905 (-576))) . T) (((-390)) . T) (((-227)) . T)) +((((-1177)) . 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T)) -(-3765 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1196))) (|has| |#1| (-1068)) (|has| |#1| (-1131)) (|has| |#1| (-1119))) +(-2835 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068)) (|has| |#1| (-1131)) (|has| |#1| (-1119))) (|has| |#1| (-1171)) ((((-927 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) ((($) . T)) @@ -3247,20 +3247,20 @@ (((#0=(-117 |#1|) $) |has| #0# (-296 #0# #0#))) (((|#1|) |has| |#1| (-174))) ((((-326 |#1|)) . T) (((-576)) . T)) -(-3765 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-2835 (|has| |#2| (-238)) (|has| |#2| (-237))) (((|#1|) . T)) ((((-874)) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-874)) . 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T)) (((|#2| |#2|) . T) ((#0=(-419 (-576)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-419 (-576))) . T) (($) . T)) @@ -3832,9 +3832,9 @@ ((((-874)) . T)) ((((-874)) . T)) ((((-874)) . T)) -(-3765 (|has| |#1| (-238)) (|has| |#1| (-237))) -(((|#1|) . T) (((-874)) . T) (((-1201)) . T)) -((((-1201)) . T)) +(-2835 (|has| |#1| (-238)) (|has| |#1| (-237))) +(((|#1|) . T) (((-874)) . T) (((-1200)) . T)) +((((-1200)) . T)) ((((-874)) . T)) ((((-115)) . T) ((|#1|) . T) (((-576)) . T)) ((((-130)) . T)) @@ -3842,60 +3842,60 @@ (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1| (-543 (-876 |#2|)) (-876 |#2|) (-792 |#1| (-876 |#2|))) . T)) (((|#1| |#2| (-245 |#1| |#2|) (-245 |#1| |#2|)) . 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T) (((-419 (-576))) |has| #0# (-38 (-419 (-576))))) ((((-874)) . T)) (((|#1| (-783) (-1101)) . T)) -((((-1254 (-576)) $) . T) (((-576) |#1|) . T)) +((((-1253 (-576)) $) . T) (((-576) |#1|) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) -((((-1254 (-576)) $) . T) (((-576) |#1|) . T)) -((((-1254 (-576)) $) . T) (((-576) |#1|) . T)) +((((-1253 (-576)) $) . T) (((-576) |#1|) . T)) +((((-1253 (-576)) $) . T) (((-576) |#1|) . T)) ((((-117 |#1|)) . T)) ((((-117 |#1|)) . T)) (((|#2|) |has| |#2| (-1068))) @@ -3948,12 +3948,12 @@ ((((-576)) . T)) ((((-576)) . T)) ((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) -((((-1178) (-1196) (-576) (-227) (-874)) . T)) +((((-1177) (-1195) (-576) (-227) (-874)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) ((((-576)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-576)) . 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T) (((-419 (-576))) . T)) (|has| |#1| (-926)) @@ -3977,15 +3977,15 @@ (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-576)) . T)) -((((-1201)) . T)) -(-3765 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-3765 (|has| |#1| (-21)) (|has| |#1| (-860))) +((((-1200)) . T)) +(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2835 (|has| |#1| (-21)) (|has| |#1| (-860))) (((|#2|) . T)) -(-3765 (|has| |#1| (-21)) (|has| |#1| (-860))) +(-2835 (|has| |#1| (-21)) (|has| |#1| (-860))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-874)) -3765 (-12 (|has| |#1| (-625 (-874))) (|has| |#2| (-625 (-874)))) (-12 (|has| |#1| (-1119)) (|has| |#2| (-1119))))) +((((-874)) -2835 (-12 (|has| |#1| (-625 (-874))) (|has| |#2| (-625 (-874)))) (-12 (|has| |#1| (-1119)) (|has| |#2| (-1119))))) ((((-419 |#2|) |#3|) . T)) ((((-419 (-576))) . T) (($) . T)) (|has| |#1| (-38 (-419 (-576)))) @@ -4001,17 +4001,17 @@ ((($) . T) (((-419 (-576))) . 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T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1|) . T)) @@ -4021,111 +4021,111 @@ (((|#1|) . T) (($) . T)) (((|#1|) . T)) ((((-876 |#1|)) . T)) -((((-1194 |#1| |#2| |#3|)) |has| |#1| (-374))) +((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) ((((-1159 |#1| |#2|)) . T)) -((((-1194 |#1| |#2| |#3|)) |has| |#1| (-374))) -(((|#2|) . T) (((-2 (|:| -2371 |#1|) (|:| -2900 |#2|))) . T)) -((((-2 (|:| -2371 (-1196)) (|:| -2900 (-52)))) . T)) +((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) +(((|#2|) . T) (((-2 (|:| -4282 |#1|) (|:| -4353 |#2|))) . T)) +((((-2 (|:| -4282 (-1195)) (|:| -4353 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1041)) -(((|#2|) . T) (((-2 (|:| -2371 |#1|) (|:| -2900 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4282 |#1|) (|:| -4353 |#2|))) . T)) ((($) . T)) ((((-874)) . 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T)) -((((-874)) -3765 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) ((((-576) |#1|) . T)) -((((-1194 |#1| |#2| |#3|)) |has| |#1| (-374))) +((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-374)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -3765 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1068))) (($) |has| |#4| (-1068)) (((-576)) -12 (|has| |#4| (-651 (-576))) (|has| |#4| (-1068)))) -(((|#2|) . T) ((|#3|) -3765 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068))) (($) |has| |#3| (-1068)) (((-576)) -12 (|has| |#3| (-651 (-576))) (|has| |#3| (-1068)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2835 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1068))) (($) |has| |#4| (-1068)) (((-576)) -12 (|has| |#4| (-651 (-576))) (|has| |#4| (-1068)))) +(((|#2|) . T) ((|#3|) -2835 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068))) (($) |has| |#3| (-1068)) (((-576)) -12 (|has| |#3| (-651 (-576))) (|has| |#3| (-1068)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-419 (-576))) |has| |#2| (-1057 (-419 (-576)))) (((-576)) |has| |#2| (-1057 (-576))) ((|#2|) . T) (((-876 |#1|)) . T)) -((((-1196)) . T) ((|#1|) . T)) +((((-1195)) . T) ((|#1|) . T)) ((((-874)) . T)) ((((-874)) . T)) ((((-874)) . T)) ((((-189)) . T) (((-874)) . T)) ((((-874)) . T)) (((|#1|) . T)) -((((-874)) -3765 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) ((((-130)) . T) (((-874)) . T)) -((((-576) |#1|) . T) (((-1254 (-576)) $) . T)) +((((-576) |#1|) . T) (((-1253 (-576)) $) . T)) ((((-130)) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) (($ $) . T) (((-576) |#1|) . T)) ((($ $) . 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T) (($) . T) (((-419 (-576))) . T)) -((((-1201)) . T)) -((((-874)) . T) (((-1201)) . T)) -((((-874)) . T) (((-1201)) . T)) -(-3765 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) -(-3765 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +((((-1200)) . T)) +((((-874)) . T) (((-1200)) . T)) +((((-874)) . T) (((-1200)) . T)) +(-2835 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) +(-2835 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((($) . T)) (((|#2| (-543 (-876 |#1|))) . T)) -((((-1201)) . T)) -((((-1201)) . T)) +((((-1200)) . T)) +((((-1200)) . T)) ((((-576) |#1|) . T)) -((((-874)) . T) (((-1201)) . T)) -((((-1201)) . T)) +((((-874)) . T) (((-1200)) . T)) +((((-1200)) . T)) (((|#2|) . T)) -((((-874)) . T) (((-1201)) . T)) -((((-1201)) . T)) -((((-874)) . T) (((-1201)) . T)) -((((-1201)) . T)) -((((-874)) . T) (((-1201)) . T)) -((((-1201)) . T)) -((((-874)) -3765 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) . T) (((-1200)) . T)) +((((-1200)) . T)) +((((-874)) . T) (((-1200)) . T)) +((((-1200)) . T)) +((((-874)) . T) (((-1200)) . T)) +((((-1200)) . T)) +((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) (((|#1|) . T)) (((|#2| (-783)) . T)) (((|#1| |#2|) . T)) -((((-1178) |#1|) . T)) +((((-1177) |#1|) . T)) ((((-419 |#2|)) . T)) ((((-419 |#2|)) . T)) (|has| |#1| (-568)) (|has| |#1| (-568)) -((((-2 (|:| -2371 |#1|) (|:| -2900 |#2|))) . T)) +((((-2 (|:| -4282 |#1|) (|:| -4353 |#2|))) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-419 (-576))) . T)) ((((-419 (-576))) . T) (($) . T)) @@ -4134,18 +4134,18 @@ ((((-576)) . T) (($) . T)) (((|#2| $) |has| |#2| (-296 |#2| |#2|))) (((|#1| (-656 |#1|)) |has| |#1| (-860))) -(-3765 (|has| |#1| (-238)) (|has| |#1| (-360))) -(-3765 (|has| |#1| (-374)) (|has| |#1| (-360))) -((((-1283 |#1|)) . T) (((-576)) . T) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-1057 (-419 (-576))))) +(-2835 (|has| |#1| (-238)) (|has| |#1| (-360))) +(-2835 (|has| |#1| (-374)) (|has| |#1| (-360))) +((((-1282 |#1|)) . T) (((-576)) . T) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-1057 (-419 (-576))))) (|has| |#1| (-1119)) (((|#1|) . T)) -((((-1283 |#1|)) . T) (((-576)) . T) (($) -3765 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) (((-1101)) . T) ((|#2|) . T) (((-419 (-576))) -3765 (|has| |#2| (-38 (-419 (-576)))) (|has| |#2| (-1057 (-419 (-576)))))) +((((-1282 |#1|)) . T) (((-576)) . T) (($) -2835 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) (((-1101)) . T) ((|#2|) . T) (((-419 (-576))) -2835 (|has| |#2| (-38 (-419 (-576)))) (|has| |#2| (-1057 (-419 (-576)))))) ((((-419 (-576))) . T) (($) . T)) -((((-1018 |#1|)) . T) ((|#1|) . T) (((-576)) -3765 (|has| (-1018 |#1|) (-1057 (-576))) (|has| |#1| (-1057 (-576)))) (((-419 (-576))) -3765 (|has| (-1018 |#1|) (-1057 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576)))))) +((((-1018 |#1|)) . T) ((|#1|) . T) (((-576)) -2835 (|has| (-1018 |#1|) (-1057 (-576))) (|has| |#1| (-1057 (-576)))) (((-419 (-576))) -2835 (|has| (-1018 |#1|) (-1057 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576)))))) ((((-927 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) -((((-1196)) |has| |#1| (-915 (-1196)))) +((((-1195)) |has| |#1| (-915 (-1195)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) ((((-927 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) @@ -4158,12 +4158,12 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1159 |#1| |#2|) #0#) |has| (-1159 |#1| |#2|) (-319 (-1159 |#1| |#2|)))) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((#0=(-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) #0#) |has| (-2 (|:| -2371 |#1|) (|:| -2900 |#2|)) (-319 (-2 (|:| -2371 |#1|) (|:| -2900 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((#0=(-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) #0#) |has| (-2 (|:| -4282 |#1|) (|:| -4353 |#2|)) (-319 (-2 (|:| -4282 |#1|) (|:| -4353 |#2|))))) (|has| |#1| (-296 |#1| |#1|)) -(-3765 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-2835 (|has| |#1| (-238)) (|has| |#1| (-237))) (((#0=(-117 |#1|)) |has| #0# (-319 #0#))) ((($ $) . T)) -(-3765 (|has| |#1| (-862)) (|has| |#1| (-1119))) +(-2835 (|has| |#1| (-862)) (|has| |#1| (-1119))) ((($ $) . T) ((#0=(-876 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-238)) ((|#2| |#1|) |has| |#1| (-238)) ((|#3| |#1|) . T) ((|#3| $) . 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-1237) T) ((-848 . -628) 193903) ((-839 . -628) 193858) ((-44 . -23) T) ((-491 . -296) 193837) ((-598 . -1119) T) ((-1316 . -102) T) ((-1165 . -1128) 193806) ((-1123 . -1122) 193758) ((-402 . -21) T) ((-402 . -25) T) ((-153 . -1131) T) ((-1231 . -729) 193655) ((-1217 . -1119) T) ((-1023 . -897) 193637) ((-1023 . -899) 193619) ((-635 . -232) 193603) ((-635 . -272) 193587) ((-633 . -21) T) ((-299 . -568) T) ((-633 . -25) T) ((-1023 . -1057) 193547) ((-723 . -729) 193512) ((-245 . -388) 193481) ((-390 . -1068) T) ((-225 . -1077) T) ((-118 . -272) 193458) ((-118 . -232) 193435) ((-59 . -296) 193387) ((-153 . -23) T) ((-528 . -296) 193339) ((-337 . -526) 193272) ((-508 . -296) 193224) ((-390 . -248) T) ((-390 . -238) T) ((-848 . -1068) T) ((-839 . -1068) T) ((-724 . -966) 193193) ((-713 . -862) T) ((-486 . -625) 193175) ((-1273 . -1070) 193080) ((-592 . -658) 193052) ((-576 . -658) 193024) ((-507 . -658) 192974) ((-839 . -238) 192953) ((-135 . -862) T) ((-1273 . -652) 192845) ((-670 . -1119) T) ((-1209 . -616) 192824) ((-562 . -1213) 192803) ((-347 . -1119) T) ((-329 . -374) 192782) ((-419 . -148) 192761) ((-419 . -146) 192740) ((-981 . -1131) 192639) ((-245 . -915) 192571) ((-827 . -1131) 192549) ((-666 . -864) 192533) ((-491 . -616) 192512) ((-562 . -107) 192462) ((-1023 . -388) 192444) ((-1023 . -349) 192426) ((-1196 . -625) 192408) ((-97 . -1119) T) ((-981 . -23) 192219) ((-489 . -21) T) ((-489 . -25) T) ((-827 . -23) 192071) ((-1196 . -626) 191993) ((-59 . -19) 191977) ((-1192 . -738) T) ((-1144 . -738) T) ((-1106 . -1119) T) ((-528 . -19) 191961) ((-508 . -19) 191945) ((-59 . -616) 191922) ((-1022 . -237) 191859) ((-918 . -102) 191837) ((-866 . -738) T) ((-794 . -1119) T) ((-528 . -616) 191814) ((-508 . -616) 191791) ((-792 . -1119) T) ((-792 . -1084) 191758) ((-473 . -1119) T) ((-466 . -1119) T) ((-598 . -729) 191733) ((-661 . -1119) T) ((-1279 . -47) 191710) ((-1273 . -102) T) ((-1272 . -47) 191680) ((-1251 . -47) 191657) ((-1231 . -174) 191608) ((-1193 . -317) 191587) ((-1187 . -317) 191566) ((-1115 . -628) 191547) ((-1109 . -628) 191528) ((-1099 . -568) 191479) ((-1099 . -1241) 191430) ((-1023 . -915) NIL) ((-1092 . -628) 191411) ((-682 . -132) T) ((-639 . -1131) T) ((-1085 . -628) 191392) ((-1055 . -628) 191373) ((-1038 . -628) 191354) ((-726 . -1075) 191324) ((-711 . -658) 191274) ((-284 . -1119) T) ((-85 . -453) T) ((-85 . -407) T) ((-724 . -909) 191177) ((-723 . -174) T) ((-50 . -1119) T) ((-607 . -47) 191154) ((-227 . -660) 191119) ((-593 . -1119) T) ((-530 . -1119) T) ((-499 . -832) T) ((-499 . -937) T) ((-370 . -1241) T) ((-364 . -1241) T) ((-356 . -1241) T) ((-329 . -1131) T) ((-326 . -1070) 191029) ((-323 . -1070) 190958) ((-108 . -1241) T) ((-638 . -628) 190939) ((-370 . -568) T) ((-219 . -937) T) ((-219 . -832) T) ((-326 . -652) 190849) ((-323 . -652) 190778) ((-364 . -568) T) ((-356 . -568) T) ((-495 . -628) 190759) ((-108 . -568) T) ((-670 . -729) 190729) ((-1187 . -1041) NIL) ((-220 . -628) 190710) ((-329 . -23) T) ((-67 . -1237) T) ((-1019 . -625) 190642) ((-706 . -272) 190624) ((-706 . -232) 190606) ((-726 . -111) 190571) ((-656 . -34) T) ((-250 . -501) 190555) ((-1316 . -1171) T) ((-1311 . -21) T) ((-1311 . -25) T) ((-1309 . -132) T) ((-1121 . -1117) 190539) ((-173 . -1119) T) ((-1307 . -132) T) ((-1300 . -102) T) ((-1283 . -625) 190505) ((-1279 . -1237) T) ((-1272 . -1237) T) ((-969 . -926) 190484) ((-1272 . -1057) 190419) ((-1251 . -1237) T) ((-1251 . -899) NIL) ((-527 . -628) 190403) ((-1251 . -897) 190355) ((-1251 . -1057) 190321) ((-1231 . -526) 190288) ((-493 . -926) 190267) ((-1209 . -626) NIL) ((-1209 . -625) 190249) ((-1106 . -729) 190098) ((-1081 . -660) 190070) ((-969 . -660) 189959) ((-609 . -502) 189940) ((-597 . -502) 189921) ((-794 . -729) 189750) ((-609 . -625) 189716) ((-597 . -625) 189682) ((-548 . -625) 189664) ((-548 . -626) 189645) ((-792 . -729) 189494) ((-1096 . -102) T) ((-392 . -25) T) ((-635 . -658) 189466) ((-392 . -21) T) ((-493 . -660) 189355) ((-473 . -729) 189326) ((-466 . -729) 189175) ((-1006 . -102) T) ((-1161 . -1142) 189120) ((-1065 . -1230) 189049) ((-918 . -319) 188987) ((-749 . -102) T) ((-118 . -658) 188917) ((-617 . -628) 188899) ((-888 . -93) T) ((-726 . -628) 188853) ((-543 . -25) T) ((-693 . -93) T) ((-688 . -93) T) ((-676 . -625) 188835) ((-657 . -502) 188816) ((-142 . -102) T) ((-44 . -132) T) ((-657 . -625) 188769) ((-607 . -1237) T) ((-354 . -1077) T) ((-299 . -1131) T) ((-490 . -93) T) ((-419 . -237) 188720) ((-366 . -625) 188702) ((-363 . -625) 188684) ((-355 . -625) 188666) ((-273 . -626) 188414) ((-273 . -625) 188396) ((-253 . -625) 188378) ((-253 . -626) 188239) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1160 . -625) 188221) ((-1139 . -652) 188208) ((-1139 . -1070) 188195) ((-831 . -738) T) ((-831 . -869) T) ((-614 . -298) 188172) ((-593 . -729) 188137) ((-491 . -626) NIL) ((-491 . -625) 188119) ((-530 . -729) 188064) ((-326 . -102) T) ((-323 . -102) T) ((-299 . -23) T) ((-153 . -132) T) ((-927 . -625) 188046) ((-927 . -626) 188028) ((-398 . -738) T) ((-884 . -1075) 187980) ((-884 . -111) 187918) ((-726 . -1068) T) ((-724 . -1263) 187902) ((-706 . -360) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-531 . -625) 187834) ((-390 . -807) T) ((-225 . -1119) T) ((-169 . -1237) T) ((-390 . -804) T) ((-227 . -806) T) ((-227 . -803) T) ((-59 . -626) 187795) ((-59 . -625) 187707) ((-227 . -738) T) ((-528 . -626) 187668) ((-528 . -625) 187580) ((-509 . -625) 187512) ((-508 . -626) 187473) ((-508 . -625) 187385) ((-1099 . -374) 187336) ((-40 . -423) 187313) ((-77 . -1237) T) ((-883 . -926) NIL) ((-370 . -339) 187297) ((-370 . -374) T) ((-364 . -339) 187281) ((-364 . -374) T) ((-356 . -339) 187265) ((-356 . -374) T) ((-326 . -294) 187244) ((-108 . -374) T) ((-70 . -1237) T) ((-1251 . -349) 187196) ((-883 . -660) 187141) ((-1251 . -388) 187093) ((-981 . -132) 186948) ((-827 . -132) 186819) ((-975 . -663) 186803) ((-1106 . -174) 186714) ((-975 . -384) 186698) ((-1081 . -806) T) ((-1081 . -803) T) ((-884 . -628) 186596) ((-794 . -174) 186487) ((-792 . -174) 186398) ((-828 . -47) 186360) ((-1081 . -738) T) ((-337 . -501) 186344) ((-969 . -738) T) ((-1300 . -319) 186282) ((-1279 . -915) 186195) ((-466 . -174) 186106) ((-250 . -296) 186058) ((-1272 . -915) 185964) ((-1271 . -1075) 185799) ((-1251 . -915) 185632) ((-493 . -738) T) ((-1250 . -1075) 185440) ((-1231 . -300) 185419) ((-1206 . -1237) T) ((-1203 . -379) T) ((-1202 . -379) T) ((-1165 . -152) 185403) ((-1139 . -102) T) ((-1137 . -1119) T) ((-1099 . -23) T) ((-1099 . -1131) T) ((-1094 . -102) T) ((-1076 . -625) 185370) ((-1022 . -421) 185342) ((-944 . -972) T) ((-749 . -319) 185280) ((-75 . -1237) T) ((-676 . -393) 185252) ((-171 . -926) 185205) ((-30 . -972) T) ((-112 . -856) T) ((-1 . -625) 185187) ((-1018 . -909) 185108) ((-129 . -663) 185090) ((-50 . -632) 185074) ((-706 . -658) 185009) ((-607 . -915) 184922) ((-450 . -102) T) ((-129 . -384) 184904) ((-142 . -319) NIL) ((-884 . -1068) T) ((-845 . -862) 184883) ((-81 . -1237) T) ((-723 . -300) T) ((-40 . -1077) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 184865) ((-171 . -660) 184739) ((-519 . -625) 184721) ((-362 . -148) 184703) ((-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) 184682) ((-1271 . -111) 184503) ((-1250 . -111) 184292) ((-250 . -1275) 184276) ((-576 . -860) T) ((-370 . -23) T) ((-365 . -360) T) ((-326 . -319) 184263) ((-323 . -319) 184204) ((-364 . -23) T) ((-329 . -132) T) ((-356 . -23) T) ((-1023 . -1041) T) ((-31 . -628) 184185) ((-108 . -23) T) ((-666 . -1070) 184169) ((-250 . -616) 184146) ((-343 . -1119) T) ((-666 . -652) 184116) ((-1273 . -38) 184008) ((-1260 . -926) 183987) ((-112 . -1119) T) ((-828 . -1237) T) ((-1054 . -102) T) ((-1260 . -660) 183876) ((-883 . -806) NIL) ((-867 . -660) 183850) ((-883 . -803) NIL) ((-828 . -899) NIL) ((-883 . -738) T) ((-1106 . -526) 183723) ((-794 . -526) 183670) ((-792 . -526) 183622) ((-583 . -660) 183609) ((-828 . -1057) 183437) ((-466 . -526) 183380) ((-400 . -401) T) ((-1271 . -628) 183193) ((-1250 . -628) 182941) ((-60 . -1237) T) ((-633 . -862) 182920) ((-512 . -673) T) ((-1165 . -995) 182889) ((-1043 . -658) 182826) ((-1022 . -464) T) ((-711 . -860) T) ((-522 . -804) T) ((-486 . -1075) 182661) ((-512 . -113) T) ((-354 . -1119) T) ((-323 . -1171) NIL) ((-299 . -132) T) ((-406 . -1119) T) ((-882 . -1077) T) ((-706 . -381) 182628) ((-365 . -658) 182558) ((-225 . -632) 182535) ((-337 . -296) 182487) ((-486 . -111) 182308) ((-1271 . -1068) T) ((-1250 . -1068) T) ((-828 . -388) 182292) ((-171 . -738) T) ((-666 . -102) T) ((-1271 . -248) 182271) ((-1271 . -238) 182223) ((-1250 . -238) 182128) ((-1250 . -248) 182107) ((-1022 . -414) NIL) ((-682 . -651) 182055) ((-326 . -38) 181965) ((-323 . -38) 181894) ((-69 . -625) 181876) ((-329 . -505) 181842) ((-48 . -658) 181792) ((-1209 . -298) 181771) ((-1245 . -862) T) ((-1132 . -1131) 181749) ((-83 . -1237) T) ((-61 . -625) 181731) ((-491 . -298) 181710) ((-1302 . -1057) 181687) ((-1184 . -1119) T) ((-1132 . -23) 181539) ((-828 . -915) 181475) ((-1260 . -738) T) ((-1121 . -1237) T) ((-486 . -628) 181301) ((-362 . -237) T) ((-1106 . -300) 181232) ((-983 . -1119) T) ((-906 . -102) T) ((-794 . -300) 181143) ((-337 . -19) 181127) ((-59 . -298) 181104) ((-792 . -300) 181035) ((-867 . -738) T) ((-118 . -860) NIL) ((-528 . -298) 181012) ((-337 . -616) 180989) ((-508 . -298) 180966) ((-466 . -300) 180897) ((-1054 . -319) 180748) ((-888 . -502) 180729) ((-888 . -625) 180695) ((-693 . -502) 180676) ((-583 . -738) T) ((-688 . -502) 180657) ((-693 . -625) 180607) ((-688 . -625) 180573) ((-674 . -625) 180555) ((-490 . -502) 180536) ((-490 . -625) 180502) ((-250 . -626) 180463) ((-250 . -502) 180440) ((-139 . -502) 180421) ((-138 . -502) 180402) ((-134 . -502) 180383) ((-250 . -625) 180275) ((-215 . -102) T) ((-139 . -625) 180241) ((-138 . -625) 180207) ((-134 . -625) 180173) ((-1166 . -34) T) ((-960 . -1237) T) ((-354 . -729) 180118) ((-682 . -25) T) ((-682 . -21) T) ((-1196 . -628) 180099) ((-486 . -1068) T) ((-647 . -429) 180064) ((-619 . -429) 180029) ((-1139 . -1171) T) ((-724 . -1070) 179852) ((-593 . -300) T) ((-530 . -300) T) ((-1272 . -317) 179831) ((-486 . -238) 179783) ((-486 . -248) 179762) ((-1251 . -317) 179741) ((-724 . -652) 179570) ((-1251 . -1041) NIL) ((-1099 . -132) T) ((-884 . -807) 179549) ((-145 . -102) T) ((-40 . -1119) T) ((-884 . -804) 179528) ((-656 . -1029) 179512) ((-592 . -1077) T) ((-576 . -1077) T) ((-507 . -1077) T) ((-419 . -464) T) ((-370 . -132) T) ((-326 . -412) 179496) ((-323 . -412) 179457) ((-364 . -132) T) ((-356 . -132) T) ((-1201 . -1119) T) ((-1139 . -38) 179444) ((-1113 . -625) 179411) ((-108 . -132) T) ((-971 . -1119) T) ((-938 . -1119) T) ((-783 . -1119) T) ((-684 . -1119) T) ((-713 . -148) T) ((-117 . -148) T) ((-1309 . -21) T) ((-1309 . -25) T) ((-1307 . -21) T) ((-1307 . -25) T) ((-676 . -1075) 179395) ((-543 . -862) T) ((-512 . -862) T) ((-366 . -1075) 179347) ((-363 . -1075) 179299) ((-355 . -1075) 179251) ((-258 . -1237) T) ((-257 . -1237) T) ((-273 . -1075) 179094) ((-253 . -1075) 178937) ((-676 . -111) 178916) ((-829 . -1241) 178895) ((-559 . -856) T) ((-326 . -917) 178861) ((-366 . -111) 178799) ((-363 . -111) 178737) ((-355 . -111) 178675) ((-273 . -111) 178504) ((-253 . -111) 178333) ((-323 . -917) NIL) ((-635 . -423) 178317) ((-44 . -21) T) ((-44 . -25) T) ((-827 . -651) 178223) ((-829 . -568) 178202) ((-258 . -1057) 178029) ((-257 . -1057) 177856) ((-127 . -120) 177840) ((-927 . -1075) 177805) ((-724 . -102) T) ((-711 . -1077) T) ((-609 . -628) 177786) ((-597 . -628) 177767) ((-548 . -630) 177670) ((-354 . -174) T) ((-88 . -625) 177652) ((-153 . -21) T) ((-153 . -25) T) ((-927 . -111) 177608) ((-40 . -729) 177553) ((-882 . -1119) T) ((-676 . -628) 177530) ((-657 . -628) 177511) ((-366 . -628) 177448) ((-363 . -628) 177385) ((-559 . -1119) T) ((-355 . -628) 177322) ((-337 . -626) 177283) ((-337 . -625) 177195) ((-273 . -628) 176948) ((-253 . -628) 176733) ((-1250 . -804) 176686) ((-1250 . -807) 176639) ((-258 . -388) 176608) ((-257 . -388) 176577) ((-666 . -38) 176547) ((-620 . -34) T) ((-494 . -1131) 176525) ((-487 . -34) T) ((-1132 . -132) 176396) ((-981 . -25) 176207) ((-927 . -628) 176157) ((-886 . -625) 176139) ((-981 . -21) 176094) ((-827 . -25) 175927) ((-827 . -21) 175838) ((-1243 . -379) T) ((-635 . -1077) T) ((-1198 . -568) 175817) ((-1192 . -47) 175794) ((-366 . -1068) T) ((-363 . -1068) T) ((-494 . -23) 175646) ((-355 . -1068) T) ((-273 . -1068) T) ((-253 . -1068) T) ((-1144 . -47) 175618) ((-118 . -1077) T) ((-1053 . -660) 175592) ((-975 . -34) T) ((-366 . -238) 175571) ((-366 . -248) T) ((-363 . -238) 175550) ((-363 . -248) T) ((-355 . -238) 175529) ((-355 . -248) T) ((-273 . -336) 175501) ((-253 . -336) 175458) ((-273 . -238) 175437) ((-1176 . -152) 175421) ((-258 . -915) 175353) ((-257 . -915) 175285) ((-1161 . -909) 175206) ((-1101 . -862) T) ((-426 . -1131) T) ((-1073 . -23) T) ((-1043 . -860) T) ((-927 . -1068) T) ((-332 . -660) 175188) ((-713 . -237) T) ((-682 . -234) 175133) ((-1231 . -1021) 175099) ((-1193 . -937) 175078) ((-1187 . -937) 175057) ((-1187 . -832) NIL) ((-1018 . -1070) 174953) ((-984 . -1237) T) ((-927 . -248) T) ((-829 . -374) 174932) ((-396 . -23) T) ((-128 . -1119) 174910) ((-122 . -1119) 174888) ((-927 . -238) T) ((-129 . -34) T) ((-390 . -660) 174853) ((-1018 . -652) 174801) ((-882 . -729) 174788) ((-1316 . -658) 174760) ((-1065 . -152) 174725) ((-1012 . -1237) T) ((-40 . -174) T) ((-706 . -423) 174707) ((-724 . -319) 174694) ((-848 . -660) 174654) ((-839 . -660) 174628) ((-329 . -25) T) ((-329 . -21) T) ((-670 . -296) 174607) ((-592 . -1119) T) ((-576 . -1119) T) ((-507 . -1119) T) ((-250 . -298) 174584) ((-1192 . -1237) T) ((-1144 . -1237) T) ((-323 . -272) 174545) ((-323 . -232) 174506) ((-1192 . -899) NIL) ((-55 . -1119) T) ((-1144 . -899) 174365) ((-130 . -862) T) ((-1192 . -1057) 174245) ((-1144 . -1057) 174128) ((-185 . -625) 174110) ((-866 . -1057) 174006) ((-794 . -296) 173933) ((-829 . -1131) T) ((-1053 . -738) T) ((-1065 . -995) 173862) ((-614 . -663) 173846) ((-1022 . -909) 173753) ((-1018 . -102) T) ((-829 . -23) T) ((-724 . -1171) 173731) ((-706 . -1077) T) ((-614 . -384) 173715) ((-362 . -464) T) ((-354 . -300) T) ((-1288 . -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) ((-1231 . -625) 173697) ((-1192 . -388) 173681) ((-1144 . -388) 173665) ((-1043 . -423) 173627) ((-142 . -231) 173609) ((-390 . -806) T) ((-390 . -803) T) ((-882 . -174) T) ((-390 . -738) T) ((-723 . -625) 173591) ((-724 . -38) 173420) ((-1287 . -1285) 173404) ((-362 . -414) T) ((-1287 . -1119) 173354) ((-1210 . -1119) T) ((-592 . -729) 173341) ((-576 . -729) 173328) ((-507 . -729) 173293) ((-1273 . -658) 173183) ((-326 . -641) 173162) ((-848 . -738) T) ((-839 . -738) T) ((-656 . -1237) T) ((-1099 . -651) 173110) ((-1192 . -915) 173053) ((-1144 . -915) 173037) ((-827 . -234) 172928) ((-674 . -1075) 172912) ((-108 . -651) 172894) ((-494 . -132) 172765) ((-1198 . -1131) T) ((-969 . -47) 172734) ((-635 . -1119) T) ((-674 . -111) 172713) ((-503 . -625) 172679) ((-337 . -298) 172656) ((-493 . -47) 172613) ((-1198 . -23) T) ((-118 . -1119) T) ((-103 . -102) 172591) ((-1299 . -1131) T) ((-560 . -862) T) ((-227 . -1237) T) ((-1073 . -132) T) ((-1043 . -1077) T) ((-1299 . -23) T) ((-831 . -1057) 172575) ((-1217 . -625) 172557) ((-1022 . -736) 172529) ((-1139 . -840) T) ((-711 . -729) 172494) ((-598 . -625) 172476) ((-398 . -1057) 172460) ((-365 . -1077) T) ((-396 . -132) T) ((-334 . -1057) 172444) ((-1124 . -1119) T) ((-1099 . -21) T) ((-1099 . -25) T) ((-227 . -899) 172426) ((-1023 . -937) T) ((-91 . -34) T) ((-1023 . -832) T) ((-931 . -937) T) ((-1018 . -319) 172391) ((-888 . -628) 172372) ((-499 . -1241) T) ((-726 . -660) 172332) ((-693 . -628) 172313) ((-688 . -628) 172294) ((-219 . 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-1057) 170973) ((-1106 . -626) NIL) ((-1106 . -625) 170955) ((-794 . -626) NIL) ((-794 . -625) 170916) ((-792 . -626) 170550) ((-792 . -625) 170464) ((-1132 . -651) 170370) ((-473 . -625) 170352) ((-466 . -625) 170334) ((-466 . -626) 170195) ((-1054 . -231) 170141) ((-884 . -926) 170120) ((-127 . -34) T) ((-829 . -132) T) ((-661 . -625) 170102) ((-590 . -102) T) ((-366 . -1306) 170086) ((-363 . -1306) 170070) ((-355 . -1306) 170054) ((-128 . -526) 169987) ((-122 . -526) 169920) ((-523 . -804) T) ((-523 . -807) T) ((-522 . -806) T) ((-103 . -319) 169858) ((-224 . -102) 169836) ((-711 . -174) T) ((-706 . -1119) T) ((-884 . -660) 169752) ((-65 . -395) T) ((-284 . -625) 169734) ((-65 . -407) T) ((-969 . -388) 169718) ((-882 . -300) T) ((-50 . -625) 169700) ((-1018 . -38) 169648) ((-1139 . -658) 169620) ((-593 . -625) 169602) ((-493 . -388) 169586) ((-593 . -626) 169568) ((-530 . -625) 169550) ((-927 . -1306) 169537) ((-883 . -1237) T) ((-713 . -464) T) ((-507 . -526) 169503) ((-499 . -374) T) ((-366 . -379) 169482) ((-363 . -379) 169461) ((-355 . -379) 169440) ((-726 . -738) T) ((-219 . -374) T) ((-117 . -464) T) ((-1310 . -1301) 169424) ((-883 . -897) 169401) ((-883 . -899) NIL) ((-981 . -862) 169300) ((-827 . -862) 169251) ((-1244 . -102) T) ((-666 . -668) 169235) ((-1223 . -34) T) ((-173 . -625) 169217) ((-1132 . -25) 169050) ((-1132 . -21) 168961) ((-883 . -1057) 168938) ((-969 . -915) 168919) ((-1260 . -47) 168896) ((-927 . -379) T) ((-59 . -663) 168880) ((-528 . -663) 168864) ((-493 . -915) 168841) ((-71 . -453) T) ((-71 . -407) T) ((-508 . -663) 168825) ((-59 . -384) 168809) ((-635 . -174) T) ((-528 . -384) 168793) ((-508 . -384) 168777) ((-839 . -720) 168761) ((-1192 . -317) 168740) ((-1198 . -132) T) ((-1161 . -1070) 168724) ((-118 . -174) T) ((-1161 . -652) 168656) ((-1165 . -319) 168594) ((-171 . -1237) T) ((-1299 . -132) T) ((-878 . -1070) 168564) ((-647 . -756) 168548) ((-619 . -756) 168532) ((-1272 . -937) 168511) ((-1251 . -937) 168490) ((-1251 . -832) NIL) ((-878 . -652) 168460) ((-706 . -729) 168410) ((-1250 . -926) 168363) ((-1043 . -1119) T) ((-883 . -388) 168340) ((-883 . -349) 168317) ((-922 . -1131) T) ((-171 . -897) 168301) ((-171 . -899) 168226) ((-1287 . -526) 168159) ((-1271 . -660) 168056) ((-1099 . -234) 167929) ((-499 . -1131) T) ((-365 . -1119) T) ((-219 . -1131) T) ((-76 . -453) T) ((-76 . -407) T) ((-171 . -1057) 167825) ((-304 . -909) 167782) ((-329 . -862) T) ((-1250 . -660) 167590) ((-884 . -806) 167569) ((-884 . -803) 167548) ((-884 . -738) T) ((-499 . -23) T) ((-370 . -234) 167521) ((-364 . -234) 167494) ((-356 . -234) 167467) ((-225 . -625) 167449) ((-176 . -464) T) ((-224 . -319) 167387) ((-86 . -453) T) ((-86 . -407) T) ((-108 . -234) 167374) ((-219 . -23) T) ((-1311 . -1304) 167353) ((-689 . -1057) 167337) ((-592 . -300) T) ((-576 . -300) T) ((-507 . -300) T) ((-137 . -482) 167292) ((-1260 . -1237) T) ((-666 . -658) 167251) ((-48 . -1119) T) ((-724 . -272) 167235) ((-724 . -232) 167219) ((-883 . -915) NIL) 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. -729) 165705) ((-227 . -1041) T) ((-1273 . -423) 165671) ((-362 . -1294) 165648) ((-1260 . -915) 165591) ((-730 . -738) T) ((-343 . -625) 165573) ((-1231 . -628) 165455) ((-1132 . -234) 165346) ((-112 . -625) 165328) ((-112 . -626) 165310) ((-730 . -485) T) ((-723 . -628) 165260) ((-1310 . -1070) 165244) ((-494 . -25) 165077) ((-128 . -501) 165061) ((-122 . -501) 165045) ((-494 . -21) 164956) ((-1310 . -652) 164926) ((-635 . -300) T) ((-598 . -1075) 164901) ((-449 . -1119) T) ((-1081 . -317) T) ((-118 . -300) T) ((-1123 . -102) T) ((-1022 . -102) T) ((-598 . -111) 164869) ((-1161 . -319) 164807) ((-1231 . -1068) T) ((-1081 . -1041) T) ((-66 . -1237) T) ((-1073 . -25) T) ((-1073 . -21) T) ((-723 . -1068) T) ((-396 . -21) T) ((-396 . -25) T) ((-706 . -526) NIL) ((-1043 . -174) T) ((-723 . -248) T) ((-1081 . -557) T) ((-724 . -658) 164717) ((-518 . -102) T) ((-514 . -102) T) ((-365 . -174) T) ((-354 . -625) 164699) ((-419 . -1070) 164651) ((-406 . -625) 164633) ((-1139 . -860) T) ((-486 . -738) T) ((-905 . -1057) 164601) ((-419 . -652) 164553) ((-108 . -862) T) ((-670 . -1075) 164537) ((-499 . -132) T) ((-1273 . -1077) T) ((-219 . -132) T) ((-1176 . -102) 164515) ((-99 . -1119) T) ((-250 . -678) 164499) ((-250 . -663) 164483) ((-670 . -111) 164462) ((-598 . -628) 164446) ((-326 . -423) 164430) ((-250 . -384) 164414) ((-1179 . -240) 164361) ((-1018 . -272) 164345) ((-1018 . -232) 164329) ((-74 . -1237) T) ((-48 . -174) T) ((-713 . -399) T) ((-713 . -144) T) ((-1310 . -102) T) ((-1217 . -628) 164311) ((-1107 . -1237) T) ((-1106 . -1075) 164154) ((-1095 . -1237) T) ((-273 . -926) 164133) ((-253 . -926) 164112) ((-794 . -1075) 163935) ((-792 . -1075) 163778) ((-620 . -1237) T) ((-1184 . -625) 163760) ((-1106 . -111) 163589) ((-1065 . -102) T) ((-487 . -1237) T) ((-473 . -1075) 163560) ((-466 . -1075) 163403) ((-676 . -660) 163387) ((-883 . -317) T) ((-794 . -111) 163196) ((-792 . -111) 163025) ((-366 . -660) 162977) ((-363 . -660) 162929) ((-355 . -660) 162881) ((-273 . 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((-792 . -628) 161002) ((-670 . -1068) T) ((-1316 . -1119) T) ((-466 . -628) 160787) ((-171 . -317) 160718) ((-430 . -23) T) ((-40 . -625) 160700) ((-40 . -626) 160684) ((-108 . -1011) 160666) ((-117 . -881) 160650) ((-661 . -628) 160634) ((-48 . -526) 160600) ((-1223 . -1029) 160584) ((-1201 . -625) 160551) ((-1209 . -34) T) ((-971 . -625) 160517) ((-938 . -625) 160499) ((-1132 . -862) 160450) ((-783 . -625) 160432) ((-684 . -625) 160414) ((-1176 . -319) 160352) ((-491 . -34) T) ((-1111 . -1237) T) ((-489 . -464) T) ((-1160 . -34) T) ((-1106 . -1068) T) ((-50 . -628) 160321) ((-794 . -1068) T) ((-792 . -1068) T) ((-659 . -240) 160305) ((-644 . -240) 160251) ((-593 . -628) 160201) ((-530 . -628) 160131) ((-494 . -234) 160022) ((-1260 . -317) 160001) ((-1106 . -336) 159962) ((-466 . -1068) T) ((-1198 . -21) T) ((-1106 . -238) 159941) ((-794 . -336) 159918) ((-794 . -238) T) ((-792 . -336) 159890) ((-743 . -1241) 159869) ((-337 . -663) 159853) ((-1198 . -25) T) ((-59 . -34) T) ((-531 . -34) T) ((-528 . -34) T) ((-466 . -336) 159832) ((-337 . -384) 159816) ((-509 . -34) T) ((-508 . -34) T) ((-1022 . -1171) NIL) ((-743 . -568) 159747) ((-647 . -102) T) ((-619 . -102) T) ((-366 . -738) T) ((-363 . -738) T) ((-355 . -738) T) ((-273 . -738) T) ((-253 . -738) T) ((-390 . -1237) T) ((-1065 . -319) 159655) ((-1299 . -21) T) ((-918 . -1119) 159633) ((-830 . -234) 159620) ((-50 . -1068) T) ((-1299 . -25) T) ((-1194 . -568) 159599) ((-1193 . -1241) 159578) ((-1193 . -568) 159529) ((-1187 . -1241) 159508) ((-1187 . -568) 159459) ((-593 . -1068) T) ((-530 . -1068) T) ((-1043 . -300) T) ((-372 . -1057) 159443) ((-332 . -1057) 159427) ((-1022 . -38) 159372) ((-390 . -899) 159354) ((-1018 . -658) 159277) ((-848 . -1237) T) ((-839 . -1237) 159256) ((-811 . -1131) T) ((-927 . -738) T) ((-593 . -248) T) ((-593 . -238) T) ((-530 . -238) T) ((-530 . -248) T) ((-1145 . -568) 159235) ((-365 . -300) T) ((-659 . -707) 159219) ((-390 . -1057) 159179) ((-304 . -1070) 159100) ((-350 . -909) 159079) ((-1139 . -1077) T) ((-103 . -126) 159063) ((-304 . -652) 159005) ((-811 . -23) T) ((-1309 . -1304) 158981) ((-1307 . -1304) 158960) ((-1287 . -296) 158912) ((-419 . -319) 158877) ((-1273 . -1119) T) ((-1161 . -917) 158800) ((-882 . -625) 158782) ((-848 . -1057) 158751) ((-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) 158733) ((-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) 158717) ((-682 . -237) 158668) ((-225 . -628) 158630) ((-110 . -862) T) ((-665 . -21) T) ((-665 . -25) T) ((-1310 . -38) 158600) ((-118 . -296) 158551) ((-1287 . -19) 158535) ((-1287 . -616) 158512) ((-1300 . -1119) T) ((-362 . -1070) 158457) ((-1096 . -1119) T) ((-1006 . -1119) T) ((-980 . -132) T) ((-829 . -234) 158444) ((-749 . -1119) T) ((-362 . -652) 158389) ((-747 . -132) T) ((-727 . -132) T) ((-523 . -805) T) ((-523 . -806) T) ((-465 . -132) T) ((-419 . -1171) 158367) ((-225 . -1068) T) ((-304 . -102) 158149) ((-142 . -1119) T) ((-711 . -1021) T) ((-1124 . -296) 158105) ((-91 . -1237) T) ((-128 . -625) 158037) ((-122 . -625) 157969) ((-1316 . -174) T) ((-1193 . -374) 157948) ((-1187 . -374) 157927) ((-326 . -1119) T) ((-430 . -132) T) ((-323 . -1119) T) ((-419 . -38) 157879) ((-1152 . -102) T) ((-1273 . -729) 157771) ((-666 . -1077) T) ((-1154 . -1282) T) ((-329 . -146) 157750) ((-329 . -148) 157729) ((-140 . -1119) T) ((-137 . -1119) T) ((-115 . -1119) T) ((-870 . -102) T) ((-592 . -625) 157711) ((-576 . -626) 157610) ((-576 . -625) 157592) ((-507 . -625) 157574) ((-507 . -626) 157519) ((-497 . -23) T) ((-494 . -862) 157470) ((-499 . -651) 157452) ((-982 . -625) 157434) ((-1022 . -917) 157343) ((-219 . -651) 157325) ((-227 . -416) T) ((-674 . -660) 157309) ((-55 . -625) 157291) ((-1192 . -937) 157270) ((-743 . -1131) T) ((-362 . -102) T) ((-1236 . -1102) T) ((-1139 . -856) T) ((-830 . -862) T) ((-743 . -23) T) ((-354 . -1075) 157215) ((-1178 . -1177) T) ((-1166 . -107) 157199) ((-1194 . -1131) T) ((-1193 . -1131) T) ((-527 . -1057) 157183) ((-1187 . -1131) T) ((-1145 . -1131) T) ((-354 . -111) 157112) ((-1023 . -1241) T) ((-127 . -1237) T) ((-931 . -1241) T) ((-1288 . -625) 157094) ((-706 . -296) NIL) ((-726 . -1237) T) ((-1194 . -23) T) ((-1193 . -23) T) ((-1187 . -23) T) ((-1161 . -272) 157078) ((-1161 . -232) 157062) ((-1023 . -568) T) ((-1145 . -23) T) ((-931 . -568) T) ((-1094 . -1119) T) ((-254 . -625) 157044) ((-827 . -237) 156941) ((-811 . -132) T) ((-722 . -625) 156923) ((-326 . -729) 156833) ((-323 . -729) 156762) ((-711 . -625) 156744) ((-711 . -626) 156689) ((-419 . -412) 156673) ((-450 . -1119) T) ((-499 . -25) T) ((-499 . -21) T) ((-1139 . -1119) T) ((-219 . -25) T) ((-219 . -21) T) ((-724 . -423) 156657) ((-726 . -1057) 156626) ((-1287 . -625) 156538) ((-1287 . -626) 156499) ((-1273 . -174) T) ((-1210 . -625) 156481) ((-250 . -34) T) ((-354 . -628) 156411) ((-406 . -628) 156393) ((-943 . -993) T) ((-1223 . -1237) T) ((-674 . -803) 156372) ((-674 . -806) 156351) ((-410 . -407) T) ((-535 . -102) 156329) ((-1054 . -1119) T) ((-419 . -917) 156252) ((-224 . -1014) 156236) ((-516 . -102) T) ((-635 . -625) 156218) ((-45 . -862) NIL) ((-635 . -626) 156195) ((-1054 . -622) 156170) ((-918 . -526) 156103) ((-329 . -237) 156055) ((-354 . -1068) T) ((-118 . -626) NIL) ((-118 . -625) 156037) ((-884 . -1237) T) ((-682 . -429) 156021) ((-682 . -1142) 155966) ((-512 . -152) 155948) ((-354 . -238) T) ((-354 . -248) T) ((-40 . -1075) 155893) ((-884 . -897) 155877) ((-884 . -899) 155802) ((-724 . -1077) T) ((-706 . -1021) NIL) ((-1271 . -47) 155772) ((-1250 . -47) 155749) ((-1160 . -1029) 155720) ((-1139 . -729) 155707) ((-3 . |UnionCategory|) T) ((-1124 . -625) 155689) ((-1099 . -148) 155668) ((-1099 . -146) 155619) ((-1023 . -374) T) 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. -1237) T) ((-507 . -1068) T) ((-608 . -23) T) ((-354 . -1306) 149778) ((-329 . -464) 149757) ((-350 . -319) 149744) ((-607 . -23) T) ((-439 . -132) T) ((-670 . -660) 149718) ((-250 . -1029) 149702) ((-884 . -317) T) ((-1311 . -1301) 149686) ((-783 . -804) T) ((-783 . -807) T) ((-713 . -38) 149673) ((-576 . -238) T) ((-507 . -248) T) ((-507 . -238) T) ((-1169 . -240) 149623) ((-1106 . -926) 149602) ((-117 . -38) 149589) ((-211 . -812) T) ((-210 . -812) T) ((-209 . -812) T) ((-208 . -812) T) ((-884 . -1041) 149567) ((-1300 . -501) 149551) ((-794 . -926) 149530) ((-792 . -926) 149509) ((-1209 . -1237) T) ((-366 . -1237) 149488) ((-363 . -1237) 149467) ((-355 . -1237) 149446) ((-273 . -1237) T) ((-253 . -1237) T) ((-466 . -926) 149425) ((-749 . -501) 149409) ((-1106 . -660) 149298) ((-711 . -628) 149233) ((-794 . -660) 149122) ((-635 . -1075) 149109) ((-491 . -1237) T) ((-354 . -379) T) ((-142 . -501) 149091) ((-792 . -660) 148980) ((-1160 . -1237) T) ((-561 . -862) T) ((-473 . -660) 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141890) ((-115 . -625) 141872) ((-489 . -38) 141837) ((-1311 . -1308) 141816) ((-1302 . -132) T) ((-1310 . -1077) T) ((-1101 . -102) T) ((-88 . -1237) T) ((-512 . -319) NIL) ((-1019 . -107) 141800) ((-902 . -1119) T) ((-898 . -1119) T) ((-1287 . -663) 141784) ((-1287 . -384) 141768) ((-337 . -1237) T) ((-605 . -862) T) ((-1161 . -1119) T) ((-1161 . -1072) 141708) ((-103 . -526) 141641) ((-944 . -625) 141623) ((-354 . -738) T) ((-30 . -625) 141605) ((-878 . -1119) T) ((-855 . -1077) 141584) ((-40 . -660) 141491) ((-227 . -1241) T) ((-419 . -1077) T) ((-1178 . -152) 141473) ((-1018 . -300) 141424) ((-629 . -1119) T) ((-227 . -568) T) ((-329 . -1268) 141408) ((-329 . -1265) 141378) ((-713 . -658) 141350) ((-1209 . -1213) 141329) ((-1094 . -625) 141311) ((-1209 . -107) 141261) ((-659 . -152) 141245) ((-644 . -152) 141191) ((-117 . -658) 141163) ((-491 . -1213) 141142) ((-499 . -148) T) ((-499 . -146) NIL) ((-1139 . -626) 141057) ((-450 . -625) 141039) ((-219 . -148) T) ((-219 . -146) NIL) 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135221) ((-883 . -23) T) ((-794 . -1057) 135080) ((-792 . -1057) 134937) ((-118 . -660) 134882) ((-466 . -1057) 134758) ((-326 . -628) 134322) ((-323 . -628) 134205) ((-402 . -658) 134174) ((-661 . -1057) 134158) ((-639 . -102) T) ((-593 . -1237) T) ((-530 . -1237) T) ((-224 . -501) 134142) ((-1287 . -34) T) ((-633 . -658) 134101) ((-299 . -1070) 134088) ((-137 . -628) 134072) ((-299 . -652) 134059) ((-647 . -729) 134043) ((-619 . -729) 134027) ((-682 . -38) 133987) ((-329 . -102) T) ((-85 . -625) 133969) ((-50 . -1057) 133953) ((-1139 . -1075) 133940) ((-1106 . -388) 133924) ((-794 . -388) 133908) ((-711 . -738) T) ((-711 . -806) T) ((-711 . -803) T) ((-593 . -1057) 133895) ((-530 . -1057) 133872) ((-60 . -57) 133834) ((-334 . -132) T) ((-326 . -1068) 133724) ((-323 . -1068) T) ((-171 . -1131) T) ((-792 . -388) 133708) ((-45 . -152) 133658) ((-1023 . -1011) 133640) ((-466 . -388) 133624) ((-419 . -174) T) ((-326 . -248) 133603) ((-323 . -248) T) ((-323 . -238) NIL) ((-304 . -1119) 133385) ((-227 . -132) T) ((-1139 . -111) 133370) ((-171 . -23) T) ((-811 . -148) 133349) ((-811 . -146) 133328) ((-258 . -651) 133234) ((-257 . -651) 133140) ((-329 . -294) 133106) ((-1176 . -526) 133039) ((-489 . -658) 132989) ((-494 . -909) 132856) ((-1152 . -1119) T) ((-227 . -1079) T) ((-827 . -319) 132794) ((-1106 . -915) 132729) ((-794 . -915) 132672) ((-792 . -915) 132656) ((-1309 . -38) 132626) ((-1307 . -38) 132596) ((-1260 . -1131) T) ((-867 . -1131) T) ((-466 . -915) 132573) ((-870 . -1119) T) ((-1260 . -23) T) ((-1139 . -628) 132545) ((-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) 132490) ((-118 . -806) NIL) ((-118 . -803) NIL) ((-118 . -738) T) ((-1065 . -526) 132391) ((-706 . -926) NIL) ((-583 . -23) T) ((-493 . -132) T) ((-430 . -237) 132342) ((-687 . -319) 132280) ((-647 . -773) T) ((-619 . -773) T) ((-1251 . -862) NIL) 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-407) T) ((-1179 . -102) T) ((-883 . -132) T) ((-496 . -102) 130985) ((-1316 . -379) T) ((-1099 . -102) T) ((-1080 . -102) T) ((-362 . -729) 130930) ((-743 . -148) 130909) ((-743 . -146) 130888) ((-666 . -628) 130806) ((-1043 . -660) 130743) ((-535 . -1119) 130721) ((-370 . -102) T) ((-364 . -102) T) ((-356 . -102) T) ((-108 . -102) T) ((-516 . -1119) T) ((-365 . -660) 130666) ((-1192 . -651) 130614) ((-1144 . -651) 130562) ((-396 . -521) 130541) ((-845 . -860) 130520) ((-390 . -1241) T) ((-706 . -738) T) ((-1251 . -1011) 130472) ((-350 . -1077) T) ((-112 . -1237) T) ((-176 . -1077) T) ((-103 . -625) 130404) ((-1194 . -146) 130383) ((-1194 . -148) 130362) ((-390 . -568) T) ((-1193 . -148) 130341) ((-1193 . -146) 130320) ((-1187 . -146) 130227) ((-419 . -300) T) ((-1187 . -148) 130134) ((-1145 . -148) 130113) ((-1145 . -146) 130092) ((-329 . -38) 129933) ((-171 . -132) T) ((-323 . -807) NIL) ((-323 . -804) NIL) ((-666 . -1068) T) ((-48 . -660) 129883) ((-1132 . -1070) 129784) ((-906 . 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. -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) 128378) ((-365 . -738) T) ((-682 . -272) 128362) ((-682 . -232) 128346) ((-593 . -317) T) ((-530 . -317) T) ((-304 . -526) 128295) ((-108 . -319) NIL) ((-72 . -407) T) ((-1132 . -102) 128047) ((-845 . -423) 128031) ((-1139 . -807) T) ((-1139 . -804) T) ((-713 . -1119) T) ((-590 . -625) 128013) ((-390 . -374) T) ((-171 . -505) 127991) ((-224 . -625) 127923) ((-135 . -1119) T) ((-117 . -1119) T) ((-983 . -1237) T) ((-48 . -738) T) ((-1065 . -501) 127888) ((-142 . -437) 127870) ((-142 . -379) T) ((-1046 . -102) T) ((-524 . -521) 127849) ((-724 . -628) 127605) ((-1194 . -237) 127564) ((-488 . -102) T) ((-475 . -102) T) ((-1193 . -237) 127516) ((-1187 . -237) 127339) ((-1053 . -1131) T) ((-329 . 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-336) 126013) ((-493 . -651) 125961) ((-40 . -1057) 125849) ((-724 . -238) T) ((-713 . -729) 125836) ((-350 . -1119) T) ((-176 . -1119) T) ((-341 . -862) T) ((-430 . -464) 125786) ((-390 . -23) T) ((-370 . -38) 125751) ((-364 . -38) 125716) ((-356 . -38) 125681) ((-80 . -453) T) ((-80 . -407) T) ((-227 . -25) T) ((-227 . -21) T) ((-848 . -1131) T) ((-108 . -38) 125631) ((-839 . -1131) T) ((-786 . -1119) T) ((-117 . -729) 125618) ((-684 . -1057) 125602) ((-624 . -102) T) ((-848 . -23) T) ((-839 . -23) T) ((-1176 . -296) 125554) ((-1132 . -319) 125492) ((-494 . -1070) 125393) ((-1121 . -240) 125377) ((-64 . -408) T) ((-64 . -407) T) ((-1170 . -102) T) ((-110 . -102) T) ((-494 . -652) 125299) ((-40 . -388) 125276) ((-96 . -102) T) ((-665 . -864) 125260) ((-1192 . -234) 125247) ((-1154 . -1102) T) ((-1081 . -21) T) ((-1081 . -25) T) ((-1073 . -1070) 125231) ((-827 . -272) 125200) ((-827 . -232) 125169) ((-969 . -25) T) ((-969 . -21) T) ((-1073 . -652) 125111) ((-633 . -1077) T) ((-1139 . -379) T) ((-1046 . -319) 125049) ((-682 . -658) 125008) ((-493 . -25) T) ((-493 . -21) T) ((-396 . -1070) 124992) ((-902 . -625) 124974) ((-898 . -625) 124956) ((-535 . -526) 124889) ((-258 . -862) 124840) ((-257 . -862) 124791) ((-396 . -652) 124761) ((-883 . -651) 124738) ((-488 . -319) 124676) ((-475 . -319) 124614) ((-362 . -300) T) ((-1176 . -1275) 124598) ((-1161 . -625) 124560) ((-1161 . -626) 124521) ((-1159 . -102) T) ((-1018 . -1075) 124417) ((-40 . -915) 124369) ((-1176 . -616) 124346) ((-1316 . -660) 124333) ((-1082 . -152) 124279) ((-499 . -909) NIL) ((-878 . -502) 124256) ((-1018 . -111) 124138) ((-884 . -1241) T) ((-219 . -909) NIL) ((-350 . -729) 124122) ((-878 . -625) 124084) ((-176 . -729) 124016) ((-884 . -568) T) ((-419 . -296) 123974) ((-245 . -237) 123871) ((-108 . -412) 123853) ((-84 . -395) T) ((-84 . -407) T) ((-713 . -174) T) ((-629 . -625) 123835) ((-99 . -738) T) ((-494 . -102) 123587) ((-99 . -485) T) ((-117 . -174) T) ((-1309 . -658) 123546) ((-1307 . -658) 123505) ((-171 . -651) 123453) ((-1099 . -917) 123324) ((-1073 . -102) T) ((-1018 . -628) 123214) ((-883 . -25) T) ((-827 . -243) 123193) ((-883 . -21) T) ((-830 . -102) T) ((-44 . -658) 123136) ((-1023 . -237) T) ((-426 . -102) T) ((-396 . -102) T) ((-110 . -319) NIL) ((-229 . -102) 123114) ((-128 . -1237) T) ((-122 . -1237) T) ((-108 . -917) NIL) ((-829 . -1070) 123065) ((-829 . -652) 123007) ((-1053 . -132) T) ((-682 . -378) 122991) ((-153 . -658) 122950) ((-647 . -296) 122908) ((-619 . -296) 122866) ((-1316 . -738) T) ((-1018 . -1068) T) ((-1260 . -651) 122814) ((-1123 . -625) 122796) ((-1022 . -625) 122778) ((-576 . -1237) T) ((-507 . -1237) T) ((-527 . -23) T) ((-522 . -23) T) ((-354 . -317) T) ((-520 . -23) T) ((-332 . -132) T) ((-3 . -1119) T) ((-1022 . -626) 122762) ((-1018 . -248) 122741) ((-1018 . -238) 122720) ((-1279 . -146) 122699) ((-1279 . -148) 122678) ((-845 . -1119) T) ((-1272 . -148) 122657) ((-1272 . -146) 122636) ((-1271 . -1241) 122615) ((-1251 . -146) 122522) ((-1251 . -148) 122429) ((-1250 . -1241) 122408) ((-390 . -132) T) ((-227 . -234) 122395) ((-576 . -899) 122377) ((0 . -1119) T) ((-176 . -174) T) ((-171 . -21) T) ((-171 . -25) T) ((-49 . -1119) T) ((-1273 . -660) 122282) ((-1271 . -568) 122233) ((-726 . -1131) T) ((-1250 . -568) 122184) ((-576 . -1057) 122166) ((-607 . -148) 122145) ((-607 . -146) 122124) ((-507 . -1057) 122067) ((-1154 . -1156) T) ((-87 . -395) T) ((-87 . -407) T) ((-884 . -374) T) ((-848 . -132) T) ((-839 . -132) T) ((-981 . -658) 122011) ((-726 . -23) T) ((-518 . -625) 121977) ((-514 . -625) 121959) ((-827 . -658) 121738) ((-1311 . -1077) T) ((-390 . -1079) T) ((-1045 . -1119) 121716) ((-55 . -1057) 121698) ((-918 . -34) T) ((-494 . -319) 121636) ((-604 . -102) T) ((-1176 . -626) 121597) ((-1176 . -625) 121529) ((-1198 . -1070) 121412) ((-45 . -102) T) ((-829 . -102) T) ((-1198 . -652) 121309) ((-1260 . -25) T) ((-1260 . -21) T) ((-1081 . -234) 121296) ((-867 . -25) T) ((-44 . -378) 121280) ((-867 . -21) T) ((-743 . -464) 121231) ((-1310 . -625) 121213) ((-1299 . -1070) 121183) ((-1073 . -319) 121121) ((-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) ((-1299 . -652) 121091) ((-633 . -1119) T) ((-711 . -899) 121073) ((-1287 . -1237) T) ((-229 . -319) 121011) ((-145 . -379) T) ((-1065 . -626) 120953) ((-1065 . -625) 120896) ((-323 . -926) NIL) ((-1245 . -856) T) ((-1132 . -917) 120765) ((-711 . -1057) 120710) ((-723 . -937) T) ((-486 . -1241) 120689) ((-1193 . -464) 120668) ((-1187 . -464) 120647) ((-340 . -102) T) ((-884 . -1131) T) ((-329 . -658) 120529) ((-326 . -660) 120258) ((-323 . -660) 120187) ((-486 . -568) 120138) ((-350 . -526) 120104) ((-562 . -152) 120054) ((-40 . -317) T) ((-855 . -625) 120036) ((-713 . -300) T) ((-884 . -23) T) ((-390 . -505) T) ((-1099 . -272) 120006) ((-1099 . -232) 119976) ((-524 . -102) T) ((-419 . -626) 119783) ((-419 . -625) 119765) 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. -1119) T) ((-392 . -1119) T) ((-1260 . -234) 117552) ((-1236 . -1119) T) ((-82 . -1237) T) ((-1132 . -272) 117521) ((-1081 . -862) T) ((-118 . -915) NIL) ((-794 . -937) 117500) ((-725 . -862) T) ((-543 . -1119) T) ((-512 . -1119) T) ((-366 . -1241) T) ((-363 . -1241) T) ((-355 . -1241) T) ((-273 . -1241) 117479) ((-253 . -1241) 117458) ((-545 . -872) T) ((-1132 . -232) 117427) ((-1178 . -840) T) ((-1161 . -1075) 117411) ((-402 . -773) T) ((-706 . -1237) T) ((-703 . -1057) 117395) ((-366 . -568) T) ((-363 . -568) T) ((-355 . -568) T) ((-273 . -568) 117326) ((-253 . -568) 117257) ((-537 . -1102) T) ((-1161 . -111) 117236) ((-465 . -756) 117206) ((-878 . -1075) 117176) ((-829 . -38) 117118) ((-706 . -897) 117100) ((-706 . -899) 117082) ((-305 . -319) 116886) ((-1176 . -298) 116863) ((-927 . -1241) T) ((-1099 . -658) 116758) ((-1023 . -464) T) ((-682 . -423) 116742) ((-878 . -111) 116707) ((-931 . -464) T) ((-706 . -1057) 116652) ((-927 . -568) T) ((-545 . -625) 116634) ((-593 . -937) T) 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-658) 107497) ((-1279 . -909) 107385) ((-1236 . -93) T) ((-362 . -1068) T) ((-227 . -237) T) ((-70 . -394) T) ((-70 . -407) T) ((-1185 . -102) T) ((-682 . -526) 107318) ((-1272 . -909) 107199) ((-1251 . -909) 106935) ((-701 . -319) 106873) ((-980 . -38) 106770) ((-1200 . -625) 106752) ((-747 . -38) 106722) ((-562 . -319) 106526) ((-1194 . -1070) 106409) ((-326 . -1237) T) ((-362 . -238) T) ((-362 . -248) T) ((-323 . -1237) T) ((-299 . -1119) T) ((-1193 . -1070) 106244) ((-1187 . -1070) 106034) ((-1145 . -1070) 105917) ((-1194 . -652) 105814) ((-1193 . -652) 105655) ((-723 . -1241) T) ((-1187 . -652) 105451) ((-1176 . -663) 105435) ((-1145 . -652) 105332) ((-1231 . -568) 105311) ((-831 . -397) 105295) ((-723 . -568) T) ((-607 . -909) 105206) ((-326 . -897) 105190) ((-326 . -899) 105115) ((-137 . -1237) T) ((-323 . -897) 105076) ((-323 . -899) NIL) ((-811 . -319) 105041) ((-329 . -729) 104882) ((-398 . -397) 104866) ((-334 . -333) 104843) ((-497 . -102) T) ((-486 . -25) T) ((-486 . -21) 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97826) ((-370 . -174) T) ((-364 . -174) T) ((-531 . -57) 97800) ((-509 . -57) 97750) ((-362 . -1306) 97727) ((-227 . -464) T) ((-329 . -300) 97678) ((-356 . -174) T) ((-176 . -248) T) ((-1250 . -862) 97577) ((-108 . -174) T) ((-884 . -1011) 97561) ((-670 . -1131) T) ((-593 . -374) T) ((-593 . -339) 97548) ((-530 . -339) 97525) ((-530 . -374) T) ((-326 . -317) 97504) ((-323 . -317) T) ((-614 . -862) 97483) ((-1132 . -729) 97425) ((-532 . -292) 97409) ((-670 . -23) T) ((-430 . -232) 97393) ((-430 . -272) 97377) ((-323 . -1041) NIL) ((-347 . -23) T) ((-103 . -1029) 97361) ((-45 . -36) 97340) ((-624 . -1119) T) ((-362 . -379) T) ((-536 . -102) T) ((-507 . -27) T) ((-245 . -319) 97278) ((-1106 . -1131) T) ((-1310 . -660) 97252) ((-794 . -1131) T) ((-792 . -1131) T) ((-1198 . -423) 97236) ((-466 . -1131) T) ((-1081 . -464) T) ((-1170 . -1119) T) ((-969 . -464) 97187) ((-1134 . -1102) T) ((-110 . -1119) T) ((-1106 . -23) T) ((-1179 . -526) 96970) ((-829 . -1077) T) ((-794 . -23) T) ((-792 . -23) T) ((-493 . -464) 96921) ((-473 . -23) T) ((-392 . -393) 96900) ((-366 . -234) 96873) ((-363 . -234) 96846) ((-355 . -234) 96819) ((-466 . -23) T) ((-273 . -234) 96764) ((-258 . -909) 96631) ((-257 . -909) 96498) ((-96 . -1119) T) ((-724 . -1237) T) ((-682 . -296) 96475) ((-496 . -526) 96408) ((-1279 . -1070) 96291) ((-1279 . -652) 96188) ((-1272 . -652) 96029) ((-1272 . -1070) 95864) ((-1251 . -652) 95660) ((-299 . -300) T) ((-1251 . -1070) 95450) ((-1101 . -625) 95432) ((-1101 . -626) 95413) ((-419 . -926) 95392) ((-1231 . -132) T) ((-50 . -1131) T) ((-1187 . -412) 95344) ((-1043 . -937) T) ((-1022 . -738) T) ((-855 . -660) 95317) ((-724 . -899) NIL) ((-608 . -1070) 95277) ((-593 . -1131) T) ((-530 . -1131) T) ((-607 . -1070) 95160) ((-1176 . -34) T) ((-1023 . -319) NIL) ((-827 . -501) 95144) ((-608 . -652) 95117) ((-365 . -937) T) ((-607 . -652) 95014) ((-927 . -234) 95001) ((-419 . -660) 94917) ((-50 . -23) T) ((-723 . -132) T) ((-724 . -1057) 94797) ((-593 . -23) T) ((-108 . -526) NIL) ((-530 . -23) T) ((-171 . -421) 94768) ((-1159 . -1119) T) ((-1302 . -1301) 94752) ((-743 . -917) 94729) ((-713 . -807) T) ((-713 . -804) T) ((-1139 . -317) T) ((-390 . -148) T) ((-290 . -625) 94711) ((-289 . -625) 94693) ((-1250 . -1011) 94663) ((-48 . -937) T) ((-687 . -501) 94647) ((-258 . -1294) 94617) ((-257 . -1294) 94587) ((-1107 . -237) T) ((-1196 . -862) T) ((-1139 . -1041) T) ((-1065 . -34) T) ((-848 . -148) 94566) ((-848 . -146) 94545) ((-749 . -107) 94529) ((-624 . -133) T) ((-1198 . -1077) T) ((-494 . -1119) 94281) ((-1194 . -917) 94194) ((-1193 . -917) 94100) ((-1187 . -917) 93861) ((-883 . -464) T) ((-85 . -1237) T) ((-142 . -107) 93843) ((-1145 . -917) 93827) ((-724 . -388) 93811) ((-845 . -628) 93679) ((-1310 . -738) T) ((-1299 . -1077) T) ((-1279 . -102) T) ((-1139 . -557) T) ((-591 . -102) T) ((-130 . -502) 93661) ((-1272 . -102) T) ((-402 . -1075) 93645) ((-1192 . -966) 93614) ((-44 . -296) 93591) ((-130 . -625) 93558) ((-52 . -625) 93540) ((-1144 . -966) 93507) ((-665 . -423) 93491) ((-1251 . -102) T) ((-1178 . -526) NIL) ((-674 . -25) T) ((-633 . -1075) 93475) ((-674 . -21) T) ((-980 . -658) 93385) ((-747 . -658) 93330) ((-727 . -658) 93302) ((-402 . -111) 93281) ((-224 . -261) 93265) ((-1073 . -1072) 93205) ((-1073 . -1119) T) ((-1023 . -1171) T) ((-830 . -1119) T) ((-465 . -658) 93120) ((-647 . -660) 93104) ((-354 . -1241) T) ((-633 . -111) 93083) ((-619 . -660) 93067) ((-608 . -102) T) ((-321 . -502) 93048) ((-598 . -132) T) ((-607 . -102) T) ((-426 . -1119) T) ((-396 . -1119) T) ((-321 . -625) 93014) ((-229 . -1119) 92992) ((-659 . -526) 92925) ((-644 . -526) 92769) ((-845 . -1068) 92748) ((-656 . -152) 92732) ((-354 . -568) T) ((-724 . -915) 92675) ((-562 . -231) 92625) ((-1279 . -294) 92591) ((-1272 . -294) 92557) ((-1099 . -300) 92508) ((-499 . -860) T) ((-225 . -1131) T) ((-1251 . -294) 92474) ((-1231 . -505) 92440) ((-1023 . -38) 92390) ((-219 . -860) T) ((-430 . -658) 92349) ((-931 . -38) 92301) ((-855 . -806) 92280) ((-855 . -803) 92259) ((-855 . -738) 92238) ((-370 . -300) T) ((-364 . -300) T) ((-356 . -300) T) ((-171 . -464) 92169) ((-439 . -38) 92153) ((-225 . -23) T) ((-108 . -300) T) ((-419 . -806) 92132) ((-419 . -803) 92111) ((-419 . -738) T) ((-512 . -298) 92086) ((-489 . -1075) 92051) ((-670 . -132) T) ((-633 . -628) 92020) ((-1132 . -526) 91953) ((-347 . -132) T) ((-171 . -414) 91932) ((-494 . -729) 91874) ((-827 . -296) 91851) ((-489 . -111) 91807) ((-665 . -1077) T) ((-1192 . -909) 91710) ((-1144 . -909) 91692) ((-828 . -1070) 91535) ((-1298 . -1102) T) ((-1260 . -464) 91466) ((-828 . -652) 91315) ((-1297 . -1102) T) ((-1106 . -132) T) ((-1073 . -729) 91257) ((-1046 . -526) 91190) ((-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 . -1237) T) ((-45 . -1119) T) ((-396 . -729) 91160) ((-829 . -1119) T) ((-488 . -526) 91093) ((-475 . -526) 91026) ((-1312 . -628) 91008) ((-465 . -378) 90978) ((-45 . -622) 90957) ((-411 . -1237) T) ((-326 . -312) T) ((-839 . -237) 90936) ((-489 . -628) 90886) ((-1251 . -319) 90771) ((-682 . -625) 90733) ((-59 . -862) 90712) ((-1023 . -412) 90694) ((-560 . -625) 90676) ((-811 . -658) 90635) ((-827 . -616) 90612) ((-528 . -862) 90591) ((-508 . -862) 90570) ((-1018 . -1057) 90466) ((-40 . -1241) T) ((-245 . -917) 90335) ((-50 . -132) T) ((-593 . -132) T) ((-530 . -132) T) ((-304 . -660) 90195) ((-354 . -339) 90172) ((-354 . -374) T) ((-332 . -333) 90149) ((-329 . -296) 90107) ((-40 . -568) T) ((-390 . -1222) T) ((-390 . -1225) T) ((-1054 . -1213) 90082) ((-1209 . -240) 90032) ((-1187 . -232) 89984) ((-1187 . -272) 89936) ((-340 . -1119) T) ((-390 . -95) T) ((-390 . -35) T) ((-1054 . -107) 89882) ((-489 . -1068) T) ((-1311 . -1075) 89866) ((-491 . -240) 89816) ((-1179 . -501) 89750) ((-1302 . -1070) 89734) ((-392 . -1075) 89718) ((-1302 . -652) 89688) ((-489 . -248) T) ((-828 . -102) T) ((-726 . -148) 89667) ((-726 . -146) 89646) 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83686) ((-713 . -660) 83658) ((-561 . -856) T) ((-219 . -1119) T) ((-326 . -937) 83637) ((-323 . -937) T) ((-323 . -832) NIL) ((-402 . -732) T) ((-882 . -23) T) ((-117 . -660) 83624) ((-486 . -146) 83603) ((-430 . -423) 83587) ((-486 . -148) 83566) ((-110 . -501) 83548) ((-321 . -628) 83529) ((-2 . -625) 83511) ((-188 . -102) T) ((-1178 . -19) 83493) ((-1178 . -616) 83468) ((-670 . -21) T) ((-670 . -25) T) ((-605 . -1163) T) ((-1132 . -296) 83445) ((-347 . -25) T) ((-347 . -21) T) ((-245 . -658) 83224) ((-507 . -374) T) ((-1309 . -1075) 83208) ((-1307 . -1075) 83192) ((-1302 . -38) 83162) ((-1271 . -1222) 83128) ((-1260 . -909) 83031) ((-1192 . -1070) 82854) ((-1161 . -1237) T) ((-1144 . -1070) 82697) ((-866 . -1070) 82681) ((-644 . -616) 82656) ((-1271 . -1225) 82622) ((-1271 . -95) 82588) ((-1271 . -237) 82540) ((-1192 . -652) 82369) ((-1144 . -652) 82218) ((-866 . -652) 82188) ((-1254 . -102) 82166) ((-1251 . -232) 82118) ((-561 . -1119) T) ((-1106 . -25) T) ((-1106 . -21) T) ((-543 . -804) T) ((-543 . -807) T) ((-118 . -1241) T) ((-980 . -1077) T) ((-635 . -568) T) ((-794 . -25) T) ((-794 . -21) T) ((-792 . -21) T) ((-792 . -25) T) ((-747 . -1077) T) ((-727 . -1077) T) ((-682 . -1075) 82102) ((-529 . -1102) T) ((-473 . -25) T) ((-118 . -568) T) ((-473 . -21) T) ((-466 . -25) T) ((-466 . -21) T) ((-1251 . -272) 82054) ((-1170 . -93) T) ((-1161 . -1057) 81950) ((-829 . -300) 81929) ((-1250 . -1222) 81895) ((-835 . -1119) T) ((-983 . -986) T) ((-682 . -111) 81874) ((-629 . -1237) T) ((-305 . -526) 81666) ((-1250 . -1225) 81632) ((-1250 . -237) 81491) ((-1245 . -379) T) ((-258 . -319) 81429) ((-257 . -319) 81367) ((-1242 . -856) T) ((-1179 . -626) NIL) ((-1179 . -625) 81349) ((-1161 . -388) 81333) ((-1139 . -832) T) ((-1139 . -937) T) ((-96 . -93) T) ((-1132 . -616) 81310) ((-1099 . -626) 81294) ((-1099 . -625) 81276) ((-1023 . -658) 81226) ((-931 . -658) 81163) ((-827 . -298) 81140) ((-496 . -625) 81072) ((-620 . -152) 81019) ((-499 . -729) 80969) ((-430 . -1077) T) 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. -111) 25114) ((-362 . -1241) T) ((-1279 . -1075) 24997) ((-1132 . -388) 24966) ((-1272 . -1075) 24801) ((-1251 . -1075) 24591) ((-1272 . -111) 24412) ((-1251 . -111) 24181) ((-1231 . -319) 24168) ((-1022 . -132) T) ((-927 . -658) 24118) ((-376 . -625) 24100) ((-362 . -568) T) ((-299 . -317) T) ((-608 . -1075) 24060) ((-607 . -1075) 23943) ((-593 . -1070) 23908) ((-530 . -1070) 23853) ((-372 . -1119) T) ((-332 . -1119) T) ((-258 . -625) 23814) ((-257 . -625) 23775) ((-593 . -652) 23740) ((-530 . -652) 23685) ((-706 . -421) 23652) ((-647 . -23) T) ((-619 . -23) T) ((-40 . -909) 23559) ((-670 . -102) T) ((-608 . -111) 23512) ((-607 . -111) 23381) ((-390 . -1119) T) ((-347 . -102) T) ((-171 . -300) 23292) ((-1250 . -860) 23245) ((-726 . -1077) T) ((-1166 . -526) 23178) ((-1210 . -847) 23162) ((-1132 . -915) 23094) ((-848 . -1119) T) ((-839 . -1119) T) ((-837 . -1119) T) ((-97 . -102) T) ((-145 . -862) T) ((-624 . -897) 23078) ((-110 . -1237) T) ((-1106 . -102) T) ((-1082 . -34) T) ((-794 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-806) T) ((-1081 . -803) T) ((-884 . -628) 186596) ((-794 . -174) 186487) ((-792 . -174) 186398) ((-828 . -47) 186360) ((-1081 . -738) T) ((-337 . -501) 186344) ((-969 . -738) T) ((-1299 . -319) 186282) ((-1278 . -915) 186195) ((-466 . -174) 186106) ((-250 . -296) 186058) ((-1271 . -915) 185964) ((-1270 . -1075) 185799) ((-1250 . -915) 185632) ((-493 . -738) T) ((-1249 . -1075) 185440) ((-1230 . -300) 185419) ((-1205 . -1236) T) ((-1202 . -379) T) ((-1201 . -379) T) ((-1165 . -152) 185403) ((-1139 . -102) T) ((-1137 . -1119) T) ((-1099 . -23) T) ((-1099 . -1131) T) ((-1094 . -102) T) ((-1076 . -625) 185370) ((-1022 . -421) 185342) ((-944 . -972) T) ((-749 . -319) 185280) ((-75 . -1236) T) ((-676 . -393) 185252) ((-171 . -926) 185205) ((-30 . -972) T) ((-112 . -856) T) ((-1 . -625) 185187) ((-1018 . -909) 185108) ((-129 . -663) 185090) ((-50 . -632) 185074) ((-706 . -658) 185009) ((-607 . -915) 184922) ((-450 . -102) T) ((-129 . -384) 184904) ((-142 . -319) NIL) ((-884 . -1068) T) ((-845 . -862) 184883) ((-81 . -1236) T) ((-723 . -300) T) ((-40 . -1077) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 184865) ((-171 . -660) 184739) ((-519 . -625) 184721) ((-362 . -148) 184703) ((-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) 184682) ((-1270 . -111) 184503) ((-1249 . -111) 184292) ((-250 . -1274) 184276) ((-576 . -860) T) ((-370 . -23) T) ((-365 . -360) T) ((-326 . -319) 184263) ((-323 . -319) 184204) ((-364 . -23) T) ((-329 . -132) T) ((-356 . -23) T) ((-1023 . -1041) T) ((-31 . -628) 184185) ((-108 . -23) T) ((-666 . -1070) 184169) ((-250 . -616) 184146) ((-343 . -1119) T) ((-666 . -652) 184116) ((-1272 . -38) 184008) ((-1259 . -926) 183987) ((-112 . -1119) T) ((-828 . -1236) T) ((-1054 . -102) T) ((-1259 . -660) 183876) ((-883 . -806) NIL) ((-867 . -660) 183850) ((-883 . -803) NIL) ((-828 . -899) NIL) ((-883 . -738) T) ((-1106 . -526) 183723) ((-794 . -526) 183670) ((-792 . -526) 183622) ((-583 . -660) 183609) ((-828 . -1057) 183437) ((-466 . -526) 183380) ((-400 . -401) T) ((-1270 . -628) 183193) ((-1249 . -628) 182941) ((-60 . -1236) T) ((-633 . -862) 182920) ((-512 . -673) T) ((-1165 . -995) 182889) ((-1043 . -658) 182826) ((-1022 . -464) T) ((-711 . -860) T) ((-522 . -804) T) ((-486 . -1075) 182661) ((-512 . -113) T) ((-354 . -1119) T) ((-323 . -1171) NIL) ((-299 . -132) T) ((-406 . -1119) T) ((-882 . -1077) T) ((-706 . -381) 182628) ((-365 . -658) 182558) ((-225 . -632) 182535) ((-337 . -296) 182487) ((-486 . -111) 182308) ((-1270 . -1068) T) ((-1249 . -1068) T) ((-828 . -388) 182292) ((-171 . -738) T) ((-666 . -102) T) ((-1270 . -248) 182271) ((-1270 . -238) 182223) ((-1249 . -238) 182128) ((-1249 . -248) 182107) ((-1022 . -414) NIL) ((-682 . -651) 182055) ((-326 . -38) 181965) ((-323 . -38) 181894) ((-69 . -625) 181876) ((-329 . -505) 181842) ((-48 . -658) 181792) ((-1208 . -298) 181771) ((-1244 . -862) T) ((-1132 . -1131) 181749) ((-83 . -1236) T) ((-61 . -625) 181731) ((-491 . -298) 181710) ((-1301 . -1057) 181687) ((-1183 . -1119) T) ((-1132 . -23) 181539) ((-828 . -915) 181475) ((-1259 . -738) T) ((-1121 . -1236) T) ((-486 . -628) 181301) ((-362 . -237) T) ((-1106 . -300) 181232) ((-983 . -1119) T) ((-906 . -102) T) ((-794 . -300) 181143) ((-337 . -19) 181127) ((-59 . -298) 181104) ((-792 . -300) 181035) ((-867 . -738) T) ((-118 . -860) NIL) ((-528 . -298) 181012) ((-337 . -616) 180989) ((-508 . -298) 180966) ((-466 . -300) 180897) ((-1054 . -319) 180748) ((-888 . -502) 180729) ((-888 . -625) 180695) ((-693 . -502) 180676) ((-583 . -738) T) ((-688 . -502) 180657) ((-693 . -625) 180607) ((-688 . -625) 180573) ((-674 . -625) 180555) ((-490 . -502) 180536) ((-490 . -625) 180502) ((-250 . -626) 180463) ((-250 . -502) 180440) ((-139 . -502) 180421) ((-138 . -502) 180402) ((-134 . -502) 180383) ((-250 . -625) 180275) ((-215 . -102) T) ((-139 . -625) 180241) ((-138 . -625) 180207) ((-134 . -625) 180173) ((-1166 . -34) T) ((-960 . -1236) T) ((-354 . -729) 180118) ((-682 . -25) T) ((-682 . -21) T) ((-1195 . -628) 180099) ((-486 . -1068) T) ((-647 . -429) 180064) ((-619 . -429) 180029) ((-1139 . -1171) T) ((-724 . -1070) 179852) ((-593 . -300) T) ((-530 . -300) T) ((-1271 . -317) 179831) ((-486 . -238) 179783) ((-486 . -248) 179762) ((-1250 . -317) 179741) ((-724 . -652) 179570) ((-1250 . -1041) NIL) ((-1099 . -132) T) ((-884 . -807) 179549) ((-145 . -102) T) ((-40 . -1119) T) ((-884 . -804) 179528) ((-656 . -1029) 179512) ((-592 . -1077) T) ((-576 . -1077) T) ((-507 . -1077) T) ((-419 . -464) T) ((-370 . -132) T) ((-326 . -412) 179496) ((-323 . -412) 179457) ((-364 . -132) T) ((-356 . -132) T) ((-1200 . -1119) T) ((-1139 . -38) 179444) ((-1113 . -625) 179411) ((-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) 179395) ((-543 . -862) T) ((-512 . -862) T) ((-366 . -1075) 179347) ((-363 . -1075) 179299) ((-355 . -1075) 179251) ((-258 . -1236) T) ((-257 . -1236) T) ((-273 . -1075) 179094) ((-253 . -1075) 178937) ((-676 . -111) 178916) ((-829 . -1240) 178895) ((-559 . -856) T) ((-326 . -917) 178861) ((-366 . -111) 178799) ((-363 . -111) 178737) ((-355 . -111) 178675) ((-273 . -111) 178504) ((-253 . -111) 178333) ((-323 . -917) NIL) ((-635 . -423) 178317) ((-44 . -21) T) ((-44 . -25) T) ((-827 . -651) 178223) ((-829 . -568) 178202) ((-258 . -1057) 178029) ((-257 . -1057) 177856) ((-127 . -120) 177840) ((-927 . -1075) 177805) ((-724 . -102) T) ((-711 . -1077) T) ((-609 . -628) 177786) ((-597 . -628) 177767) ((-548 . -630) 177670) ((-354 . -174) T) ((-88 . -625) 177652) ((-153 . -21) T) ((-153 . -25) T) ((-927 . -111) 177608) ((-40 . -729) 177553) ((-882 . -1119) T) ((-676 . -628) 177530) ((-657 . -628) 177511) ((-366 . -628) 177448) ((-363 . -628) 177385) ((-559 . -1119) T) ((-355 . -628) 177322) ((-337 . -626) 177283) ((-337 . -625) 177195) ((-273 . -628) 176948) ((-253 . -628) 176733) ((-1249 . -804) 176686) ((-1249 . -807) 176639) ((-258 . -388) 176608) ((-257 . -388) 176577) ((-666 . -38) 176547) ((-620 . -34) T) ((-494 . -1131) 176525) ((-487 . -34) T) ((-1132 . -132) 176396) ((-981 . -25) 176207) ((-927 . -628) 176157) ((-886 . -625) 176139) ((-981 . -21) 176094) ((-827 . -25) 175927) ((-827 . -21) 175838) ((-1242 . -379) T) ((-635 . -1077) T) ((-1197 . -568) 175817) ((-1191 . -47) 175794) ((-366 . -1068) T) ((-363 . -1068) T) ((-494 . -23) 175646) ((-355 . -1068) T) ((-273 . -1068) T) ((-253 . -1068) T) ((-1144 . -47) 175618) ((-118 . -1077) T) ((-1053 . -660) 175592) ((-975 . -34) T) ((-366 . -238) 175571) ((-366 . -248) T) ((-363 . -238) 175550) ((-363 . -248) T) ((-355 . -238) 175529) ((-355 . -248) T) ((-273 . -336) 175501) ((-253 . -336) 175458) ((-273 . -238) 175437) ((-1176 . -152) 175421) ((-258 . -915) 175353) ((-257 . -915) 175285) ((-1161 . -909) 175206) ((-1101 . -862) T) ((-426 . -1131) T) ((-1073 . -23) T) ((-1043 . -860) T) ((-927 . -1068) T) ((-332 . -660) 175188) ((-713 . -237) T) ((-682 . -234) 175133) ((-1230 . -1021) 175099) ((-1192 . -937) 175078) ((-1186 . -937) 175057) ((-1186 . -832) NIL) ((-1018 . -1070) 174953) ((-984 . -1236) T) ((-927 . -248) T) ((-829 . -374) 174932) ((-396 . -23) T) ((-128 . -1119) 174910) ((-122 . -1119) 174888) ((-927 . -238) T) ((-129 . -34) T) ((-390 . -660) 174853) ((-1018 . -652) 174801) ((-882 . -729) 174788) ((-1315 . -658) 174760) ((-1065 . -152) 174725) ((-1012 . -1236) T) ((-40 . -174) T) ((-706 . -423) 174707) ((-724 . -319) 174694) ((-848 . -660) 174654) ((-839 . -660) 174628) ((-329 . -25) T) ((-329 . -21) T) ((-670 . -296) 174607) ((-592 . -1119) T) ((-576 . -1119) T) ((-507 . -1119) T) ((-250 . -298) 174584) ((-1191 . -1236) T) ((-1144 . -1236) T) ((-323 . -272) 174545) ((-323 . -232) 174506) ((-1191 . -899) NIL) ((-55 . -1119) T) ((-1144 . -899) 174365) ((-130 . -862) T) ((-1191 . -1057) 174245) ((-1144 . -1057) 174128) ((-185 . -625) 174110) ((-866 . -1057) 174006) ((-794 . -296) 173933) ((-829 . -1131) T) ((-1053 . -738) T) ((-1065 . -995) 173862) ((-614 . -663) 173846) ((-1022 . -909) 173753) ((-1018 . -102) T) ((-829 . -23) T) ((-724 . -1171) 173731) ((-706 . -1077) T) ((-614 . -384) 173715) ((-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) 173697) ((-1191 . -388) 173681) ((-1144 . -388) 173665) ((-1043 . -423) 173627) ((-142 . -231) 173609) ((-390 . -806) T) ((-390 . -803) T) ((-882 . -174) T) ((-390 . -738) T) ((-723 . -625) 173591) ((-724 . -38) 173420) ((-1286 . -1284) 173404) ((-362 . -414) T) ((-1286 . -1119) 173354) ((-1209 . -1119) T) ((-592 . -729) 173341) ((-576 . -729) 173328) ((-507 . -729) 173293) ((-1272 . -658) 173183) ((-326 . -641) 173162) ((-848 . -738) T) ((-839 . -738) T) ((-656 . -1236) T) ((-1099 . -651) 173110) ((-1191 . -915) 173053) ((-1144 . -915) 173037) ((-827 . -234) 172928) ((-674 . -1075) 172912) ((-108 . -651) 172894) ((-494 . -132) 172765) ((-1197 . -1131) T) ((-969 . -47) 172734) ((-635 . -1119) T) ((-674 . -111) 172713) ((-503 . -625) 172679) ((-337 . -298) 172656) ((-493 . -47) 172613) ((-1197 . -23) T) ((-118 . -1119) T) ((-103 . -102) 172591) ((-1298 . -1131) T) ((-560 . -862) T) ((-227 . -1236) T) ((-1073 . -132) T) ((-1043 . -1077) T) ((-1298 . -23) T) ((-831 . -1057) 172575) ((-1216 . -625) 172557) ((-1022 . -736) 172529) ((-1139 . -840) T) ((-711 . -729) 172494) ((-598 . -625) 172476) ((-398 . -1057) 172460) ((-365 . -1077) T) ((-396 . -132) T) ((-334 . -1057) 172444) ((-1124 . -1119) T) ((-1099 . -21) T) ((-1099 . -25) T) ((-227 . -899) 172426) ((-1023 . -937) T) ((-91 . -34) T) ((-1023 . -832) T) ((-931 . -937) T) ((-1018 . -319) 172391) ((-888 . -628) 172372) ((-499 . -1240) T) ((-726 . -660) 172332) ((-693 . -628) 172313) ((-688 . -628) 172294) ((-219 . -1240) T) ((-419 . -909) 172215) ((-227 . -1057) 172175) ((-40 . -300) T) ((-499 . -568) T) ((-490 . -628) 172156) ((-370 . -25) T) ((-326 . -658) 171811) ((-323 . -658) 171725) ((-370 . -21) T) ((-364 . -25) T) ((-364 . -21) T) ((-219 . -568) T) ((-356 . -25) T) ((-356 . -21) T) ((-329 . -234) 171671) ((-250 . -628) 171648) ((-139 . -628) 171629) ((-138 . -628) 171610) ((-134 . -628) 171591) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1077) T) ((-592 . -174) T) ((-576 . -174) T) ((-507 . -174) T) ((-1081 . -1236) T) ((-969 . -1236) T) ((-670 . -625) 171573) ((-493 . -1236) T) ((-749 . -748) 171557) ((-347 . -625) 171539) ((-68 . -394) T) ((-68 . -407) T) ((-1121 . -107) 171523) ((-1081 . -899) 171505) ((-969 . -899) 171430) ((-665 . -1131) T) ((-635 . -729) 171417) ((-493 . -899) NIL) ((-1165 . -102) T) ((-1113 . -630) 171401) ((-1081 . -1057) 171383) ((-97 . -625) 171365) ((-489 . -148) T) ((-969 . -1057) 171245) ((-118 . -729) 171190) ((-724 . -917) 171097) ((-665 . -23) T) ((-493 . -1057) 170973) ((-1106 . -626) NIL) ((-1106 . -625) 170955) ((-794 . -626) NIL) ((-794 . -625) 170916) ((-792 . -626) 170550) ((-792 . -625) 170464) ((-1132 . -651) 170370) ((-473 . -625) 170352) ((-466 . -625) 170334) ((-466 . -626) 170195) ((-1054 . -231) 170141) ((-884 . -926) 170120) ((-127 . -34) T) ((-829 . -132) T) ((-661 . -625) 170102) ((-590 . -102) T) ((-366 . -1305) 170086) ((-363 . -1305) 170070) ((-355 . -1305) 170054) ((-128 . -526) 169987) ((-122 . -526) 169920) ((-523 . -804) T) ((-523 . -807) T) ((-522 . -806) T) ((-103 . -319) 169858) ((-224 . -102) 169836) ((-711 . -174) T) ((-706 . -1119) T) ((-884 . -660) 169752) ((-65 . -395) T) ((-284 . -625) 169734) ((-65 . -407) T) ((-969 . -388) 169718) ((-882 . -300) T) ((-50 . -625) 169700) ((-1018 . -38) 169648) ((-1139 . -658) 169620) ((-593 . -625) 169602) ((-493 . -388) 169586) ((-593 . -626) 169568) ((-530 . -625) 169550) ((-927 . -1305) 169537) ((-883 . -1236) T) ((-713 . -464) T) ((-507 . -526) 169503) ((-499 . -374) T) ((-366 . -379) 169482) ((-363 . -379) 169461) ((-355 . -379) 169440) ((-726 . -738) T) ((-219 . -374) T) ((-117 . -464) T) ((-1309 . -1300) 169424) ((-883 . -897) 169401) ((-883 . -899) NIL) ((-981 . -862) 169300) ((-827 . -862) 169251) ((-1243 . -102) T) ((-666 . -668) 169235) ((-1222 . -34) T) ((-173 . -625) 169217) ((-1132 . -25) 169050) ((-1132 . -21) 168961) ((-883 . -1057) 168938) ((-969 . -915) 168919) ((-1259 . -47) 168896) ((-927 . -379) T) ((-59 . -663) 168880) ((-528 . -663) 168864) ((-493 . -915) 168841) ((-71 . -453) T) ((-71 . -407) T) ((-508 . -663) 168825) ((-59 . -384) 168809) ((-635 . -174) T) ((-528 . -384) 168793) ((-508 . -384) 168777) ((-839 . -720) 168761) ((-1191 . -317) 168740) ((-1197 . -132) T) ((-1161 . -1070) 168724) ((-118 . -174) T) ((-1161 . -652) 168656) ((-1165 . -319) 168594) ((-171 . -1236) T) ((-1298 . -132) T) ((-878 . -1070) 168564) ((-647 . -756) 168548) ((-619 . -756) 168532) ((-1271 . -937) 168511) ((-1250 . -937) 168490) ((-1250 . -832) NIL) ((-878 . -652) 168460) ((-706 . -729) 168410) ((-1249 . -926) 168363) ((-1043 . -1119) T) ((-883 . -388) 168340) ((-883 . -349) 168317) ((-922 . -1131) T) ((-171 . -897) 168301) ((-171 . -899) 168226) ((-1286 . -526) 168159) ((-1270 . -660) 168056) ((-1099 . -234) 167929) ((-499 . -1131) T) ((-365 . -1119) T) ((-219 . -1131) T) ((-76 . -453) T) ((-76 . -407) T) ((-171 . -1057) 167825) ((-304 . -909) 167782) ((-329 . -862) T) ((-1249 . -660) 167590) ((-884 . -806) 167569) ((-884 . -803) 167548) ((-884 . -738) T) ((-499 . -23) T) ((-370 . -234) 167521) ((-364 . -234) 167494) ((-356 . -234) 167467) ((-225 . -625) 167449) ((-176 . -464) T) ((-224 . -319) 167387) ((-86 . -453) T) ((-86 . -407) T) ((-108 . -234) 167374) ((-219 . -23) T) ((-1310 . -1303) 167353) ((-689 . -1057) 167337) ((-592 . -300) T) ((-576 . -300) T) ((-507 . -300) T) ((-137 . -482) 167292) ((-1259 . -1236) T) ((-666 . -658) 167251) ((-48 . -1119) T) ((-724 . -272) 167235) 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((-1270 . -738) T) ((-1249 . -738) T) ((-48 . -729) 165705) ((-227 . -1041) T) ((-1272 . -423) 165671) ((-362 . -1293) 165648) ((-1259 . -915) 165591) ((-730 . -738) T) ((-343 . -625) 165573) ((-1230 . -628) 165455) ((-1132 . -234) 165346) ((-112 . -625) 165328) ((-112 . -626) 165310) ((-730 . -485) T) ((-723 . -628) 165260) ((-1309 . -1070) 165244) ((-494 . -25) 165077) ((-128 . -501) 165061) ((-122 . -501) 165045) ((-494 . -21) 164956) ((-1309 . -652) 164926) ((-635 . -300) T) ((-598 . -1075) 164901) ((-449 . -1119) T) ((-1081 . -317) T) ((-118 . -300) T) ((-1123 . -102) T) ((-1022 . -102) T) ((-598 . -111) 164869) ((-1161 . -319) 164807) ((-1230 . -1068) T) ((-1081 . -1041) T) ((-66 . -1236) T) ((-1073 . -25) T) ((-1073 . -21) T) ((-723 . -1068) T) ((-396 . -21) T) ((-396 . -25) T) ((-706 . -526) NIL) ((-1043 . -174) T) ((-723 . -248) T) ((-1081 . -557) T) ((-724 . -658) 164717) ((-518 . -102) T) ((-514 . -102) T) ((-365 . -174) T) ((-354 . -625) 164699) ((-419 . -1070) 164651) 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. -660) 162929) ((-355 . -660) 162881) ((-273 . -660) 162770) ((-253 . -660) 162659) ((-1177 . -862) T) ((-1107 . -1057) 162643) ((-473 . -111) 162604) ((-466 . -111) 162433) ((-1095 . -1057) 162410) ((-1019 . -34) T) ((-983 . -625) 162392) ((-975 . -1236) T) ((-127 . -1029) 162376) ((-980 . -1131) T) ((-883 . -1041) NIL) ((-747 . -1131) T) ((-727 . -1131) T) ((-670 . -628) 162294) ((-1286 . -501) 162278) ((-1161 . -38) 162238) ((-980 . -23) T) ((-927 . -660) 162203) ((-877 . -1119) T) ((-855 . -102) T) ((-829 . -21) T) ((-647 . -1070) 162187) ((-619 . -1070) 162171) ((-829 . -25) T) ((-747 . -23) T) ((-727 . -23) T) ((-647 . -652) 162155) ((-110 . -673) T) ((-619 . -652) 162139) ((-593 . -1075) 162104) ((-530 . -1075) 162049) ((-229 . -57) 162007) ((-465 . -23) T) ((-419 . -102) T) ((-270 . -102) T) ((-110 . -113) T) ((-706 . -300) T) ((-878 . -38) 161977) ((-593 . -111) 161933) ((-530 . -111) 161862) ((-1106 . -628) 161598) ((-430 . -1131) T) ((-326 . -1077) 161488) ((-323 . -1077) 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T) ((-1230 . -660) 152232) ((-1022 . -658) 152162) ((-980 . -21) T) ((-980 . -25) T) ((-747 . -21) T) ((-747 . -25) T) ((-727 . -21) T) ((-727 . -25) T) ((-723 . -660) 152127) ((-465 . -21) T) ((-465 . -25) T) ((-350 . -102) T) ((-176 . -102) T) ((-1018 . -1077) T) ((-882 . -1068) T) ((-786 . -102) T) ((-1271 . -374) 152106) ((-1270 . -915) 152012) ((-1250 . -374) 151991) ((-1249 . -915) 151842) ((-1043 . -625) 151824) ((-419 . -840) 151777) ((-1193 . -505) 151743) ((-171 . -937) 151674) ((-1192 . -505) 151640) ((-1186 . -505) 151606) ((-724 . -1119) T) ((-1145 . -505) 151572) ((-592 . -1075) 151559) ((-576 . -1075) 151546) ((-507 . -1075) 151511) ((-326 . -300) 151490) ((-323 . -300) T) ((-365 . -625) 151472) ((-430 . -25) T) ((-430 . -21) T) ((-99 . -296) 151451) ((-592 . -111) 151436) ((-576 . -111) 151421) ((-507 . -111) 151377) ((-1195 . -899) 151344) ((-918 . -501) 151328) ((-48 . -625) 151310) ((-48 . -626) 151255) ((-245 . -132) 151126) ((-1309 . -658) 151085) ((-1259 . -937) 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-1075) 146649) ((-1311 . -102) T) ((-1278 . -132) T) ((-1271 . -132) T) ((-1250 . -132) T) ((-1193 . -25) T) ((-1161 . -423) 146633) ((-647 . -378) 146565) ((-619 . -378) 146497) ((-1176 . -1168) 146481) ((-103 . -1119) 146459) ((-1193 . -21) T) ((-1192 . -21) T) ((-877 . -625) 146441) ((-1018 . -729) 146389) ((-225 . -660) 146356) ((-706 . -111) 146290) ((-50 . -738) T) ((-1192 . -25) T) ((-362 . -360) T) ((-1186 . -21) T) ((-1099 . -464) 146241) ((-1186 . -25) T) ((-724 . -526) 146188) ((-593 . -738) T) ((-530 . -738) T) ((-1145 . -21) T) ((-1145 . -25) T) ((-608 . -132) T) ((-607 . -132) T) ((-304 . -658) 145923) ((-494 . -237) 145820) ((-370 . -464) T) ((-364 . -464) T) ((-356 . -464) T) ((-486 . -317) 145799) ((-1244 . -102) T) ((-323 . -296) 145734) ((-108 . -464) T) ((-79 . -453) T) ((-79 . -407) T) ((-489 . -102) T) ((-703 . -628) 145718) ((-1315 . -625) 145700) ((-1315 . -626) 145682) ((-1099 . -414) 145661) ((-1054 . -501) 145592) ((-137 . -296) 145569) ((-576 . -807) T) 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143169) ((-354 . -660) 143114) ((-1299 . -625) 143076) ((-633 . -38) 143060) ((-1299 . -626) 143021) ((-1193 . -234) 142974) ((-1096 . -625) 142956) ((-1043 . -248) T) ((-365 . -1068) T) ((-827 . -1293) 142926) ((-258 . -23) T) ((-257 . -23) T) ((-1006 . -625) 142908) ((-1192 . -234) 142854) ((-1186 . -234) 142671) ((-749 . -626) 142632) ((-749 . -625) 142614) ((-1178 . -152) 142561) ((-811 . -862) 142540) ((-1023 . -25) T) ((-1018 . -526) 142452) ((-365 . -238) T) ((-365 . -248) T) ((-400 . -628) 142433) ((-927 . -317) T) ((-142 . -625) 142415) ((-142 . -626) 142374) ((-329 . -909) 142278) ((-1023 . -21) T) ((-990 . -25) T) ((-931 . -21) T) ((-931 . -25) T) ((-439 . -21) T) ((-439 . -25) T) ((-855 . -423) 142262) ((-48 . -1068) T) ((-1308 . -1300) 142246) ((-1306 . -1300) 142230) ((-1054 . -616) 142205) ((-326 . -626) 142066) ((-326 . -625) 142048) ((-323 . -626) NIL) ((-323 . -625) 142030) ((-48 . -248) T) ((-48 . -238) T) ((-666 . -296) 141991) ((-562 . -240) 141941) ((-140 . -625) 141908) ((-137 . -625) 141890) ((-115 . -625) 141872) ((-489 . -38) 141837) ((-1310 . -1307) 141816) ((-1301 . -132) T) ((-1309 . -1077) T) ((-1101 . -102) T) ((-88 . -1236) T) ((-512 . -319) NIL) ((-1019 . -107) 141800) ((-902 . -1119) T) ((-898 . -1119) T) ((-1286 . -663) 141784) ((-1286 . -384) 141768) ((-337 . -1236) T) ((-605 . -862) T) ((-1161 . -1119) T) ((-1161 . -1072) 141708) ((-103 . -526) 141641) ((-944 . -625) 141623) ((-354 . -738) T) ((-30 . -625) 141605) ((-878 . -1119) T) ((-855 . -1077) 141584) ((-40 . -660) 141491) ((-227 . -1240) T) ((-419 . -1077) T) ((-1177 . -152) 141473) ((-1018 . -300) 141424) ((-629 . -1119) T) ((-227 . -568) T) ((-329 . -1267) 141408) ((-329 . -1264) 141378) ((-713 . -658) 141350) ((-1208 . -1212) 141329) ((-1094 . -625) 141311) ((-1208 . -107) 141261) ((-659 . -152) 141245) ((-644 . -152) 141191) ((-117 . -658) 141163) ((-491 . -1212) 141142) ((-499 . -148) T) ((-499 . -146) NIL) ((-1139 . -626) 141057) ((-450 . -625) 141039) ((-219 . -148) T) ((-219 . -146) NIL) ((-1139 . -625) 141021) ((-130 . -102) T) ((-52 . -102) T) ((-1250 . -651) 140973) ((-491 . -107) 140923) ((-1012 . -23) T) ((-1310 . -38) 140893) ((-1191 . -1131) T) ((-1144 . -1131) T) ((-1081 . -1240) T) ((-245 . -234) 140784) ((-321 . -102) T) ((-866 . -1131) T) ((-969 . -1240) 140763) ((-493 . -1240) 140742) ((-1081 . -568) T) ((-969 . -568) 140673) ((-1191 . -23) T) ((-1170 . -1102) T) ((-1144 . -23) T) ((-866 . -23) T) ((-493 . -568) 140604) ((-1161 . -729) 140536) ((-682 . -1070) 140520) ((-1165 . -526) 140453) ((-682 . -652) 140437) ((-1054 . -626) NIL) ((-1054 . -625) 140419) ((-96 . -1102) T) ((-1315 . -1075) 140406) ((-878 . -729) 140376) ((-1315 . -111) 140361) ((-1230 . -47) 140330) ((-1186 . -862) NIL) ((-258 . -132) T) ((-257 . -132) T) ((-1123 . -1119) T) ((-1022 . -1119) T) ((-62 . -625) 140312) ((-1099 . -909) 140181) ((-1043 . -804) T) ((-1043 . -807) T) ((-1278 . -25) T) ((-1278 . -21) T) ((-1271 . -21) T) ((-1271 . -25) T) ((-882 . -660) 140168) ((-1250 . -21) T) ((-1250 . -25) T) ((-1046 . -152) 140152) ((-1023 . -234) 140139) ((-884 . -832) 140118) ((-884 . -937) T) ((-724 . -296) 140045) ((-608 . -21) T) ((-350 . -658) 140004) ((-108 . -909) NIL) ((-608 . -25) T) ((-607 . -21) T) ((-176 . -658) 139921) ((-40 . -738) T) ((-224 . -526) 139854) ((-607 . -25) T) ((-488 . -152) 139838) ((-475 . -152) 139822) ((-938 . -806) T) ((-938 . -738) T) ((-783 . -805) T) ((-783 . -806) T) ((-518 . -1119) T) ((-514 . -1119) T) ((-783 . -738) T) ((-227 . -374) T) ((-1308 . -1070) 139806) ((-1306 . -1070) 139790) ((-1308 . -652) 139760) ((-1176 . -1119) 139738) ((-883 . -1240) T) ((-1306 . -652) 139708) ((-666 . -625) 139690) ((-883 . -568) T) ((-706 . -379) NIL) ((-44 . -1070) 139674) ((-1315 . -628) 139656) ((-1309 . -1119) T) ((-682 . -102) T) ((-370 . -1293) 139640) ((-364 . -1293) 139624) ((-44 . -652) 139608) ((-356 . -1293) 139592) ((-560 . -102) T) ((-1230 . -1236) T) ((-532 . -862) 139571) ((-499 . -237) T) ((-219 . -237) T) 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((-1012 . -132) T) ((-44 . -102) T) ((-245 . -862) 138060) ((-1259 . -1240) 138039) ((-103 . -501) 138023) ((-1309 . -729) 137993) ((-1106 . -47) 137954) ((-1081 . -1131) T) ((-969 . -1131) T) ((-128 . -34) T) ((-122 . -34) T) ((-794 . -47) 137931) ((-792 . -47) 137903) ((-1259 . -568) 137814) ((-365 . -379) T) ((-493 . -1131) T) ((-1191 . -132) T) ((-1144 . -132) T) ((-466 . -47) 137793) ((-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) 137726) ((-604 . -1102) T) ((-598 . -1057) 137710) ((-1272 . -628) 137584) ((-493 . -23) T) ((-362 . -1077) T) ((-1230 . -915) 137565) ((-682 . -319) 137503) ((-1132 . -1293) 137473) ((-711 . -660) 137438) ((-1023 . -862) T) ((-1022 . -174) T) ((-980 . -146) 137417) ((-647 . -1119) T) ((-619 . -1119) T) ((-980 . -148) 137396) ((-747 . -148) 137375) ((-747 . -146) 137354) ((-670 . -1236) T) ((-990 . -862) T) ((-1278 . -234) 137307) ((-1271 . -234) 137253) ((-1250 . -234) 137070) ((-845 . -658) 136987) ((-486 . -937) 136966) ((-329 . -1070) 136801) ((-326 . -1075) 136711) ((-323 . -1075) 136640) ((-1018 . -296) 136598) ((-419 . -729) 136550) ((-329 . -652) 136391) ((-607 . -234) 136344) ((-713 . -860) T) ((-1272 . -1068) T) ((-326 . -111) 136240) ((-323 . -111) 136153) ((-981 . -102) T) ((-827 . -102) 135905) ((-724 . -626) NIL) ((-724 . -625) 135887) ((-1272 . -336) 135831) ((-670 . -1057) 135727) ((-1106 . -1236) T) ((-1054 . -298) 135702) ((-592 . -738) T) ((-576 . -806) T) ((-171 . -374) 135653) ((-576 . -803) T) ((-576 . -738) T) ((-507 . -738) T) ((-794 . -1236) T) ((-792 . -1236) T) ((-1165 . -501) 135637) ((-466 . -1236) T) ((-1106 . -899) NIL) ((-883 . -1131) T) ((-118 . -926) NIL) ((-1308 . -1307) 135613) ((-1306 . -1307) 135592) ((-794 . -899) NIL) ((-792 . -899) 135451) ((-1301 . -25) T) ((-1301 . -21) T) ((-1233 . -102) 135429) ((-1125 . -407) T) ((-635 . -660) 135416) ((-466 . -899) NIL) ((-687 . -102) 135394) ((-1106 . -1057) 135221) ((-883 . -23) T) ((-794 . -1057) 135080) ((-792 . -1057) 134937) ((-118 . -660) 134882) ((-466 . -1057) 134758) ((-326 . -628) 134322) ((-323 . -628) 134205) ((-402 . -658) 134174) ((-661 . -1057) 134158) ((-639 . -102) T) ((-593 . -1236) T) ((-530 . -1236) T) ((-224 . -501) 134142) ((-1286 . -34) T) ((-633 . -658) 134101) ((-299 . -1070) 134088) ((-137 . -628) 134072) ((-299 . -652) 134059) ((-647 . -729) 134043) ((-619 . -729) 134027) ((-682 . -38) 133987) ((-329 . -102) T) ((-85 . -625) 133969) ((-50 . -1057) 133953) ((-1139 . -1075) 133940) ((-1106 . -388) 133924) ((-794 . -388) 133908) ((-711 . -738) T) ((-711 . -806) T) ((-711 . -803) T) ((-593 . -1057) 133895) ((-530 . -1057) 133872) ((-60 . -57) 133834) ((-334 . -132) T) ((-326 . -1068) 133724) ((-323 . -1068) T) ((-171 . -1131) T) ((-792 . -388) 133708) ((-45 . -152) 133658) ((-1023 . -1011) 133640) ((-466 . -388) 133624) ((-419 . -174) T) ((-326 . -248) 133603) ((-323 . -248) T) ((-323 . -238) NIL) ((-304 . -1119) 133385) ((-227 . -132) T) ((-1139 . -111) 133370) ((-171 . -23) T) ((-811 . -148) 133349) ((-811 . -146) 133328) ((-258 . -651) 133234) ((-257 . -651) 133140) ((-329 . -294) 133106) ((-1176 . -526) 133039) ((-489 . -658) 132989) ((-494 . -909) 132856) ((-1152 . -1119) T) ((-227 . -1079) T) ((-827 . -319) 132794) ((-1106 . -915) 132729) ((-794 . -915) 132672) ((-792 . -915) 132656) ((-1308 . -38) 132626) ((-1306 . -38) 132596) ((-1259 . -1131) T) ((-867 . -1131) T) ((-466 . -915) 132573) ((-870 . -1119) T) ((-1259 . -23) T) ((-1139 . -628) 132545) ((-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) 132490) ((-118 . -806) NIL) ((-118 . -803) NIL) ((-118 . -738) T) ((-1065 . -526) 132391) ((-706 . -926) NIL) ((-583 . -23) T) ((-493 . -132) T) ((-430 . -237) 132342) ((-687 . -319) 132280) ((-647 . -773) T) ((-619 . -773) T) ((-1250 . -862) NIL) ((-1099 . -1070) 132190) ((-1022 . -300) T) ((-706 . -660) 132140) ((-258 . -25) T) ((-362 . -1119) T) ((-258 . -21) T) ((-257 . -25) T) ((-257 . -21) T) ((-153 . -38) 132124) ((-2 . -102) T) ((-927 . -937) T) ((-1099 . -652) 131992) ((-494 . -1293) 131962) ((-1139 . -1068) T) ((-723 . -317) T) ((-370 . -1070) 131914) ((-364 . -1070) 131866) ((-356 . -1070) 131818) ((-370 . -652) 131770) ((-225 . -1057) 131747) ((-364 . -652) 131699) ((-108 . -1070) 131649) ((-356 . -652) 131601) ((-304 . -729) 131543) ((-713 . -1077) T) ((-499 . -464) T) ((-419 . -526) 131455) ((-108 . -652) 131405) ((-219 . -464) T) ((-1139 . -238) T) ((-305 . -152) 131355) ((-1018 . -626) 131316) ((-1018 . -625) 131298) ((-1008 . -625) 131280) ((-117 . -1077) T) ((-666 . -1075) 131264) ((-227 . -505) T) ((-411 . -625) 131246) ((-411 . -626) 131223) ((-1073 . -1293) 131193) ((-666 . -111) 131172) ((-682 . -917) 131095) ((-1161 . -501) 131079) ((-1310 . -658) 131038) ((-392 . -658) 131007) ((-63 . -453) T) ((-63 . -407) T) ((-1178 . -102) T) ((-883 . -132) T) ((-496 . -102) 130985) ((-1315 . -379) T) ((-1099 . -102) T) ((-1080 . -102) T) ((-362 . -729) 130930) ((-743 . -148) 130909) ((-743 . -146) 130888) ((-666 . -628) 130806) ((-1043 . -660) 130743) ((-535 . -1119) 130721) ((-370 . -102) T) ((-364 . -102) T) ((-356 . -102) T) ((-108 . -102) T) ((-516 . -1119) T) ((-365 . -660) 130666) ((-1191 . -651) 130614) ((-1144 . -651) 130562) ((-396 . -521) 130541) ((-845 . -860) 130520) ((-390 . -1240) T) ((-706 . -738) T) ((-1250 . -1011) 130472) ((-350 . -1077) T) ((-112 . -1236) T) ((-176 . -1077) T) ((-103 . -625) 130404) ((-1193 . -146) 130383) ((-1193 . -148) 130362) ((-390 . -568) T) ((-1192 . -148) 130341) ((-1192 . -146) 130320) ((-1186 . -146) 130227) ((-419 . -300) T) ((-1186 . -148) 130134) ((-1145 . -148) 130113) ((-1145 . -146) 130092) ((-329 . -38) 129933) ((-171 . -132) T) ((-323 . -807) NIL) ((-323 . -804) NIL) ((-666 . -1068) T) ((-48 . -660) 129883) ((-1132 . -1070) 129784) 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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) 128378) ((-365 . -738) T) ((-682 . -272) 128362) ((-682 . -232) 128346) ((-593 . -317) T) ((-530 . -317) T) ((-304 . -526) 128295) ((-108 . -319) NIL) ((-72 . -407) T) ((-1132 . -102) 128047) ((-845 . -423) 128031) ((-1139 . -807) T) ((-1139 . -804) T) ((-713 . -1119) T) ((-590 . -625) 128013) ((-390 . -374) T) ((-171 . -505) 127991) ((-224 . -625) 127923) ((-135 . -1119) T) ((-117 . -1119) T) ((-983 . -1236) T) ((-48 . -738) T) ((-1065 . -501) 127888) ((-142 . -437) 127870) ((-142 . -379) T) ((-1046 . -102) T) ((-524 . -521) 127849) ((-724 . -628) 127605) ((-1193 . -237) 127564) ((-488 . -102) T) ((-475 . -102) T) ((-1192 . -237) 127516) ((-1186 . -237) 127339) ((-1053 . -1131) T) 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-21) T) ((-743 . -464) 121231) ((-1309 . -625) 121213) ((-1298 . -1070) 121183) ((-1073 . -319) 121121) ((-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) 121091) ((-633 . -1119) T) ((-711 . -899) 121073) ((-1286 . -1236) T) ((-229 . -319) 121011) ((-145 . -379) T) ((-1065 . -626) 120953) ((-1065 . -625) 120896) ((-323 . -926) NIL) ((-1244 . -856) T) ((-1132 . -917) 120765) ((-711 . -1057) 120710) ((-723 . -937) T) ((-486 . -1240) 120689) ((-1192 . -464) 120668) ((-1186 . -464) 120647) ((-340 . -102) T) ((-884 . -1131) T) ((-329 . -658) 120529) ((-326 . -660) 120258) ((-323 . -660) 120187) ((-486 . -568) 120138) ((-350 . -526) 120104) ((-562 . -152) 120054) ((-40 . -317) T) ((-855 . -625) 120036) ((-713 . -300) T) ((-884 . -23) T) ((-390 . -505) T) ((-1099 . -272) 120006) ((-1099 . -232) 119976) ((-524 . -102) T) ((-419 . -626) 119783) ((-419 . -625) 119765) ((-270 . -625) 119747) ((-117 . -300) T) ((-1272 . -738) T) ((-635 . -1236) T) ((-1311 . -1119) T) ((-1270 . -374) 119726) ((-1249 . -374) 119705) ((-1299 . -34) T) ((-1244 . -1119) T) ((-118 . -1236) T) ((-108 . -272) 119687) ((-108 . -232) 119669) ((-1197 . -102) T) ((-489 . -1119) T) ((-535 . -501) 119653) ((-749 . -34) T) ((-665 . -1070) 119637) ((-665 . -652) 119607) ((-883 . -234) NIL) ((-142 . -34) T) ((-118 . -897) 119584) ((-118 . -899) NIL) ((-635 . -1057) 119467) ((-1298 . -102) T) ((-1278 . -237) 119426) ((-656 . -862) 119405) ((-1271 . -237) 119357) ((-1250 . -237) 119180) ((-305 . -102) T) ((-724 . -379) 119159) ((-118 . -1057) 119136) ((-402 . -729) 119120) ((-607 . -237) 119079) ((-633 . -729) 119063) ((-1124 . -1236) T) ((-45 . -319) 118867) ((-828 . -146) 118846) ((-828 . -148) 118825) ((-299 . -658) 118797) ((-1309 . -393) 118776) ((-831 . -862) T) ((-1288 . -1119) T) ((-1178 . -231) 118723) ((-398 . -862) 118702) ((-1278 . -35) 118668) ((-1278 . -1224) 118634) ((-1278 . -1221) 118600) ((-1271 . -1221) 118566) ((-527 . -132) T) ((-1271 . -1224) 118532) ((-1250 . -1221) 118498) ((-1250 . -1224) 118464) ((-1278 . -95) 118430) ((-1271 . -95) 118396) ((-430 . -909) 118317) ((-647 . -625) 118286) ((-619 . -625) 118255) ((-227 . -862) T) ((-1271 . -35) 118221) ((-1270 . -1131) T) ((-1250 . -95) 118187) ((-1139 . -660) 118159) ((-1250 . -35) 118125) ((-1249 . -1131) T) ((-605 . -152) 118107) ((-1099 . -360) 118086) ((-176 . -300) T) ((-118 . -388) 118063) ((-118 . -349) 118040) ((-171 . -234) 117965) ((-882 . -317) T) ((-323 . -806) NIL) ((-323 . -803) NIL) ((-326 . -738) 117814) ((-323 . -738) T) ((-486 . -374) 117793) ((-370 . -360) 117772) ((-364 . -360) 117751) ((-356 . -360) 117730) ((-326 . -485) 117709) ((-1270 . -23) T) ((-1249 . -23) T) ((-730 . -1131) T) ((-726 . -132) T) ((-665 . -102) T) ((-489 . -729) 117674) ((-45 . -292) 117624) ((-105 . -1119) T) ((-68 . -625) 117606) ((-989 . -102) T) ((-876 . -102) T) ((-635 . -915) 117565) 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-937) T) ((-499 . -1070) 116584) ((-486 . -1131) T) ((-530 . -937) T) ((-494 . -917) 116453) ((-65 . -625) 116435) ((-219 . -1070) 116385) ((-499 . -652) 116335) ((-370 . -658) 116272) ((-364 . -658) 116209) ((-356 . -658) 116146) ((-644 . -231) 116092) ((-219 . -652) 116042) ((-108 . -658) 115992) ((-486 . -23) T) ((-1139 . -806) T) ((-884 . -132) T) ((-1139 . -803) T) ((-1301 . -1303) 115971) ((-1139 . -738) T) ((-666 . -660) 115945) ((-304 . -625) 115686) ((-1161 . -628) 115604) ((-1054 . -34) T) ((-828 . -237) 115555) ((-592 . -317) T) ((-576 . -317) T) ((-507 . -317) T) ((-1310 . -729) 115525) ((-706 . -388) 115507) ((-706 . -349) 115489) ((-489 . -174) T) ((-392 . -729) 115459) ((-878 . -628) 115394) ((-883 . -862) NIL) ((-576 . -1041) T) ((-507 . -1041) T) ((-1152 . -625) 115376) ((-1132 . -243) 115355) ((-216 . -102) T) ((-1169 . -102) T) ((-71 . -625) 115337) ((-1161 . -1068) T) ((-1197 . -38) 115234) ((-870 . -625) 115216) ((-576 . -557) T) ((-682 . -1077) T) ((-743 . -966) 115169) ((-365 . -1236) T) ((-1161 . -238) 115148) ((-1101 . -1119) T) ((-1053 . -25) T) ((-1053 . -21) T) ((-1022 . -1075) 115093) ((-922 . -102) T) ((-878 . -1068) T) ((-706 . -915) NIL) ((-366 . -339) 115077) ((-366 . -374) T) ((-363 . -339) 115061) ((-363 . -374) T) ((-355 . -339) 115045) ((-355 . -374) T) ((-499 . -102) T) ((-1298 . -38) 115015) ((-558 . -862) T) ((-535 . -699) 114965) ((-219 . -102) T) ((-1043 . -1057) 114845) ((-1022 . -111) 114774) ((-1193 . -992) 114743) ((-1192 . -992) 114705) ((-532 . -152) 114689) ((-1099 . -381) 114668) ((-362 . -625) 114650) ((-332 . -21) T) ((-365 . -1057) 114627) ((-332 . -25) T) ((-1186 . -992) 114596) ((-48 . -1236) T) ((-76 . -625) 114578) ((-1145 . -992) 114545) ((-711 . -317) T) ((-130 . -856) T) ((-927 . -374) T) ((-390 . -25) T) ((-390 . -21) T) ((-927 . -339) 114532) ((-86 . -625) 114514) ((-711 . -1041) T) ((-689 . -862) T) ((-1270 . -132) T) ((-1249 . -132) T) ((-918 . -1029) 114498) ((-848 . -21) T) ((-48 . -1057) 114441) 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-238) 113014) ((-1022 . -248) T) ((-1145 . -909) 112996) ((-118 . -1041) NIL) ((-927 . -1131) T) ((-1271 . -464) 112975) ((-1250 . -464) 112954) ((-535 . -625) 112886) ((-724 . -660) 112775) ((-419 . -1075) 112727) ((-516 . -625) 112709) ((-927 . -23) T) ((-499 . -319) NIL) ((-1309 . -628) 112665) ((-486 . -132) T) ((-219 . -319) NIL) ((-419 . -111) 112603) ((-827 . -1077) 112581) ((-749 . -1117) 112565) ((-1270 . -505) 112531) ((-1249 . -505) 112497) ((-560 . -856) T) ((-142 . -1117) 112479) ((-489 . -300) T) ((-1309 . -1068) T) ((-258 . -237) 112376) ((-257 . -237) 112273) ((-1241 . -102) T) ((-1082 . -102) T) ((-855 . -628) 112141) ((-512 . -526) NIL) ((-494 . -243) 112120) ((-419 . -628) 112018) ((-980 . -1070) 111901) ((-747 . -1070) 111871) ((-980 . -652) 111768) ((-1191 . -146) 111747) ((-747 . -652) 111717) ((-465 . -1070) 111687) ((-1191 . -148) 111666) ((-1144 . -148) 111645) ((-1144 . -146) 111624) ((-647 . -1075) 111608) ((-619 . -1075) 111592) ((-465 . -652) 111562) 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110650) ((-245 . -909) 110517) ((-135 . -625) 110499) ((-117 . -625) 110481) ((-158 . -25) T) ((-1308 . -1119) T) ((-884 . -651) 110429) ((-1306 . -1119) T) ((-980 . -102) T) ((-747 . -102) T) ((-727 . -102) T) ((-465 . -102) T) ((-828 . -464) 110380) ((-44 . -1119) T) ((-1107 . -862) T) ((-1082 . -319) 110231) ((-676 . -132) T) ((-1073 . -658) 110200) ((-682 . -729) 110184) ((-299 . -1077) T) ((-366 . -132) T) ((-363 . -132) T) ((-355 . -132) T) ((-273 . -132) T) ((-253 . -132) T) ((-396 . -658) 110153) ((-430 . -102) T) ((-153 . -1119) T) ((-45 . -231) 110103) ((-1023 . -909) NIL) ((-811 . -1070) 110087) ((-975 . -862) 110066) ((-1018 . -660) 109968) ((-811 . -652) 109952) ((-245 . -1293) 109922) ((-1043 . -317) T) ((-304 . -1075) 109843) ((-927 . -132) T) ((-40 . -937) T) ((-499 . -412) 109825) ((-365 . -317) T) ((-219 . -412) 109807) ((-1099 . -423) 109791) ((-304 . -111) 109707) ((-1202 . -862) T) ((-1201 . -862) T) ((-884 . -25) T) ((-884 . -21) T) ((-1272 . -47) 109651) ((-350 . -625) 109633) ((-1191 . -237) T) ((-227 . -148) T) ((-176 . -625) 109615) ((-786 . -625) 109597) ((-129 . -862) T) ((-620 . -240) 109544) ((-487 . -240) 109494) ((-1308 . -729) 109464) ((-48 . -317) T) ((-1306 . -729) 109434) ((-65 . -628) 109363) ((-981 . -1119) T) ((-827 . -1119) 109115) ((-322 . -102) T) ((-918 . -1236) T) ((-48 . -1041) T) ((-1249 . -651) 109023) ((-701 . -102) 109001) ((-44 . -729) 108985) ((-562 . -102) T) ((-304 . -628) 108916) ((-67 . -394) T) ((-499 . -917) NIL) ((-67 . -407) T) ((-219 . -917) NIL) ((-674 . -23) T) ((-829 . -658) 108852) ((-682 . -773) T) ((-1233 . -1119) 108830) ((-362 . -1075) 108775) ((-687 . -1119) 108753) ((-1081 . -148) T) ((-969 . -148) 108732) ((-969 . -146) 108711) ((-811 . -102) T) ((-153 . -729) 108695) ((-493 . -148) 108674) ((-493 . -146) 108653) ((-362 . -111) 108582) ((-1099 . -1077) T) ((-332 . -862) 108561) ((-1278 . -992) 108530) ((-639 . -1119) T) ((-1271 . -992) 108492) ((-523 . -132) T) ((-519 . -132) T) ((-305 . -231) 108442) ((-370 . -1077) T) ((-364 . -1077) T) ((-356 . -1077) T) ((-304 . -1068) 108384) ((-1250 . -992) 108353) ((-390 . -862) T) ((-108 . -1077) T) ((-1018 . -738) T) ((-882 . -937) T) ((-855 . -807) 108332) ((-855 . -804) 108311) ((-430 . -319) 108250) ((-480 . -102) T) ((-607 . -992) 108219) ((-329 . -1119) T) ((-419 . -807) 108198) ((-419 . -804) 108177) ((-512 . -501) 108159) ((-1272 . -1057) 108125) ((-1270 . -21) T) ((-1270 . -25) T) ((-1249 . -21) T) ((-1249 . -25) T) ((-827 . -729) 108067) ((-362 . -628) 107997) ((-711 . -416) T) ((-1299 . -1236) T) ((-1132 . -423) 107966) ((-618 . -102) T) ((-1096 . -1236) T) ((-1022 . -379) NIL) ((-683 . -102) T) ((-182 . -102) T) ((-162 . -102) T) ((-157 . -102) T) ((-155 . -102) T) ((-103 . -34) T) ((-1197 . -658) 107876) ((-749 . -1236) T) ((-743 . -1070) 107719) ((-44 . -773) T) ((-743 . -652) 107568) ((-605 . -102) T) ((-665 . -668) 107552) ((-77 . -408) T) ((-77 . -407) T) ((-142 . -1236) T) ((-883 . -148) T) ((-883 . -146) NIL) 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-102) T) ((-1192 . -102) T) ((-1186 . -102) T) ((-1178 . -1119) T) ((-1145 . -102) T) ((-224 . -34) T) ((-299 . -729) 103728) ((-1178 . -622) 103704) ((-605 . -319) NIL) ((-1278 . -1277) 103688) ((-496 . -1119) 103666) ((-1169 . -231) 103616) ((-402 . -625) 103598) ((-522 . -862) T) ((-1139 . -1236) T) ((-1278 . -1264) 103575) ((-1271 . -1269) 103536) ((-1271 . -1264) 103506) ((-1271 . -1267) 103490) ((-1250 . -1248) 103451) ((-1250 . -1264) 103428) ((-1250 . -1246) 103412) ((-633 . -625) 103394) ((-1193 . -294) 103360) ((-711 . -937) T) ((-1192 . -294) 103326) ((-1186 . -294) 103292) ((-1145 . -294) 103258) ((-1099 . -1119) T) ((-1080 . -1119) T) ((-48 . -312) T) ((-326 . -915) 103224) ((-323 . -915) NIL) ((-1080 . -1087) 103203) ((-1139 . -899) 103185) ((-811 . -38) 103169) ((-273 . -651) 103117) ((-253 . -651) 103065) ((-713 . -1075) 103052) ((-607 . -1264) 103029) ((-1139 . -1057) 103011) ((-329 . -174) 102942) ((-370 . -1119) T) ((-364 . -1119) T) ((-356 . -1119) T) ((-512 . -19) 102924) ((-1121 . -152) 102908) ((-883 . -237) NIL) ((-108 . -1119) T) ((-117 . -1075) 102895) ((-723 . -374) T) ((-512 . -616) 102870) ((-713 . -111) 102855) ((-1311 . -625) 102822) ((-1311 . -502) 102804) ((-1270 . -234) 102750) ((-1249 . -234) 102603) ((-448 . -102) T) ((-888 . -1281) T) ((-256 . -102) T) ((-45 . -1168) 102553) ((-117 . -111) 102538) ((-1288 . -625) 102520) ((-1259 . -237) T) ((-1244 . -625) 102502) ((-1242 . -862) T) ((-647 . -732) T) ((-619 . -732) T) ((-1230 . -1131) T) ((-1230 . -23) T) ((-1191 . -464) 102433) ((-1186 . -319) 102318) ((-1185 . -1119) T) ((-827 . -526) 102251) ((-1054 . -1236) T) ((-245 . -1070) 102152) ((-1177 . -1119) T) ((-1161 . -660) 102090) ((-960 . -152) 102074) ((-1145 . -319) 102061) ((-1144 . -464) 102012) ((-245 . -652) 101934) ((-1106 . -568) 101865) ((-1106 . -1240) 101844) ((-1099 . -729) 101712) ((-537 . -102) T) ((-532 . -102) 101662) ((-1023 . -1070) 101612) ((-1013 . -1119) T) ((-828 . -909) 101508) ((-794 . -1240) 101487) 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-1119) 100449) ((-644 . -622) 100424) ((-644 . -1119) T) ((-593 . -1240) T) ((-593 . -568) T) ((-530 . -1240) T) ((-530 . -568) T) ((-499 . -658) 100374) ((-486 . -234) 100320) ((-439 . -1070) 100304) ((-439 . -652) 100288) ((-370 . -729) 100240) ((-364 . -729) 100192) ((-350 . -1075) 100176) ((-356 . -729) 100128) ((-350 . -111) 100107) ((-176 . -1075) 100039) ((-219 . -658) 99989) ((-176 . -111) 99900) ((-108 . -729) 99850) ((-283 . -1119) T) ((-282 . -1119) T) ((-281 . -1119) T) ((-280 . -1119) T) ((-279 . -1119) T) ((-278 . -1119) T) ((-277 . -1119) T) ((-214 . -1119) T) ((-213 . -1119) T) ((-171 . -1224) 99828) ((-171 . -1221) 99806) ((-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) 99558) ((-171 . -35) 99536) ((-171 . -95) 99514) ((-666 . -1057) 99410) ((-494 . -1077) 99388) ((-1132 . -1119) 99140) ((-1161 . -34) T) ((-682 . -501) 99124) ((-73 . -1236) T) ((-105 . -625) 99106) ((-1310 . -625) 99088) ((-392 . -625) 99070) ((-350 . -628) 99022) ((-176 . -628) 98939) ((-1235 . -502) 98920) ((-743 . -38) 98769) ((-583 . -1224) T) ((-583 . -1221) T) ((-543 . -625) 98751) ((-532 . -319) 98689) ((-512 . -625) 98671) ((-512 . -626) 98653) ((-1235 . -625) 98619) ((-1186 . -1171) NIL) ((-1046 . -1090) 98588) ((-1046 . -1119) T) ((-1023 . -102) T) ((-990 . -102) T) ((-931 . -102) T) ((-906 . -1057) 98565) ((-1161 . -738) T) ((-1022 . -660) 98472) ((-488 . -1119) T) ((-475 . -1119) T) ((-598 . -23) T) ((-583 . -35) T) ((-583 . -95) T) ((-439 . -102) T) ((-1082 . -231) 98418) ((-1193 . -38) 98315) ((-878 . -738) T) ((-706 . -937) T) ((-523 . -25) T) ((-519 . -21) T) ((-519 . -25) T) ((-1192 . -38) 98156) ((-350 . -1068) T) ((-1186 . -38) 97952) ((-1099 . -174) T) ((-176 . -1068) T) ((-1145 . -38) 97849) ((-724 . -47) 97826) ((-370 . -174) T) ((-364 . -174) T) ((-531 . -57) 97800) ((-509 . -57) 97750) ((-362 . -1305) 97727) ((-227 . -464) T) ((-329 . -300) 97678) ((-356 . -174) T) ((-176 . -248) T) ((-1249 . -862) 97577) ((-108 . -174) T) ((-884 . -1011) 97561) ((-670 . -1131) T) ((-593 . -374) T) ((-593 . -339) 97548) ((-530 . -339) 97525) ((-530 . -374) T) ((-326 . -317) 97504) ((-323 . -317) T) ((-614 . -862) 97483) ((-1132 . -729) 97425) ((-532 . -292) 97409) ((-670 . -23) T) ((-430 . -232) 97393) ((-430 . -272) 97377) ((-323 . -1041) NIL) ((-347 . -23) T) ((-103 . -1029) 97361) ((-45 . -36) 97340) ((-624 . -1119) T) ((-362 . -379) T) ((-536 . -102) T) ((-507 . -27) T) ((-245 . -319) 97278) ((-1106 . -1131) T) ((-1309 . -660) 97252) ((-794 . -1131) T) ((-792 . -1131) T) ((-1197 . -423) 97236) ((-466 . -1131) T) ((-1081 . -464) T) ((-1170 . -1119) T) ((-969 . -464) 97187) ((-1134 . -1102) T) ((-110 . -1119) T) ((-1106 . -23) T) ((-1178 . -526) 96970) ((-829 . -1077) T) ((-794 . -23) T) 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-806) 92280) ((-855 . -803) 92259) ((-855 . -738) 92238) ((-370 . -300) T) ((-364 . -300) T) ((-356 . -300) T) ((-171 . -464) 92169) ((-439 . -38) 92153) ((-225 . -23) T) ((-108 . -300) T) ((-419 . -806) 92132) ((-419 . -803) 92111) ((-419 . -738) T) ((-512 . -298) 92086) ((-489 . -1075) 92051) ((-670 . -132) T) ((-633 . -628) 92020) ((-1132 . -526) 91953) ((-347 . -132) T) ((-171 . -414) 91932) ((-494 . -729) 91874) ((-827 . -296) 91851) ((-489 . -111) 91807) ((-665 . -1077) T) ((-1191 . -909) 91710) ((-1144 . -909) 91692) ((-828 . -1070) 91535) ((-1297 . -1102) T) ((-1259 . -464) 91466) ((-828 . -652) 91315) ((-1296 . -1102) T) ((-1106 . -132) T) ((-1073 . -729) 91257) ((-1046 . -526) 91190) ((-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) 91160) ((-829 . -1119) T) ((-488 . -526) 91093) ((-475 . -526) 91026) ((-1311 . -628) 91008) ((-465 . -378) 90978) ((-45 . -622) 90957) ((-411 . -1236) T) ((-326 . -312) T) ((-839 . -237) 90936) ((-489 . -628) 90886) ((-1250 . -319) 90771) ((-682 . -625) 90733) ((-59 . -862) 90712) ((-1023 . -412) 90694) ((-560 . -625) 90676) ((-811 . -658) 90635) ((-827 . -616) 90612) ((-528 . -862) 90591) ((-508 . -862) 90570) ((-1018 . -1057) 90466) ((-40 . -1240) T) ((-245 . -917) 90335) ((-50 . -132) T) ((-593 . -132) T) ((-530 . -132) T) ((-304 . -660) 90195) ((-354 . -339) 90172) ((-354 . -374) T) ((-332 . -333) 90149) ((-329 . -296) 90107) ((-40 . -568) T) ((-390 . -1221) T) ((-390 . -1224) T) ((-1054 . -1212) 90082) ((-1208 . -240) 90032) ((-1186 . -232) 89984) ((-1186 . -272) 89936) ((-340 . -1119) T) ((-390 . -95) T) ((-390 . -35) T) ((-1054 . -107) 89882) ((-489 . -1068) T) ((-1310 . -1075) 89866) ((-491 . -240) 89816) ((-1178 . -501) 89750) ((-1301 . -1070) 89734) ((-392 . -1075) 89718) ((-1301 . -652) 89688) ((-489 . -248) T) ((-828 . -102) T) ((-726 . -148) 89667) 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T) ((-398 . -102) T) ((-334 . -102) T) ((-220 . -1102) T) ((-980 . -1119) T) ((-153 . -1068) T) ((-743 . -423) 76496) ((-118 . -23) T) ((-1022 . -915) 76448) ((-747 . -1119) T) ((-727 . -1119) T) ((-1278 . -658) 76358) ((-465 . -1119) T) ((-419 . -1236) T) ((-326 . -442) 76342) ((-604 . -93) T) ((-1271 . -658) 76224) ((-1046 . -626) 76185) ((-1043 . -1240) T) ((-227 . -102) T) ((-1046 . -625) 76147) ((-828 . -272) 76131) ((-828 . -232) 76115) ((-827 . -628) 75913) ((-1250 . -658) 75750) ((-1043 . -568) T) ((-845 . -660) 75723) ((-365 . -1240) T) ((-488 . -625) 75685) ((-488 . -626) 75646) ((-475 . -626) 75607) ((-475 . -625) 75569) ((-608 . -658) 75528) ((-419 . -897) 75512) ((-329 . -1075) 75347) ((-419 . -899) 75272) ((-607 . -658) 75182) ((-855 . -1057) 75078) ((-499 . -526) NIL) ((-494 . -616) 75055) ((-593 . -234) 75042) ((-365 . -568) T) ((-530 . -234) 75029) ((-219 . -526) NIL) ((-884 . -464) T) ((-430 . -1119) T) ((-419 . -1057) 74893) ((-329 . -111) 74714) ((-706 . -374) T) 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. -660) 72798) ((-322 . -1119) T) ((-299 . -1075) 72785) ((-110 . -625) 72767) ((-110 . -626) 72749) ((-465 . -729) 72719) ((-828 . -260) 72658) ((-701 . -1119) 72636) ((-562 . -1119) T) ((-1193 . -1077) T) ((-1192 . -1077) T) ((-96 . -502) 72617) ((-1186 . -1077) T) ((-299 . -111) 72602) ((-1145 . -1077) T) ((-562 . -622) 72581) ((-96 . -625) 72547) ((-1023 . -860) T) ((-229 . -699) 72505) ((-706 . -1131) T) ((-1230 . -752) 72481) ((-1043 . -374) T) ((-850 . -847) 72463) ((-845 . -806) 72442) ((-419 . -915) 72401) ((-329 . -1068) T) ((-354 . -25) T) ((-354 . -21) T) ((-171 . -1070) 72311) ((-68 . -1236) T) ((-845 . -803) 72290) ((-430 . -729) 72264) ((-811 . -1119) T) ((-724 . -937) 72243) ((-711 . -132) T) ((-171 . -652) 72071) ((-706 . -23) T) ((-499 . -300) T) ((-845 . -738) 72050) ((-329 . -238) 72002) ((-329 . -248) 71981) ((-219 . -300) T) ((-130 . -379) T) ((-1270 . -464) 71960) ((-1249 . -464) 71939) ((-365 . -339) 71916) ((-365 . -374) T) ((-1159 . -625) 71898) ((-45 . -1274) 71848) ((-883 . -102) T) ((-656 . -292) 71832) ((-711 . -1079) T) ((-1297 . -102) T) ((-1296 . -102) T) ((-489 . -660) 71797) ((-480 . -1119) T) ((-45 . -616) 71722) ((-1177 . -298) 71697) ((-299 . -628) 71669) ((-40 . -651) 71608) ((-1259 . -1070) 71431) ((-867 . -1070) 71415) ((-48 . -374) T) ((-1125 . -625) 71397) ((-1259 . -652) 71226) ((-867 . -652) 71196) ((-644 . -298) 71171) ((-828 . -658) 71081) ((-583 . -1070) 71068) ((-494 . -625) 70761) ((-245 . -423) 70730) ((-969 . -319) 70717) ((-583 . -652) 70704) ((-65 . -1236) T) ((-1191 . -917) 70611) ((-1184 . -1119) T) ((-1082 . -526) 70455) ((-683 . -1119) T) ((-635 . -132) T) ((-493 . -319) 70442) ((-618 . -1119) T) ((-558 . -102) T) ((-118 . -132) T) ((-299 . -1068) T) ((-182 . -1119) T) ((-162 . -1119) T) ((-157 . -1119) T) ((-155 . -1119) T) ((-465 . -773) T) ((-31 . -1102) T) ((-980 . -174) 70393) ((-1144 . -917) 70377) ((-989 . -93) T) ((-1132 . -298) 70354) ((-1099 . -1075) 70264) ((-633 . -806) 70243) ((-605 . -1119) T) 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. -521) 64744) ((-884 . -909) 64665) ((-499 . -296) NIL) ((-494 . -298) 64642) ((-430 . -300) T) ((-365 . -132) T) ((-219 . -296) NIL) ((-706 . -505) NIL) ((-99 . -1131) T) ((-40 . -234) 64573) ((-171 . -38) 64401) ((-969 . -917) 64382) ((-1270 . -992) 64344) ((-1166 . -319) 64282) ((-493 . -917) 64259) ((-1249 . -992) 64228) ((-927 . -414) T) ((-1132 . -1068) 64206) ((-1272 . -568) T) ((-1169 . -616) 64185) ((-112 . -862) T) ((-1082 . -501) 64116) ((-592 . -21) T) ((-592 . -25) T) ((-576 . -21) T) ((-576 . -25) T) ((-507 . -25) T) ((-507 . -21) T) ((-1259 . -1171) 64094) ((-1132 . -238) 64046) ((-48 . -132) T) ((-1217 . -102) T) ((-245 . -1119) 63798) ((-883 . -412) 63775) ((-1107 . -102) T) ((-1095 . -102) T) ((-620 . -102) T) ((-487 . -102) T) ((-1259 . -38) 63604) ((-867 . -38) 63574) ((-1053 . -1070) 63548) ((-743 . -174) 63459) ((-665 . -625) 63441) ((-657 . -1102) T) ((-1053 . -652) 63425) ((-583 . -38) 63412) ((-989 . -502) 63393) ((-989 . -625) 63359) ((-975 . -102) 63309) 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. -111) 25114) ((-362 . -1240) T) ((-1278 . -1075) 24997) ((-1132 . -388) 24966) ((-1271 . -1075) 24801) ((-1250 . -1075) 24591) ((-1271 . -111) 24412) ((-1250 . -111) 24181) ((-1230 . -319) 24168) ((-1022 . -132) T) ((-927 . -658) 24118) ((-376 . -625) 24100) ((-362 . -568) T) ((-299 . -317) T) ((-608 . -1075) 24060) ((-607 . -1075) 23943) ((-593 . -1070) 23908) ((-530 . -1070) 23853) ((-372 . -1119) T) ((-332 . -1119) T) ((-258 . -625) 23814) ((-257 . -625) 23775) ((-593 . -652) 23740) ((-530 . -652) 23685) ((-706 . -421) 23652) ((-647 . -23) T) ((-619 . -23) T) ((-40 . -909) 23559) ((-670 . -102) T) ((-608 . -111) 23512) ((-607 . -111) 23381) ((-390 . -1119) T) ((-347 . -102) T) ((-171 . -300) 23292) ((-1249 . -860) 23245) ((-726 . -1077) T) ((-1166 . -526) 23178) ((-1209 . -847) 23162) ((-1132 . -915) 23094) ((-848 . -1119) T) ((-839 . -1119) T) ((-837 . -1119) T) ((-97 . -102) T) ((-145 . -862) T) ((-624 . -897) 23078) ((-110 . -1236) T) ((-1106 . -102) T) ((-1082 . -34) T) ((-794 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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 8abfc6e6..03c94a1d 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3486501422) -(4465 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3486517508) +(4464 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -430,7 +430,7 @@ |SquareFreeRegularTriangularSet| |Stack| |StreamAggregate&| |StreamAggregate| |SparseTable| |StepAst| |StepThrough| |StreamInfiniteProduct| |StreamFunctions1| |StreamFunctions2| - |StreamFunctions3| |Stream| |StringCategory| |String| |StringTable| + |StreamFunctions3| |Stream| |String| |StringTable| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctionsNonCommutative| |StreamTranscendentalFunctions| |SubResultantPackage| |SubSpace| @@ -488,665 +488,671 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |changeThreshhold| |imagK| |setleft!| |property| - |length| |OMserve| |string?| |toseSquareFreePart| |primeFrobenius| - |basisOfCentroid| |extendedEuclidean| |kernels| |linearDependence| - |getProperties| |leftScalarTimes!| |scripts| |ord| |reorder| |linear?| - |df2mf| |overbar| |maxrank| |ocf2ocdf| |operator| |acoshIfCan| - |clipParametric| LODO2FUN |const| |tanh2coth| |leadingExponent| - |resultantEuclideannaif| |dequeue| |componentUpperBound| |delta| - |changeName| |dfRange| |multiset| |doubleRank| |alternatingGroup| - |semiLastSubResultantEuclidean| |commutator| |reify| |primitivePart| - |univariate| |direction| |arg1| |zeroSquareMatrix| |po| - |viewDeltaXDefault| |modifyPoint| |leftAlternative?| |scale| - |gcdPrimitive| |arg2| |denominators| |subspace| |applyRules| - |categoryMode| |pair?| |stoseInvertibleSet| |realRoots| |digamma| - |interval| |push| |putProperty| |fortranReal| |wholeRagits| |element?| - |unvectorise| |monicRightDivide| |subresultantSequence| |factor| - |drawCurves| |conditions| |pToDmp| |trim| |OMgetEndApp| |cycleTail| - |aromberg| |exponentialOrder| |euclideanGroebner| |c02agf| |sqrt| - |match| |ran| |internalSubPolSet?| |expressIdealMember| |userOrdered?| - |removeRoughlyRedundantFactorsInPol| |setPoly| |squareFreePrim| |is?| - |totalfract| |algDsolve| |real| |increment| |complete| - |readLineIfCan!| |more?| |tree| |lazyResidueClass| |read!| |makeEq| - |leftRegularRepresentation| |e02bef| |lambda| |algebraicOf| |imag| - |radicalOfLeftTraceForm| |viewSizeDefault| |doubleResultant| - |curryRight| |list?| |nthFlag| Y |OMParseError?| |removeZeroes| - |padecf| |maxRowIndex| |directProduct| |harmonic| |inverseColeman| - |critM| |tanSum| |linearlyDependent?| |getProperty| |asinIfCan| - |solve1| |monicDecomposeIfCan| |alternative?| |isAnd| |fibonacci| - |noValueMode| |listexp| |csc2sin| |tubePlot| |branchPoint?| |swap| - |curve?| |brace| |pointColor| |quasiRegular?| |polyRicDE| |B1solve| - |d03faf| |rarrow| |meshPar1Var| |cosh2sech| |basisOfRightNucloid| - |expPot| |destruct| |absolutelyIrreducible?| |ip4Address| - |semiResultantEuclidean2| |repeating| |OMputBind| |polygon| - |setTopPredicate| |extendIfCan| |hypergeometric0F1| - |showTheSymbolTable| |nonLinearPart| |localIntegralBasis| |cotIfCan| - |antisymmetric?| |tValues| |evaluate| |genericRightTraceForm| - |iterationVar| |denominator| |RittWuCompare| |ptree| - |commutativeEquality| |mightHaveRoots| |edf2df| |relativeApprox| - |minordet| |flatten| |finiteBound| |showAllElements| |rootBound| - |component| |plus| |rename| |convert| |upperCase?| |iiasec| |d01apf| - |s18adf| |modTree| |euclideanNormalForm| |unaryFunction| |f07fef| - |hasTopPredicate?| |getCurve| |lp| |options| |monomial| |readUInt8!| - |fortranTypeOf| |expint| |power| |mainExpression| |divideIfCan!| - |laguerreL| |pointData| |eigenMatrix| |subscript| |multivariate| - |s13aaf| |before?| |traceMatrix| |isOr| |numericIfCan| |variable?| - |univariatePolynomialsGcds| |simplifyLog| |order| |times| - |currentScope| |variables| |elliptic?| |sechIfCan| |sylvesterMatrix| - |s20adf| |failed?| |curve| |multiple?| |viewDefaults| |chebyshevT| - |semiIndiceSubResultantEuclidean| |string| |f02aff| |primitiveElement| - |continuedFraction| |cycleSplit!| |schwerpunkt| |iiasin| |zerosOf| - |fortranComplex| |completeHensel| |outputList| |tanAn| |prologue| - |perfectNthRoot| |evenInfiniteProduct| |modulus| |compactFraction| - |OMputSymbol| |setAdaptive| |showScalarValues| |rur| |swapRows!| - |rewriteSetWithReduction| |genericRightDiscriminant| |cyclicEqual?| - |environment| |f07adf| |acotIfCan| |rightRank| |realEigenvalues| - |roughEqualIdeals?| |part?| |completeHermite| |monom| |divisor| - |squareFreePart| |sin?| |squareFreePolynomial| |poisson| |elliptic| - |rotatey| |sturmSequence| |inR?| |dominantTerm| |taylor| |reduction| - |kmax| |alternating| |ldf2vmf| |solveInField| |outerProduct| - |OMputEndObject| |atoms| |selectPDERoutines| |collectUpper| |open?| - |laurent| |ddFact| |mix| |randomLC| |e02zaf| |printingInfo?| - |isobaric?| |variable| |pade| |headRemainder| |startTableGcd!| - |common| |clipSurface| |puiseux| |measure2Result| |rspace| |npcoef| - |numberOfVariables| |separateFactors| |close| |e02ajf| |iterators| - |stopTable!| |laurentIfCan| |iibinom| |euler| F2FG |nextColeman| - |factorset| |hostByteOrder| |constantToUnaryFunction| - |rewriteIdealWithHeadRemainder| |s14baf| |OMsend| |setEpilogue!| - |monicRightFactorIfCan| |inv| |df2ef| |minGbasis| |leastPower| - |chebyshevU| |outputBinaryFile| |display| |iifact| |An| - |rationalIfCan| |insertionSort!| |terms| |countable?| |ground?| - |declare!| |nullity| |dot| |iiatanh| |f01ref| - |primPartElseUnitCanonical| |leviCivitaSymbol| |s17def| |arity| - |computeInt| |getIdentifier| |zeroOf| |ground| |f2df| |primlimintfrac| - |polarCoordinates| |makeYoungTableau| |nextsubResultant2| - |fortranDouble| |rischNormalize| |startTableInvSet!| |extract!| - |eulerPhi| |leadingMonomial| |mapExpon| |rk4f| - |leftCharacteristicPolynomial| |middle| |integralMatrix| |scan| - |rootProduct| |problemPoints| |removeDuplicates| |c06fqf| - |leadingCoefficient| |d01akf| |fortranCompilerName| |power!| - |setStatus| |cTanh| |showSummary| |irreducibleFactor| - |SturmHabichtCoefficients| |stronglyReduced?| |basisOfLeftNucloid| - |btwFact| |primitiveMonomials| |zero| |skewSFunction| |lex| - |stoseSquareFreePart| |epilogue| |input| |pastel| |rdHack1| - |flagFactor| |leftRecip| |oddintegers| |lazyGintegrate| |reductum| - |OMgetFloat| |probablyZeroDim?| |quotient| |triangularSystems| - |library| |abelianGroup| |fixedDivisor| |ScanFloatIgnoreSpaces| - |OMputApp| |lflimitedint| |complexExpand| |And| |setnext!| |value| - |semiResultantEuclidean1| |tryFunctionalDecomposition| |triangSolve| - |addPoint2| |totalDegree| |getSyntaxFormsFromFile| - |univariatePolynomial| |sortConstraints| |f01maf| |Or| - |integralDerivationMatrix| |localAbs| |limitedint| |segment| - |OMgetEndObject| |optimize| |trigs2explogs| |showAttributes| |members| - |crushedSet| |purelyAlgebraicLeadingMonomial?| |numberOfDivisors| - |myDegree| |Not| |subst| |linGenPos| |copy!| |findConstructor| - |binomial| |degreeSubResultantEuclidean| |column| |qfactor| - |testModulus| |factorial| |selectAndPolynomials| |iomode| - |clipPointsDefault| |ranges| |kernel| |e01bff| |singularitiesOf| - |binaryTree| |hasSolution?| |OMgetEndAttr| |root| |assert| |getOrder| - |copies| |integralBasisAtInfinity| |selectODEIVPRoutines| |groebSolve| - |list| |routines| |colorFunction| |iicsc| |euclideanSize| |ode1| - |conditionP| |lhs| |draw| |putColorInfo| |mappingMode| - |numberOfCycles| |f04qaf| |insertMatch| |cAcot| |denomLODE| |getCode| - |coerceImages| |d02bbf| |Beta| |f01qcf| |rhs| |iiatan| |setColumn!| - |scripted?| |nextNormalPrimitivePoly| |UP2ifCan| |one?| |coordinate| - |leadingIdeal| |orbits| |unmakeSUP| |cAsinh| - |indicialEquationAtInfinity| |distdfact| |leftZero| - |branchPointAtInfinity?| |updatF| |li| |radicalRoots| |currentEnv| - |packageCall| |c05pbf| |wordsForStrongGenerators| |integerIfCan| - |resultantEuclidean| |objects| |iiacosh| |numberOfMonomials| - |cyclotomicFactorization| |dictionary| |regime| |numberOfComponents| - |elColumn2!| |resultantReduit| |goto| |OMsupportsCD?| |makeObject| - |base| |e04fdf| |solve| |printCode| |normalize| |fractionPart| - |pushup| |critB| |PDESolve| |charClass| |invertible?| |GospersMethod| - |uniform| |realSolve| |closed| |coef| |readable?| |nextPartition| - |messagePrint| |solveRetract| |iiacot| |gcdprim| |find| |iitanh| - |inputBinaryFile| |cPower| |permutations| |mkIntegral| |rubiksGroup| - |unrankImproperPartitions0| |scalarTypeOf| |constantIfCan| - |constructor| |stoseLastSubResultant| |headReduced?| - |listRepresentation| |LazardQuotient2| |splitSquarefree| |newLine| - |OMputEndApp| |realZeros| |viewThetaDefault| |musserTrials| - |interpretString| |highCommonTerms| |s20acf| |normDeriv2| - |createRandomElement| |wrregime| |OMgetBind| |leftNorm| - |semiResultantReduitEuclidean| |rectangularMatrix| |lazyPseudoDivide| - |algebraicVariables| |integralCoordinates| |merge!| |digit| - |magnitude| |coerceListOfPairs| |pascalTriangle| |Si| |f02wef| - |topPredicate| |eq?| |flexibleArray| |s18def| |useSingleFactorBound| - |integral| |safeFloor| |twist| |test| |c02aff| |coth2trigh| - |minimumDegree| |vectorise| |c06gcf| |numberOfFractionalTerms| - |writable?| UTS2UP |OMmakeConn| |universe| |realElementary| |d03edf| - |bivariate?| |meatAxe| |ParCond| |isAbsolutelyIrreducible?| - |oneDimensionalArray| |exponents| |droot| |s17ahf| |sayLength| |width| - |rootOf| |trunc| |dim| |externalList| |bits| |lazyIrreducibleFactors| - |critMonD1| |ksec| |compiledFunction| |e02baf| |pureLex| |OMgetAtp| - |compose| |innerEigenvectors| |outputForm| |numberOfNormalPoly| - |rightQuotient| |exteriorDifferential| |partialFraction| |partitions| - |discriminant| |d01fcf| |s13acf| |cCosh| |startStats!| - |pmComplexintegrate| |minColIndex| |zero?| |secIfCan| |rootSimp| - |compound?| |critpOrder| |OMencodingXML| |type| |indicialEquation| - |exponential| |makeMulti| |expt| |prefix| |setRealSteps| |rem| - |e02akf| |complexIntegrate| |plus!| |number?| |table| |blankSeparate| - |predicate| |showFortranOutputStack| |octon| |setLabelValue| |quo| - |infix| |drawComplexVectorField| |removeSinSq| |scopes| - |stopTableInvSet!| |new| |antisymmetricTensors| |splitNodeOf!| - |readInt32!| |nil?| |viewPosDefault| |obj| |basis| - |representationType| |f02agf| |squareFreeLexTriangular| |optional| - |subCase?| |rules| |inverseIntegralMatrixAtInfinity| - |OMUnknownSymbol?| |getlo| |deepExpand| |rCoord| |chineseRemainder| - |div| |index?| |cache| |even?| |isPlus| |substitute| |slash| |d01alf| - |intensity| |e01saf| |exquo| |internalIntegrate| |setScreenResolution| - |f01qef| |sh| |zeroDimensional?| |diagonals| |logGamma| |prevPrime| - |binding| |OMgetAttr| |stiffnessAndStabilityOfODEIF| ~= |hMonic| - |palginfieldint| |erf| |directSum| |monicModulo| |purelyAlgebraic?| - |yCoordinates| |subQuasiComponent?| |children| |lyndonIfCan| - |cyclicCopy| |unknown| |cAtan| |#| |reducedQPowers| |palgint| |iExquo| - |pattern| |printTypes| |removeSinhSq| |meshFun2Var| |getGraph| - |primeFactor| |determinant| |symmetricSquare| ~ |OMgetSymbol| - |fortranInteger| |commaSeparate| |getRef| |closed?| |hconcat| - |integers| |formula| |infieldint| |dilog| |rightMult| |d01aqf| - |bracket| |solveLinearPolynomialEquation| |cot2trig| |lowerCase?| - |minIndex| |f01mcf| |getPickedPoints| |torsion?| |physicalLength| - |dequeue!| |nextItem| |sin| |points| |s17dhf| |outputArgs| - |parameters| |closedCurve| |resetNew| |leftDivide| |isList| - |lfinfieldint| |/\\| |e04ycf| |level| |realEigenvectors| |message| - |cos| |squareFree| |ratDsolve| |tanhIfCan| |acschIfCan| - |LazardQuotient| |minrank| |initials| |\\/| |chvar| |OMReadError?| - |mapUnivariateIfCan| |tan| |appendPoint| |cAcosh| |left| - |currentCategoryFrame| |concat!| |addMatchRestricted| |setref| - |conical| |exprHasWeightCosWXorSinWX| |sPol| |s17dlf| |cot| |cot2tan| - |hasoln| |nrows| |complementaryBasis| |right| |mkAnswer| |OMgetBVar| - |search| |isImplies| |ideal| |deleteProperty!| |permutation| |pow| - |linearMatrix| |sec| |zeroDimPrimary?| |ncols| |lowerPolynomial| - |fixedPoint| |iprint| |squareTop| |readUInt32!| |toScale| |cschIfCan| - |d02kef| |csc| |nextPrimitivePoly| |anticoord| |heapSort| - |perfectSqrt| |airyAi| |OMgetEndBind| |pop!| |withPredicates| |lazy?| - |polyred| |d01amf| |asin| |central?| |fprindINFO| |critMTonD1| - |palgLODE0| |setPrologue!| |lazyIntegrate| |karatsubaDivide| |dual| - |balancedFactorisation| |iisqrt3| |normal?| |acos| |dihedral| - |pseudoRemainder| |just| |changeWeightLevel| - |tableForDiscreteLogarithm| |getOperands| |conditionsForIdempotents| - |contains?| |e02aef| |companionBlocks| |atan| |linearPart| - |integralBasis| |symbolTable| |univariate?| |makeSUP| |any?| |paren| - |algint| |double?| |chiSquare| |acot| |autoReduced?| |att2Result| - |refine| |iilog| |cscIfCan| |OMgetEndBVar| |quartic| |hasPredicate?| - |quadraticNorm| |setMaxPoints3D| |incrementKthElement| |asec| - |mapCoef| |lfextlimint| |complexRoots| |pushFortranOutputStack| - |cycleLength| |localReal?| |cardinality| |mat| |external?| |powmod| - |SturmHabichtMultiple| |outputAsTex| |acsc| F |primintegrate| - |lazyPseudoQuotient| |irreducible?| |popFortranOutputStack| - |increasePrecision| |bombieriNorm| |bright| |setAttributeButtonStep| - |showTheIFTable| |outputSpacing| |algintegrate| |divide| |mainContent| - |deepestInitial| |sinh| |hermiteH| |wordInStrongGenerators| - |basisOfRightNucleus| |oblateSpheroidal| |toseLastSubResultant| - |curryLeft| |readLine!| |checkPrecision| |selectIntegrationRoutines| - |hspace| |size| |pol| |substring?| |precision| |cycleEntry| - |normalizedDivide| |cosh| |systemCommand| |truncate| - |integralAtInfinity?| |c06ebf| |symbol| |eval| |hitherPlane| - |commutative?| |adaptive| |bringDown| |mindegTerm| |mainForm| |tanh| - |lquo| |invmod| |torsionIfCan| |thenBranch| |expression| - |expextendedint| |createGenericMatrix| |palgintegrate| - |stripCommentsAndBlanks| |binarySearchTree| |suffix?| |sumOfSquares| - |lllip| |expIfCan| |coth| |removeRoughlyRedundantFactorsInContents| - |shape| |integer| |elRow1!| |pushucoef| |expintfldpoly| |f04atf| - |separant| |iisin| |pomopo!| |minimize| |orthonormalBasis| |sech| - |inverse| |normal| |error| |OMopenFile| |weierstrass| |setleaves!| - |laguerre| |binary| |prefix?| |prepareDecompose| - |numericalOptimization| |linearPolynomials| |csch| |dimensionsOf| - |removeCoshSq| |brillhartIrreducible?| |primaryDecomp| |OMgetError| - |viewpoint| |ParCondList| |stirling1| |oddlambert| |asinh| - |listOfLists| |redPo| |lazyEvaluate| |pr2dmp| |stFunc2| |s15aef| - |splitDenominator| |generateIrredPoly| |iicos| |deepestTail| FG2F - |acosh| |OMclose| |OMsupportsSymbol?| |edf2efi| |collectUnder| - |inrootof| |subresultantVector| |f01rdf| |numberOfHues| |listLoops| - |stoseIntegralLastSubResultant| |atanh| |dualSignature| |mathieu11| - |imagJ| |lift| |whitePoint| |d01bbf| |cyclicParents| - |permutationGroup| |extractTop!| |makeSeries| |pseudoQuotient| |acoth| - |rightFactorIfCan| |df2fi| |viewPhiDefault| |node| |LyndonBasis| - |stFuncN| |reduce| |optional?| |insert!| |bandedJacobian| - |extractIfCan| |keys| |stoseInvertible?reg| |bernoulli| |color| - |asech| |degree| |nextLatticePermutation| |key| |s17agf| |prod| - |createNormalPrimitivePoly| |identityMatrix| |s18aef| |infix?| - |retract| |rightTrace| |elseBranch| |setelt!| |removeConstantTerm| - |e04gcf| |byteBuffer| |radPoly| |s19aaf| |redpps| |unravel| |filename| - |shrinkable| |mask| |vark| |numeric| |d02cjf| |multiple| - |constantLeft| |node?| |sort| |padicFraction| |aLinear| |newReduc| - |elem?| |clip| |tanQ| |radical| |qPot| |applyQuote| |setDifference| - |sequences| |selectMultiDimensionalRoutines| |e01bhf| |baseRDE| - |cycle| |schema| |genericRightMinimalPolynomial| |leftUnits| - |intcompBasis| |gcdcofact| |returnTypeOf| |OMgetString| |parse| |null| - |genericLeftTraceForm| |setTex!| |shanksDiscLogAlgorithm| - |complexLimit| |light| |point?| |getMatch| |coefficient| - |HermiteIntegrate| |singRicDE| |not| |module| |primextendedint| - |computeCycleLength| |horizConcat| |cAcoth| |qualifier| |pToHdmp| - |tanIfCan| |ruleset| |createLowComplexityTable| |inverseLaplace| |and| - |random| |createMultiplicationTable| |ptFunc| |swap!| |totalLex| - |measure| |birth| |multinomial| |symmetric?| |idealiserMatrix| - |airyBi| |or| |jokerMode| |mainVariable?| |elementary| - |internalInfRittWu?| |subscriptedVariables| |makeViewport2D| |resize| - |palgextint0| |setfirst!| |gensym| |e04naf| |shellSort| |delete| - |characteristic| |leftTraceMatrix| |drawStyle| |doubleDisc| - |setLegalFortranSourceExtensions| |taylorQuoByVar| |map| |square?| - |suchThat| |karatsuba| |SturmHabicht| |loopPoints| |weight| - |solveLinear| |cartesian| |recolor| |setStatus!| |subResultantGcd| - |retractable?| |dmpToP| |hostPlatform| |cyclic?| |byte| ** |bindings| - |e01sff| |LagrangeInterpolation| |hdmpToDmp| |callForm?| |imaginary| - |removeCosSq| |void| |monomials| |pquo| |sincos| |createNormalElement| - |lexTriangular| |scaleRoots| |stFunc1| |equation| |clikeUniv| - |zeroSetSplitIntoTriangularSystems| |freeOf?| |rationalPower| |e02def| - |rightFactorCandidate| |totalDifferential| |complexSolve| |var2Steps| - |getZechTable| |imagE| |partialDenominators| |d02gaf| |say| |minPoly| - |ODESolve| |rotate!| |idealSimplify| |computeBasis| |firstNumer| - |delete!| |OMputInteger| |OMputError| |noLinearFactor?| - |divisorCascade| |groebnerIdeal| |removeRedundantFactorsInPols| - |ef2edf| |jacobian| |sqfrFactor| |addPointLast| |LiePoly| |approxSqrt| - |iipow| |normalDenom| |socf2socdf| |discreteLog| |rightDiscriminant| - |PollardSmallFactor| |index| |reset| |s17aef| |center| |nullary| - |fractRadix| |d01gaf| |opeval| |decrease| |c06ecf| - |leadingCoefficientRicDE| |completeSmith| |parseString| - |extractClosed| |unparse| |mvar| |equiv| |zeroSetSplit| - |hyperelliptic| |omError| |write| |scanOneDimSubspaces| - |rootDirectory| |unitCanonical| |components| |fullPartialFraction| - |int| |taylorIfCan| |in?| |shiftLeft| |maxdeg| |identity| |generator| - |pdf2df| |save| |irreducibleRepresentation| |pair| |move| - |extensionDegree| |tRange| |boundOfCauchy| |unary?| |ReduceOrder| - |setEmpty!| |nextsousResultant2| |rischDEsys| |leftPower| |setvalue!| - |subTriSet?| |positiveSolve| |rightLcm| |setMaxPoints| - |exportedOperators| |goodPoint| |pushNewContour| |numerators| - |evaluateInverse| |iicosh| |moebius| |nextIrreduciblePoly| |OMputAttr| - |pointLists| |s17akf| |green| |jordanAlgebra?| |s14abf| |log10| - |OMgetApp| |reducedDiscriminant| SEGMENT |setMinPoints| |besselK| - |OMgetVariable| |roughSubIdeal?| |besselI| |interactiveEnv| - |fixedPoints| |decomposeFunc| |fintegrate| |nextPrime| |lifting| - |indiceSubResultant| |inf| |split!| |stoseInternalLastSubResultant| - |OMputEndAttr| |usingTable?| |partialNumerators| |BasicMethod| - |integralLastSubResultant| |space| |e02dcf| |isMult| |empty| - |printInfo!| |transpose| |shiftRoots| |setIntersection| |f02aaf| - |showArrayValues| |lazyPremWithDefault| |multiEuclidean| |failed| - |indicialEquations| |whatInfinity| |quoted?| |parametric?| |minus!| - |parabolic| |adaptive?| |cosIfCan| |incr| |moduleSum| |delay| - |rowEchelon| |tab| |rotate| |permutationRepresentation| |sec2cos| - |isOpen?| |constant| |sn| |hi| |cSin| |shufflein| |eigenvectors| - |halfExtendedSubResultantGcd1| |varList| |innerSolve1| |reflect| - |OMread| |fortran| |getOperator| |makeCrit| |nand| - |combineFeatureCompatibility| |groebner| |symmetricGroup| |makeSin| - |zCoord| |apply| |squareFreeFactors| |iitan| RF2UTS |degreePartition| - |s17acf| |bivariatePolynomials| |OMcloseConn| |sin2csc| |singular?| - |nil| |first| |imports| |log| |explimitedint| |printInfo| - |rewriteSetByReducingWithParticularGenerators| |ref| |lazyPrem| - |rootNormalize| |createIrreduciblePoly| |invertibleElseSplit?| |rest| - |intermediateResultsIF| |bumptab| |f2st| |degreeSubResultant| - |variationOfParameters| |OMreadStr| |numFunEvals3D| |setClosed| - |basisOfCommutingElements| |exQuo| |associative?| |graeffe| |prime?| - |max| |coHeight| |approximate| |setright!| |s18acf| |mainMonomials| - |completeEchelonBasis| |float| |kovacic| |prindINFO| |OMgetEndAtp| - |algebraicDecompose| |complex| |newSubProgram| |quasiComponent| - |tubePointsDefault| |standardBasisOfCyclicSubmodule| |maxColIndex| - |prinpolINFO| |inverseIntegralMatrix| |sup| |pushdterm| |ode| |f01bsf| - |approximants| |basicSet| |curveColor| |subNode?| |meshPar2Var| - |mappingAst| |showIntensityFunctions| |getBadValues| |vedf2vef| - |explicitEntries?| |semiSubResultantGcdEuclidean1| |sorted?| |e02ddf| - |graphStates| |dAndcExp| |removeRoughlyRedundantFactorsInPols| - |ffactor| |linearlyDependentOverZ?| |uncouplingMatrices| - |listBranches| |tensorProduct| |chiSquare1| |explicitlyEmpty?| - |recoverAfterFail| |fortranLiteral| |intPatternMatch| |over| |fTable| - |OMputEndAtp| |diagonalMatrix| |sizePascalTriangle| |s21baf| |iiGamma| - |iiabs| |f04faf| |gradient| |cCoth| |f04axf| |iisech| |gbasis| - |generate| |cCot| |collectQuasiMonic| |times!| |semicolonSeparate| - |extendedSubResultantGcd| |setValue!| |countRealRootsMultiple| - |closedCurve?| |tanintegrate| |optpair| |OMputEndBVar| |maxPoints3D| - |associatedEquations| |sncndn| |trace2PowMod| |infiniteProduct| - |transcendentalDecompose| |printHeader| |dihedralGroup| |vspace| - |rootPower| |incrementBy| |algebraicCoefficients?| |powern| - |setImagSteps| GE |typeList| |hermite| |argument| |simplifyExp| - |irCtor| |tanNa| |HenselLift| |expand| |lfunc| |divergence| |rroot| GT - |linSolve| |tablePow| |makeResult| |sech2cosh| |eulerE| |findBinding| - |size?| |f01brf| |numericalIntegration| |contours| LE - |definingPolynomial| UP2UTS |tanh2trigh| |extend| |digit?| |midpoints| - |logical?| |d03eef| |leastMonomial| |diagonal?| LT |concat| - |trapezoidal| |symbolIfCan| |errorInfo| |wordInGenerators| |maxrow| - |imagj| |f01qdf| |polygon?| |OMencodingSGML| |rightGcd| |minset| - |monic?| |OMputAtp| |extractIndex| |lieAdmissible?| |infinite?| - |complex?| |e01daf| |expr| |getConstant| |infinityNorm| - |explogs2trigs| |isQuotient| |collect| |tracePowMod| |low| - |binaryFunction| |OMunhandledSymbol| |alphanumeric| - |definingEquations| |pushdown| |cCos| |matrixConcat3D| |symFunc| - |raisePolynomial| |cSinh| |diagonalProduct| |outputMeasure| |dmp2rfi| - |createLowComplexityNormalBasis| |remove| |KrullNumber| |aQuartic| - |OMputBVar| |mathieu12| |exprToXXP| |useEisensteinCriterion?| - |factorOfDegree| |entry| |tubePoints| |subResultantGcdEuclidean| - |spherical| |overlap| |initializeGroupForWordProblem| - |viewDeltaYDefault| |thetaCoord| |submod| |pointColorDefault| - |quasiAlgebraicSet| |inconsistent?| |last| |rk4a| |stoseInvertible?| - |mapUnivariate| |cross| |Gamma| |fill!| |stronglyReduce| |range| - |rowEchLocal| |assoc| |infieldIntegrate| |stoseInvertible?sqfreg| - |writeByte!| |eyeDistance| |height| |script| |headAst| - |axesColorDefault| |compdegd| |triangular?| |f02fjf| - |var2StepsDefault| |rewriteIdealWithQuasiMonicGenerators| - |invmultisect| |fortranCharacter| |roughBasicSet| - |reciprocalPolynomial| |zeroDim?| |f04mcf| |s15adf| |OMgetInteger| - |semiDegreeSubResultantEuclidean| |heap| |satisfy?| |associates?| - |reduceByQuasiMonic| |lexico| |writeInt8!| |zoom| |elements| - |halfExtendedSubResultantGcd2| |id| |permanent| |Lazard| |untab| - |fixedPointExquo| |tex| |polar| |rischDE| |d02ejf| |f01rcf| - |mainVariables| |denomRicDE| |call| |addmod| |mergeDifference| |lo| - |rightExactQuotient| |parents| |singleFactorBound| |simpson| - |retractIfCan| |bumprow| |selectfirst| |constantCoefficientRicDE| - |d02bhf| |car| |localUnquote| |minPoints| |figureUnits| |duplicates| - |c05nbf| |cup| |youngGroup| |whileLoop| |exprHasAlgebraicWeight| - |jacobiIdentity?| |basisOfNucleus| |replaceKthElement| |exptMod| - |cAcsc| |ListOfTerms| |UnVectorise| |resultant| |radicalEigenvalues| - |rootRadius| |beauzamyBound| |showTheFTable| |unitVector| - |unitNormalize| |mainValue| |subset?| |top| |represents| |lepol| - |randomR| |isTimes| |leadingTerm| |prefixRagits| |iisinh| |hue| - |continue| |expandTrigProducts| |rightTraceMatrix| |setAdaptive3D| - |genericLeftTrace| |totolex| |explicitlyFinite?| |function| - |OMconnInDevice| |derivative| |convergents| |noKaratsuba| |s19adf| - |directory| |tube| |factorSquareFree| |minPol| |bat| |setchildren!| - |asinhIfCan| |supRittWu?| |palgint0| |prolateSpheroidal| |lighting| - |ipow| |rightScalarTimes!| |cyclotomicDecomposition| |lintgcd| - |diophantineSystem| |mesh| |radicalSimplify| |exprToGenUPS| - |rightRecip| |extractBottom!| |OMlistCDs| |cAsech| |palglimint| - |simpsono| |numberOfChildren| |tail| |makeUnit| |factorsOfDegree| - |quadraticForm| |reverseLex| |factorSFBRlcUnit| |replace| |entries| - |internalLastSubResultant| |transcendenceDegree| |rightUnits| - |lagrange| |iisec| |factorList| |declare| |coerceS| - |encodingDirectory| |fixPredicate| |integral?| |nsqfree| |label| - |areEquivalent?| |frobenius| |coefficients| |mulmod| |maxPoints| - |multiplyCoefficients| |supDimElseRittWu?| |typeForm| |odd?| - |BumInSepFFE| |traverse| |setVariableOrder| |bytes| |super| - |principalAncestors| |removeRedundantFactorsInContents| |putGraph| EQ - |setFieldInfo| |cSech| |bezoutMatrix| |plot| |hasHi| GF2FG - |prepareSubResAlgo| |createZechTable| |symmetricPower| - |matrixDimensions| |quadratic?| |less?| |functorData| |f04arf| - |atrapezoidal| |makeprod| |addBadValue| - |removeIrreducibleRedundantFactors| |palglimint0| |conjunction| - |polyRDE| |cAtanh| |preprocess| |mapBivariate| |iicsch| |lcm| - |viewZoomDefault| |distFact| |conjugates| |cAsin| - |unrankImproperPartitions1| |viewport2D| |OMgetEndError| |OMputString| - |nthr| |s17adf| |normFactors| |reverse!| |gethi| |adjoint| - |solveLinearPolynomialEquationByRecursion| |rootSplit| |sub| |iiacoth| - |distance| |option?| |append| |hash| |changeVar| |binomThmExpt| - |gcdPolynomial| |signAround| |option| |rightCharacteristicPolynomial| - |clearTheFTable| |outlineRender| |perfectNthPower?| |gcd| |count| - |category| |diag| |Vectorise| |changeBase| |rangePascalTriangle| - |basisOfCenter| |nonSingularModel| |nthFactor| |false| |cfirst| - |domain| |fractionFreeGauss!| |box| |minimalPolynomial| |lambert| - |positiveRemainder| |ldf2lst| |e02bcf| |exp1| |useEisensteinCriterion| - |package| |lookupFunction| |choosemon| |quasiMonicPolynomials| - |exponent| |exprToUPS| |limitPlus| |isExpt| |recip| |isEquiv| - |consnewpol| |difference| |write!| |drawToScale| |setMinPoints3D| - |intChoose| |e01baf| |radicalEigenvector| |region| |signatureAst| - |normalizeAtInfinity| |exprex| |condition| |largest| |laurentRep| - |print| |symmetricProduct| |dark| |readIfCan!| |dimensions| |belong?| - |numberOfOperations| |factorGroebnerBasis| |outputAsScript| - |decompose| |redPol| |vertConcat| |resolve| |expenseOfEvaluationIF| - |laplacian| |voidMode| |showTheRoutinesTable| |getExplanations| - |prinb| |groebner?| |makeFR| |f04adf| |useNagFunctions| |quote| - |coshIfCan| |yCoord| |clearTable!| |unitsColorDefault| |outputFixed| - |lookup| |basisOfMiddleNucleus| |anfactor| |LyndonWordsList| - |exactQuotient!| |mapGen| |OMencodingBinary| |checkRur| - |resultantnaif| |debug3D| |possiblyInfinite?| |createThreeSpace| - |fullDisplay| |badValues| |updatD| |readInt16!| |checkForZero| - |screenResolution| |subHeight| |morphism| |toseInvertibleSet| - |clearCache| |findCycle| |powerSum| |cCsc| |nodeOf?| |SFunction| - |quasiRegular| |deleteRoutine!| |isConnected?| |sum| |drawComplex| - |merge| |simplifyPower| |relationsIdeal| |nthRootIfCan| |iiasech| - |decreasePrecision| |atom?| |fortranCarriageReturn| |cosSinInfo| - |notelem| |iFTable| |coleman| |coercePreimagesImages| |disjunction| - |initTable!| |clipBoolean| |dec| |normalizeIfCan| |Is| - |patternVariable| |dimensionOfIrreducibleRepresentation| |eq| - |seriesSolve| |blue| |setButtonValue| |factorPolynomial| - |resetVariableOrder| |iter| |cothIfCan| |someBasis| |coordinates| - |latex| |rightDivide| |dmpToHdmp| |reducedContinuedFraction| |every?| - |perfectSquare?| |style| |modularFactor| |elRow2!| |matrix| |shift| - |stoseInvertibleSetsqfreg| |c06frf| |f02akf| |bfKeys| |mainMonomial| - |step| |characteristicSerie| |decimal| |imagI| |solid| |ignore?| - |yellow| |ScanRoman| |f04maf| |mirror| |setErrorBound| |has?| - |partialQuotients| |ravel| |operation| |makeop| - |unprotectedRemoveRedundantFactors| |sinhcosh| |htrigs| |f07fdf| - |ScanFloatIgnoreSpacesIfCan| |supersub| |ratDenom| |rangeIsFinite| - |cn| |compile| |approxNthRoot| |red| |reshape| - |factorSquareFreeByRecursion| |check| |leftUnit| |UpTriBddDenomInv| - |pointColorPalette| |outputFloating| |makeTerm| |OMbindTCP| |mapdiv| - |systemSizeIF| |create| |setRow!| |complexNumericIfCan| |logpart| - |roughBase?| |branchIfCan| |cSec| |sinh2csch| |zeroDimPrime?| - |separate| |exp| |leftFactor| |nthRoot| |stoseInvertibleSetreg| - |second| |linkToFortran| |sumOfDivisors| |inRadical?| |connect| - |sort!| |trailingCoefficient| |acosIfCan| |internalSubQuasiComponent?| - |deref| |third| |generic| |leadingSupport| |subResultantChain| - |insert| |empty?| |makeFloatFunction| |units| |nullary?| - |extractSplittingLeaf| |inGroundField?| |medialSet| |genus| |romberg| - |polygamma| |update| |enterInCache| |hex| |iiexp| |f02axf| - |controlPanel| |specialTrigs| |iiperm| |product| |double| - |linearAssociatedOrder| |shallowExpand| |mainCoefficients| |tableau| - |d01asf| |startTable!| |fglmIfCan| |selectOrPolynomials| |besselY| - |generalizedInverse| |upperCase| |mainVariable| |signature| - |graphState| |palgLODE| |leftExtendedGcd| |d01ajf| |rk4qc| - |symmetricTensors| |s01eaf| |bumptab1| |cyclePartition| |edf2fi| |Ci| - |setOrder| |changeNameToObjf| |point| |makeSketch| |factor1| - |generalizedEigenvector| |polCase| |abs| |code| |roughUnitIdeal?| - |character?| |s19acf| |zag| |complexZeros| |sumOfKthPowerDivisors| - |create3Space| |irreducibleFactors| |position| |c06ekf| |filterWhile| - |viewWriteAvailable| |reducedForm| |startPolynomial| |zeroVector| - |noncommutativeJordanAlgebra?| |critBonD| |iidprod| - |solveLinearPolynomialEquationByFractions| |parametersOf| - |filterUntil| |leader| |df2st| |getMultiplicationMatrix| - |lastSubResultantEuclidean| |hexDigit?| |series| - |rationalApproximation| |colorDef| |critT| |cAcsch| |cdr| |select| - |cycles| |f02adf| |baseRDEsys| |sizeMultiplication| |setProperty| - |shallowCopy| |e02ahf| |uniform01| |graphImage| - |univariatePolynomials| |inHallBasis?| |showAll?| |sqfree| - |multiEuclideanTree| |outputAsFortran| |initial| |block| |FormatRoman| - |setlast!| |coth2tanh| |f02bjf| |plotPolar| |powers| - |basisOfLeftNucleus| |setsubMatrix!| |scalarMatrix| |rightZero| - |setOfMinN| |alphabetic?| |neglist| |lazyVariations| |integerBound| - |reopen!| |lifting1| |min| |wreath| |toseInvertible?| |e02bbf| - |tubeRadiusDefault| |corrPoly| |fmecg| |fortranLiteralLine| |unit| - |LowTriBddDenomInv| |badNum| |init| |addiag| |endSubProgram| - |primitive?| |surface| |vconcat| |cAcos| |seriesToOutputForm| |s21bdf| - |e02adf| |normalForm| |inputOutputBinaryFile| |cylindrical| - |clearTheIFTable| |leftRankPolynomial| |compBound| |makeRecord| - |rightRemainder| |OMgetObject| |trivialIdeal?| |maxint| - |ellipticCylindrical| |imagi| |lowerBound| |lSpaceBasis| |unitNormal| - |getButtonValue| |quasiMonic?| |cond| |reduced?| |mapDown!| - |internal?| |functionIsFracPolynomial?| |setPredicates| |pmintegrate| - |minPoints3D| |ode2| |d01anf| |addMatch| |argumentList!| - |constantOperator| |readInt8!| |asimpson| |lprop| |algSplitSimple| - |OMconnectTCP| |enterPointData| |matrixGcd| |youngDiagram| |nlde| - |shuffle| |halfExtendedResultant1| |pdf2ef| |domainTemplate| - |functionIsOscillatory| |associatorDependence| |c06gbf| |normalDeriv| - |indiceSubResultantEuclidean| |irForm| |csch2sinh| |splitLinear| - |semiResultantEuclideannaif| |isAtom| |positive?| |moduloP| |depth| - |separateDegrees| |nativeModuleExtension| |goodnessOfFit| - |patternMatchTimes| |tryFunctionalDecomposition?| |minimumExponent| - |inspect| |stosePrepareSubResAlgo| |equality| |radicalSolve| - |listYoungTableaus| |output| |copyInto!| |subNodeOf?| - |radicalEigenvectors| |geometric| |intersect| |polyPart| |primes| - |support| |sinIfCan| |attributeData| |genericPosition| - |initiallyReduced?| |leastAffineMultiple| |duplicates?| |generators| - |integrate| |primitivePart!| |palgRDE0| |isOp| |reduceBasisAtInfinity| - |vector| |close!| |nthFractionalTerm| |f02bbf| |s17dgf| |midpoint| - |xn| |nothing| |increase| |connectTo| |charthRoot| |groebnerFactorize| - |differentiate| |s18aff| |linearDependenceOverZ| |e01bgf| |normalise| - |integralMatrixAtInfinity| |complexEigenvectors| |host| - |exprHasLogarithmicWeights| |wronskianMatrix| |assign| - |rightExtendedGcd| |overlabel| |laplace| |lazyPquo| |c06fpf| |cyclic| - |shade| |nary?| |FormatArabic| |commonDenominator| |constantKernel| - |constant?| |monomialIntPoly| |purelyTranscendental?| |mesh?| - |polynomialZeros| |numberOfPrimitivePoly| |dioSolve| |listOfMonoms| - |rotatex| |bitTruth| |conjugate| |countRealRoots| - |numberOfComputedEntries| |OMlistSymbols| |zeroMatrix| |d02gbf| - |viewWriteDefault| |leftTrace| |eisensteinIrreducible?| |dom| |sample| - |alphanumeric?| |rootPoly| |nextNormalPoly| |moreAlgebraic?| - |stopTableGcd!| |set| |multMonom| |errorKind| |iisqrt2| |expintegrate| - |dimension| |monicLeftDivide| |properties| |nthExpon| |asechIfCan| - |palgRDE| |seed| |normalizedAssociate| |bitLength| BY |rootKerSimp| - |Aleph| |addPoint| |tubeRadius| |translate| |child?| |cos2sec| - |homogeneous?| |quadratic| |cRationalPower| |reducedSystem| |bag| - |jacobi| |linears| |leftMinimalPolynomial| |innerSolve| - |rowEchelonLocal| |bandedHessian| |enumerate| |build| |c05adf| - |stirling2| |leaves| |key?| |back| |genericLeftNorm| |limit| - |mainCharacterization| |relerror| |sts2stst| |restorePrecision| - |bottom!| |open| |charpol| |infRittWu?| |child| |negative?| |content| - |title| |simpleBounds?| |virtualDegree| |mdeg| |bezoutResultant| - |s19abf| |setLength!| |high| |setprevious!| |distribute| |expandLog| - |cyclicEntries| |removeSuperfluousCases| |rootOfIrreduciblePoly| - |OMputObject| |firstUncouplingMatrix| |cCsch| |rst| |s21bcf| |aCubic| - |complexForm| |nonQsign| |complement| |integer?| |bsolve| |OMgetType| - |roman| |modularGcdPrimitive| |numberOfComposites| |setrest!| - |internalIntegrate0| |computePowers| |subPolSet?| |limitedIntegrate| - |getVariableOrder| |e| |powerAssociative?| |result| NOT - |regularRepresentation| |oddInfiniteProduct| |ramified?| |getDatabase| - |redmat| |mkPrim| |operations| |totalGroebner| |coefChoose| - |triangulate| |identification| OR |c06gsf| |f02ajf| |setFormula!| - |partition| |numberOfIrreduciblePoly| |antiCommutator| |iicot| - |elaborateFile| |OMwrite| |discriminantEuclidean| |setPosition| AND - |numberOfImproperPartitions| |show| |calcRanges| |leaf?| - |complexElementary| |normalElement| |moebiusMu| |mapMatrixIfCan| - |c06fuf| |nextSubsetGray| |subtractIfCan| |makeVariable| - |bivariateSLPEBR| |factors| |e02agf| |arbitrary| - |characteristicPolynomial| |clearFortranOutputStack| |inc| |sequence| - |LyndonCoordinates| |coerceP| |dflist| |e02daf| |psolve| |trace| - |OMsetEncoding| |ScanArabic| |capacity| |setClipValue| - |normInvertible?| |complexNormalize| |jordanAdmissible?| - |knownInfBasis| |fortranLogical| |selectFiniteRoutines| |interpret| - |factorByRecursion| |enqueue!| |qelt| |gcdcofactprim| |squareMatrix| - |rotatez| |bothWays| |finiteBasis| |expandPower| |iidsum| |orbit| - |monomRDE| |qsetelt| |validExponential| |arguments| |invertIfCan| - |select!| |pile| |push!| |generic?| |quickSort| - |halfExtendedResultant2| |bitand| |char| |e01sef| |pole?| |xRange| - |var1StepsDefault| |primlimitedint| |returnType!| |readUInt16!| |lllp| - |Frobenius| |Ei| |algebraicSort| |bitior| |computeCycleEntry| - |strongGenerators| |coord| |yRange| |biRank| |e04mbf| |e04ucf| - |aspFilename| |readBytes!| |invertibleSet| |cubic| - |setScreenResolution3D| |rational?| |zRange| |nullSpace| |c06gqf| - |makingStats?| |irDef| |internalAugment| |createPrimitiveElement| - |normalized?| |defineProperty| |shiftRight| |map!| |taylorRep| - |bfEntry| |littleEndian| |null?| |Hausdorff| |LiePolyIfCan| - |nilFactor| |s17dcf| * |imagk| |doubleComplex?| |showRegion| - |bipolarCylindrical| |qsetelt!| |topFortranOutputStack| |mathieu23| - |fillPascalTriangle| |floor| |constantRight| |numer| |overset?| - |radix| |irVar| |setUnion| |multisect| |previous| |unexpand| |nthCoef| - |lieAlgebra?| |s13adf| |denom| |repeatUntilLoop| |linear| |categories| - |firstDenom| |readByte!| |associator| |identitySquareMatrix| - |normal01| |s21bbf| |fracPart| |e01sbf| |isNot| |lastSubResultant| = - |exponential1| |s17aff| |mr| |splitConstant| |nextSublist| - |structuralConstants| |pi| |kind| |polynomial| |e02bdf| |split| - |leadingIndex| |getGoodPrime| |c06eaf| |sign| |selectsecond| - |henselFact| |infinity| |parent| |complexEigenvalues| |op| |presub| - |wholePart| |updateStatus!| < |acsch| |graphCurves| |OMopenString| - |logIfCan| |fractRagits| |loadNativeModule| |useSingleFactorBound?| - |rightPower| |revert| |primPartElseUnitCanonical!| > |rombergo| - |generalizedContinuumHypothesisAssumed| |currentSubProgram| - |comparison| |genericLeftDiscriminant| |sdf2lst| |genericRightTrace| - |digits| |slex| |ricDsolve| <= |symbolTableOf| |mapExponents| - |monomRDEsys| |stopMusserTrials| |mathieu22| |typeLists| - |binaryTournament| |bitCoef| |subResultantsChain| |e04jaf| >= - |twoFactor| |OMputVariable| |legendre| |position!| |mpsode| - |upperCase!| |quotedOperators| |monicCompleteDecompose| |quotientByP| - |headReduce| |cLog| |head| |member?| |characteristicSet| |buildSyntax| - |sumSquares| |credPol| |pushuconst| |removeZero| |setProperties| - |writeLine!| |primextintfrac| |semiSubResultantGcdEuclidean2| - |selectPolynomials| |factorsOfCyclicGroupSize| |derivationCoordinates| - |getMeasure| |monicDivide| |union| + |recur| |f02aef| |coerceL| - |evenlambert| |generalTwoFactor| |comp| |idealiser| |ratpart| - |selectSumOfSquaresRoutines| |composites| - |OMputFloat| - |singularAtInfinity?| |safeCeiling| |gderiv| |extendedIntegrate| - |mkcomm| |accuracyIF| |dn| |iicoth| / |llprop| |leftRemainder| - |bounds| |argscript| |infLex?| |generalizedEigenvectors| |finite?| - |leftFactorIfCan| |cons| |makeViewport3D| |superHeight| |simplify| - |basisOfLeftAnnihilator| |factorFraction| |trueEqual| |insertTop!| - |rightNorm| |e02dff| |f02xef| |phiCoord| |rank| |stack| |arrayStack| - |getMultiplicationTable| |e02gaf| |iroot| |doublyTransitive?| - |leftQuotient| |associatedSystem| |tan2trig| |row| |completeEval| - |ratPoly| |leftOne| |elaborate| |principalIdeal| |rquo| |queue| - |generalLambert| |paraboloidal| |OMputEndBind| |extendedint| - |padicallyExpand| |monomialIntegrate| |alphabetic| |root?| |cAsec| - |asecIfCan| |clearDenominator| |f02abf| |brillhartTrials| - |adaptive3D?| |next| |printStats!| |cycleRagits| |newTypeLists| - |conjug| |quatern| |exists?| |augment| |allRootsOf| |divideIfCan| - |qroot| |coerce| |weakBiRank| |categoryFrame| |makeGraphImage| - |s14aaf| |source| |cTan| |univcase| |printStatement| |algebraic?| - |diff| |construct| |createNormalPoly| |varselect| |unknownEndian| - |atanIfCan| |implies| |log2| |predicates| |numberOfFactors| |reverse| - |lfintegrate| |rightRegularRepresentation| |perspective| |iiacsc| - |resultantReduitEuclidean| |lists| |weighted| |mainPrimitivePart| - |genericLeftMinimalPolynomial| |upperBound| |wholeRadix| |name| - |crest| |RemainderList| |ramifiedAtInfinity?| |pointPlot| - |interReduce| |lowerCase| |safetyMargin| |bat1| |rightOne| |hexDigit| - |rewriteIdealWithRemainder| |body| |fi2df| - |removeSuperfluousQuasiComponents| |aQuadratic| |backOldPos| |bipolar| - |e01bef| |eigenvector| |factorials| |testDim| |acothIfCan| - |extendedResultant| |target| |mapSolve| |clearTheSymbolTable| - |iflist2Result| |endOfFile?| |principal?| |innerint| |returns| - |entry?| |modifyPointData| |trapezoidalo| |OMconnOutDevice| - |nthExponent| |OMUnknownCD?| |generalPosition| |rightUnit| - |leftExactQuotient| |prime| |extractProperty| |leftDiscriminant| - |rename!| |maximumExponent| |gramschmidt| |showClipRegion| |solveid| - |cyclicGroup| |top!| |subMatrix| |lexGroebner| |se2rfi| - |basisOfRightAnnihilator| |ceiling| |semiDiscriminantEuclidean| - |s17ajf| |cyclicSubmodule| |leadingBasisTerm| |changeMeasure| - |contract| |primintfldpoly| |definingInequation| - |generalInfiniteProduct| |rootsOf| |rule| |lazyPseudoRemainder| - |isPower| |fortranDoubleComplex| |mainSquareFreePart| |insertRoot!| - |hessian| |createPrimitivePoly| |internalZeroSetSplit| |besselJ| - |functionIsContinuousAtEndPoints| |prinshINFO| |port| |lyndon| - |lastSubResultantElseSplit| |doubleFloatFormat| |extension| - |flexible?| |mathieu24| |multiplyExponents| |curry| |float?| - |linearAssociatedLog| |groebgen| |ridHack1| |pseudoDivide| - |linearAssociatedExp| |minRowIndex| |nextPrimitiveNormalPoly| - |writeBytes!| |t| |csubst| |hclf| |OMreadFile| |argumentListOf| - |generalSqFr| |e04dgf| |repeating?| |internalDecompose| - |rationalPoints| |swapColumns!| |iiacsch| |constDsolve| |quoByVar| - |OMencodingUnknown| |genericRightNorm| |leftLcm| |superscript| - |rightRankPolynomial| |sinhIfCan| |atanhIfCan| |reseed| - |chainSubResultants| |leftRank| |macroExpand| |OMreceive| |viewport3D| - |rationalFunction| |setelt| |putProperties| |LyndonWordsList1| - |forLoop| |norm| |symmetricRemainder| |factorSquareFreePolynomial| - |clipWithRanges| |sparsityIF| |mapmult| |modularGcd| - |mainDefiningPolynomial| |parts| |eof?| |lowerCase!| |mergeFactors| - |expenseOfEvaluation| |rowEch| |rational| |interpolate| |copy| |any| - |iiasinh| |xCoord| |numerator| |transcendent?| |numFunEvals| |debug| - |bit?| |firstSubsetGray| |exactQuotient| |xor| |hdmpToP| |Lazard2| - |closeComponent| |reindex| |pleskenSplit| |symbol?| D - |constantOpIfCan| |SturmHabichtSequence| |setCondition!| |bigEndian| - |case| |escape| |outputGeneral| |pdct| |subSet| |f02awf| - |OMputEndError| |extractPoint| |tan2cot| |Zero| |mindeg| |saturate| - |nodes| |cap| |univariateSolve| |unit?| |iCompose| |edf2ef| |tab1| - |One| |janko2| |mapUp!| |stiffnessAndStabilityFactor| |Nul| |maxIndex| - |true| |match?| |selectOptimizationRoutines| |lyndon?| |froot| - |selectNonFiniteRoutines| |cycleElt| |autoCoerce| - |parabolicCylindrical| |rdregime| |bezoutDiscriminant| |round| - |balancedBinaryTree| |removeDuplicates!| |axes| |monomial?| - |differentialVariables| |var1Steps| |removeSquaresIfCan| - |upDateBranches| |graphs| |lineColorDefault| |plusInfinity| |qqq| - |antiAssociative?| |pointSizeDefault| |karatsubaOnce| |divisors| - |insertBottom!| |contractSolve| |rationalPoint?| |palgextint| - |mainKernel| |operators| |f04mbf| |minusInfinity| |composite| - |solveLinearlyOverQ| |curveColorPalette| |frst| |eigenvalues| - |lfextendedint| |summation| |optAttributes| |factorAndSplit| - |datalist| |physicalLength!| |removeRedundantFactors| |leftMult| - |bubbleSort!| |createPrimitiveNormalPoly| |elt| |iteratedInitials| - |symmetricDifference| |plenaryPower| |front| |s18dcf| |comment| - |qinterval| |patternMatch| |remove!| |deriv| |rightMinimalPolynomial| - |makeCos| |elaboration| |particularSolution| |integralRepresents| - |iiacos| |reduceLODE| |tower| |f04asf| |diagonal| |smith| |transform| - |resetBadValues| |stop| |presuper| |antiCommutative?| |postfix| - |initiallyReduce| |deepCopy| |solid?| |real?| |listConjugateBases| - 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|halfExtendedSubResultantGcd1| |leadingSupport| |iilog| + |currentEnv| |ideal| |numberOfDivisors| |bumptab| |airyBi| + |reduceByQuasiMonic| |currentScope| |updateStatus!| |torsion?| + |physicalLength!| |semiResultantEuclideannaif| |credPol| |someBasis| + |testDim| |s15aef| |unitsColorDefault| |plotPolar| |deepCopy| + |makeObject| |eq?| |isEquiv| |basisOfLeftNucloid| |sincos| + |infieldIntegrate| |qelt| |uncouplingMatrices| |e01sef| |firstDenom| + |selectMultiDimensionalRoutines| |selectPDERoutines| |linear| + |selectOrPolynomials| |coef| |factors| |isTimes| |LyndonBasis| + |generalInfiniteProduct| |qsetelt| |factorSFBRlcUnit| |iidsum| + |extend| |mkcomm| |diagonalMatrix| |printStatement| + |integralAtInfinity?| |rightExtendedGcd| |newSubProgram| |drawComplex| + |create3Space| |partialFraction| |xRange| |functionIsFracPolynomial?| + |pr2dmp| |sizeLess?| |splitSquarefree| |outputFloating| |arity| + |polynomial| |zoom| |resetAttributeButtons| |mvar| |associatedSystem| + |pointData| |s14abf| |yRange| |startTable!| |gcdprim| |minPoints| + |jokerMode| |orbits| |augment| |list?| |iomode| |rationalFunction| + |distFact| |karatsubaDivide| |zRange| |seed| |divisorCascade| + |realElementary| |shellSort| |maxint| |e02bcf| |f01rcf| |sort| + |lifting1| |squareFreePart| |rootPower| |intensity| |map!| |mindeg| + |genericLeftNorm| |duplicates?| |trapezoidalo| |acothIfCan| |integers| + |factorSquareFree| |dec| |makeop| |setTex!| |innerSolve1| |taylorRep| + |qsetelt!| |s14baf| |nextPrimitiveNormalPoly| |number?| |iterationVar| + |f2st| |calcRanges| |rightRegularRepresentation| |divide| |s21bcf| + |PDESolve| |minimize| |iiasin| |deleteProperty!| |traverse| + |setFormula!| |prime?| |euclideanGroebner| |collect| + |createNormalElement| |removeRedundantFactors| |subResultantChain| + |cscIfCan| |outputFixed| |orbit| |solid?| |realRoots| |random| + |asinIfCan| |graphCurves| |btwFact| |isAtom| |pushuconst| + |coordinates| |sizePascalTriangle| |listBranches| |myDegree| + |collectUpper| |leadingTerm| |physicalLength| |rootsOf| + |irreducibleFactors| |stoseInvertible?sqfreg| |digit?| |kind| + |computeInt| |pole?| |makeTerm| |e01bhf| |flexibleArray| |consnewpol| + |eigenMatrix| |stFuncN| |partitions| |acsch| |readByte!| |op| + |ellipticCylindrical| |unmakeSUP| |c06ebf| |powers| |e02agf| + |overlabel| |factor| |dual| |tan2trig| |replace| |newLine| + |setPredicates| |mainVariable?| |allRootsOf| |algebraic?| |comp| + |e01saf| SEGMENT |equiv| |quasiComponent| |sqrt| |merge| + |normalizedAssociate| |figureUnits| |extendedResultant| + |characteristic| |nthFlag| |minPol| |bfEntry| |putProperties| + |createMultiplicationMatrix| |real| |conjugates| |OMgetApp| |rules| + |groebnerIdeal| |OMconnOutDevice| |blankSeparate| |exp1| |d03edf| + |reflect| |sin?| |clipPointsDefault| |imag| |algebraicCoefficients?| + |saturate| |generators| |denominator| |setVariableOrder| |infieldint| + |real?| |charClass| |wreath| |unprotectedRemoveRedundantFactors| + |directProduct| |aCubic| |OMsend| |writeBytes!| |permutation| + |monomRDE| |max| |open?| |shanksDiscLogAlgorithm| |mainContent| + |lexTriangular| |leftMult| |orthonormalBasis| |zerosOf| |union| + |lookup| |tensorProduct| |OMbindTCP| |leaf?| |skewSFunction| + |tracePowMod| |perspective| |brace| |positive?| |empty?| |arguments| + |getIdentifier| |OMgetEndBVar| |s21baf| |numeric| |screenResolution3D| + |hitherPlane| |arbitrary| |c06ekf| |OMopenString| + |lazyPseudoRemainder| |destruct| |stirling1| |writeByte!| |elementary| + |latex| |radical| |var1StepsDefault| |linGenPos| |divideIfCan| + |solve1| |laplace| |optional?| |subscript| |linearAssociatedOrder| + |removeZero| |associator| |cAsinh| |imagi| |basisOfLeftNucleus| + |bivariate?| |s18def| |dequeue!| |balancedFactorisation| |row| + |entries| |selectSumOfSquaresRoutines| |midpoints| |leftTraceMatrix| + |mapSolve| |baseRDE| |bat| |copy| |prefixRagits| |difference| + |simplifyPower| |internalIntegrate| |semiDegreeSubResultantEuclidean| + |discriminant| |duplicates| |showFortranOutputStack| |pmintegrate| + |rotatex| |diff| |littleEndian| |c02agf| |zeroSetSplit| |cAsin| + |monomial| |setRealSteps| |bitLength| |OMputEndApp| |nthExponent| + |bytes| |OMParseError?| |tRange| |LyndonWordsList1| + |tubePointsDefault| |multivariate| |OMread| |powern| |bandedHessian| + |reducedDiscriminant| |validExponential| |RittWuCompare| + |useEisensteinCriterion| |listConjugateBases| |f07aef| + |squareFreePolynomial| |variables| |invertible?| |complexForm| |nodes| + |multiplyCoefficients| |rightExactQuotient| |basisOfMiddleNucleus| + |chiSquare1| |rightMult| |ddFact| |scaleRoots| |ranges| + |makeFloatFunction| |deepestInitial| |bubbleSort!| |condition| + |usingTable?| |match?| |ODESolve| |zeroOf| |pow| |commutative?| + |complexElementary| |autoCoerce| |complexLimit| |sinhcosh| |dequeue| + |moduloP| |parabolicCylindrical| |setEpilogue!| |intersect| |iiGamma| + |clearTheSymbolTable| |mapdiv| |coHeight| |shallowExpand| |isPower| + |lex| |interpret| |inverse| |lineColorDefault| |principalAncestors| + |primlimitedint| |qroot| |randnum| |solid| |makeRecord| |s13aaf| + |debug| |insert!| |setProperties| |oddlambert| |any?| |octon| + |indicialEquationAtInfinity| |copy!| |setchildren!| |iisqrt3| + |primintegrate| |heap| D |taylor| |viewWriteAvailable| |eyeDistance| + |close| |multiple?| |push| |setsubMatrix!| |minPoints3D| F |meatAxe| + |c06eaf| |completeEval| |relationsIdeal| |laurent| |d01fcf| + |composites| |patternVariable| |bitTruth| |cycle| |OMputAtp| + |setImagSteps| |e02akf| |puiseux| |setScreenResolution| |display| + |internalLastSubResultant| |polar| |iiasinh| |vedf2vef| + |createNormalPoly| |boundOfCauchy| |showTheFTable| |null?| + |unrankImproperPartitions1| |rootKerSimp| |supDimElseRittWu?| + |argscript| |df2mf| |fortranLogical| |remainder| |removeZeroes| + |merge!| |GospersMethod| |inv| |getOperator| |partialNumerators| + |setMinPoints| |singleFactorBound| |hypergeometric0F1| |cExp| + |lookupFunction| |mix| |e01bgf| |ground?| |cap| |enumerate| + |rubiksGroup| |sPol| |conditionP| |systemSizeIF| |d01aqf| |opeval| + |distribute| |nullSpace| |ground| |nullary?| |rdregime| |polyPart| + |createMultiplicationTable| |groebner?| |setright!| |adaptive| + |fortran| |rightRankPolynomial| |goto| |tab| |input| |leadingMonomial| + |numericIfCan| |monicRightFactorIfCan| |rotate!| |mapExponents| + |e02adf| |weakBiRank| |normalElement| |leadingExponent| |f07adf| + |writeInt8!| |solveLinearlyOverQ| |library| |leadingCoefficient| + |OMopenFile| |mainCoefficients| |gcdPrimitive| |OMputBVar| + |rewriteIdealWithRemainder| |size| EQ |ignore?| + |functionIsOscillatory| |d01akf| |primitiveMonomials| |print| + |headAst| |listOfLists| |qqq| |iiatan| |meshPar1Var| |f02abf| + |showAll?| |lazyPseudoQuotient| |polCase| |e01sff| |resolve| + |reductum| |OMputFloat| |writeLine!| |viewDefaults| + |numberOfOperations| |internalInfRittWu?| |groebgen| |lyndonIfCan| + |extractIndex| |semiDiscriminantEuclidean| |cyclicParents| |s13acf| + |satisfy?| |dimensionOfIrreducibleRepresentation| |lowerBound| + |initials| |makeEq| |gcdPolynomial| |sign| |f02xef| |getCurve| |set| + |paren| |explicitEntries?| |overbar| |nonSingularModel| + |explimitedint| |digit| |curveColorPalette| |polyred| |headReduce| + |simpson| |xCoord| |selectFiniteRoutines| |getDatabase| |determinant| + |generator| |palglimint0| |unitVector| |categories| |findCycle| + |palglimint| |unrankImproperPartitions0| |showTheSymbolTable| + |divideExponents| |numberOfIrreduciblePoly| |diagonal| |decrease| + |associatedEquations| |rCoord| |OMgetAtp| |primes| |makeFR| + |putColorInfo| |variationOfParameters| |dominantTerm| |normalise| + |c06gqf| |expandLog| |iisqrt2| |idealSimplify| |ptFunc| |s17dlf| + |radPoly| |localAbs| |sinhIfCan| |OMsupportsCD?| |rotate| |moebius| + |denominators| |mathieu12| |normalForm| |newReduc| |f02adf| |node| + |acotIfCan| |fortranCompilerName| |resultantEuclideannaif| + |outputGeneral| |fi2df| |seriesSolve| |monomRDEsys| |true| + |brillhartTrials| |sqfree| |category| |yellow| |associatorDependence| + |permutationGroup| |euler| |antiAssociative?| |setColumn!| |cosh2sech| + |signAround| |ridHack1| |domain| |irreducible?| + |LagrangeInterpolation| |abs| |sort!| |chebyshevT| |chvar| + |subscriptedVariables| |leftRegularRepresentation| |cyclicCopy| + |package| |lieAdmissible?| |s17ajf| |phiCoord| |elRow1!| |isQuotient| + |insert| |wholeRagits| |lSpaceBasis| |factorGroebnerBasis| |nthFactor| + |redmat| |selectsecond| |readUInt8!| |chineseRemainder| |cLog| + |search| |show| |algint| |factorByRecursion| |maxrank| + |symmetricSquare| |rewriteSetByReducingWithParticularGenerators| + |incr| |unitNormalize| |powerSum| |conjunction| |script| |cross| + |f01brf| |semiSubResultantGcdEuclidean1| |numerator| |antiCommutator| + |smith| |hi| |magnitude| |d01amf| |permutationRepresentation| + |simpsono| |trace| |multisect| |nonLinearPart| |mappingMode| + |reduction| |OMreadStr| |directory| |integralMatrixAtInfinity| + |sncndn| |cyclicEntries| |compose| |scalarTypeOf| + |inputOutputBinaryFile| |f04adf| |limitedint| |s19aaf| + |nextIrreduciblePoly| |c06ecf| |frst| |makingStats?| |tex| |height| + |bumprow| |swap!| |cot2tan| |multiEuclideanTree| |baseRDEsys| + |atanhIfCan| |power!| |c06gbf| |expintegrate| |computeBasis| + |exprToXXP| |removeSuperfluousQuasiComponents| |elem?| |adaptive3D?| + |rightRank| |extractTop!| |e04fdf| |pdct| |units| |outerProduct| + |support| |stopMusserTrials| |OMReadError?| + |rightCharacteristicPolynomial| |e02bef| |increasePrecision| + |hdmpToDmp| |roughUnitIdeal?| F2FG |pointSizeDefault| |unitNormal| + |outputAsScript| |cAtan| |OMgetSymbol| |equation| |ScanRoman| |point| + |arrayStack| |cyclicSubmodule| |trailingCoefficient| |element?| + |sorted?| |scripted?| |mkPrim| |cfirst| |infinite?| |index?| + |fortranTypeOf| |pushucoef| |comment| + |semiIndiceSubResultantEuclidean| |enqueue!| |unvectorise| |iicot| + |ref| |center| |henselFact| |central?| |polyRDE| |head| |double?| + |numberOfCycles| |makeViewport2D| |transform| |numFunEvals3D| + |coerceListOfPairs| |series| |cCsc| |removeSuperfluousCases| |code| + |Gamma| |blue| |cylindrical| |ocf2ocdf| |kmax| |OMgetEndObject| + |declare| |mainValue| |trace2PowMod| |sec2cos| |innerEigenvectors| + |numericalIntegration| |totalLex| |transcendent?| |clip| + |sizeMultiplication| |complexEigenvectors| |eigenvalues| |irDef| + |numberOfChildren| |block| |log10| |unexpand| |aQuadratic| + |localIntegralBasis| |redpps| |rule| |generate| |build| + |leadingCoefficientRicDE| |callForm?| |setStatus| |OMputAttr| + |constantIfCan| |bitand| |useNagFunctions| |mapUnivariateIfCan| + |categoryFrame| |printStats!| |BasicMethod| |min| |reseed| + |character?| |solve| |dimension| |bitior| |selectfirst| |hasoln| + |decompose| |totalGroebner| |algebraicOf| |incrementBy| |normalDeriv| + |realEigenvalues| |makeSeries| |matrix| |subSet| |firstNumer| + |nextNormalPrimitivePoly| |gcdcofactprim| |fortranInteger| |lazyPrem| + |tail| |expand| |leadingBasisTerm| |bombieriNorm| + |getMultiplicationTable| |printInfo| |nextColeman| |sinIfCan| + |getButtonValue| |e02ddf| |fractionFreeGauss!| |resetBadValues| + |filterWhile| |f04maf| |cAtanh| |expint| |expintfldpoly| + |karatsubaOnce| |f04qaf| |resize| |elaborateFile| |alternating| + |filterUntil| |complex?| |fprindINFO| |even?| |acosIfCan| + |setButtonValue| |clearTheIFTable| |numFunEvals| |setProperty| + |setClosed| |select| |parent| |rootOfIrreduciblePoly| |nodeOf?| + |fill!| |f02aff| |measure| |acoshIfCan| |unravel| |tanQ| |properties| + |pascalTriangle| |isOpen?| |internalAugment| |lift| |member?| + |chiSquare| |backOldPos| |cotIfCan| |trigs2explogs| |cycleRagits| + |host| |lfextendedint| |infiniteProduct| |translate| |reduce| + |makeUnit| |nthCoef| |complementaryBasis| |redPol| |result| + |derivative| |FormatRoman| |subset?| |printCode| |cTanh| |outputForm| + |contours| |appendPoint| |quote| |makeGraphImage| + |numberOfFractionalTerms| |completeSmith| |imaginary| |s19acf| + |pointLists| |constantCoefficientRicDE| |intPatternMatch| + |squareMatrix| |radicalOfLeftTraceForm| |rootNormalize| + |chainSubResultants| |indiceSubResultantEuclidean| |pseudoQuotient| + |monicLeftDivide| |stoseLastSubResultant| |push!| |graphStates| + |minimalPolynomial| |coefChoose| |roughEqualIdeals?| |e02gaf| + |changeMeasure| |f02awf| |delete!| |UP2ifCan| |insertMatch| + |commaSeparate| |presuper| Y |setAttributeButtonStep| |isPlus| |power| + |factorset| |attributeData| |leftRankPolynomial| |palgextint0| + |basisOfCommutingElements| |ldf2vmf| |mirror| |SFunction| |preprocess| + |f04atf| |shrinkable| |primitiveElement| |quasiMonic?| |birth| |label| + |OMwrite| |e01daf| |critMTonD1| |cSin| |internalSubQuasiComponent?| + |clipParametric| |bipolar| |members| |shallowCopy| + |complexEigenvalues| |createPrimitiveElement| |OMputObject| + |stronglyReduce| |empty| |rotatez| |bit?| |qPot| |newTypeLists| + |exprHasLogarithmicWeights| |summation| |transcendentalDecompose| + |characteristicSet| |monomial?| |parents| |cAcosh| |antisymmetric?| + |convergents| |setlast!| |represents| |irreducibleFactor| |normalize| + |numberOfNormalPoly| |elliptic?| |mkAnswer| |vertConcat| |writable?| + |s14aaf| |byte| |irForm| |zag| |factorsOfDegree| |accuracyIF| + |dAndcExp| |coshIfCan| |createIrreduciblePoly| |viewSizeDefault| + |increase| |removeCosSq| |rightFactorIfCan| |nthExpon| |elements| + |multinomial| |over| |getRef| |triangulate| |rightDiscriminant| + |iroot| |contract| |constructor| |s17akf| |find| |compBound| + |generic?| |antiCommutative?| |lambert| |constDsolve| |categoryMode| + |mainExpression| |OMputEndError| |mainVariables| |option| |exQuo| + |solveInField| |subspace| |showSummary| |mapBivariate| |palgLODE0| + |outputList| |hostByteOrder| |limit| |primitive?| |linearDependence| + |vark| |discriminantEuclidean| |bfKeys| |substitute| |quasiRegular| + |separant| |stack| |printInfo!| |cAcoth| |lowerCase!| |e02ahf| + |double| |crushedSet| |rur| |showAttributes| |shufflein| |printHeader| + |deref| |differentialVariables| |semiResultantEuclidean2| + |interReduce| |setDifference| |conjug| |mat| |int| |range| + |leftAlternative?| |setClipValue| |leftUnit| |coth2tanh| |noKaratsuba| + |structuralConstants| |updatD| |f02agf| |pointColor| |rightTrim| + |buildSyntax| |round| |sechIfCan| |cycleEntry| |name| |signature| + |cTan| UTS2UP |polygon?| |aspFilename| |less?| |sdf2lst| + |rightQuotient| |leftTrim| |univariatePolynomialsGcds| |disjunction| + |laurentRep| |body| |doubleResultant| |identification| |dim| + |UnVectorise| |vector| |parabolic| |setValue!| |redPo| |output| + |quadraticForm| |companionBlocks| |diagonalProduct| |squareFree| + |null| |semiResultantReduitEuclidean| |differentiate| + |cyclotomicFactorization| |mdeg| |tableau| |asechIfCan| |dn| + |identity| |subNode?| |s18aef| |addPoint2| |shift| |not| + |PollardSmallFactor| |rationalPoint?| |subResultantGcd| |green| BY + |halfExtendedSubResultantGcd2| |denomLODE| |status| + |monomialIntegrate| |d02gaf| |declare!| |and| |connectTo| + |integralMatrix| |youngDiagram| |extractPoint| |iitanh| + |getProperties| |routines| |directSum| |radicalEigenvectors| |or| + |quoByVar| |top!| |Ci| |denomRicDE| |surface| |mesh?| |flexible?| + |sub| |xor| |applyRules| |s18adf| |stoseIntegralLastSubResultant| + |rootPoly| |mainCharacterization| |mergeFactors| |qualifier| + |increment| |limitedIntegrate| |case| |basisOfLeftAnnihilator| + |swapRows!| |readInt16!| |assert| |symbol?| |transpose| |port| + |lowerCase| |repeating| |perfectNthPower?| |s17acf| |pattern| |Zero| + |external?| |functorData| |perfectSqrt| |numberOfVariables| + |var1Steps| |outputMeasure| |quasiRegular?| |elaboration| |iExquo| + |One| |mainMonomial| |readBytes!| |squareFreeLexTriangular| + |binarySearchTree| |symmetricProduct| |scale| |normalizedDivide| |t| + |abelianGroup| |overset?| |linears| NOT |e02bdf| |bezoutResultant| + |countRealRootsMultiple| |nthRoot| |sylvesterMatrix| |rightTrace| + |ratDsolve| |UpTriBddDenomInv| |lyndon?| |sech2cosh| |rischDE| + |segment| OR |OMencodingSGML| |dictionary| |adaptive?| |mpsode| + |linearPart| |cond| |rationalApproximation| |delta| + |genericRightTrace| |meshPar2Var| |totalDegree| |message| + |solveRetract| |nullity| AND |rectangularMatrix| |palgextint| + |retractable?| |pointColorDefault| |initTable!| |getCode| + |normInvertible?| |alphabetic| |mathieu24| |specialTrigs| |resultant| + |dualSignature| |nlde| |exprToGenUPS| |iicoth| + |generalizedContinuumHypothesisAssumed?| |polynomialZeros| |iiacoth| + |complete| |OMgetError| |elt| |s17aef| |subMatrix| |scan| |critMonD1| + |permanent| |colorFunction| |pdf2df| |diag| |monicModulo| |f04mcf| + |second| |charthRoot| |modTree| |setOrder| |goodPoint| |suchThat| + |call| |expenseOfEvaluation| |vconcat| |bivariatePolynomials| + |printTypes| |third| |generalTwoFactor| |OMencodingUnknown| + |checkForZero| |factorFraction| |nextNormalPoly| |inputBinaryFile| + |leftScalarTimes!| |pToHdmp| |eulerE| |getVariableOrder| + |leftMinimalPolynomial| |rewriteSetWithReduction| |f04arf| |airyAi| + |constantOpIfCan| |cons| |void| |relerror| |safetyMargin| |OMputBind| + |radix| |particularSolution| |exponential| |powmod| |invertibleSet| + |subCase?| |sumOfSquares| |shiftRoots| |systemCommand| |polyRicDE| + |digits| |getSyntaxFormsFromFile| |fixedDivisor| |coefficients| + |characteristicSerie| |s19abf| |closedCurve?| |separateFactors| + |removeSquaresIfCan| |dark| |dmp2rfi| |elseBranch| |d02cjf| |key?| + |split!| |rightGcd| |regime| |cosIfCan| |leaves| + |stoseInvertibleSetreg| |s20adf| |coerceImages| |tanhIfCan| + |uniform01| |colorDef| |e02dcf| |froot| * |split| |mainKernel| + |shuffle| |quasiAlgebraicSet| |ord| |clipBoolean| |mappingAst| + |Vectorise| |normal| |root?| |dot| |rootProduct| |radicalEigenvalues| + |macroExpand| |dmpToP| |iiacot| |upperCase!| |integralBasis| + |numberOfPrimitivePoly| |complexNormalize| |distance| + |multiplyExponents| |iiperm| |expr| |lazyPseudoDivide| + |changeNameToObjf| |lexGroebner| |ksec| |source| |Lazard| + |irreducibleRepresentation| |d01gbf| |purelyAlgebraic?| + |primitivePart| |viewpoint| |groebnerFactorize| = + |euclideanNormalForm| |mathieu11| |rightRecip| |llprop| |iicsc| + |rowEch| |powerAssociative?| |readLineIfCan!| |idealiser| |nullary| + |trueEqual| |OMgetEndBind| |pushNewContour| |addmod| |plusInfinity| + |cAcos| |polygon| |OMcloseConn| |removeSinhSq| |s15adf| + |genericRightNorm| < |inverseIntegralMatrixAtInfinity| + |screenResolution| |moreAlgebraic?| |cPower| |minusInfinity| + |tanIfCan| |setref| |integralRepresents| |irVar| |mulmod| |char| + |variable| |genericRightDiscriminant| > |tanintegrate| |atrapezoidal| + |singularAtInfinity?| |SturmHabichtSequence| |upDateBranches| + |showTheRoutinesTable| |bat1| |ScanFloatIgnoreSpaces| |findBinding| + |makeMulti| |iterators| |decimal| <= |setLength!| |cubic| + |associates?| |e02ajf| |target| |failed?| + |createLowComplexityNormalBasis| |B1solve| |critT| + |univariatePolynomial| |innerSolve| >= |SturmHabichtMultiple| + |moduleSum| |numberOfComponents| |linkToFortran| |normalizeIfCan| + |acschIfCan| |slex| |graphImage| |setelt!| + |stoseInternalLastSubResultant| |leadingIndex| |operators| + |halfExtendedResultant1| |lllip| |univariate?| |d02bbf| |readIfCan!| + |cAsec| |constantLeft| |selectNonFiniteRoutines| |minset| |makeSketch| + |hostPlatform| |inconsistent?| |type| |leftRemainder| |dioSolve| + |jordanAdmissible?| |option?| |curry| |iiatanh| |id| |rootRadius| + + |problemPoints| |se2rfi| |quotedOperators| |untab| + |showIntensityFunctions| |move| |yCoordinates| |meshFun2Var| + |ParCondList| |lo| |algebraicVariables| - |float| |unaryFunction| + |imagJ| |extractBottom!| |mergeDifference| |toroidal| |reorder| + |regularRepresentation| |direction| |product| |s18aff| / |insertTop!| + |subHeight| |compiledFunction| |permutations| |euclideanSize| + |rational| |sin2csc| |more?| |ratpart| |fractRadix| |OMUnknownSymbol?| + |pop!| |numerators| |minPoly| |createLowComplexityTable| + |setTopPredicate| |iiacos| |changeBase| |OMgetInteger| |leftLcm| + |optpair| |makeprod| |stopTableGcd!| |size?| |geometric| |conical| + |seriesToOutputForm| |keys| |OMputApp| |maxPoints| |cyclicEqual?| + |setScreenResolution3D| |high| |setCondition!| |value| |symbolTable| + |graphs| |rightOne| |getExplanations| |removeConstantTerm| |setUnion| + |expt| |imagI| |elColumn2!| |delay| |stopTable!| |curve| |d03faf| + |ricDsolve| |sortConstraints| |cAcsch| |rowEchelonLocal| |outputAsTex| + |pdf2ef| |f04mbf| |sumOfDivisors| |pushFortranOutputStack| |Is| + |LazardQuotient| |KrullNumber| |univariatePolynomials| |asecIfCan| + |OMputEndAttr| |getGoodPrime| |removeDuplicates| |cyclic?| |expIfCan| + |popFortranOutputStack| |makeSUP| |Beta| |dimensions| |changeVar| + |node?| |cycleElt| |monic?| GE |basisOfRightAnnihilator| |factor1| + |rk4a| |bounds| |outputAsFortran| |knownInfBasis| |listOfMonoms| + |changeName| |subQuasiComponent?| |f01ref| |integralCoordinates| GT + |f07fef| |whitePoint| |monicCompleteDecompose| |fixedPointExquo| + |getBadValues| |extensionDegree| |singular?| |float?| |beauzamyBound| + LE |morphism| |rightNorm| |e02baf| |mkIntegral| |rk4| |linear?| + |lazyResidueClass| |oddInfiniteProduct| |d01gaf| LT |getlo| + |withPredicates| |OMlistCDs| |interpolate| |ode1| + |rangePascalTriangle| |reduceLODE| |open| |linearDependenceOverZ| + |OMputEndBVar| |addBadValue| |multMonom| |inverseLaplace| + |extendIfCan| |lflimitedint| |getGraph| |tree| |superscript| + |setprevious!| |rational?| |evaluateInverse| + |exprHasWeightCosWXorSinWX| |s21bdf| |const| |f01maf| |environment| + |resultantReduit| |rowEchelon| |bigEndian| |hexDigit| |sn| |prinb| + |inHallBasis?| |e04gcf| |bindings| |composite| |laurentIfCan| |rarrow| + |aQuartic| |padicFraction| |cdr| |index| |symbolIfCan| |operations| + |generalizedEigenvector| |domainTemplate| |inRadical?| |belong?| + |symbolTableOf| |dfRange| |clearDenominator| |isNot| |precision| + |c06fqf| |ceiling| |removeRoughlyRedundantFactorsInContents| |f01qcf| + |minrank| |binomThmExpt| |linearAssociatedLog| |jacobiIdentity?| + |lazy?| |d01bbf| |quotientByP| |read!| |children| |pair| |s20acf| + |e02dff| |hasTopPredicate?| |stoseInvertible?| |bright| + |radicalEigenvector| |primPartElseUnitCanonical!| |basisOfCenter| + |ramified?| |approxSqrt| |deepExpand| |toseInvertibleSet| |cAsech| + |genericLeftTrace| |resetNew| |primeFactor| |imports| + |nthFractionalTerm| |maxPoints3D| |removeIrreducibleRedundantFactors| + |pureLex| |dflist| |FormatArabic| |eval| |f04asf| |degreeSubResultant| + |width| |repeating?| |iicosh| |pushdterm| |coth2trigh| |byteBuffer| + |removeDuplicates!| |partition| |modularFactor| |lazyPremWithDefault| + |showAllElements| |errorKind| |indices| |components| + |integralDerivationMatrix| |cycles| |modulus| |readUInt32!| + |startTableInvSet!| |escape| |checkPrecision| |sparsityIF| |error| + |root| |order| |aLinear| |tanh2coth| |lfextlimint| |edf2efi| + |resultantnaif| |iibinom| |subst| |unit| |string?| |fglmIfCan| + |errorInfo| |computeCycleEntry| |d01ajf| |connect| |optimize| |mr| + |rangeIsFinite| |singRicDE| |queue| |userOrdered?| |gbasis| + |lastSubResultant| |function| |infLex?| |shape| |curryLeft| + |wholeRadix| |notelem| |normFactors| |optional| |viewDeltaXDefault| + GF2FG |c05pbf| |mapUnivariate| |cCos| |csc2sin| |prevPrime| + |getOperands| |basisOfNucleus| |asimpson| |splitNodeOf!| |rombergo| + |leftDivide| |HenselLift| |alternatingGroup| |any| |normDeriv2| + |multiEuclidean| |loopPoints| |branchIfCan| |fullPartialFraction| + |region| |makeSin| |showRegion| |varList| |iipow| |rename!| + |infRittWu?| |spherical| |objects| |totolex| |e02daf| + |totalDifferential| |modularGcdPrimitive| |f02bbf| |extract!| + |rootBound| |subResultantsChain| |base| |minimumDegree| |ode| + |qinterval| |stosePrepareSubResAlgo| |internalDecompose| |toScale| + |rk4qc| |sayLength| |rightAlternative?| |commonDenominator| + |functionIsContinuousAtEndPoints| |po| |polygamma| |complexRoots| + |debug3D| |collectUnder| |rightScalarTimes!| |rem| + |toseSquareFreePart| |getOrder| |removeRoughlyRedundantFactorsInPol| + |oddintegers| |rewriteIdealWithQuasiMonicGenerators| |compactFraction| + |generalizedEigenvectors| |cCot| |setvalue!| |flatten| |quo| |module| + |mapmult| |conditionsForIdempotents| + |solveLinearPolynomialEquationByFractions| |getMeasure| |elRow2!| + |readInt32!| |strongGenerators| |viewWriteDefault| + |basisOfRightNucloid| |LowTriBddDenomInv| |iFTable| + |nextLatticePermutation| |encodingDirectory| |wordInGenerators| + |wordsForStrongGenerators| |prepareSubResAlgo| |hdmpToP| |div| + |approxNthRoot| |crest| |bipolarCylindrical| |generalLambert| |ravel| + |secIfCan| |weight| |exponential1| |lcm| |indicialEquations| + |startTableGcd!| |tubePlot| |exquo| |delete| |readLine!| |binding| + |lfunc| |reshape| |quadratic| |modifyPoint| |lprop| |child| + |thenBranch| ~= |generalizedContinuumHypothesisAssumed| |isList| + |complexExpand| |reverse!| |decomposeFunc| |eulerPhi| + |createRandomElement| |append| |maximumExponent| |cSec| |#| + |matrixConcat3D| |signatureAst| |equality| + |semiLastSubResultantEuclidean| |mapUp!| |apply| |inrootof| + |replaceKthElement| |component| |gcd| |overlap| |zero| ~ + |primeFrobenius| |f01bsf| |complexSolve| |zCoord| |An| |first| + |normalDenom| |false| |cschIfCan| |symmetricTensors| |e04jaf| + |constantKernel| |psolve| |prinshINFO| |numberOfComposites| + |linearPolynomials| |rest| |s17dgf| |finite?| |possiblyInfinite?| + |cyclotomicDecomposition| |previous| |And| |plus| |legendreP| + |explicitlyFinite?| |setPoly| |patternMatch| |enterInCache| |update| + |rationalPoints| |createZechTable| |coord| |rootOf| |Or| |/\\| + |copies| |vectorise| |contains?| |lazyGintegrate| |monicDivide| |next| + |OMputSymbol| |nil?| |collectQuasiMonic| |leftTrace| |Not| |\\/| + |primextendedint| |taylorIfCan| |s17agf| |coleman| |invmultisect| + |datalist| |stoseInvertibleSetsqfreg| |algSplitSimple| |whatInfinity| + |subTriSet?| |modularGcd| |badNum| |topFortranOutputStack| + |parametersOf| |rootSimp| |times| |coerce| |cycleLength| + |integerIfCan| |negative?| |Lazard2| |expPot| |RemainderList| + |paraboloidal| |divergence| |fixPredicate| |construct| |s17aff| + |solveLinear| |mapExpon| |clipSurface| |lexico| |branchPoint?| |red| + |setnext!| |gethi| |cRationalPower| |position| |maxrow| |s01eaf| + |gramschmidt| |expextendedint| |gderiv| |normalizeAtInfinity| + |selectIntegrationRoutines| |var2Steps| |OMgetAttr| |fintegrate| + |exptMod| |rename| |subresultantVector| |sinh2csch| |lambda| + |lfinfieldint| |symFunc| |squareFreeFactors| |radicalSolve| + |stiffnessAndStabilityFactor| |monom| |rank| |wrregime| |d02kef| + |leftFactorIfCan| |initializeGroupForWordProblem| |approximants| + |currentSubProgram| |lyndon| |setrest!| |rationalIfCan| |socf2socdf| + |symmetricPower| |createThreeSpace| |twoFactor| |c06gcf| + |OMsetEncoding| |squareFreePrim| |remove!| |hex| |midpoint| |biRank| + |viewPosDefault| |lintgcd| |OMconnInDevice| |trigs| |e02aef| + |OMgetFloat| |common| |dimensionsOf| |bezoutDiscriminant| + |swapColumns!| |times!| |quoted?| |trunc| |integralBasisAtInfinity| + |in?| |df2st| |coercePreimagesImages| |fortranCharacter| |variable?| + |localReal?| |d02ejf| |content| |resultantEuclidean| + |eisensteinIrreducible?| |computeCycleLength| |constant?| |prod| + |mathieu23| |recur| |isMult| |setAdaptive| |cartesian| |divisors| + |positiveSolve| |basisOfCentroid| |addiag| |OMputEndBind| |rroot| + |integral?| |splitConstant| |back| |rk4f| |OMconnectTCP| + |closeComponent| |ramifiedAtInfinity?| |mainDefiningPolynomial| + |stiffnessAndStabilityOfODEIF| |semiResultantEuclidean1| |compound?| + |loadNativeModule| |lists| |c06frf| |axes| |f01rdf| |showClipRegion| + |measure2Result| |swap| |absolutelyIrreducible?| |getZechTable| + |adjoint| |reducedSystem| |imagj| |upperCase?| |bumptab1| + |zeroDimPrime?| |exprex| |hspace| |iitan| |listYoungTableaus| + |lazyEvaluate| |nextPrime| |cAcsc| |nextPrimitivePoly| + |makeViewport3D| |createGenericMatrix| |erf| |plus!| |e04ycf| + |factorSquareFreeByRecursion| |internalIntegrate0| + |lastSubResultantElseSplit| |Nul| |d01asf| |log| |OMgetBind| + |fullDisplay| |basis| |OMputVariable| |comparison| |ScanArabic| + |BumInSepFFE| |is?| |deriv| |insertionSort!| |discreteLog| + |matrixDimensions| |e04mbf| |li| |viewDeltaYDefault| |raisePolynomial| + |basicSet| |fillPascalTriangle| |probablyZeroDim?| |iiexp| |setelt| + |xn| |reverse| |simpleBounds?| |semicolonSeparate| |diophantineSystem| + |dilog| |extendedEuclidean| |certainlySubVariety?| + |getMultiplicationMatrix| |linSolve| |removeCoshSq| |iiacsch| + |iiacosh| |parametric?| |externalList| |sin| |monomialIntPoly| + |selectODEIVPRoutines| |createNormalPrimitivePoly| + |tryFunctionalDecomposition| |f02aef| |showScalarValues| + |insertBottom!| |recolor| |rightLcm| |cos| |horizConcat| |shiftLeft| + |copyInto!| |extendedint| |roughBasicSet| |cardinality| + |leftCharacteristicPolynomial| |enterPointData| |unknown| |sample| + |tan| |eof?| |endSubProgram| |hMonic| |imagE| |bag| |f02akf| + |numberOfHues| |solveid| |reindex| |cot| |ip4Address| |pointPlot| + |doubleFloatFormat| |solveLinearPolynomialEquationByRecursion| + |critpOrder| |f01qdf| |iiasec| |cyclePartition| |rspace| |sec| |pol| + |curve?| |computePowers| |totalfract| |nsqfree| |nextSublist| + |anticoord| |superHeight| |palgintegrate| |csc| |realEigenvectors| + |check| |reducedQPowers| RF2UTS |lifting| |leftNorm| |quadratic?| + |badValues| |separate| |asin| |test| |genericLeftDiscriminant| + |largest| |rightMinimalPolynomial| |clearTheFTable| |maxIndex| + |representationType| |ListOfTerms| |complexIntegrate| |e04ucf| + |legendre| |acos| |capacity| |cSinh| |tablePow| |quotient| |parts| + |terms| |virtualDegree| |odd?| |extendedSubResultantGcd| |thetaCoord| + |atan| |curveColor| |cAcot| |identityMatrix| |floor| + |brillhartIrreducible?| |removeRedundantFactorsInPols| |minus!| + |numberOfMonomials| |bits| |acot| |operation| |cyclotomic| + |purelyTranscendental?| |lastSubResultantEuclidean| |triangSolve| + |f02axf| |integrate| |matrixGcd| |contractSolve| |mesh| |asec| + |groebSolve| |maxdeg| |partialDenominators| |padicallyExpand| + |reciprocalPolynomial| |csubst| |middle| |setStatus!| |alphanumeric?| + |cn| |acsc| |rootSplit| |subNodeOf?| |coerceL| |fortranComplex| + |edf2fi| |cyclicGroup| |prefix| |setMaxPoints| |sinh| |logIfCan| + |toseInvertible?| |extension| |palginfieldint| |OMencodingXML| + |rightDivide| |d01apf| |listLoops| |pleskenSplit| |cosh| |iiacsc| + |low| |degreePartition| |algDsolve| |tower| |areEquivalent?| |quartic| + |heapSort| |simplify| |npcoef| |iisinh| |tanh| |ran| |eq| |leader| + |palgint| |subPolSet?| |jacobi| |identitySquareMatrix| |remove| + |leftFactor| |hyperelliptic| |coth| |iter| |monicDecomposeIfCan| + |makeCos| |outlineRender| |indiceSubResultant| |logical?| + |explicitlyEmpty?| |drawStyle| |obj| |stripCommentsAndBlanks| |sech| + |write!| |useSingleFactorBound| |constantRight| |triangularSystems| + |selectOptimizationRoutines| |c05nbf| |last| |invertIfCan| + |OMUnknownCD?| |position!| |cache| |csch| |lazyPquo| |nextItem| + |hexDigit?| |makeResult| |countable?| |assoc| |realZeros| |f2df| + |commutativeEquality| |submod| |asinh| |forLoop| + |characteristicPolynomial| |primaryDecomp| |complexNumeric| |ef2edf| + |linearMatrix| |besselY| |lazyIrreducibleFactors| |acosh| + |standardBasisOfCyclicSubmodule| |changeThreshhold| |separateDegrees| + |nonQsign| |controlPanel| |primitivePart!| |anfactor| + |splitDenominator| |radicalSimplify| |atanh| |bernoulliB| |poisson| + |createPrimitiveNormalPoly| |stFunc1| |kernels| |zeroDim?| |hclf| + |iflist2Result| |iiabs| |exportedOperators| |acoth| |e01bff| + |hermiteH| |fortranDoubleComplex| |componentUpperBound| |operator| + |evenlambert| |completeHensel| |setLabelValue| |returnType!| |c05adf| + |e02bbf| |asech| |level| |htrigs| |exp| |before?| + |stoseSquareFreePart| |inf| |hasPredicate?| |distdfact| + |removeRedundantFactorsInContents| |ParCond| |sturmVariationsOf| + |binaryFunction| |light| |integralLastSubResultant| |normal?| + |subresultantSequence| |frobenius| |univariate| |dmpToHdmp| |select!| + |doubleDisc| |findConstructor| |asinhIfCan| |multiple| + |resultantReduitEuclidean| |fractRagits| |reducedForm| |nthRootIfCan| + |indicialEquation| |d03eef| |recoverAfterFail| |ode2| |unary?| + |schema| |alternative?| |applyQuote| |compile| |integral| + |bandedJacobian| |typeList| |table| |normal01| |generalPosition| + |primlimintfrac| |conjugate| |scalarMatrix| |drawToScale| |hue| + |ratPoly| |Hausdorff| |transcendenceDegree| |new| |cup| + |zeroDimPrimary?| |generalizedInverse| |nor| |varselect| |c06fpf| + |points| |f01qef| |uniform| |Aleph| |viewThetaDefault| + |generateIrredPoly| |mightHaveRoots| |randomLC| |padecf| |ruleset| + |clearFortranOutputStack| |omError| |nativeModuleExtension| + |viewport2D| |besselK| |palgRDE0| |retract| |LyndonWordsList| + |endOfFile?| |bringDown| |choosemon| |imagK| |maxColIndex| + |complement| |clikeUniv| |univariateSolve| |jacobian| |readUInt16!| + |infix| |bracket| |create| |pack!| |norm| |makeCrit| + |mainSquareFreePart| |df2ef| |convert| |OMreadFile| |f04faf| + |putGraph| |moebiusMu| |commutator| |singularitiesOf| |elliptic| + |traceMatrix| |iteratedInitials| |extractSplittingLeaf| |tanAn| + |putProperty| |leftZero| |s18acf| |isAbsolutelyIrreducible?| + |typeForm| |nil| |f07fdf| |point?| |dihedral| |epilogue| |weierstrass| + |reducedContinuedFraction| |setLegalFortranSourceExtensions| + |fortranLiteral| |box| |writeUInt8!| |supRittWu?| + |wordInStrongGenerators| |tubeRadiusDefault| |iiasech| |drawCurves| + |primextintfrac| |quadraticNorm| |d01anf| |pile| |ReduceOrder| + |binomial| |useSingleFactorBound?| |multiset| |startPolynomial| + |hermite| |axesColorDefault| |s21bbf| |polarCoordinates| |rightUnit| + |rightZero| |countRealRoots| |approximate| |OMunhandledSymbol| + |weighted| |extractIfCan| |LiePolyIfCan| |rightUnits| |leastMonomial| + |iicos| |edf2df| |genericRightMinimalPolynomial| |d02raf| |complex| + |leftOne| |safeFloor| |isAnd| |stop| |realSolve| |cCosh| |left| + |musserTrials| |lowerPolynomial| |upperCase| |unknownEndian| |e02zaf| + |s17dhf| |expandTrigProducts| |OMgetEndError| |goodnessOfFit| + |OMgetVariable| |right| |youngGroup| |principal?| |exactQuotient!| + |setRow!| |maxRowIndex| |cyclic| |setMinPoints3D| + |zeroSetSplitIntoTriangularSystems| |sh| |addPoint| |sqfrFactor| + |drawComplexVectorField| |gradient| |solveLinearPolynomialEquation| + |mindegTerm| |failed| |insertRoot!| |prinpolINFO| + |scanOneDimSubspaces| |nand| |initial| |unit?| |isOp| |setFieldInfo| + |lllp| |useEisensteinCriterion?| |quasiMonicPolynomials| |setleft!| + |sequence| |decreasePrecision| |integer?| |minGbasis| |argumentListOf| + |branchPointAtInfinity?| |fortranReal| |mapMatrixIfCan| |mathieu22| + |symmetricRemainder| |acscIfCan| |isOr| |symmetricDifference| + |setleaves!| |prologue| |taylorQuoByVar| |makeYoungTableau| + |oneDimensionalArray| |mainMonomials| |binaryTree| |rotatey| + |nilFactor| |pastel| |inGroundField?| |every?| |addMatch| + |mainVariable| |reify| |f04jgf| |basisOfRightNucleus| |corrPoly| + |pToDmp| |pseudoRemainder| |compdegd| |setMaxPoints3D| + |leftExactQuotient| |deepestTail| |palgint0| + |degreeSubResultantEuclidean| |ScanFloatIgnoreSpacesIfCan| |getMatch| + |zeroVector| |argument| |semiSubResultantGcdEuclidean2| |fracPart| + |innerint| |relativeApprox| |leftUnits| |numberOfComputedEntries| + |doubleRank| |alphanumeric| |closed| |stoseInvertible?reg| + |startStats!| |diagonal?| |cSech| |mapGen| |setOfMinN| |setEmpty!| + |rightPower| |mainPrimitivePart| |elaborate| |freeOf?| |lagrange| + |whileLoop| |fixedPoint| |removeSinSq| |hcrf| |atanIfCan| + |rightTraceMatrix| |fibonacci| |zeroDimensional?| |patternMatchTimes| + |tubeRadius| |symbol| |reduceBasisAtInfinity| |cCoth| + |setIntersection| |length| |harmonic| |printingInfo?| |twist| + |intChoose| |hessian| |OMputString| |roughSubIdeal?| |expression| + |scripts| |interpretString| |sts2stst| |Frobenius| |exponent| + |complexNumericIfCan| |outputArgs| |shade| + |combineFeatureCompatibility| |just| |iCompose| |integer| |key| + |addPointLast| |updatF| FG2F |mainForm| |cot2trig| + |inverseIntegralMatrix| |rootDirectory| |bsolve| |atom?| |leastPower| + |generalSqFr| |square?| |nextsubResultant2| |factorOfDegree| |c06fuf| + |LyndonCoordinates| |factorSquareFreePolynomial| |plenaryPower| + |s17dcf| |laguerre| |filename| |super| |perfectNthRoot| + |argumentList!| |graphState| |completeEchelonBasis| |typeLists| + |processTemplate| |property| |rdHack1| |simplifyExp| |medialSet| + |perfectSquare?| |returns| |prime| |prolateSpheroidal| + |possiblyNewVariety?| |hasSolution?| |sturmSequence| |readable?| + |trim| |triangular?| |parse| |bezoutMatrix| |incrementKthElement| + |depth| |minordet| |exponents| |column| |oblateSpheroidal| + |coefficient| |noncommutativeJordanAlgebra?| + |tryFunctionalDecomposition?| |selectPolynomials| |e01sbf| |scopes| + |iprint| |alphabetic?| |OMlistSymbols| |supersub| |fmecg| |bernoulli| + |rationalPower| |iisec| |trapezoidal| |f02aaf| |OMencodingBinary| + |intcompBasis| |nextsousResultant2| |genericLeftMinimalPolynomial| + |entry| |definingEquations| |createPrimitivePoly| |principalIdeal| + |say| |pmComplexintegrate| |exprHasAlgebraicWeight| |Ei| + |restorePrecision| |leftGcd| |implies| |arg1| |noValueMode| |revert| + |nthr| |internalSubPolSet?| |child?| |highCommonTerms| |fortranDouble| + |f04axf| |lowerCase?| |isobaric?| |nary?| |arg2| + |fortranCarriageReturn| |e01baf| |reset| |diagonals| |besselI| + |close!| |palgLODE| |radicalRoots| |logpart| |inverseColeman| |sum| + |c02aff| |closedCurve| |groebner| |changeWeightLevel| |edf2ef| |inc| + |LiePoly| |constantOperator| |OMclose| |exprToUPS| |lquo| |coerceP| + |conditions| |irCtor| |setAdaptive3D| |OMgetType| |write| |chebyshevU| + |e04dgf| |entry?| |karatsuba| |binaryTournament| |nextSubsetGray| + |save| |unitCanonical| |match| |imagk| |sup| |front| |options| |genus| + |lp| |evenInfiniteProduct| |plot| |extractProperty| |tubePoints| + |kovacic| |dom| |clipWithRanges| |sylvesterSequence| |flagFactor| + |nextPartition| |binary| |style| |finiteBound| |stopTableInvSet!| + |droot| |getStream| |OMgetEndAttr| |OMserve| |critBonD| + |minimumExponent| |factorsOfCyclicGroupSize| |mapCoef| |nil| + |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -3765 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -3765 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-35) |has| |#1| (-1222)) ((-95) |has| |#1| (-1222)) ((-102) . T) ((-111 #0# #0#) -3765 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -3765 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -3765 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -3765 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-625 (-874)) . T) ((-174) . T) ((-626 (-171 (-227))) |has| |#1| (-1041)) ((-626 (-171 (-390))) |has| |#1| (-1041)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-905 (-390))) |has| |#1| (-626 (-905 (-390)))) ((-626 (-905 (-576))) |has| |#1| (-626 (-905 (-576)))) ((-626 #1=(-1192 |#1|)) . 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T) ((-464) -3765 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-505) |has| |#1| (-1222)) ((-526 (-1196) |#1|) |has| |#1| (-526 (-1196) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) -3765 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-658 #0#) -3765 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) -3765 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-660 #2=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) -3765 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-652 |#1|) . T) ((-652 $) -3765 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-651 #2#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) -3765 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-729 |#1|) . T) ((-729 $) -3765 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-736 |#1| #1#) . T) ((-738) . T) ((-909 $ #3=(-1196)) -3765 (|has| |#1| (-917 (-1196))) (|has| |#1| (-915 (-1196)))) ((-915 (-1196)) |has| |#1| (-915 (-1196))) ((-917 #3#) -3765 (|has| |#1| (-917 (-1196))) (|has| |#1| (-915 (-1196)))) ((-899 (-390)) |has| |#1| (-899 (-390))) ((-899 (-576)) |has| |#1| (-899 (-576))) ((-897 |#1|) . T) ((-926) -12 (|has| |#1| (-317)) (|has| |#1| (-926))) ((-937) -3765 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-1021) -12 (|has| |#1| (-1021)) (|has| |#1| (-1222))) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 |#1|) . T) ((-1070 #0#) -3765 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1070 |#1|) . T) ((-1070 $) . T) ((-1075 #0#) -3765 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1075 |#1|) . T) ((-1075 $) . T) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-360)) ((-1222) |has| |#1| (-1222)) ((-1225) |has| |#1| (-1222)) ((-1237) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-35) |has| |#1| (-1221)) ((-95) |has| |#1| (-1221)) ((-102) . T) ((-111 #0# #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2835 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -2835 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-625 (-874)) . T) ((-174) . T) ((-626 (-171 (-227))) |has| |#1| (-1041)) ((-626 (-171 (-390))) |has| |#1| (-1041)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-905 (-390))) |has| |#1| (-626 (-905 (-390)))) ((-626 (-905 (-576))) |has| |#1| (-626 (-905 (-576)))) ((-626 #1=(-1191 |#1|)) . 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T) ((-464) -2835 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-505) |has| |#1| (-1221)) ((-526 (-1195) |#1|) |has| |#1| (-526 (-1195) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) -2835 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-658 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-660 #2=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-652 |#1|) . T) ((-652 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-651 #2#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-729 |#1|) . T) ((-729 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-736 |#1| #1#) . T) ((-738) . T) ((-909 $ #3=(-1195)) -2835 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-917 #3#) -2835 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-899 (-390)) |has| |#1| (-899 (-390))) ((-899 (-576)) |has| |#1| (-899 (-576))) ((-897 |#1|) . T) ((-926) -12 (|has| |#1| (-317)) (|has| |#1| (-926))) ((-937) -2835 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-1021) -12 (|has| |#1| (-1021)) (|has| |#1| (-1221))) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 |#1|) . T) ((-1070 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1070 |#1|) . T) ((-1070 $) . T) ((-1075 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1075 |#1|) . T) ((-1075 $) . T) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-360)) ((-1221) |has| |#1| (-1221)) ((-1224) |has| |#1| (-1221)) ((-1236) . 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T) ((-102) -3765 (|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))) ((-111 |#2| |#2|) -3765 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-132) -3765 (|has| |#2| (-1068)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-628 #0=(-419 (-576))) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119))) ((-628 (-576)) -3765 (|has| |#2| (-1068)) (-12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119)))) ((-628 |#2|) |has| |#2| (-1119)) ((-625 (-874)) -3765 (|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| (-625 (-874))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-625 (-1287 |#2|)) . T) ((-234 $) -3765 (-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) -3765 (-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)) -3765 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -3765 (|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|) -3765 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1068)) ((-652 |#2|) -3765 (|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|) -3765 (|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) -3765 (|has| |#2| (-862)) (|has| |#2| (-805))) ((-909 $ #3=(-1196)) -3765 (-12 (|has| |#2| (-917 (-1196))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1196))) (|has| |#2| (-1068)))) ((-915 (-1196)) -12 (|has| |#2| (-915 (-1196))) (|has| |#2| (-1068))) ((-917 #3#) -3765 (-12 (|has| |#2| (-917 (-1196))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1196))) (|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|) -3765 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1075 |#2|) -3765 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1068) |has| |#2| (-1068)) ((-1077) |has| |#2| (-1068)) ((-1131) |has| |#2| (-1068)) ((-1119) -3765 (|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))) ((-1237) . T) ((-1294 |#2|) |has| |#2| (-374))) -((-1687 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-2359 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-2477 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) -(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -1687 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2359 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2477 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-783) (-1237) (-1237)) (T -244)) -((-2477 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1237)) (-4 *7 (-1237)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-2359 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1237)) (-4 *2 (-1237)) (-5 *1 (-244 *5 *6 *2)))) (-1687 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-783)) (-4 *7 (-1237)) (-4 *5 (-1237)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-102) -2835 (|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))) ((-111 |#2| |#2|) -2835 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-132) -2835 (|has| |#2| (-1068)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-628 #0=(-419 (-576))) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119))) ((-628 (-576)) -2835 (|has| |#2| (-1068)) (-12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119)))) ((-628 |#2|) |has| |#2| (-1119)) ((-625 (-874)) -2835 (|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| (-625 (-874))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-625 (-1286 |#2|)) . T) ((-234 $) -2835 (-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) -2835 (-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)) -2835 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -2835 (|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|) -2835 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1068)) ((-652 |#2|) -2835 (|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|) -2835 (|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) -2835 (|has| |#2| (-862)) (|has| |#2| (-805))) ((-909 $ #3=(-1195)) -2835 (-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#) -2835 (-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|) -2835 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1075 |#2|) -2835 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1068) |has| |#2| (-1068)) ((-1077) |has| |#2| (-1068)) ((-1131) |has| |#2| (-1068)) ((-1119) -2835 (|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))) +((-2874 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-2521 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-1632 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) +(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -2874 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2521 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -1632 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-783) (-1236) (-1236)) (T -244)) +((-1632 (*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)))) (-2521 (*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)))) (-2874 (*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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((-102) . T) ((-111 #0# #0#) |has| |#1| (-568)) ((-111 |#1| |#1|) |has| |#1| (-174)) ((-111 $ $) |has| |#1| (-568)) ((-132) -3765 (|has| |#1| (-1068)) (|has| |#1| (-568)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146)) (|has| |#1| (-21))) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) -3765 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-568))) ((-628 #1=(-419 (-969 |#1|))) |has| |#1| (-568)) ((-628 (-576)) -3765 (|has| |#1| (-1068)) (|has| |#1| (-1057 (-576))) (|has| |#1| (-568)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146))) ((-628 #2=(-624 $)) . T) ((-628 #3=(-969 |#1|)) |has| |#1| (-1068)) ((-628 #4=(-1196)) . T) ((-628 |#1|) . T) ((-628 $) |has| |#1| (-568)) ((-625 (-874)) . T) ((-174) |has| |#1| (-568)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-905 (-390))) |has| |#1| (-626 (-905 (-390)))) ((-626 (-905 (-576))) |has| |#1| (-626 (-905 (-576)))) ((-248) |has| |#1| (-568)) ((-300) |has| |#1| (-568)) ((-317) |has| |#1| (-568)) ((-319 $) . T) ((-312) . T) ((-374) |has| |#1| (-568)) ((-388 |#1|) |has| |#1| (-1068)) ((-412 |#1|) . T) ((-423 |#1|) . T) ((-464) |has| |#1| (-568)) ((-485) |has| |#1| (-485)) ((-526 (-624 $) $) . T) ((-526 $ $) . 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T) ((-937) |has| |#1| (-568)) ((-1057 (-419 (-576))) -3765 (|has| |#1| (-1057 (-419 (-576)))) (-12 (|has| |#1| (-568)) (|has| |#1| (-1057 (-576))))) ((-1057 #1#) |has| |#1| (-568)) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 #2#) . T) ((-1057 #3#) |has| |#1| (-1068)) ((-1057 #4#) . T) ((-1057 |#1|) . T) ((-1070 #0#) |has| |#1| (-568)) ((-1070 |#1|) |has| |#1| (-174)) ((-1070 $) |has| |#1| (-568)) ((-1075 #0#) |has| |#1| (-568)) ((-1075 |#1|) |has| |#1| (-174)) ((-1075 $) |has| |#1| (-568)) ((-1068) -3765 (|has| |#1| (-1068)) (|has| |#1| (-568)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146))) ((-1077) -3765 (|has| |#1| (-1068)) (|has| |#1| (-568)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146))) ((-1131) -3765 (|has| |#1| (-1131)) (|has| |#1| (-1068)) (|has| |#1| (-568)) (|has| |#1| (-485)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146))) ((-1119) . T) ((-1237) . 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T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -3765 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -3765 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -3765 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -3765 (|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) -3765 (-12 (|has| |#1| (-374)) (|has| |#2| (-862))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-909 $ #4=(-1196)) -3765 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1196)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1196)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1196))))) ((-915 (-1196)) -3765 (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1196)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1196))))) ((-917 #4#) -3765 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1196)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1196)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1196))))) ((-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 (-1196)))) ((-1057 |#2|) . T) ((-1070 #1#) -3765 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1070 |#1|) . T) ((-1070 |#2|) |has| |#1| (-374)) ((-1070 $) -3765 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) -3765 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1075 |#1|) . T) ((-1075 |#2|) |has| |#1| (-374)) ((-1075 $) -3765 (|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))) ((-1222) |has| |#1| (-38 (-419 (-576)))) ((-1225) |has| |#1| (-38 (-419 (-576)))) ((-1237) . T) ((-1241) |has| |#1| (-374)) ((-1247 |#1|) . T) ((-1265 |#1| #0#) . 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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 $) -3765 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3765 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) -3765 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1101)) . T) ((-628 |#1|) . T) ((-628 $) -3765 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-625 (-874)) . 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T) ((-568) -3765 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-658 #1#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #1#) |has| |#1| (-38 (-419 (-576)))) ((-660 #3=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #1#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -3765 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-651 #3#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #1#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -3765 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-738) . T) ((-909 $ #2#) . T) ((-909 $ #4=(-1196)) -3765 (|has| |#1| (-917 (-1196))) (|has| |#1| (-915 (-1196)))) ((-915 #2#) . T) ((-915 (-1196)) |has| |#1| (-915 (-1196))) ((-917 #2#) . T) ((-917 #4#) -3765 (|has| |#1| (-917 (-1196))) (|has| |#1| (-915 (-1196)))) ((-899 (-390)) -12 (|has| (-1101) (-899 (-390))) (|has| |#1| (-899 (-390)))) ((-899 (-576)) -12 (|has| (-1101) (-899 (-576))) (|has| |#1| (-899 (-576)))) ((-966 |#1| #0# #2#) . T) ((-926) |has| |#1| (-926)) ((-937) |has| |#1| (-374)) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 #2#) . T) ((-1057 |#1|) . T) ((-1070 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -3765 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -3765 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-1171)) ((-1237) . 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T) ((-652 #0#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) |has| |#1| (-568)) ((-729 #0#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) |has| |#1| (-568)) ((-738) . T) ((-909 $ #1=(-1196)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-915 (-1196)))) ((-915 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-915 (-1196)))) ((-917 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-915 (-1196)))) ((-992 |#1| |#2| (-1101)) . T) ((-1070 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -3765 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1075 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -3765 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1237) . 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T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -2835 (|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) -2835 (-12 (|has| |#1| (-374)) (|has| |#2| (-862))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-909 $ #4=(-1195)) -2835 (-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)) -2835 (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-917 #4#) -2835 (-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#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1070 |#1|) . T) ((-1070 |#2|) |has| |#1| (-374)) ((-1070 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1075 |#1|) . T) ((-1075 |#2|) |has| |#1| (-374)) ((-1075 $) -2835 (|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) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) -2835 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1101)) . T) ((-628 |#1|) . T) ((-628 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-625 (-874)) . 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T) ((-568) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-658 #1#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #1#) |has| |#1| (-38 (-419 (-576)))) ((-660 #3=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #1#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-651 #3#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #1#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-738) . T) ((-909 $ #2#) . T) ((-909 $ #4=(-1195)) -2835 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-915 #2#) . T) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-917 #2#) . T) ((-917 #4#) -2835 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-899 (-390)) -12 (|has| (-1101) (-899 (-390))) (|has| |#1| (-899 (-390)))) ((-899 (-576)) -12 (|has| (-1101) (-899 (-576))) (|has| |#1| (-899 (-576)))) ((-966 |#1| #0# #2#) . T) ((-926) |has| |#1| (-926)) ((-937) |has| |#1| (-374)) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 #2#) . T) ((-1057 |#1|) . T) ((-1070 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-1171)) ((-1236) . T) ((-1240) |has| |#1| (-926))) +((-1991 (((-656 (-1101)) $) 34)) (-2166 (($ $) 31)) (-1970 (($ |#2| |#3|) NIL) (($ $ (-1101) |#3|) 28) (($ $ (-656 (-1101)) (-656 |#3|)) 27)) (-2129 (($ $) 14)) (-2142 ((|#2| $) 12)) (-1433 ((|#3| $) 10))) +(((-1263 |#1| |#2| |#3|) (-10 -8 (-15 -1991 ((-656 (-1101)) |#1|)) (-15 -1970 (|#1| |#1| (-656 (-1101)) (-656 |#3|))) (-15 -1970 (|#1| |#1| (-1101) |#3|)) (-15 -2166 (|#1| |#1|)) (-15 -1970 (|#1| |#2| |#3|)) (-15 -1433 (|#3| |#1|)) (-15 -2129 (|#1| |#1|)) (-15 -2142 (|#2| |#1|))) (-1264 |#2| |#3|) (-1068) (-804)) (T -1263)) +NIL +(-10 -8 (-15 -1991 ((-656 (-1101)) |#1|)) (-15 -1970 (|#1| |#1| (-656 (-1101)) (-656 |#3|))) (-15 -1970 (|#1| |#1| (-1101) |#3|)) (-15 -2166 (|#1| |#1|)) (-15 -1970 (|#1| |#2| |#3|)) (-15 -1433 (|#3| |#1|)) (-15 -2129 (|#1| |#1|)) (-15 -2142 (|#2| |#1|))) +((-3474 (((-112) $ $) 7)) (-1454 (((-112) $) 17)) (-1991 (((-656 (-1101)) $) 86)) (-3022 (((-1195) $) 118)) (-2362 (((-2 (|:| -3341 $) (|:| -4448 $) (|:| |associate| $)) 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) |has| |#1| (-568)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2835 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) |has| |#1| (-38 (-419 (-576)))) ((-628 (-576)) . T) ((-628 |#1|) |has| |#1| (-174)) ((-628 $) |has| |#1| (-568)) ((-625 (-874)) . T) ((-174) -2835 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-234 $) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-238) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-237) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-296 |#2| |#1|) . T) ((-296 $ $) |has| |#2| (-1131)) ((-300) |has| |#1| (-568)) ((-568) |has| |#1| (-568)) ((-658 #0#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) |has| |#1| (-38 (-419 (-576)))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) |has| |#1| (-568)) ((-729 #0#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) |has| |#1| (-568)) ((-738) . T) ((-909 $ #1=(-1195)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-915 (-1195)))) ((-915 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-915 (-1195)))) ((-917 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-915 (-1195)))) ((-992 |#1| |#2| (-1101)) . T) ((-1070 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1075 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1236) . 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3128392 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1270 3110891 3117687 3117749 "UPXSCCA" 3118323 NIL UPXSCCA (NIL T T) -9 NIL 3118556 NIL) (-1269 3110529 3110614 3110788 "UPXSCCA-" 3110793 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1268 3099788 3106357 3106400 "UPXSCAT" 3107048 NIL UPXSCAT (NIL T) -9 NIL 3107657 NIL) (-1267 3099218 3099297 3099476 "UPXS2" 3099703 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1266 3097872 3098125 3098476 "UPSQFREE" 3098961 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1265 3091080 3094140 3094195 "UPSCAT" 3095275 NIL UPSCAT (NIL T T) -9 NIL 3096040 NIL) (-1264 3090284 3090491 3090818 "UPSCAT-" 3090823 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1263 3075374 3083411 3083454 "UPOLYC" 3085555 NIL UPOLYC (NIL T) -9 NIL 3086776 NIL) (-1262 3066702 3069128 3072275 "UPOLYC-" 3072280 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1261 3066329 3066372 3066505 "UPOLYC2" 3066653 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1260 3057872 3066012 3066141 "UP" 3066248 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1259 3057211 3057318 3057482 "UPMP" 3057761 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1258 3056764 3056845 3056984 "UPDIVP" 3057124 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1257 3055332 3055581 3055897 "UPDECOMP" 3056513 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1256 3054563 3054675 3054861 "UPCDEN" 3055216 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1255 3054082 3054151 3054300 "UP2" 3054488 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1254 3052549 3053286 3053563 "UNISEG" 3053840 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1253 3051764 3051891 3052096 "UNISEG2" 3052392 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1252 3050824 3051004 3051230 "UNIFACT" 3051580 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1251 3033584 3050136 3050378 "ULS" 3050640 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3021222 3033488 3033560 "ULSCONS" 3033565 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1249 3002058 3014410 3014472 "ULSCCAT" 3015110 NIL ULSCCAT (NIL T T) -9 NIL 3015399 NIL) (-1248 3001108 3001353 3001741 "ULSCCAT-" 3001746 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1247 2990172 2996655 2996698 "ULSCAT" 2997561 NIL ULSCAT (NIL T) -9 NIL 2998292 NIL) (-1246 2989602 2989681 2989860 "ULS2" 2990087 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1245 2988721 2989231 2989338 "UINT8" 2989449 T UINT8 (NIL) -8 NIL NIL 2989534) (-1244 2987839 2988349 2988456 "UINT64" 2988567 T UINT64 (NIL) -8 NIL NIL 2988652) (-1243 2986957 2987467 2987574 "UINT32" 2987685 T UINT32 (NIL) -8 NIL NIL 2987770) (-1242 2986075 2986585 2986692 "UINT16" 2986803 T UINT16 (NIL) -8 NIL NIL 2986888) (-1241 2984378 2985335 2985365 "UFD" 2985577 T UFD (NIL) -9 NIL 2985691 NIL) (-1240 2984172 2984218 2984313 "UFD-" 2984318 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1239 2983254 2983437 2983653 "UDVO" 2983978 T UDVO (NIL) -7 NIL NIL NIL) (-1238 2981070 2981479 2981950 "UDPO" 2982818 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1237 2981003 2981008 2981038 "TYPE" 2981043 T TYPE (NIL) -9 NIL NIL NIL) (-1236 2980763 2980958 2980989 "TYPEAST" 2980994 T TYPEAST (NIL) -8 NIL NIL NIL) (-1235 2979734 2979936 2980176 "TWOFACT" 2980557 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1234 2978757 2979143 2979378 "TUPLE" 2979534 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1233 2976448 2976967 2977506 "TUBETOOL" 2978240 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1232 2975297 2975502 2975743 "TUBE" 2976241 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1231 2970026 2974269 2974552 "TS" 2975049 NIL TS (NIL T) -8 NIL NIL NIL) (-1230 2958666 2962785 2962882 "TSETCAT" 2968151 NIL TSETCAT (NIL T T T T) -9 NIL 2969682 NIL) (-1229 2953398 2954998 2956889 "TSETCAT-" 2956894 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1228 2948037 2948884 2949813 "TRMANIP" 2952534 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1227 2947478 2947541 2947704 "TRIMAT" 2947969 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1226 2945344 2945581 2945938 "TRIGMNIP" 2947227 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1225 2944864 2944977 2945007 "TRIGCAT" 2945220 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1224 2944533 2944612 2944753 "TRIGCAT-" 2944758 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1223 2941378 2943391 2943672 "TREE" 2944287 NIL TREE (NIL T) -8 NIL NIL NIL) (-1222 2940652 2941180 2941210 "TRANFUN" 2941245 T TRANFUN (NIL) -9 NIL 2941311 NIL) (-1221 2939931 2940122 2940402 "TRANFUN-" 2940407 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1220 2939735 2939767 2939828 "TOPSP" 2939892 T TOPSP (NIL) -7 NIL NIL NIL) (-1219 2939083 2939198 2939352 "TOOLSIGN" 2939616 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1218 2937717 2938260 2938499 "TEXTFILE" 2938866 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1217 2935629 2936170 2936599 "TEX" 2937310 T TEX (NIL) -8 NIL NIL NIL) (-1216 2935410 2935441 2935513 "TEX1" 2935592 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1215 2935058 2935121 2935211 "TEMUTL" 2935342 T TEMUTL (NIL) -7 NIL NIL NIL) (-1214 2933212 2933492 2933817 "TBCMPPK" 2934781 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1213 2924989 2931372 2931428 "TBAGG" 2931828 NIL TBAGG (NIL T T) -9 NIL 2932039 NIL) (-1212 2920059 2921547 2923301 "TBAGG-" 2923306 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1211 2919443 2919550 2919695 "TANEXP" 2919948 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1210 2918954 2919218 2919308 "TALGOP" 2919388 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1209 2912344 2918811 2918904 "TABLE" 2918909 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1208 2911756 2911855 2911993 "TABLEAU" 2912241 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1207 2906364 2907584 2908832 "TABLBUMP" 2910542 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1206 2905586 2905733 2905914 "SYSTEM" 2906205 T SYSTEM (NIL) -8 NIL NIL NIL) (-1205 2902045 2902744 2903527 "SYSSOLP" 2904837 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1204 2901843 2902000 2902031 "SYSPTR" 2902036 T SYSPTR (NIL) -8 NIL NIL NIL) (-1203 2900879 2901384 2901503 "SYSNNI" 2901689 NIL SYSNNI (NIL NIL) -8 NIL NIL 2901774) (-1202 2900178 2900637 2900716 "SYSINT" 2900776 NIL SYSINT (NIL NIL) -8 NIL NIL 2900821) (-1201 2896510 2897456 2898166 "SYNTAX" 2899490 T SYNTAX (NIL) -8 NIL NIL NIL) (-1200 2893668 2894270 2894902 "SYMTAB" 2895900 T SYMTAB (NIL) -8 NIL NIL NIL) (-1199 2888917 2889819 2890802 "SYMS" 2892707 T SYMS (NIL) -8 NIL NIL NIL) (-1198 2886152 2888375 2888605 "SYMPOLY" 2888722 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1197 2885669 2885744 2885867 "SYMFUNC" 2886064 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1196 2881689 2882981 2883794 "SYMBOL" 2884878 T SYMBOL (NIL) -8 NIL NIL NIL) (-1195 2875228 2876917 2878637 "SWITCH" 2879991 T SWITCH (NIL) -8 NIL NIL NIL) (-1194 2868572 2874184 2874478 "SUTS" 2874992 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1193 2860748 2867954 2868218 "SUPXS" 2868366 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1192 2852239 2860366 2860492 "SUP" 2860657 NIL SUP (NIL T) -8 NIL NIL NIL) (-1191 2851398 2851525 2851742 "SUPFRACF" 2852107 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1190 2851019 2851078 2851191 "SUP2" 2851333 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1189 2849467 2849741 2850097 "SUMRF" 2850718 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1188 2848802 2848868 2849060 "SUMFS" 2849388 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1187 2831597 2848114 2848356 "SULS" 2848618 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1186 2831199 2831419 2831489 "SUCHTAST" 2831549 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1185 2830494 2830724 2830864 "SUCH" 2831107 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1184 2824361 2825400 2826359 "SUBSPACE" 2829582 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1183 2823791 2823881 2824045 "SUBRESP" 2824249 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1182 2817159 2818456 2819767 "STTF" 2822527 NIL STTF (NIL T) -7 NIL NIL NIL) (-1181 2811332 2812452 2813599 "STTFNC" 2816059 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1180 2802645 2804514 2806308 "STTAYLOR" 2809573 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1179 2795775 2802509 2802592 "STRTBL" 2802597 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1178 2790979 2795730 2795761 "STRING" 2795766 T STRING (NIL) -8 NIL NIL NIL) (-1177 2785406 2790081 2790111 "STRICAT" 2790226 T STRICAT (NIL) -9 NIL 2790303 NIL) (-1176 2778159 2783025 2783636 "STREAM" 2784830 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1175 2777669 2777746 2777890 "STREAM3" 2778076 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1174 2776651 2776834 2777069 "STREAM2" 2777482 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1173 2776339 2776391 2776484 "STREAM1" 2776593 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1172 2775355 2775536 2775767 "STINPROD" 2776155 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1171 2774907 2775117 2775147 "STEP" 2775227 T STEP (NIL) -9 NIL 2775305 NIL) (-1170 2774094 2774396 2774544 "STEPAST" 2774781 T STEPAST (NIL) -8 NIL NIL NIL) (-1169 2767526 2773993 2774070 "STBL" 2774075 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1168 2762621 2766717 2766760 "STAGG" 2766913 NIL STAGG (NIL T) -9 NIL 2767002 NIL) (-1167 2760323 2760925 2761797 "STAGG-" 2761802 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1166 2758470 2760093 2760185 "STACK" 2760266 NIL STACK (NIL T) -8 NIL NIL NIL) (-1165 2751165 2756611 2757067 "SREGSET" 2758100 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1164 2743590 2744959 2746472 "SRDCMPK" 2749771 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1163 2736475 2741000 2741030 "SRAGG" 2742333 T SRAGG (NIL) -9 NIL 2742941 NIL) (-1162 2735492 2735747 2736126 "SRAGG-" 2736131 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1161 2729684 2734439 2734860 "SQMATRIX" 2735118 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1160 2723369 2726402 2727129 "SPLTREE" 2729029 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1159 2719332 2720025 2720671 "SPLNODE" 2722795 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1158 2718379 2718612 2718642 "SPFCAT" 2719086 T SPFCAT (NIL) -9 NIL NIL NIL) (-1157 2717116 2717326 2717590 "SPECOUT" 2718137 T SPECOUT (NIL) -7 NIL NIL NIL) (-1156 2708226 2710098 2710128 "SPADXPT" 2714804 T SPADXPT (NIL) -9 NIL 2716968 NIL) (-1155 2707987 2708027 2708096 "SPADPRSR" 2708179 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1154 2706036 2707942 2707973 "SPADAST" 2707978 T SPADAST (NIL) -8 NIL NIL NIL) (-1153 2697981 2699754 2699797 "SPACEC" 2704170 NIL SPACEC (NIL T) -9 NIL 2705986 NIL) (-1152 2696111 2697913 2697962 "SPACE3" 2697967 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1151 2694863 2695034 2695325 "SORTPAK" 2695916 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1150 2692955 2693258 2693670 "SOLVETRA" 2694527 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1149 2692005 2692227 2692488 "SOLVESER" 2692728 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1148 2687309 2688197 2689192 "SOLVERAD" 2691057 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1147 2683124 2683733 2684462 "SOLVEFOR" 2686676 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1146 2677394 2682473 2682570 "SNTSCAT" 2682575 NIL SNTSCAT (NIL T T T T) -9 NIL 2682645 NIL) (-1145 2671500 2675717 2676108 "SMTS" 2677084 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1144 2665917 2671388 2671465 "SMP" 2671470 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1143 2664076 2664377 2664775 "SMITH" 2665614 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1142 2656188 2660655 2660758 "SMATCAT" 2662109 NIL SMATCAT (NIL NIL T T T) -9 NIL 2662659 NIL) (-1141 2652402 2653439 2654873 "SMATCAT-" 2654878 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1140 2650068 2651638 2651681 "SKAGG" 2651942 NIL SKAGG (NIL T) -9 NIL 2652077 NIL) (-1139 2646266 2649541 2649725 "SINT" 2649877 T SINT (NIL) -8 NIL NIL 2650039) (-1138 2646038 2646076 2646142 "SIMPAN" 2646222 T SIMPAN (NIL) -7 NIL NIL NIL) (-1137 2645317 2645573 2645713 "SIG" 2645920 T SIG (NIL) -8 NIL NIL NIL) (-1136 2644155 2644376 2644651 "SIGNRF" 2645076 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1135 2642988 2643139 2643423 "SIGNEF" 2643984 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1134 2642294 2642571 2642695 "SIGAST" 2642886 T SIGAST (NIL) -8 NIL NIL NIL) (-1133 2639984 2640438 2640944 "SHP" 2641835 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1132 2633818 2639885 2639961 "SHDP" 2639966 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1131 2633391 2633583 2633613 "SGROUP" 2633706 T SGROUP (NIL) -9 NIL 2633768 NIL) (-1130 2633249 2633275 2633348 "SGROUP-" 2633353 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1129 2630040 2630738 2631461 "SGCF" 2632548 T SGCF (NIL) -7 NIL NIL NIL) (-1128 2624408 2629487 2629584 "SFRTCAT" 2629589 NIL SFRTCAT (NIL T T T T) -9 NIL 2629628 NIL) (-1127 2617829 2618847 2619983 "SFRGCD" 2623391 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1126 2610955 2612028 2613214 "SFQCMPK" 2616762 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1125 2610575 2610664 2610775 "SFORT" 2610896 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1124 2609693 2610415 2610536 "SEXOF" 2610541 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1123 2608800 2609574 2609642 "SEX" 2609647 T SEX (NIL) -8 NIL NIL NIL) (-1122 2604581 2605296 2605391 "SEXCAT" 2608013 NIL SEXCAT (NIL T T T T T) -9 NIL 2608573 NIL) (-1121 2601734 2604515 2604563 "SET" 2604568 NIL SET (NIL T) -8 NIL NIL NIL) (-1120 2599958 2600447 2600752 "SETMN" 2601475 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1119 2599454 2599606 2599636 "SETCAT" 2599812 T SETCAT (NIL) -9 NIL 2599922 NIL) (-1118 2599146 2599224 2599354 "SETCAT-" 2599359 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1117 2595507 2597607 2597650 "SETAGG" 2598520 NIL SETAGG (NIL T) -9 NIL 2598860 NIL) (-1116 2594965 2595081 2595318 "SETAGG-" 2595323 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1115 2594408 2594661 2594762 "SEQAST" 2594886 T SEQAST (NIL) -8 NIL NIL NIL) (-1114 2593607 2593901 2593962 "SEGXCAT" 2594248 NIL SEGXCAT (NIL T T) -9 NIL 2594368 NIL) (-1113 2592613 2593273 2593455 "SEG" 2593460 NIL SEG (NIL T) -8 NIL NIL NIL) (-1112 2591592 2591806 2591849 "SEGCAT" 2592371 NIL SEGCAT (NIL T) -9 NIL 2592592 NIL) (-1111 2590524 2590955 2591163 "SEGBIND" 2591419 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1110 2590145 2590204 2590317 "SEGBIND2" 2590459 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1109 2589718 2589946 2590023 "SEGAST" 2590090 T SEGAST (NIL) -8 NIL NIL NIL) (-1108 2588937 2589063 2589267 "SEG2" 2589562 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1107 2588308 2588872 2588919 "SDVAR" 2588924 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1106 2580567 2588078 2588208 "SDPOL" 2588213 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1105 2579160 2579426 2579745 "SCPKG" 2580282 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1104 2578324 2578496 2578688 "SCOPE" 2578990 T SCOPE (NIL) -8 NIL NIL NIL) (-1103 2577544 2577678 2577857 "SCACHE" 2578179 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1102 2577190 2577376 2577406 "SASTCAT" 2577411 T SASTCAT (NIL) -9 NIL 2577424 NIL) (-1101 2576677 2577025 2577101 "SAOS" 2577136 T SAOS (NIL) -8 NIL NIL NIL) (-1100 2576242 2576277 2576450 "SAERFFC" 2576636 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1099 2569913 2576139 2576219 "SAE" 2576224 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1098 2569506 2569541 2569700 "SAEFACT" 2569872 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1097 2567827 2568141 2568542 "RURPK" 2569172 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1096 2566464 2566770 2567075 "RULESET" 2567661 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1095 2563687 2564217 2564675 "RULE" 2566145 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1094 2563299 2563481 2563564 "RULECOLD" 2563639 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1093 2563089 2563117 2563188 "RTVALUE" 2563250 T RTVALUE (NIL) -8 NIL NIL NIL) (-1092 2562560 2562806 2562900 "RSTRCAST" 2563017 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1091 2557408 2558203 2559123 "RSETGCD" 2561759 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1090 2546638 2551717 2551814 "RSETCAT" 2555933 NIL RSETCAT (NIL T T T T) -9 NIL 2557030 NIL) (-1089 2544565 2545104 2545928 "RSETCAT-" 2545933 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1088 2536951 2538327 2539847 "RSDCMPK" 2543164 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1087 2534930 2535397 2535471 "RRCC" 2536557 NIL RRCC (NIL T T) -9 NIL 2536901 NIL) (-1086 2534281 2534455 2534734 "RRCC-" 2534739 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1085 2533724 2533977 2534078 "RPTAST" 2534202 T RPTAST (NIL) -8 NIL NIL NIL) (-1084 2507208 2516836 2516903 "RPOLCAT" 2527569 NIL RPOLCAT (NIL T T T) -9 NIL 2530729 NIL) (-1083 2498706 2501046 2504168 "RPOLCAT-" 2504173 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1082 2489637 2496917 2497399 "ROUTINE" 2498246 T ROUTINE (NIL) -8 NIL NIL NIL) (-1081 2486306 2489263 2489403 "ROMAN" 2489519 T ROMAN (NIL) -8 NIL NIL NIL) (-1080 2484550 2485166 2485426 "ROIRC" 2486111 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1079 2480782 2483066 2483096 "RNS" 2483400 T RNS (NIL) -9 NIL 2483674 NIL) (-1078 2479291 2479674 2480208 "RNS-" 2480283 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1077 2478694 2479102 2479132 "RNG" 2479137 T RNG (NIL) -9 NIL 2479158 NIL) (-1076 2477697 2478059 2478261 "RNGBIND" 2478545 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1075 2477096 2477484 2477527 "RMODULE" 2477532 NIL RMODULE (NIL T) -9 NIL 2477559 NIL) (-1074 2475932 2476026 2476362 "RMCAT2" 2476997 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1073 2472782 2475278 2475575 "RMATRIX" 2475694 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1072 2465609 2467869 2467984 "RMATCAT" 2471343 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2472325 NIL) (-1071 2464984 2465131 2465438 "RMATCAT-" 2465443 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1070 2464613 2464785 2464828 "RLINSET" 2464890 NIL RLINSET (NIL T) -9 NIL 2464934 NIL) (-1069 2464180 2464255 2464383 "RINTERP" 2464532 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1068 2463238 2463792 2463822 "RING" 2463878 T RING (NIL) -9 NIL 2463970 NIL) (-1067 2463030 2463074 2463171 "RING-" 2463176 NIL RING- (NIL T) -8 NIL NIL NIL) (-1066 2461871 2462108 2462366 "RIDIST" 2462794 T RIDIST (NIL) -7 NIL NIL NIL) (-1065 2453160 2461339 2461545 "RGCHAIN" 2461719 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1064 2452510 2452916 2452957 "RGBCSPC" 2453015 NIL RGBCSPC (NIL T) -9 NIL 2453067 NIL) (-1063 2451668 2452049 2452090 "RGBCMDL" 2452322 NIL RGBCMDL (NIL T) -9 NIL 2452436 NIL) (-1062 2448662 2449276 2449946 "RF" 2451032 NIL RF (NIL T) -7 NIL NIL NIL) (-1061 2448308 2448371 2448474 "RFFACTOR" 2448593 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1060 2448033 2448068 2448165 "RFFACT" 2448267 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1059 2446150 2446514 2446896 "RFDIST" 2447673 T RFDIST (NIL) -7 NIL NIL NIL) (-1058 2445603 2445695 2445858 "RETSOL" 2446052 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1057 2445239 2445319 2445362 "RETRACT" 2445495 NIL RETRACT (NIL T) -9 NIL 2445582 NIL) (-1056 2445088 2445113 2445200 "RETRACT-" 2445205 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1055 2444690 2444910 2444980 "RETAST" 2445040 T RETAST (NIL) -8 NIL NIL NIL) (-1054 2437428 2444343 2444470 "RESULT" 2444585 T RESULT (NIL) -8 NIL NIL NIL) (-1053 2436019 2436697 2436896 "RESRING" 2437331 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1052 2435655 2435704 2435802 "RESLATC" 2435956 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1051 2435360 2435395 2435502 "REPSQ" 2435614 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1050 2432782 2433362 2433964 "REP" 2434780 T REP (NIL) -7 NIL NIL NIL) (-1049 2432479 2432514 2432625 "REPDB" 2432741 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1048 2426379 2427768 2428991 "REP2" 2431291 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1047 2422756 2423437 2424245 "REP1" 2425606 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1046 2415452 2420897 2421353 "REGSET" 2422386 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1045 2414217 2414600 2414850 "REF" 2415237 NIL REF (NIL T) -8 NIL NIL NIL) (-1044 2413594 2413697 2413864 "REDORDER" 2414101 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1043 2409562 2412807 2413034 "RECLOS" 2413422 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1042 2408614 2408795 2409010 "REALSOLV" 2409369 T REALSOLV (NIL) -7 NIL NIL NIL) (-1041 2408460 2408501 2408531 "REAL" 2408536 T REAL (NIL) -9 NIL 2408571 NIL) (-1040 2404943 2405745 2406629 "REAL0Q" 2407625 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1039 2400544 2401532 2402593 "REAL0" 2403924 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1038 2400015 2400261 2400355 "RDUCEAST" 2400472 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1037 2399420 2399492 2399699 "RDIV" 2399937 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1036 2398488 2398662 2398875 "RDIST" 2399242 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1035 2397085 2397372 2397744 "RDETRS" 2398196 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1034 2394897 2395351 2395889 "RDETR" 2396627 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1033 2393522 2393800 2394197 "RDEEFS" 2394613 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1032 2392031 2392337 2392762 "RDEEF" 2393210 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1031 2386092 2389012 2389042 "RCFIELD" 2390337 T RCFIELD (NIL) -9 NIL 2391068 NIL) (-1030 2384156 2384660 2385356 "RCFIELD-" 2385431 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1029 2380425 2382257 2382300 "RCAGG" 2383384 NIL RCAGG (NIL T) -9 NIL 2383849 NIL) (-1028 2380053 2380147 2380310 "RCAGG-" 2380315 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1027 2379388 2379500 2379665 "RATRET" 2379937 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1026 2378941 2379008 2379129 "RATFACT" 2379316 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1025 2378249 2378369 2378521 "RANDSRC" 2378811 T RANDSRC (NIL) -7 NIL NIL NIL) (-1024 2377983 2378027 2378100 "RADUTIL" 2378198 T RADUTIL (NIL) -7 NIL NIL NIL) (-1023 2370819 2376814 2377125 "RADIX" 2377706 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1022 2361287 2370661 2370791 "RADFF" 2370796 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1021 2360934 2361009 2361039 "RADCAT" 2361199 T RADCAT (NIL) -9 NIL NIL NIL) (-1020 2360716 2360764 2360864 "RADCAT-" 2360869 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1019 2358814 2360486 2360578 "QUEUE" 2360659 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1018 2355083 2358747 2358795 "QUAT" 2358800 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1017 2354714 2354757 2354888 "QUATCT2" 2355034 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1016 2347548 2351164 2351206 "QUATCAT" 2351997 NIL QUATCAT (NIL T) -9 NIL 2352763 NIL) (-1015 2343687 2344724 2346114 "QUATCAT-" 2346210 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1014 2341152 2342763 2342806 "QUAGG" 2343187 NIL QUAGG (NIL T) -9 NIL 2343362 NIL) (-1013 2340754 2340974 2341044 "QQUTAST" 2341104 T QQUTAST (NIL) -8 NIL NIL NIL) (-1012 2339767 2340267 2340432 "QFORM" 2340635 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1011 2330162 2335669 2335711 "QFCAT" 2336379 NIL QFCAT (NIL T) -9 NIL 2337380 NIL) (-1010 2325003 2326418 2328268 "QFCAT-" 2328364 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1009 2324634 2324677 2324808 "QFCAT2" 2324954 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1008 2324089 2324199 2324331 "QEQUAT" 2324524 T QEQUAT (NIL) -8 NIL NIL NIL) (-1007 2317215 2318288 2319474 "QCMPACK" 2323022 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1006 2314753 2315201 2315631 "QALGSET" 2316870 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1005 2313988 2314164 2314400 "QALGSET2" 2314571 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1004 2312673 2312897 2313216 "PWFFINTB" 2313761 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1003 2310848 2311016 2311372 "PUSHVAR" 2312487 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1002 2306737 2307791 2307834 "PTRANFN" 2309745 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1001 2305128 2305419 2305743 "PTPACK" 2306448 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1000 2304757 2304814 2304925 "PTFUNC2" 2305065 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-999 2299202 2303599 2303640 "PTCAT" 2303936 NIL PTCAT (NIL T) -9 NIL 2304089 NIL) (-998 2298860 2298895 2299019 "PSQFR" 2299161 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-997 2297455 2297753 2298087 "PSEUDLIN" 2298558 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-996 2284218 2286589 2288913 "PSETPK" 2295215 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-995 2277236 2279976 2280072 "PSETCAT" 2283093 NIL PSETCAT (NIL T T T T) -9 NIL 2283907 NIL) (-994 2275072 2275706 2276527 "PSETCAT-" 2276532 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-993 2274421 2274586 2274614 "PSCURVE" 2274882 T PSCURVE (NIL) -9 NIL 2275049 NIL) (-992 2270419 2271935 2272000 "PSCAT" 2272844 NIL PSCAT (NIL T T T) -9 NIL 2273084 NIL) (-991 2269482 2269698 2270098 "PSCAT-" 2270103 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-990 2267841 2268551 2268814 "PRTITION" 2269239 T PRTITION (NIL) -8 NIL NIL NIL) (-989 2267316 2267562 2267654 "PRTDAST" 2267769 T PRTDAST (NIL) -8 NIL NIL NIL) (-988 2256406 2258620 2260808 "PRS" 2265178 NIL PRS (NIL T T) -7 NIL NIL NIL) (-987 2254217 2255756 2255796 "PRQAGG" 2255979 NIL PRQAGG (NIL T) -9 NIL 2256081 NIL) (-986 2253553 2253858 2253886 "PROPLOG" 2254025 T PROPLOG (NIL) -9 NIL 2254140 NIL) (-985 2253157 2253214 2253337 "PROPFUN2" 2253476 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-984 2252472 2252593 2252765 "PROPFUN1" 2253018 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-983 2250653 2251219 2251516 "PROPFRML" 2252208 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-982 2250122 2250229 2250357 "PROPERTY" 2250545 T PROPERTY (NIL) -8 NIL NIL NIL) (-981 2244180 2248288 2249108 "PRODUCT" 2249348 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-980 2241458 2243638 2243872 "PR" 2243991 NIL PR (NIL T T) -8 NIL NIL NIL) (-979 2241254 2241286 2241345 "PRINT" 2241419 T PRINT (NIL) -7 NIL NIL NIL) (-978 2240594 2240711 2240863 "PRIMES" 2241134 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-977 2238659 2239060 2239526 "PRIMELT" 2240173 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-976 2238388 2238437 2238465 "PRIMCAT" 2238589 T PRIMCAT (NIL) -9 NIL NIL NIL) (-975 2234503 2238326 2238371 "PRIMARR" 2238376 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-974 2233510 2233688 2233916 "PRIMARR2" 2234321 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-973 2233153 2233209 2233320 "PREASSOC" 2233448 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-972 2232628 2232761 2232789 "PPCURVE" 2232994 T PPCURVE (NIL) -9 NIL 2233130 NIL) (-971 2232223 2232423 2232506 "PORTNUM" 2232565 T PORTNUM (NIL) -8 NIL NIL NIL) (-970 2229582 2229981 2230573 "POLYROOT" 2231804 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-969 2223496 2229186 2229346 "POLY" 2229455 NIL POLY (NIL T) -8 NIL NIL NIL) (-968 2222879 2222937 2223171 "POLYLIFT" 2223432 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-967 2219154 2219603 2220232 "POLYCATQ" 2222424 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-966 2205504 2210901 2210966 "POLYCAT" 2214480 NIL POLYCAT (NIL T T T) -9 NIL 2216358 NIL) (-965 2198227 2200303 2202943 "POLYCAT-" 2202948 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-964 2197814 2197882 2198002 "POLY2UP" 2198153 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-963 2197446 2197503 2197612 "POLY2" 2197751 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-962 2196131 2196370 2196646 "POLUTIL" 2197220 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-961 2194486 2194763 2195094 "POLTOPOL" 2195853 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-960 2189951 2194422 2194468 "POINT" 2194473 NIL POINT (NIL T) -8 NIL NIL NIL) (-959 2188138 2188495 2188870 "PNTHEORY" 2189596 T PNTHEORY (NIL) -7 NIL NIL NIL) (-958 2186596 2186893 2187292 "PMTOOLS" 2187836 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-957 2186189 2186267 2186384 "PMSYM" 2186512 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-956 2185697 2185766 2185941 "PMQFCAT" 2186114 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-955 2185052 2185162 2185318 "PMPRED" 2185574 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-954 2184445 2184531 2184693 "PMPREDFS" 2184953 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-953 2183109 2183317 2183695 "PMPLCAT" 2184207 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-952 2182641 2182720 2182872 "PMLSAGG" 2183024 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-951 2182114 2182190 2182372 "PMKERNEL" 2182559 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-950 2181731 2181806 2181919 "PMINS" 2182033 NIL PMINS (NIL T) -7 NIL NIL NIL) (-949 2181173 2181242 2181451 "PMFS" 2181656 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-948 2180401 2180519 2180724 "PMDOWN" 2181050 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-947 2179568 2179726 2179907 "PMASS" 2180240 T PMASS (NIL) -7 NIL NIL NIL) (-946 2178841 2178951 2179114 "PMASSFS" 2179455 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-945 2178496 2178564 2178658 "PLOTTOOL" 2178767 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-944 2173103 2174307 2175455 "PLOT" 2177368 T PLOT (NIL) -8 NIL NIL NIL) (-943 2168907 2169951 2170872 "PLOT3D" 2172202 T PLOT3D (NIL) -8 NIL NIL NIL) (-942 2167819 2167996 2168231 "PLOT1" 2168711 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-941 2143210 2147885 2152736 "PLEQN" 2163085 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-940 2142528 2142650 2142830 "PINTERP" 2143075 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-939 2142221 2142268 2142371 "PINTERPA" 2142475 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-938 2141437 2141985 2142072 "PI" 2142112 T PI (NIL) -8 NIL NIL 2142179) (-937 2139734 2140709 2140737 "PID" 2140919 T PID (NIL) -9 NIL 2141053 NIL) (-936 2139485 2139522 2139597 "PICOERCE" 2139691 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-935 2138805 2138944 2139120 "PGROEB" 2139341 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-934 2134392 2135206 2136111 "PGE" 2137920 T PGE (NIL) -7 NIL NIL NIL) (-933 2132515 2132762 2133128 "PGCD" 2134109 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-932 2131853 2131956 2132117 "PFRPAC" 2132399 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-931 2128493 2130401 2130754 "PFR" 2131532 NIL PFR (NIL T) -8 NIL NIL NIL) (-930 2126882 2127126 2127451 "PFOTOOLS" 2128240 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-929 2125415 2125654 2126005 "PFOQ" 2126639 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-928 2123916 2124128 2124484 "PFO" 2125199 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-927 2120469 2123805 2123874 "PF" 2123879 NIL PF (NIL NIL) -8 NIL NIL NIL) (-926 2117803 2119074 2119102 "PFECAT" 2119687 T PFECAT (NIL) -9 NIL 2120071 NIL) (-925 2117248 2117402 2117616 "PFECAT-" 2117621 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-924 2115851 2116103 2116404 "PFBRU" 2116997 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-923 2113717 2114069 2114501 "PFBR" 2115502 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-922 2109763 2111229 2111876 "PERM" 2113103 NIL PERM (NIL T) -8 NIL NIL NIL) (-921 2104997 2105970 2106840 "PERMGRP" 2108926 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-920 2103116 2104076 2104117 "PERMCAT" 2104517 NIL PERMCAT (NIL T) -9 NIL 2104815 NIL) (-919 2102769 2102810 2102934 "PERMAN" 2103069 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-918 2100257 2102434 2102556 "PENDTREE" 2102680 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-917 2099186 2099401 2099442 "PDSPC" 2099975 NIL PDSPC (NIL T) -9 NIL 2100220 NIL) (-916 2098289 2098507 2098869 "PDSPC-" 2098874 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-915 2097171 2097939 2097980 "PDRING" 2097985 NIL PDRING (NIL T) -9 NIL 2098013 NIL) (-914 2096058 2096676 2096730 "PDMOD" 2096735 NIL PDMOD (NIL T T) -9 NIL 2096839 NIL) (-913 2093273 2094051 2094719 "PDEPROB" 2095410 T PDEPROB (NIL) -8 NIL NIL NIL) (-912 2090818 2091322 2091877 "PDEPACK" 2092738 T PDEPACK (NIL) -7 NIL NIL NIL) (-911 2089730 2089920 2090171 "PDECOMP" 2090617 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-910 2087309 2088152 2088180 "PDECAT" 2088967 T PDECAT (NIL) -9 NIL 2089680 NIL) (-909 2086938 2086993 2087047 "PDDOM" 2087212 NIL PDDOM (NIL T T) -9 NIL 2087292 NIL) (-908 2086757 2086787 2086894 "PDDOM-" 2086899 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-907 2086508 2086541 2086631 "PCOMP" 2086718 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-906 2084686 2085309 2085606 "PBWLB" 2086237 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-905 2077159 2078759 2080097 "PATTERN" 2083369 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-904 2076791 2076848 2076957 "PATTERN2" 2077096 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-903 2074548 2074936 2075393 "PATTERN1" 2076380 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-902 2071916 2072497 2072978 "PATRES" 2074113 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-901 2071480 2071547 2071679 "PATRES2" 2071843 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-900 2069363 2069768 2070175 "PATMATCH" 2071147 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-899 2068873 2069082 2069123 "PATMAB" 2069230 NIL PATMAB (NIL T) -9 NIL 2069313 NIL) (-898 2067391 2067727 2067985 "PATLRES" 2068678 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-897 2066937 2067060 2067101 "PATAB" 2067106 NIL PATAB (NIL T) -9 NIL 2067278 NIL) (-896 2065119 2065514 2065937 "PARTPERM" 2066534 T PARTPERM (NIL) -7 NIL NIL NIL) (-895 2064740 2064803 2064905 "PARSURF" 2065050 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-894 2064372 2064429 2064538 "PARSU2" 2064677 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-893 2064136 2064176 2064243 "PARSER" 2064325 T PARSER (NIL) -7 NIL NIL NIL) (-892 2063757 2063820 2063922 "PARSCURV" 2064067 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-891 2063389 2063446 2063555 "PARSC2" 2063694 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-890 2063028 2063086 2063183 "PARPCURV" 2063325 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-889 2062660 2062717 2062826 "PARPC2" 2062965 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-888 2061721 2062033 2062215 "PARAMAST" 2062498 T PARAMAST (NIL) -8 NIL NIL NIL) (-887 2061241 2061327 2061446 "PAN2EXPR" 2061622 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-886 2060018 2060362 2060590 "PALETTE" 2061033 T PALETTE (NIL) -8 NIL NIL NIL) (-885 2058411 2059023 2059383 "PAIR" 2059704 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-884 2052011 2057668 2057863 "PADICRC" 2058265 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-883 2044935 2051355 2051540 "PADICRAT" 2051858 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-882 2043250 2044872 2044917 "PADIC" 2044922 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-881 2040360 2041924 2041964 "PADICCT" 2042545 NIL PADICCT (NIL NIL) -9 NIL 2042827 NIL) (-880 2039317 2039517 2039785 "PADEPAC" 2040147 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-879 2038529 2038662 2038868 "PADE" 2039179 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-878 2036916 2037737 2038017 "OWP" 2038333 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-877 2036409 2036622 2036719 "OVERSET" 2036839 T OVERSET (NIL) -8 NIL NIL NIL) (-876 2035455 2036014 2036186 "OVAR" 2036277 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-875 2034719 2034840 2035001 "OUT" 2035314 T OUT (NIL) -7 NIL NIL NIL) (-874 2023591 2025828 2028028 "OUTFORM" 2032539 T OUTFORM (NIL) -8 NIL NIL NIL) (-873 2022927 2023188 2023315 "OUTBFILE" 2023484 T OUTBFILE (NIL) -8 NIL NIL NIL) (-872 2022234 2022399 2022427 "OUTBCON" 2022745 T OUTBCON (NIL) -9 NIL 2022911 NIL) (-871 2021835 2021947 2022104 "OUTBCON-" 2022109 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-870 2021215 2021564 2021653 "OSI" 2021766 T OSI (NIL) -8 NIL NIL NIL) (-869 2020745 2021083 2021111 "OSGROUP" 2021116 T OSGROUP (NIL) -9 NIL 2021138 NIL) (-868 2019490 2019717 2020002 "ORTHPOL" 2020492 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-867 2017041 2019325 2019446 "OREUP" 2019451 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-866 2014444 2016732 2016859 "ORESUP" 2016983 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-865 2011972 2012472 2013033 "OREPCTO" 2013933 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-864 2005658 2007859 2007900 "OREPCAT" 2010248 NIL OREPCAT (NIL T) -9 NIL 2011352 NIL) (-863 2002805 2003587 2004645 "OREPCAT-" 2004650 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-862 2001956 2002254 2002282 "ORDSET" 2002591 T ORDSET (NIL) -9 NIL 2002755 NIL) (-861 2001387 2001535 2001759 "ORDSET-" 2001764 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-860 1999952 2000743 2000771 "ORDRING" 2000973 T ORDRING (NIL) -9 NIL 2001098 NIL) (-859 1999597 1999691 1999835 "ORDRING-" 1999840 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 1998977 1999440 1999468 "ORDMON" 1999473 T ORDMON (NIL) -9 NIL 1999494 NIL) (-857 1998139 1998286 1998481 "ORDFUNS" 1998826 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1997477 1997896 1997924 "ORDFIN" 1997989 T ORDFIN (NIL) -9 NIL 1998063 NIL) (-855 1994036 1996063 1996472 "ORDCOMP" 1997101 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1993302 1993429 1993615 "ORDCOMP2" 1993896 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1989883 1990793 1991607 "OPTPROB" 1992508 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1986685 1987324 1988028 "OPTPACK" 1989199 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1984372 1985138 1985166 "OPTCAT" 1985985 T OPTCAT (NIL) -9 NIL 1986635 NIL) (-850 1983756 1984049 1984154 "OPSIG" 1984287 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1983524 1983563 1983629 "OPQUERY" 1983710 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1980655 1981835 1982339 "OP" 1983053 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1980029 1980255 1980296 "OPERCAT" 1980508 NIL OPERCAT (NIL T) -9 NIL 1980605 NIL) (-846 1979784 1979840 1979957 "OPERCAT-" 1979962 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1976597 1978581 1978950 "ONECOMP" 1979448 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1975902 1976017 1976191 "ONECOMP2" 1976469 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1975321 1975427 1975557 "OMSERVER" 1975792 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1972183 1974761 1974801 "OMSAGG" 1974862 NIL OMSAGG (NIL T) -9 NIL 1974926 NIL) (-841 1970806 1971069 1971351 "OMPKG" 1971921 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1970236 1970339 1970367 "OM" 1970666 T OM (NIL) -9 NIL NIL NIL) (-839 1968783 1969785 1969954 "OMLO" 1970117 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1967743 1967890 1968110 "OMEXPR" 1968609 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1967034 1967289 1967425 "OMERR" 1967627 T OMERR (NIL) -8 NIL NIL NIL) (-836 1966185 1966455 1966615 "OMERRK" 1966894 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1965636 1965862 1965970 "OMENC" 1966097 T OMENC (NIL) -8 NIL NIL NIL) (-834 1959531 1960716 1961887 "OMDEV" 1964485 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1958600 1958771 1958965 "OMCONN" 1959357 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1957121 1958097 1958125 "OINTDOM" 1958130 T OINTDOM (NIL) -9 NIL 1958151 NIL) (-831 1954459 1955809 1956146 "OFMONOID" 1956816 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1953831 1954396 1954441 "ODVAR" 1954446 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1951254 1953576 1953731 "ODR" 1953736 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1943567 1951030 1951156 "ODPOL" 1951161 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1937371 1943439 1943544 "ODP" 1943549 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1936137 1936352 1936627 "ODETOOLS" 1937145 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1933104 1933762 1934478 "ODESYS" 1935470 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1927986 1928894 1929919 "ODERTRIC" 1932179 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1927412 1927494 1927688 "ODERED" 1927898 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1924300 1924848 1925525 "ODERAT" 1926835 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1921259 1921724 1922321 "ODEPRRIC" 1923829 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1919202 1919798 1920284 "ODEPROB" 1920793 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1915722 1916207 1916854 "ODEPRIM" 1918681 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1914971 1915073 1915333 "ODEPAL" 1915614 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1911133 1911924 1912788 "ODEPACK" 1914127 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1910194 1910301 1910523 "ODEINT" 1911022 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1904295 1905720 1907167 "ODEIFTBL" 1908767 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1899693 1900479 1901431 "ODEEF" 1903454 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1899042 1899131 1899354 "ODECONST" 1899598 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1897167 1897828 1897856 "ODECAT" 1898461 T ODECAT (NIL) -9 NIL 1898992 NIL) (-811 1894022 1896872 1896994 "OCT" 1897077 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1893660 1893703 1893830 "OCTCT2" 1893973 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1888271 1890706 1890746 "OC" 1891843 NIL OC (NIL T) -9 NIL 1892701 NIL) (-808 1885498 1886246 1887236 "OC-" 1887330 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1884850 1885318 1885346 "OCAMON" 1885351 T OCAMON (NIL) -9 NIL 1885372 NIL) (-806 1884381 1884722 1884750 "OASGP" 1884755 T OASGP (NIL) -9 NIL 1884775 NIL) (-805 1883642 1884131 1884159 "OAMONS" 1884199 T OAMONS (NIL) -9 NIL 1884242 NIL) (-804 1883056 1883489 1883517 "OAMON" 1883522 T OAMON (NIL) -9 NIL 1883542 NIL) (-803 1882314 1882832 1882860 "OAGROUP" 1882865 T OAGROUP (NIL) -9 NIL 1882885 NIL) (-802 1882004 1882054 1882142 "NUMTUBE" 1882258 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1875577 1877095 1878631 "NUMQUAD" 1880488 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1871333 1872321 1873346 "NUMODE" 1874572 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1868688 1869568 1869596 "NUMINT" 1870519 T NUMINT (NIL) -9 NIL 1871283 NIL) (-798 1867636 1867833 1868051 "NUMFMT" 1868490 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1853995 1856940 1859472 "NUMERIC" 1865143 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1848365 1853444 1853539 "NTSCAT" 1853544 NIL NTSCAT (NIL T T T T) -9 NIL 1853583 NIL) (-795 1847559 1847724 1847917 "NTPOLFN" 1848204 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1835368 1844384 1845196 "NSUP" 1846780 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1835000 1835057 1835166 "NSUP2" 1835305 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1824958 1834774 1834907 "NSMP" 1834912 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1823390 1823691 1824048 "NREP" 1824646 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1821981 1822233 1822591 "NPCOEF" 1823133 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1821047 1821162 1821378 "NORMRETR" 1821862 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1819088 1819378 1819787 "NORMPK" 1820755 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1818773 1818801 1818925 "NORMMA" 1819054 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1818573 1818730 1818759 "NONE" 1818764 T NONE (NIL) -8 NIL NIL NIL) (-785 1818362 1818391 1818460 "NONE1" 1818537 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1817859 1817921 1818100 "NODE1" 1818294 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1816140 1816991 1817246 "NNI" 1817593 T NNI (NIL) -8 NIL NIL 1817828) (-782 1814560 1814873 1815237 "NLINSOL" 1815808 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1810801 1811796 1812695 "NIPROB" 1813681 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1809558 1809792 1810094 "NFINTBAS" 1810563 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1808732 1809208 1809249 "NETCLT" 1809421 NIL NETCLT (NIL T) -9 NIL 1809503 NIL) (-778 1807440 1807671 1807952 "NCODIV" 1808500 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1807202 1807239 1807314 "NCNTFRAC" 1807397 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1805382 1805746 1806166 "NCEP" 1806827 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1804233 1805006 1805034 "NASRING" 1805144 T NASRING (NIL) -9 NIL 1805224 NIL) (-774 1804028 1804072 1804166 "NASRING-" 1804171 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1803135 1803660 1803688 "NARNG" 1803805 T NARNG (NIL) -9 NIL 1803896 NIL) (-772 1802827 1802894 1803028 "NARNG-" 1803033 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1801706 1801913 1802148 "NAGSP" 1802612 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1792978 1794662 1796335 "NAGS" 1800053 T NAGS (NIL) -7 NIL NIL NIL) (-769 1791526 1791834 1792165 "NAGF07" 1792667 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1786064 1787355 1788662 "NAGF04" 1790239 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1779032 1780646 1782279 "NAGF02" 1784451 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1774256 1775356 1776473 "NAGF01" 1777935 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1767884 1769450 1771035 "NAGE04" 1772691 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1759053 1761174 1763304 "NAGE02" 1765774 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1755006 1755953 1756917 "NAGE01" 1758109 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1752801 1753335 1753893 "NAGD03" 1754468 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1744551 1746479 1748433 "NAGD02" 1750867 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1738362 1739787 1741227 "NAGD01" 1743131 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1734571 1735393 1736230 "NAGC06" 1737545 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1733036 1733368 1733724 "NAGC05" 1734235 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1732412 1732531 1732675 "NAGC02" 1732912 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1731371 1731954 1731994 "NAALG" 1732073 NIL NAALG (NIL T) -9 NIL 1732134 NIL) (-755 1731206 1731235 1731325 "NAALG-" 1731330 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1725156 1726264 1727451 "MULTSQFR" 1730102 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1724475 1724550 1724734 "MULTFACT" 1725068 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1717146 1721060 1721113 "MTSCAT" 1722183 NIL MTSCAT (NIL T T) -9 NIL 1722698 NIL) (-751 1716858 1716912 1717004 "MTHING" 1717086 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1716650 1716683 1716743 "MSYSCMD" 1716818 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1712732 1715405 1715725 "MSET" 1716363 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1709801 1712293 1712334 "MSETAGG" 1712339 NIL MSETAGG (NIL T) -9 NIL 1712373 NIL) (-747 1705643 1707180 1707925 "MRING" 1709101 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1705209 1705276 1705407 "MRF2" 1705570 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1704827 1704862 1705006 "MRATFAC" 1705168 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1702439 1702734 1703165 "MPRFF" 1704532 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1696468 1702293 1702390 "MPOLY" 1702395 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1695958 1695993 1696201 "MPCPF" 1696427 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1695472 1695515 1695699 "MPC3" 1695909 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1694667 1694748 1694969 "MPC2" 1695387 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1692968 1693305 1693695 "MONOTOOL" 1694327 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1692193 1692510 1692538 "MONOID" 1692757 T MONOID (NIL) -9 NIL 1692904 NIL) (-737 1691739 1691858 1692039 "MONOID-" 1692044 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1681295 1687517 1687576 "MONOGEN" 1688250 NIL MONOGEN (NIL T T) -9 NIL 1688706 NIL) (-735 1678513 1679248 1680248 "MONOGEN-" 1680367 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1677346 1677792 1677820 "MONADWU" 1678212 T MONADWU (NIL) -9 NIL 1678450 NIL) (-733 1676718 1676877 1677125 "MONADWU-" 1677130 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1676077 1676321 1676349 "MONAD" 1676556 T MONAD (NIL) -9 NIL 1676668 NIL) (-731 1675762 1675840 1675972 "MONAD-" 1675977 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1674051 1674675 1674954 "MOEBIUS" 1675515 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1673329 1673733 1673773 "MODULE" 1673778 NIL MODULE (NIL T) -9 NIL 1673817 NIL) (-728 1672897 1672993 1673183 "MODULE-" 1673188 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1670577 1671261 1671588 "MODRING" 1672721 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1667521 1668682 1669203 "MODOP" 1670106 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1666109 1666588 1666865 "MODMONOM" 1667384 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1655885 1664400 1664814 "MODMON" 1665746 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1653041 1654729 1655005 "MODFIELD" 1655760 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1652018 1652322 1652512 "MMLFORM" 1652871 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1651544 1651587 1651766 "MMAP" 1651969 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1649623 1650390 1650431 "MLO" 1650854 NIL MLO (NIL T) -9 NIL 1651096 NIL) (-719 1646989 1647505 1648107 "MLIFT" 1649104 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1646380 1646464 1646618 "MKUCFUNC" 1646900 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1645979 1646049 1646172 "MKRECORD" 1646303 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1645026 1645188 1645416 "MKFUNC" 1645790 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1644414 1644518 1644674 "MKFLCFN" 1644909 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1643691 1643793 1643978 "MKBCFUNC" 1644307 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1640288 1643245 1643381 "MINT" 1643575 T MINT (NIL) -8 NIL NIL NIL) (-712 1639100 1639343 1639620 "MHROWRED" 1640043 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1634480 1637635 1638040 "MFLOAT" 1638715 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1633837 1633913 1634084 "MFINFACT" 1634392 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1630152 1631000 1631884 "MESH" 1632973 T MESH (NIL) -7 NIL NIL NIL) (-708 1628542 1628854 1629207 "MDDFACT" 1629839 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1625337 1627701 1627742 "MDAGG" 1627997 NIL MDAGG (NIL T) -9 NIL 1628140 NIL) (-706 1614039 1624630 1624837 "MCMPLX" 1625150 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1613176 1613322 1613523 "MCDEN" 1613888 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1611066 1611336 1611716 "MCALCFN" 1612906 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1609991 1610231 1610464 "MAYBE" 1610872 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1607603 1608126 1608688 "MATSTOR" 1609462 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1603560 1606975 1607223 "MATRIX" 1607388 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1599326 1600033 1600769 "MATLIN" 1602917 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1589432 1592618 1592695 "MATCAT" 1597575 NIL MATCAT (NIL T T T) -9 NIL 1598992 NIL) (-698 1585788 1586809 1588165 "MATCAT-" 1588170 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1584382 1584535 1584868 "MATCAT2" 1585623 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1582494 1582818 1583202 "MAPPKG3" 1584057 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1581475 1581648 1581870 "MAPPKG2" 1582318 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1579974 1580258 1580585 "MAPPKG1" 1581181 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1579053 1579380 1579557 "MAPPAST" 1579817 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1578664 1578722 1578845 "MAPHACK3" 1578989 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1578256 1578317 1578431 "MAPHACK2" 1578596 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1577694 1577797 1577939 "MAPHACK1" 1578147 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1575773 1576394 1576698 "MAGMA" 1577422 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1575252 1575497 1575588 "MACROAST" 1575702 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1571670 1573491 1573952 "M3D" 1574824 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1565745 1570009 1570050 "LZSTAGG" 1570832 NIL LZSTAGG (NIL T) -9 NIL 1571127 NIL) (-685 1561703 1562876 1564333 "LZSTAGG-" 1564338 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1558790 1559594 1560081 "LWORD" 1561248 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1558366 1558594 1558669 "LSTAST" 1558735 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1551264 1558137 1558271 "LSQM" 1558276 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1550488 1550627 1550855 "LSPP" 1551119 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1548300 1548601 1549057 "LSMP" 1550177 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1545079 1545753 1546483 "LSMP1" 1547602 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1538925 1544216 1544257 "LSAGG" 1544319 NIL LSAGG (NIL T) -9 NIL 1544397 NIL) (-677 1535620 1536544 1537757 "LSAGG-" 1537762 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1533219 1534764 1535013 "LPOLY" 1535415 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1532801 1532886 1533009 "LPEFRAC" 1533128 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1531122 1531895 1532148 "LO" 1532633 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1530774 1530886 1530914 "LOGIC" 1531025 T LOGIC (NIL) -9 NIL 1531106 NIL) (-672 1530636 1530659 1530730 "LOGIC-" 1530735 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1529829 1529969 1530162 "LODOOPS" 1530492 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1527252 1529745 1529811 "LODO" 1529816 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1525790 1526025 1526378 "LODOF" 1526999 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1521994 1524425 1524466 "LODOCAT" 1524904 NIL LODOCAT (NIL T) -9 NIL 1525115 NIL) (-667 1521727 1521785 1521912 "LODOCAT-" 1521917 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1519047 1521568 1521686 "LODO2" 1521691 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1516482 1518984 1519029 "LODO1" 1519034 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1515363 1515528 1515833 "LODEEF" 1516305 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1510666 1513557 1513598 "LNAGG" 1514460 NIL LNAGG (NIL T) -9 NIL 1514895 NIL) (-662 1509813 1510027 1510369 "LNAGG-" 1510374 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1505949 1506738 1507377 "LMOPS" 1509228 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1505352 1505740 1505781 "LMODULE" 1505786 NIL LMODULE (NIL T) -9 NIL 1505812 NIL) (-659 1502550 1504997 1505120 "LMDICT" 1505262 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1502182 1502354 1502395 "LLINSET" 1502456 NIL LLINSET (NIL T) -9 NIL 1502500 NIL) (-657 1501881 1502090 1502150 "LITERAL" 1502155 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1495044 1500815 1501119 "LIST" 1501610 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1494569 1494643 1494782 "LIST3" 1494964 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1493576 1493754 1493982 "LIST2" 1494387 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1491710 1492022 1492421 "LIST2MAP" 1493223 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1491355 1491543 1491584 "LINSET" 1491589 NIL LINSET (NIL T) -9 NIL 1491623 NIL) (-651 1489790 1490396 1490437 "LINEXP" 1490927 NIL LINEXP (NIL T) -9 NIL 1491200 NIL) (-650 1488367 1488627 1488938 "LINDEP" 1489542 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1485134 1485853 1486630 "LIMITRF" 1487622 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1483437 1483733 1484142 "LIMITPS" 1484829 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1477865 1482948 1483176 "LIE" 1483258 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1476813 1477282 1477322 "LIECAT" 1477462 NIL LIECAT (NIL T) -9 NIL 1477613 NIL) (-645 1476654 1476681 1476769 "LIECAT-" 1476774 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1469241 1476194 1476350 "LIB" 1476518 T LIB (NIL) -8 NIL NIL NIL) (-643 1464876 1465759 1466694 "LGROBP" 1468358 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1462874 1463148 1463498 "LF" 1464597 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1461714 1462406 1462434 "LFCAT" 1462641 T LFCAT (NIL) -9 NIL 1462780 NIL) (-640 1458616 1459246 1459934 "LEXTRIPK" 1461078 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1455360 1456186 1456689 "LEXP" 1458196 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1454836 1455081 1455173 "LETAST" 1455288 T LETAST (NIL) -8 NIL NIL NIL) (-637 1453234 1453547 1453948 "LEADCDET" 1454518 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1452424 1452498 1452727 "LAZM3PK" 1453155 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1447341 1450501 1451039 "LAUPOL" 1451936 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1446920 1446964 1447125 "LAPLACE" 1447291 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1444859 1446021 1446272 "LA" 1446753 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1443853 1444437 1444478 "LALG" 1444540 NIL LALG (NIL T) -9 NIL 1444599 NIL) (-631 1443567 1443626 1443762 "LALG-" 1443767 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1443402 1443426 1443467 "KVTFROM" 1443529 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1442325 1442769 1442954 "KTVLOGIC" 1443237 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1442160 1442184 1442225 "KRCFROM" 1442287 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1441064 1441251 1441550 "KOVACIC" 1441960 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1440899 1440923 1440964 "KONVERT" 1441026 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1440734 1440758 1440799 "KOERCE" 1440861 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1438565 1439327 1439704 "KERNEL" 1440390 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1438061 1438142 1438274 "KERNEL2" 1438479 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1431831 1436600 1436654 "KDAGG" 1437031 NIL KDAGG (NIL T T) -9 NIL 1437237 NIL) (-621 1431360 1431484 1431689 "KDAGG-" 1431694 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1424508 1431021 1431176 "KAFILE" 1431238 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1418936 1424019 1424247 "JORDAN" 1424329 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1418315 1418585 1418706 "JOINAST" 1418835 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1418161 1418220 1418275 "JAVACODE" 1418280 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1414413 1416366 1416420 "IXAGG" 1417349 NIL IXAGG (NIL T T) -9 NIL 1417808 NIL) (-615 1413332 1413638 1414057 "IXAGG-" 1414062 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1408862 1413254 1413313 "IVECTOR" 1413318 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1407628 1407865 1408131 "ITUPLE" 1408629 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1406130 1406307 1406602 "ITRIGMNP" 1407450 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1404875 1405079 1405362 "ITFUN3" 1405906 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1404507 1404564 1404673 "ITFUN2" 1404812 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1403666 1403987 1404161 "ITFORM" 1404353 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1401627 1402686 1402964 "ITAYLOR" 1403421 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1390572 1395764 1396927 "ISUPS" 1400497 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1389676 1389816 1390052 "ISUMP" 1390419 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1385051 1389621 1389662 "ISTRING" 1389667 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1384527 1384772 1384864 "ISAST" 1384979 T ISAST (NIL) -8 NIL NIL NIL) (-603 1383736 1383818 1384034 "IRURPK" 1384441 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1382672 1382873 1383113 "IRSN" 1383516 T IRSN (NIL) -7 NIL NIL NIL) (-601 1380743 1381098 1381527 "IRRF2F" 1382310 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1380490 1380528 1380604 "IRREDFFX" 1380699 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1379105 1379364 1379663 "IROOT" 1380223 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1375709 1376789 1377481 "IR" 1378445 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1374914 1375202 1375353 "IRFORM" 1375578 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1372527 1373022 1373588 "IR2" 1374392 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1371627 1371740 1371954 "IR2F" 1372410 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1371418 1371452 1371512 "IPRNTPK" 1371587 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1367999 1371307 1371376 "IPF" 1371381 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1366326 1367924 1367981 "IPADIC" 1367986 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1365638 1365886 1366016 "IP4ADDR" 1366216 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1365012 1365267 1365399 "IOMODE" 1365526 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1364085 1364609 1364736 "IOBFILE" 1364905 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1363573 1363989 1364017 "IOBCON" 1364022 T IOBCON (NIL) -9 NIL 1364043 NIL) (-587 1363084 1363142 1363325 "INVLAPLA" 1363509 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1352732 1355086 1357472 "INTTR" 1360748 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1349067 1349809 1350674 "INTTOOLS" 1351917 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1348653 1348744 1348861 "INTSLPE" 1348970 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1346606 1348576 1348635 "INTRVL" 1348640 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1344208 1344720 1345295 "INTRF" 1346091 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1343619 1343716 1343858 "INTRET" 1344106 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1341616 1342005 1342475 "INTRAT" 1343227 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1338879 1339462 1340081 "INTPM" 1341101 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1335624 1336223 1336961 "INTPAF" 1338265 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1330803 1331765 1332816 "INTPACK" 1334593 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1327623 1330600 1330709 "INT" 1330714 T INT (NIL) -8 NIL NIL NIL) (-575 1326875 1327027 1327235 "INTHERTR" 1327465 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1326314 1326394 1326582 "INTHERAL" 1326789 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1324160 1324603 1325060 "INTHEORY" 1325877 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1315566 1317187 1318959 "INTG0" 1322512 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1296139 1300929 1305739 "INTFTBL" 1310776 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1295388 1295526 1295699 "INTFACT" 1295998 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1292815 1293261 1293818 "INTEF" 1294942 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1291182 1291921 1291949 "INTDOM" 1292250 T INTDOM (NIL) -9 NIL 1292457 NIL) (-567 1290551 1290725 1290967 "INTDOM-" 1290972 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1286939 1288867 1288921 "INTCAT" 1289720 NIL INTCAT (NIL T) -9 NIL 1290041 NIL) (-565 1286411 1286514 1286642 "INTBIT" 1286831 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1285110 1285264 1285571 "INTALG" 1286256 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1284593 1284683 1284840 "INTAF" 1285014 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1277936 1284403 1284543 "INTABL" 1284548 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1277269 1277735 1277800 "INT8" 1277834 T INT8 (NIL) -8 NIL NIL 1277879) (-560 1276601 1277067 1277132 "INT64" 1277166 T INT64 (NIL) -8 NIL NIL 1277211) (-559 1275933 1276399 1276464 "INT32" 1276498 T INT32 (NIL) -8 NIL NIL 1276543) (-558 1275265 1275731 1275796 "INT16" 1275830 T INT16 (NIL) -8 NIL NIL 1275875) (-557 1269982 1272826 1272854 "INS" 1273788 T INS (NIL) -9 NIL 1274453 NIL) (-556 1267222 1267993 1268967 "INS-" 1269040 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1265997 1266224 1266522 "INPSIGN" 1266975 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1265115 1265232 1265429 "INPRODPF" 1265877 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1264009 1264126 1264363 "INPRODFF" 1264995 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1263009 1263161 1263421 "INNMFACT" 1263845 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1262206 1262303 1262491 "INMODGCD" 1262908 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1260714 1260959 1261283 "INFSP" 1261951 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1259898 1260015 1260198 "INFPROD0" 1260594 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1256753 1257963 1258478 "INFORM" 1259391 T INFORM (NIL) -8 NIL NIL NIL) (-547 1256363 1256423 1256521 "INFORM1" 1256688 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1255886 1255975 1256089 "INFINITY" 1256269 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1255062 1255606 1255707 "INETCLTS" 1255805 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1253678 1253928 1254249 "INEP" 1254810 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1252927 1253575 1253640 "INDE" 1253645 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1252491 1252559 1252676 "INCRMAPS" 1252854 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1251309 1251760 1251966 "INBFILE" 1252305 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1246608 1247545 1248489 "INBFF" 1250397 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1245516 1245785 1245813 "INBCON" 1246326 T INBCON (NIL) -9 NIL 1246592 NIL) (-538 1244768 1244991 1245267 "INBCON-" 1245272 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1244247 1244492 1244583 "INAST" 1244697 T INAST (NIL) -8 NIL NIL NIL) (-536 1243674 1243926 1244032 "IMPTAST" 1244161 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1240120 1243518 1243622 "IMATRIX" 1243627 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1238828 1238951 1239267 "IMATQF" 1239976 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1237048 1237275 1237612 "IMATLIN" 1238584 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1231626 1236972 1237030 "ILIST" 1237035 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1229531 1231486 1231599 "IIARRAY2" 1231604 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1224929 1229442 1229506 "IFF" 1229511 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1224276 1224546 1224662 "IFAST" 1224833 T IFAST (NIL) -8 NIL NIL NIL) (-528 1219271 1223568 1223756 "IFARRAY" 1224133 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1218451 1219175 1219248 "IFAMON" 1219253 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1218035 1218100 1218154 "IEVALAB" 1218361 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1217710 1217778 1217938 "IEVALAB-" 1217943 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1217341 1217624 1217687 "IDPO" 1217692 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1216591 1217230 1217305 "IDPOAMS" 1217310 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1215898 1216480 1216555 "IDPOAM" 1216560 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214957 1215233 1215286 "IDPC" 1215699 NIL IDPC (NIL T T) -9 NIL 1215848 NIL) (-520 1214426 1214849 1214922 "IDPAM" 1214927 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1213802 1214318 1214391 "IDPAG" 1214396 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1213447 1213638 1213713 "IDENT" 1213747 T IDENT (NIL) -8 NIL NIL NIL) (-517 1209702 1210550 1211445 "IDECOMP" 1212604 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1202539 1203625 1204672 "IDEAL" 1208738 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1201699 1201811 1202011 "ICDEN" 1202423 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1200770 1201179 1201326 "ICARD" 1201572 T ICARD (NIL) -8 NIL NIL NIL) (-513 1198830 1199143 1199548 "IBPTOOLS" 1200447 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1194437 1198450 1198563 "IBITS" 1198749 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1191160 1191736 1192431 "IBATOOL" 1193854 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1188939 1189401 1189934 "IBACHIN" 1190695 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1186768 1188785 1188888 "IARRAY2" 1188893 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1182874 1186694 1186751 "IARRAY1" 1186756 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1176742 1181286 1181767 "IAN" 1182413 T IAN (NIL) -8 NIL NIL NIL) (-506 1176253 1176310 1176483 "IALGFACT" 1176679 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1175781 1175894 1175922 "HYPCAT" 1176129 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1175319 1175436 1175622 "HYPCAT-" 1175627 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1174914 1175114 1175197 "HOSTNAME" 1175256 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1174759 1174796 1174837 "HOMOTOP" 1174842 NIL HOMOTOP (NIL T) -9 NIL 1174875 NIL) (-501 1171391 1172769 1172810 "HOAGG" 1173791 NIL HOAGG (NIL T) -9 NIL 1174470 NIL) (-500 1169985 1170384 1170910 "HOAGG-" 1170915 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1163709 1169578 1169728 "HEXADEC" 1169855 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1162457 1162679 1162942 "HEUGCD" 1163486 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1161533 1162294 1162424 "HELLFDIV" 1162429 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1159712 1161310 1161398 "HEAP" 1161477 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1158975 1159264 1159398 "HEADAST" 1159598 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1152823 1158890 1158952 "HDP" 1158957 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1146543 1152458 1152610 "HDMP" 1152724 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1145867 1146007 1146171 "HB" 1146399 T HB (NIL) -7 NIL NIL NIL) (-491 1139253 1145713 1145817 "HASHTBL" 1145822 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1138729 1138974 1139066 "HASAST" 1139181 T HASAST (NIL) -8 NIL NIL NIL) (-489 1136507 1138351 1138533 "HACKPI" 1138567 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1132175 1136360 1136473 "GTSET" 1136478 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1125590 1132053 1132151 "GSTBL" 1132156 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1117977 1124755 1125011 "GSERIES" 1125390 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1117118 1117535 1117563 "GROUP" 1117766 T GROUP (NIL) -9 NIL 1117900 NIL) (-484 1116484 1116643 1116894 "GROUP-" 1116899 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1114851 1115172 1115559 "GROEBSOL" 1116161 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1113765 1114053 1114104 "GRMOD" 1114633 NIL GRMOD (NIL T T) -9 NIL 1114801 NIL) (-481 1113533 1113569 1113697 "GRMOD-" 1113702 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1108823 1109887 1110887 "GRIMAGE" 1112553 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1107289 1107550 1107874 "GRDEF" 1108519 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1106733 1106849 1106990 "GRAY" 1107168 T GRAY (NIL) -7 NIL NIL NIL) (-477 1105920 1106326 1106377 "GRALG" 1106530 NIL GRALG (NIL T T) -9 NIL 1106623 NIL) (-476 1105581 1105654 1105817 "GRALG-" 1105822 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1102358 1105166 1105344 "GPOLSET" 1105488 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1101712 1101769 1102027 "GOSPER" 1102295 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1097444 1098150 1098676 "GMODPOL" 1101411 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1096449 1096633 1096871 "GHENSEL" 1097256 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1090605 1091448 1092468 "GENUPS" 1095533 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1090302 1090353 1090442 "GENUFACT" 1090548 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1089714 1089791 1089956 "GENPGCD" 1090220 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1089188 1089223 1089436 "GENMFACT" 1089673 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1087754 1088011 1088318 "GENEEZ" 1088931 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1081634 1087365 1087527 "GDMP" 1087677 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1070977 1075405 1076511 "GCNAALG" 1080617 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1069304 1070166 1070194 "GCDDOM" 1070449 T GCDDOM (NIL) -9 NIL 1070606 NIL) (-463 1068774 1068901 1069116 "GCDDOM-" 1069121 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1067446 1067631 1067935 "GB" 1068553 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1056062 1058392 1060784 "GBINTERN" 1065137 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1053899 1054191 1054612 "GBF" 1055737 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1052680 1052845 1053112 "GBEUCLID" 1053715 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1052029 1052154 1052303 "GAUSSFAC" 1052551 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1050396 1050698 1051012 "GALUTIL" 1051748 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1048704 1048978 1049302 "GALPOLYU" 1050123 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1046069 1046359 1046766 "GALFACTU" 1048401 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1037875 1039374 1040982 "GALFACT" 1044501 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1035263 1035921 1035949 "FVFUN" 1037105 T FVFUN (NIL) -9 NIL 1037825 NIL) (-452 1034529 1034711 1034739 "FVC" 1035030 T FVC (NIL) -9 NIL 1035213 NIL) (-451 1034172 1034354 1034422 "FUNDESC" 1034481 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1033787 1033969 1034050 "FUNCTION" 1034124 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1031531 1032109 1032575 "FT" 1033341 T FT (NIL) -8 NIL NIL NIL) (-448 1030322 1030832 1031035 "FTEM" 1031348 T FTEM (NIL) -8 NIL NIL NIL) (-447 1028613 1028902 1029299 "FSUPFACT" 1030013 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1027010 1027299 1027631 "FST" 1028301 T FST (NIL) -8 NIL NIL NIL) (-445 1026209 1026315 1026503 "FSRED" 1026892 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1024908 1025164 1025511 "FSPRMELT" 1025924 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1022214 1022652 1023138 "FSPECF" 1024471 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1003287 1011988 1012029 "FS" 1015913 NIL FS (NIL T) -9 NIL 1018202 NIL) (-441 991930 994923 998980 "FS-" 999280 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 991458 991512 991682 "FSINT" 991871 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 989750 990451 990754 "FSERIES" 991237 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 988792 988908 989132 "FSCINT" 989630 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 985000 987736 987777 "FSAGG" 988147 NIL FSAGG (NIL T) -9 NIL 988406 NIL) (-436 982762 983363 984159 "FSAGG-" 984254 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 981804 981947 982174 "FSAGG2" 982615 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 979482 979762 980310 "FS2UPS" 981522 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 979116 979159 979288 "FS2" 979433 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 977994 978165 978467 "FS2EXPXP" 978941 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 977420 977535 977687 "FRUTIL" 977874 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 968833 972915 974273 "FR" 976094 NIL FR (NIL T) -8 NIL NIL NIL) (-429 963847 966522 966562 "FRNAALG" 967882 NIL FRNAALG (NIL T) -9 NIL 968480 NIL) (-428 959520 960596 961871 "FRNAALG-" 962621 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 959158 959201 959328 "FRNAAF2" 959471 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 957533 958007 958303 "FRMOD" 958970 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 955276 955908 956226 "FRIDEAL" 957324 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 954467 954554 954845 "FRIDEAL2" 955183 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 953600 954014 954055 "FRETRCT" 954060 NIL FRETRCT (NIL T) -9 NIL 954236 NIL) (-422 952712 952943 953294 "FRETRCT-" 953299 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 949800 951010 951069 "FRAMALG" 951951 NIL FRAMALG (NIL T T) -9 NIL 952243 NIL) (-420 947934 948389 949019 "FRAMALG-" 949242 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 941585 947407 947684 "FRAC" 947689 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 941221 941278 941385 "FRAC2" 941522 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 940857 940914 941021 "FR2" 941158 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 935370 938263 938291 "FPS" 939410 T FPS (NIL) -9 NIL 939967 NIL) (-415 934819 934928 935092 "FPS-" 935238 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 932121 933790 933818 "FPC" 934043 T FPC (NIL) -9 NIL 934185 NIL) (-413 931914 931954 932051 "FPC-" 932056 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 930704 931402 931443 "FPATMAB" 931448 NIL FPATMAB (NIL T) -9 NIL 931600 NIL) (-411 928943 929446 929793 "FPARFRAC" 930420 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 924337 924835 925517 "FORTRAN" 928375 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 922053 922553 923092 "FORT" 923818 T FORT (NIL) -7 NIL NIL NIL) (-408 919729 920291 920319 "FORTFN" 921379 T FORTFN (NIL) -9 NIL 922003 NIL) (-407 919493 919543 919571 "FORTCAT" 919630 T FORTCAT (NIL) -9 NIL 919692 NIL) (-406 917599 918109 918499 "FORMULA" 919123 T FORMULA (NIL) -8 NIL NIL NIL) (-405 917387 917417 917486 "FORMULA1" 917563 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 916910 916962 917135 "FORDER" 917329 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 916006 916170 916363 "FOP" 916737 T FOP (NIL) -7 NIL NIL NIL) (-402 914587 915286 915460 "FNLA" 915888 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 913316 913731 913759 "FNCAT" 914219 T FNCAT (NIL) -9 NIL 914479 NIL) (-400 912855 913275 913303 "FNAME" 913308 T FNAME (NIL) -8 NIL NIL NIL) (-399 911418 912381 912409 "FMTC" 912414 T FMTC (NIL) -9 NIL 912450 NIL) (-398 910164 911354 911400 "FMONOID" 911405 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 906992 908160 908201 "FMONCAT" 909418 NIL FMONCAT (NIL T) -9 NIL 910023 NIL) (-396 906184 906734 906883 "FM" 906888 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 903608 904254 904282 "FMFUN" 905426 T FMFUN (NIL) -9 NIL 906134 NIL) (-394 902877 903058 903086 "FMC" 903376 T FMC (NIL) -9 NIL 903558 NIL) (-393 899956 900816 900870 "FMCAT" 902065 NIL FMCAT (NIL T T) -9 NIL 902560 NIL) (-392 898822 899722 899822 "FM1" 899901 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 896596 897012 897506 "FLOATRP" 898373 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 890174 894325 894946 "FLOAT" 895995 T FLOAT (NIL) -8 NIL NIL NIL) (-389 887612 888112 888690 "FLOATCP" 889641 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 886282 887218 887259 "FLINEXP" 887264 NIL FLINEXP (NIL T) -9 NIL 887357 NIL) (-387 884710 885159 885743 "FLINEXP-" 885748 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883786 883930 884154 "FLASORT" 884562 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880902 881770 881822 "FLALG" 883049 NIL FLALG (NIL T T) -9 NIL 883516 NIL) (-384 874606 878358 878399 "FLAGG" 879661 NIL FLAGG (NIL T) -9 NIL 880313 NIL) (-383 873332 873671 874161 "FLAGG-" 874166 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 872374 872517 872744 "FLAGG2" 873185 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 869225 870233 870292 "FINRALG" 871420 NIL FINRALG (NIL T T) -9 NIL 871928 NIL) (-380 868385 868614 868953 "FINRALG-" 868958 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867765 868004 868032 "FINITE" 868228 T FINITE (NIL) -9 NIL 868335 NIL) (-378 860122 862309 862349 "FINAALG" 866016 NIL FINAALG (NIL T) -9 NIL 867469 NIL) (-377 855454 856504 857648 "FINAALG-" 859027 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854822 855209 855312 "FILE" 855384 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 853480 853818 853872 "FILECAT" 854556 NIL FILECAT (NIL T T) -9 NIL 854772 NIL) (-374 851196 852724 852752 "FIELD" 852792 T FIELD (NIL) -9 NIL 852872 NIL) (-373 849816 850201 850712 "FIELD-" 850717 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 847666 848451 848798 "FGROUP" 849502 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846756 846920 847140 "FGLMICPK" 847498 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 842588 846681 846738 "FFX" 846743 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 842189 842250 842385 "FFSLPE" 842521 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 838179 838961 839757 "FFPOLY" 841425 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837683 837719 837928 "FFPOLY2" 838137 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 833529 837602 837665 "FFP" 837670 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828927 833440 833504 "FF" 833509 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 824053 828270 828460 "FFNBX" 828781 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818981 823188 823446 "FFNBP" 823907 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 813614 818265 818476 "FFNB" 818814 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 812446 812644 812959 "FFINTBAS" 813411 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 808472 810693 810721 "FFIELDC" 811341 T FFIELDC (NIL) -9 NIL 811717 NIL) (-359 807134 807505 808002 "FFIELDC-" 808007 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806703 806749 806873 "FFHOM" 807076 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 804398 804885 805402 "FFF" 806218 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 800016 804140 804241 "FFCGX" 804341 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 795638 799748 799855 "FFCGP" 799959 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790821 795365 795473 "FFCG" 795574 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 770302 780497 780583 "FFCAT" 785748 NIL FFCAT (NIL T T T) -9 NIL 787199 NIL) (-352 765499 766547 767861 "FFCAT-" 769091 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764910 764953 765188 "FFCAT2" 765450 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 754233 757882 759102 "FEXPR" 763762 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 753195 753630 753671 "FEVALAB" 753755 NIL FEVALAB (NIL T) -9 NIL 754016 NIL) (-348 752354 752564 752902 "FEVALAB-" 752907 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750920 751737 751940 "FDIV" 752253 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747940 748681 748796 "FDIVCAT" 750364 NIL FDIVCAT (NIL T T T T) -9 NIL 750801 NIL) (-345 747702 747729 747899 "FDIVCAT-" 747904 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746922 747009 747286 "FDIV2" 747609 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745896 746217 746419 "FCTRDATA" 746740 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 744582 744841 745130 "FCPAK1" 745627 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743681 744082 744223 "FCOMP" 744473 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 727386 730831 734369 "FC" 740163 T FC (NIL) -8 NIL NIL NIL) (-339 719665 723693 723733 "FAXF" 725535 NIL FAXF (NIL T) -9 NIL 726227 NIL) (-338 716942 717599 718424 "FAXF-" 718889 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711994 716318 716494 "FARRAY" 716799 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706888 708955 709008 "FAMR" 710031 NIL FAMR (NIL T T) -9 NIL 710491 NIL) (-335 705778 706080 706515 "FAMR-" 706520 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704947 705700 705753 "FAMONOID" 705758 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702733 703443 703496 "FAMONC" 704437 NIL FAMONC (NIL T T) -9 NIL 704823 NIL) (-332 701397 702487 702624 "FAGROUP" 702629 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 699192 699511 699914 "FACUTIL" 701078 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 698291 698476 698698 "FACTFUNC" 699002 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690713 697594 697793 "EXPUPXS" 698147 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 688196 688736 689322 "EXPRTUBE" 690147 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 684467 685059 685789 "EXPRODE" 687535 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669959 683116 683545 "EXPR" 684071 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 664513 665100 665906 "EXPR2UPS" 669257 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 664145 664202 664311 "EXPR2" 664450 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 655150 663296 663587 "EXPEXPAN" 663981 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654950 655107 655136 "EXIT" 655141 T EXIT (NIL) -8 NIL NIL NIL) (-321 654430 654674 654765 "EXITAST" 654879 T EXITAST (NIL) -8 NIL NIL NIL) (-320 654057 654119 654232 "EVALCYC" 654362 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 653598 653716 653757 "EVALAB" 653927 NIL EVALAB (NIL T) -9 NIL 654031 NIL) (-318 653079 653201 653422 "EVALAB-" 653427 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 650447 651749 651777 "EUCDOM" 652332 T EUCDOM (NIL) -9 NIL 652682 NIL) (-316 648852 649294 649884 "EUCDOM-" 649889 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 636391 639150 641900 "ESTOOLS" 646122 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 636023 636080 636189 "ESTOOLS2" 636328 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635774 635816 635896 "ESTOOLS1" 635975 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629811 631419 631447 "ES" 634215 T ES (NIL) -9 NIL 635625 NIL) (-311 624758 626045 627862 "ES-" 628026 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 621132 621893 622673 "ESCONT" 623998 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620877 620909 620991 "ESCONT1" 621094 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 620552 620602 620702 "ES2" 620821 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 620182 620240 620349 "ES1" 620488 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 619398 619527 619703 "ERROR" 620026 T ERROR (NIL) -7 NIL NIL NIL) (-305 612790 619257 619348 "EQTBL" 619353 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 605293 608104 609553 "EQ" 611374 NIL -3091 (NIL T) -8 NIL NIL NIL) (-303 604925 604982 605091 "EQ2" 605230 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 600216 601263 602356 "EP" 603864 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598816 599107 599413 "ENV" 599930 T ENV (NIL) -8 NIL NIL NIL) (-300 597910 598464 598492 "ENTIRER" 598497 T ENTIRER (NIL) -9 NIL 598543 NIL) (-299 594604 596092 596453 "EMR" 597718 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593734 593919 593973 "ELTAGG" 594353 NIL ELTAGG (NIL T T) -9 NIL 594564 NIL) (-297 593453 593515 593656 "ELTAGG-" 593661 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 593217 593246 593300 "ELTAB" 593384 NIL ELTAB (NIL T T) -9 NIL 593436 NIL) (-295 592343 592489 592688 "ELFUTS" 593068 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 592085 592141 592169 "ELEMFUN" 592274 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591955 591976 592044 "ELEMFUN-" 592049 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586769 590025 590066 "ELAGG" 591006 NIL ELAGG (NIL T) -9 NIL 591469 NIL) (-291 585054 585488 586151 "ELAGG-" 586156 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 584366 584503 584659 "ELABOR" 584918 T ELABOR (NIL) -8 NIL NIL NIL) (-289 583027 583306 583600 "ELABEXPR" 584092 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575861 577664 578493 "EFUPXS" 582302 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 569309 571110 571921 "EFULS" 575136 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566794 567152 567624 "EFSTRUC" 568941 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 556585 558151 559699 "EF" 565309 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 555659 556070 556219 "EAB" 556456 T EAB (NIL) -8 NIL NIL NIL) (-283 554841 555618 555646 "E04UCFA" 555651 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 554023 554800 554828 "E04NAFA" 554833 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 553205 553982 554010 "E04MBFA" 554015 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 552387 553164 553192 "E04JAFA" 553197 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 551571 552346 552374 "E04GCFA" 552379 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550755 551530 551558 "E04FDFA" 551563 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549937 550714 550742 "E04DGFA" 550747 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 544110 545462 546826 "E04AGNT" 548593 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542881 543424 543464 "DVARCAT" 543805 NIL DVARCAT (NIL T) -9 NIL 543968 NIL) (-274 542085 542297 542611 "DVARCAT-" 542616 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534954 541884 542013 "DSMP" 542018 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 533377 534096 534137 "DSEXT" 534500 NIL DSEXT (NIL T) -9 NIL 534794 NIL) (-271 531662 532090 532756 "DSEXT-" 532761 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 526443 527607 528675 "DROPT" 530614 T DROPT (NIL) -8 NIL NIL NIL) (-269 526108 526167 526265 "DROPT1" 526378 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 521223 522349 523486 "DROPT0" 524991 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 519568 519893 520279 "DRAWPT" 520857 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 514155 515078 516157 "DRAW" 518542 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513788 513841 513959 "DRAWHACK" 514096 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 512519 512788 513079 "DRAWCX" 513517 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 512034 512103 512254 "DRAWCURV" 512445 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 502502 504464 506579 "DRAWCFUN" 509939 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 499266 501195 501236 "DQAGG" 501865 NIL DQAGG (NIL T) -9 NIL 502139 NIL) (-260 486739 493477 493560 "DPOLCAT" 495412 NIL DPOLCAT (NIL T T T T) -9 NIL 495957 NIL) (-259 481576 482924 484882 "DPOLCAT-" 484887 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474931 481437 481535 "DPMO" 481540 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 468189 474711 474878 "DPMM" 474883 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 467759 467973 468062 "DOMTMPLT" 468120 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 467192 467561 467641 "DOMCTOR" 467699 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 466404 466672 466823 "DOMAIN" 467061 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 460124 466039 466191 "DMP" 466305 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 458069 459191 459232 "DMEXT" 459237 NIL DMEXT (NIL T) -9 NIL 459413 NIL) (-251 457669 457725 457869 "DLP" 458007 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 451491 456996 457186 "DLIST" 457511 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 448288 450344 450385 "DLAGG" 450935 NIL DLAGG (NIL T) -9 NIL 451165 NIL) (-248 446964 447628 447656 "DIVRING" 447748 T DIVRING (NIL) -9 NIL 447831 NIL) (-247 446201 446391 446691 "DIVRING-" 446696 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 444303 444660 445066 "DISPLAY" 445815 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 438171 444217 444280 "DIRPROD" 444285 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 437019 437222 437487 "DIRPROD2" 437964 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 425774 431805 431858 "DIRPCAT" 432116 NIL DIRPCAT (NIL NIL T) -9 NIL 432991 NIL) (-242 422374 423230 424367 "DIRPCAT-" 424704 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421661 421821 422007 "DIOSP" 422208 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418316 420573 420614 "DIOPS" 421048 NIL DIOPS (NIL T) -9 NIL 421277 NIL) (-239 417865 417979 418170 "DIOPS-" 418175 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 416916 417544 417572 "DIFRING" 417577 T DIFRING (NIL) -9 NIL 417599 NIL) (-237 416588 416662 416690 "DIFFSPC" 416809 T DIFFSPC (NIL) -9 NIL 416884 NIL) (-236 416233 416311 416463 "DIFFSPC-" 416468 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415289 415767 415808 "DIFFMOD" 415813 NIL DIFFMOD (NIL T) -9 NIL 415911 NIL) (-234 414997 415042 415083 "DIFFDOM" 415204 NIL DIFFDOM (NIL T) -9 NIL 415272 NIL) (-233 414850 414874 414958 "DIFFDOM-" 414963 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412782 414054 414095 "DIFEXT" 414100 NIL DIFEXT (NIL T) -9 NIL 414253 NIL) (-231 410057 412314 412355 "DIAGG" 412360 NIL DIAGG (NIL T) -9 NIL 412380 NIL) (-230 409441 409598 409850 "DIAGG-" 409855 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404858 408400 408677 "DHMATRIX" 409210 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400470 401379 402389 "DFSFUN" 403868 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395548 399401 399713 "DFLOAT" 400178 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393811 394092 394481 "DFINTTLS" 395256 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390840 391832 392232 "DERHAM" 393477 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388641 390615 390704 "DEQUEUE" 390784 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 387895 388028 388211 "DEGRED" 388503 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384325 385070 385916 "DEFINTRF" 387123 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 381880 382349 382941 "DEFINTEF" 383844 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 381230 381500 381615 "DEFAST" 381785 T DEFAST (NIL) -8 NIL NIL NIL) (-219 374954 380823 380973 "DECIMAL" 381100 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372466 372924 373430 "DDFACT" 374498 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 372062 372105 372256 "DBLRESP" 372417 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 369930 370292 370653 "DBASE" 371828 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 369172 369410 369556 "DATAARY" 369829 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368278 369131 369159 "D03FAFA" 369164 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367385 368237 368265 "D03EEFA" 368270 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365335 365801 366290 "D03AGNT" 366916 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364624 365294 365322 "D02EJFA" 365327 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 363913 364583 364611 "D02CJFA" 364616 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 363202 363872 363900 "D02BHFA" 363905 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362491 363161 363189 "D02BBFA" 363194 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355688 357277 358883 "D02AGNT" 360905 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353456 353979 354525 "D01WGTS" 355162 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352523 353415 353443 "D01TRNS" 353448 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351591 352482 352510 "D01GBFA" 352515 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350659 351550 351578 "D01FCFA" 351583 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349727 350618 350646 "D01ASFA" 350651 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348795 349686 349714 "D01AQFA" 349719 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347863 348754 348782 "D01APFA" 348787 T D01APFA (NIL) -8 NIL NIL NIL) (-199 346931 347822 347850 "D01ANFA" 347855 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 345999 346890 346918 "D01AMFA" 346923 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 345067 345958 345986 "D01ALFA" 345991 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 344135 345026 345054 "D01AKFA" 345059 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 343203 344094 344122 "D01AJFA" 344127 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336498 338051 339612 "D01AGNT" 341662 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335835 335963 336115 "CYCLOTOM" 336366 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332568 333283 334010 "CYCLES" 335128 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331880 332014 332185 "CVMP" 332429 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329721 329979 330348 "CTRIGMNP" 331608 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 329157 329515 329588 "CTOR" 329668 T CTOR (NIL) -8 NIL NIL NIL) (-188 328666 328888 328989 "CTORKIND" 329076 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 327957 328273 328301 "CTORCAT" 328483 T CTORCAT (NIL) -9 NIL 328596 NIL) (-186 327555 327666 327825 "CTORCAT-" 327830 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 327017 327229 327337 "CTORCALL" 327479 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326391 326490 326643 "CSTTOOLS" 326914 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 322190 322847 323605 "CRFP" 325703 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321665 321911 322003 "CRCEAST" 322118 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320712 320897 321125 "CRAPACK" 321469 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 320096 320197 320401 "CPMATCH" 320588 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319821 319849 319955 "CPIMA" 320062 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 316169 316841 317560 "COORDSYS" 319156 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315581 315702 315844 "CONTOUR" 316047 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311472 313584 314076 "CONTFRAC" 315121 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311352 311373 311401 "CONDUIT" 311438 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310440 310994 311022 "COMRING" 311027 T COMRING (NIL) -9 NIL 311079 NIL) (-173 309494 309798 309982 "COMPPROP" 310276 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 309155 309190 309318 "COMPLPAT" 309453 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298466 308964 309073 "COMPLEX" 309078 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 298102 298159 298266 "COMPLEX2" 298403 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297441 297562 297722 "COMPILER" 297962 T COMPILER (NIL) -8 NIL NIL NIL) (-168 297159 297194 297292 "COMPFACT" 297400 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279446 290863 290903 "COMPCAT" 291907 NIL COMPCAT (NIL T) -9 NIL 293255 NIL) (-166 268232 271373 275256 "COMPCAT-" 275612 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 267961 267989 268092 "COMMUPC" 268198 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 267755 267789 267848 "COMMONOP" 267922 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 267311 267506 267593 "COMM" 267688 T COMM (NIL) -8 NIL NIL NIL) (-162 266887 267115 267190 "COMMAAST" 267256 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266136 266330 266358 "COMBOPC" 266696 T COMBOPC (NIL) -9 NIL 266871 NIL) (-160 265032 265242 265484 "COMBINAT" 265926 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 261489 262063 262690 "COMBF" 264454 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 260247 260605 260840 "COLOR" 261274 T COLOR (NIL) -8 NIL NIL NIL) (-157 259723 259968 260060 "COLONAST" 260175 T COLONAST (NIL) -8 NIL NIL NIL) (-156 259363 259410 259535 "CMPLXRT" 259670 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 258811 259063 259162 "CLLCTAST" 259284 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 254313 255341 256421 "CLIP" 257751 T CLIP (NIL) -7 NIL NIL NIL) (-153 252654 253414 253654 "CLIF" 254140 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 248829 250800 250841 "CLAGG" 251770 NIL CLAGG (NIL T) -9 NIL 252306 NIL) (-151 247251 247708 248291 "CLAGG-" 248296 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 246795 246880 247020 "CINTSLPE" 247160 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 244296 244767 245315 "CHVAR" 246323 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 243470 244024 244052 "CHARZ" 244057 T CHARZ (NIL) -9 NIL 244072 NIL) (-147 243224 243264 243342 "CHARPOL" 243424 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 242282 242869 242897 "CHARNZ" 242944 T CHARNZ (NIL) -9 NIL 243000 NIL) (-145 240188 240936 241289 "CHAR" 241949 T CHAR (NIL) -8 NIL NIL NIL) (-144 239914 239975 240003 "CFCAT" 240114 T CFCAT (NIL) -9 NIL NIL NIL) (-143 239155 239266 239449 "CDEN" 239798 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 235120 238308 238588 "CCLASS" 238895 T CCLASS (NIL) -8 NIL NIL NIL) (-141 234371 234528 234705 "CATEGORY" 234963 T -10 (NIL) -8 NIL NIL NIL) (-140 233944 234290 234338 "CATCTOR" 234343 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 233395 233647 233745 "CATAST" 233866 T CATAST (NIL) -8 NIL NIL NIL) (-138 232871 233116 233208 "CASEAST" 233323 T CASEAST (NIL) -8 NIL NIL NIL) (-137 228009 229028 229772 "CARTEN" 232183 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227117 227265 227486 "CARTEN2" 227856 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 225433 226267 226524 "CARD" 226880 T CARD (NIL) -8 NIL NIL NIL) (-134 225009 225237 225312 "CAPSLAST" 225378 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 224513 224721 224749 "CACHSET" 224881 T CACHSET (NIL) -9 NIL 224959 NIL) (-132 223983 224305 224333 "CABMON" 224383 T CABMON (NIL) -9 NIL 224439 NIL) (-131 223456 223687 223797 "BYTEORD" 223893 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 222433 222985 223127 "BYTE" 223290 T BYTE (NIL) -8 NIL NIL 223412) (-129 217783 221938 222110 "BYTEBUF" 222281 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 215292 217475 217582 "BTREE" 217709 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 212741 214940 215062 "BTOURN" 215202 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210111 212211 212252 "BTCAT" 212320 NIL BTCAT (NIL T) -9 NIL 212397 NIL) (-125 209778 209858 210007 "BTCAT-" 210012 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 205157 209037 209065 "BTAGG" 209179 T BTAGG (NIL) -9 NIL 209289 NIL) (-123 204647 204772 204978 "BTAGG-" 204983 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 201642 203925 204140 "BSTREE" 204464 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 200780 200906 201090 "BRILL" 201498 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 197432 199506 199547 "BRAGG" 200196 NIL BRAGG (NIL T) -9 NIL 200454 NIL) (-119 195961 196367 196922 "BRAGG-" 196927 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 188885 195305 195490 "BPADICRT" 195808 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 187200 188822 188867 "BPADIC" 188872 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 186898 186928 187042 "BOUNDZRO" 187164 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 182126 183324 184236 "BOP" 186006 T BOP (NIL) -8 NIL NIL NIL) (-114 179907 180311 180786 "BOP1" 181684 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 179608 179669 179697 "BOOLE" 179808 T BOOLE (NIL) -9 NIL 179890 NIL) (-112 178433 179182 179331 "BOOLEAN" 179479 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 177712 178116 178170 "BMODULE" 178175 NIL BMODULE (NIL T T) -9 NIL 178240 NIL) (-110 173513 177510 177583 "BITS" 177659 T BITS (NIL) -8 NIL NIL NIL) (-109 172934 173053 173193 "BINDING" 173393 T BINDING (NIL) -8 NIL NIL NIL) (-108 166661 172529 172678 "BINARY" 172805 T BINARY (NIL) -8 NIL NIL NIL) (-107 164441 165916 165957 "BGAGG" 166217 NIL BGAGG (NIL T) -9 NIL 166354 NIL) (-106 164272 164304 164395 "BGAGG-" 164400 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 163343 163656 163861 "BFUNCT" 164087 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 162033 162211 162499 "BEZOUT" 163167 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 158502 160885 161215 "BBTREE" 161736 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158236 158289 158317 "BASTYPE" 158436 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 158088 158117 158190 "BASTYPE-" 158195 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 157522 157598 157750 "BALFACT" 157999 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156378 156937 157123 "AUTOMOR" 157367 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 156104 156109 156135 "ATTREG" 156140 T ATTREG (NIL) -9 NIL NIL NIL) (-97 154356 154801 155153 "ATTRBUT" 155770 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 153964 154184 154250 "ATTRAST" 154308 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 153500 153613 153639 "ATRIG" 153840 T ATRIG (NIL) -9 NIL NIL NIL) (-94 153309 153350 153437 "ATRIG-" 153442 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 152954 153140 153166 "ASTCAT" 153171 T ASTCAT (NIL) -9 NIL 153201 NIL) (-92 152681 152740 152859 "ASTCAT-" 152864 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 150830 152457 152545 "ASTACK" 152624 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 149335 149632 149997 "ASSOCEQ" 150512 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 148367 148994 149118 "ASP9" 149242 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 148130 148315 148354 "ASP8" 148359 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 146998 147735 147877 "ASP80" 148019 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 145896 146633 146765 "ASP7" 146897 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 144850 145573 145691 "ASP78" 145809 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 143819 144530 144647 "ASP77" 144764 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 142731 143457 143588 "ASP74" 143719 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 141631 142366 142498 "ASP73" 142630 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 140735 141457 141557 "ASP6" 141562 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139682 140412 140530 "ASP55" 140648 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 138631 139356 139475 "ASP50" 139594 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 137719 138332 138442 "ASP4" 138552 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 136807 137420 137530 "ASP49" 137640 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 135591 136346 136514 "ASP42" 136696 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 134368 135124 135294 "ASP41" 135478 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 133318 134045 134163 "ASP35" 134281 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 133083 133266 133305 "ASP34" 133310 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 132820 132887 132963 "ASP33" 133038 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 131714 132455 132587 "ASP31" 132719 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 131479 131662 131701 "ASP30" 131706 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 131214 131283 131359 "ASP29" 131434 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 130979 131162 131201 "ASP28" 131206 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 130744 130927 130966 "ASP27" 130971 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 129828 130442 130553 "ASP24" 130664 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 128905 129630 129742 "ASP20" 129747 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 127993 128606 128716 "ASP1" 128826 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 126936 127667 127786 "ASP19" 127905 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126673 126740 126816 "ASP12" 126891 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 125525 126272 126416 "ASP10" 126560 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 123376 125369 125460 "ARRAY2" 125465 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 119141 123024 123138 "ARRAY1" 123293 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 118173 118346 118567 "ARRAY12" 118964 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 112485 114403 114478 "ARR2CAT" 117108 NIL ARR2CAT (NIL T T T) -9 NIL 117866 NIL) (-56 109919 110663 111617 "ARR2CAT-" 111622 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 109236 109546 109671 "ARITY" 109812 T ARITY (NIL) -8 NIL NIL NIL) (-54 108012 108164 108463 "APPRULE" 109072 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107663 107711 107830 "APPLYORE" 107958 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 107017 107256 107376 "ANY" 107561 T ANY (NIL) -8 NIL NIL NIL) (-51 106295 106418 106575 "ANY1" 106891 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 103825 104732 105059 "ANTISYM" 106019 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 103317 103532 103628 "ANON" 103747 T ANON (NIL) -8 NIL NIL NIL) (-48 97325 101856 102310 "AN" 102881 T AN (NIL) -8 NIL NIL NIL) (-47 93223 94611 94662 "AMR" 95410 NIL AMR (NIL T T) -9 NIL 96010 NIL) (-46 92335 92556 92919 "AMR-" 92924 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 76774 92252 92313 "ALIST" 92318 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73579 76368 76537 "ALGSC" 76692 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70135 70689 71296 "ALGPKG" 73019 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69412 69513 69697 "ALGMFACT" 70021 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65447 66026 66620 "ALGMANIP" 68996 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55666 65073 65223 "ALGFF" 65380 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54862 54993 55172 "ALGFACT" 55524 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53803 54403 54441 "ALGEBRA" 54446 NIL ALGEBRA (NIL T) -9 NIL 54487 NIL) (-37 53521 53580 53712 "ALGEBRA-" 53717 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35584 51493 51545 "ALAGG" 51681 NIL ALAGG (NIL T T) -9 NIL 51842 NIL) (-35 35120 35233 35259 "AHYP" 35460 T AHYP (NIL) -9 NIL NIL NIL) (-34 34051 34299 34325 "AGG" 34824 T AGG (NIL) -9 NIL 35103 NIL) (-33 33485 33647 33861 "AGG-" 33866 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31291 31714 32119 "AF" 33127 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30771 31016 31106 "ADDAST" 31219 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30039 30298 30454 "ACPLOT" 30633 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18670 26971 27009 "ACFS" 27616 NIL ACFS (NIL T) -9 NIL 27855 NIL) (-28 16697 17187 17949 "ACFS-" 17954 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12815 14744 14770 "ACF" 15649 T ACF (NIL) -9 NIL 16062 NIL) (-26 11519 11853 12346 "ACF-" 12351 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11091 11286 11312 "ABELSG" 11404 T ABELSG (NIL) -9 NIL 11469 NIL) (-24 10958 10983 11049 "ABELSG-" 11054 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10301 10588 10614 "ABELMON" 10784 T ABELMON (NIL) -9 NIL 10896 NIL) (-22 9965 10049 10187 "ABELMON-" 10192 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9313 9685 9711 "ABELGRP" 9783 T ABELGRP (NIL) -9 NIL 9858 NIL) (-20 8776 8905 9121 "ABELGRP-" 9126 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8085 8124 "A1AGG" 8129 NIL A1AGG (NIL T) -9 NIL 8169 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3261370 3261375 3261380 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3261355 3261360 3261365 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3261340 3261345 3261350 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3261325 3261330 3261335 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1315 3260468 3261200 3261277 "ZMOD" 3261282 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1314 3259522 3259686 3259909 "ZLINDEP" 3260300 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1313 3248822 3250590 3252562 "ZDSOLVE" 3257652 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1312 3248068 3248209 3248398 "YSTREAM" 3248668 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1311 3247496 3247742 3247855 "YDIAGRAM" 3247977 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1310 3245270 3246797 3247001 "XRPOLY" 3247339 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1309 3241823 3243141 3243716 "XPR" 3244742 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1308 3239544 3241154 3241358 "XPOLY" 3241654 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1307 3237197 3238565 3238620 "XPOLYC" 3238908 NIL XPOLYC (NIL T T) -9 NIL 3239021 NIL) (-1306 3233573 3235714 3236102 "XPBWPOLY" 3236855 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1305 3229268 3231563 3231605 "XF" 3232226 NIL XF (NIL T) -9 NIL 3232626 NIL) (-1304 3228889 3228977 3229146 "XF-" 3229151 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1303 3224085 3225374 3225429 "XFALG" 3227601 NIL XFALG (NIL T T) -9 NIL 3228390 NIL) (-1302 3223218 3223322 3223527 "XEXPPKG" 3223977 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1301 3221327 3223068 3223164 "XDPOLY" 3223169 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3220134 3220734 3220777 "XALG" 3220782 NIL XALG (NIL T) -9 NIL 3220893 NIL) (-1299 3213576 3218111 3218605 "WUTSET" 3219726 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1298 3211832 3212628 3212951 "WP" 3213387 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1297 3211434 3211654 3211724 "WHILEAST" 3211784 T WHILEAST (NIL) -8 NIL NIL NIL) (-1296 3210906 3211151 3211245 "WHEREAST" 3211362 T WHEREAST (NIL) -8 NIL NIL NIL) (-1295 3209792 3209990 3210285 "WFFINTBS" 3210703 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1294 3207696 3208123 3208585 "WEIER" 3209364 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1293 3206742 3207192 3207234 "VSPACE" 3207370 NIL VSPACE (NIL T) -9 NIL 3207444 NIL) (-1292 3206580 3206607 3206698 "VSPACE-" 3206703 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1291 3206389 3206431 3206499 "VOID" 3206534 T VOID (NIL) -8 NIL NIL NIL) (-1290 3204525 3204884 3205290 "VIEW" 3206005 T VIEW (NIL) -7 NIL NIL NIL) (-1289 3200949 3201588 3202325 "VIEWDEF" 3203810 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1288 3190253 3192497 3194670 "VIEW3D" 3198798 T VIEW3D (NIL) -8 NIL NIL NIL) (-1287 3182504 3184164 3185743 "VIEW2D" 3188696 T VIEW2D (NIL) -8 NIL NIL NIL) (-1286 3177857 3182274 3182366 "VECTOR" 3182447 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1285 3176434 3176693 3177011 "VECTOR2" 3177587 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1284 3169876 3174185 3174228 "VECTCAT" 3175223 NIL VECTCAT (NIL T) -9 NIL 3175810 NIL) (-1283 3168890 3169144 3169534 "VECTCAT-" 3169539 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1282 3168344 3168541 3168661 "VARIABLE" 3168805 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1281 3168277 3168282 3168312 "UTYPE" 3168317 T UTYPE (NIL) -9 NIL NIL NIL) (-1280 3167107 3167261 3167523 "UTSODETL" 3168103 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1279 3164547 3165007 3165531 "UTSODE" 3166648 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1278 3156495 3162308 3162788 "UTS" 3164125 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3147059 3152429 3152472 "UTSCAT" 3153584 NIL UTSCAT (NIL T) -9 NIL 3154342 NIL) (-1276 3144407 3145129 3146118 "UTSCAT-" 3146123 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1275 3144034 3144077 3144210 "UTS2" 3144358 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1274 3138260 3140872 3140915 "URAGG" 3142985 NIL URAGG (NIL T) -9 NIL 3143708 NIL) (-1273 3135199 3136062 3137185 "URAGG-" 3137190 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1272 3130908 3133834 3134299 "UPXSSING" 3134863 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1271 3123084 3130290 3130554 "UPXS" 3130702 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1270 3116157 3122988 3123060 "UPXSCONS" 3123065 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1269 3105564 3112360 3112422 "UPXSCCA" 3112996 NIL UPXSCCA (NIL T T) -9 NIL 3113229 NIL) (-1268 3105202 3105287 3105461 "UPXSCCA-" 3105466 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1267 3094461 3101030 3101073 "UPXSCAT" 3101721 NIL UPXSCAT (NIL T) -9 NIL 3102330 NIL) (-1266 3093891 3093970 3094149 "UPXS2" 3094376 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1265 3092545 3092798 3093149 "UPSQFREE" 3093634 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1264 3085753 3088813 3088868 "UPSCAT" 3089948 NIL UPSCAT (NIL T T) -9 NIL 3090713 NIL) (-1263 3084957 3085164 3085491 "UPSCAT-" 3085496 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1262 3070047 3078084 3078127 "UPOLYC" 3080228 NIL UPOLYC (NIL T) -9 NIL 3081449 NIL) (-1261 3061375 3063801 3066948 "UPOLYC-" 3066953 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1260 3061002 3061045 3061178 "UPOLYC2" 3061326 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1259 3052545 3060685 3060814 "UP" 3060921 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1258 3051884 3051991 3052155 "UPMP" 3052434 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1257 3051437 3051518 3051657 "UPDIVP" 3051797 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1256 3050005 3050254 3050570 "UPDECOMP" 3051186 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1255 3049236 3049348 3049534 "UPCDEN" 3049889 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1254 3048755 3048824 3048973 "UP2" 3049161 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1253 3047222 3047959 3048236 "UNISEG" 3048513 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1252 3046437 3046564 3046769 "UNISEG2" 3047065 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1251 3045497 3045677 3045903 "UNIFACT" 3046253 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1250 3028257 3044809 3045051 "ULS" 3045313 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1249 3015895 3028161 3028233 "ULSCONS" 3028238 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1248 2996731 3009083 3009145 "ULSCCAT" 3009783 NIL ULSCCAT (NIL T T) -9 NIL 3010072 NIL) (-1247 2995781 2996026 2996414 "ULSCCAT-" 2996419 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1246 2984845 2991328 2991371 "ULSCAT" 2992234 NIL ULSCAT (NIL T) -9 NIL 2992965 NIL) (-1245 2984275 2984354 2984533 "ULS2" 2984760 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1244 2983394 2983904 2984011 "UINT8" 2984122 T UINT8 (NIL) -8 NIL NIL 2984207) (-1243 2982512 2983022 2983129 "UINT64" 2983240 T UINT64 (NIL) -8 NIL NIL 2983325) (-1242 2981630 2982140 2982247 "UINT32" 2982358 T UINT32 (NIL) -8 NIL NIL 2982443) (-1241 2980748 2981258 2981365 "UINT16" 2981476 T UINT16 (NIL) -8 NIL NIL 2981561) (-1240 2979051 2980008 2980038 "UFD" 2980250 T UFD (NIL) -9 NIL 2980364 NIL) (-1239 2978845 2978891 2978986 "UFD-" 2978991 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1238 2977927 2978110 2978326 "UDVO" 2978651 T UDVO (NIL) -7 NIL NIL NIL) (-1237 2975743 2976152 2976623 "UDPO" 2977491 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1236 2975676 2975681 2975711 "TYPE" 2975716 T TYPE (NIL) -9 NIL NIL NIL) (-1235 2975436 2975631 2975662 "TYPEAST" 2975667 T TYPEAST (NIL) -8 NIL NIL NIL) (-1234 2974407 2974609 2974849 "TWOFACT" 2975230 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1233 2973430 2973816 2974051 "TUPLE" 2974207 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1232 2971121 2971640 2972179 "TUBETOOL" 2972913 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1231 2969970 2970175 2970416 "TUBE" 2970914 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1230 2964699 2968942 2969225 "TS" 2969722 NIL TS (NIL T) -8 NIL NIL NIL) (-1229 2953339 2957458 2957555 "TSETCAT" 2962824 NIL TSETCAT (NIL T T T T) -9 NIL 2964355 NIL) (-1228 2948071 2949671 2951562 "TSETCAT-" 2951567 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1227 2942710 2943557 2944486 "TRMANIP" 2947207 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1226 2942151 2942214 2942377 "TRIMAT" 2942642 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1225 2940017 2940254 2940611 "TRIGMNIP" 2941900 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1224 2939537 2939650 2939680 "TRIGCAT" 2939893 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1223 2939206 2939285 2939426 "TRIGCAT-" 2939431 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1222 2936051 2938064 2938345 "TREE" 2938960 NIL TREE (NIL T) -8 NIL NIL NIL) (-1221 2935325 2935853 2935883 "TRANFUN" 2935918 T TRANFUN (NIL) -9 NIL 2935984 NIL) (-1220 2934604 2934795 2935075 "TRANFUN-" 2935080 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1219 2934408 2934440 2934501 "TOPSP" 2934565 T TOPSP (NIL) -7 NIL NIL NIL) (-1218 2933756 2933871 2934025 "TOOLSIGN" 2934289 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1217 2932390 2932933 2933172 "TEXTFILE" 2933539 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1216 2930302 2930843 2931272 "TEX" 2931983 T TEX (NIL) -8 NIL NIL NIL) (-1215 2930083 2930114 2930186 "TEX1" 2930265 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1214 2929731 2929794 2929884 "TEMUTL" 2930015 T TEMUTL (NIL) -7 NIL NIL NIL) (-1213 2927885 2928165 2928490 "TBCMPPK" 2929454 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1212 2919662 2926045 2926101 "TBAGG" 2926501 NIL TBAGG (NIL T T) -9 NIL 2926712 NIL) (-1211 2914732 2916220 2917974 "TBAGG-" 2917979 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1210 2914116 2914223 2914368 "TANEXP" 2914621 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1209 2913627 2913891 2913981 "TALGOP" 2914061 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1208 2907017 2913484 2913577 "TABLE" 2913582 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1207 2906429 2906528 2906666 "TABLEAU" 2906914 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1206 2901037 2902257 2903505 "TABLBUMP" 2905215 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1205 2900259 2900406 2900587 "SYSTEM" 2900878 T SYSTEM (NIL) -8 NIL NIL NIL) (-1204 2896718 2897417 2898200 "SYSSOLP" 2899510 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1203 2896516 2896673 2896704 "SYSPTR" 2896709 T SYSPTR (NIL) -8 NIL NIL NIL) (-1202 2895552 2896057 2896176 "SYSNNI" 2896362 NIL SYSNNI (NIL NIL) -8 NIL NIL 2896447) (-1201 2894851 2895310 2895389 "SYSINT" 2895449 NIL SYSINT (NIL NIL) -8 NIL NIL 2895494) (-1200 2891183 2892129 2892839 "SYNTAX" 2894163 T SYNTAX (NIL) -8 NIL NIL NIL) (-1199 2888341 2888943 2889575 "SYMTAB" 2890573 T SYMTAB (NIL) -8 NIL NIL NIL) (-1198 2883590 2884492 2885475 "SYMS" 2887380 T SYMS (NIL) -8 NIL NIL NIL) (-1197 2880825 2883048 2883278 "SYMPOLY" 2883395 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1196 2880342 2880417 2880540 "SYMFUNC" 2880737 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1195 2876362 2877654 2878467 "SYMBOL" 2879551 T SYMBOL (NIL) -8 NIL NIL NIL) (-1194 2869901 2871590 2873310 "SWITCH" 2874664 T SWITCH (NIL) -8 NIL NIL NIL) (-1193 2863245 2868857 2869151 "SUTS" 2869665 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1192 2855421 2862627 2862891 "SUPXS" 2863039 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2846912 2855039 2855165 "SUP" 2855330 NIL SUP (NIL T) -8 NIL NIL NIL) (-1190 2846071 2846198 2846415 "SUPFRACF" 2846780 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1189 2845692 2845751 2845864 "SUP2" 2846006 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1188 2844140 2844414 2844770 "SUMRF" 2845391 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1187 2843475 2843541 2843733 "SUMFS" 2844061 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1186 2826270 2842787 2843029 "SULS" 2843291 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1185 2825872 2826092 2826162 "SUCHTAST" 2826222 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1184 2825167 2825397 2825537 "SUCH" 2825780 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1183 2819034 2820073 2821032 "SUBSPACE" 2824255 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1182 2818464 2818554 2818718 "SUBRESP" 2818922 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1181 2811832 2813129 2814440 "STTF" 2817200 NIL STTF (NIL T) -7 NIL NIL NIL) (-1180 2806005 2807125 2808272 "STTFNC" 2810732 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1179 2797318 2799187 2800981 "STTAYLOR" 2804246 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1178 2790448 2797182 2797265 "STRTBL" 2797270 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1177 2785406 2790157 2790256 "STRING" 2790371 T STRING (NIL) -8 NIL NIL NIL) (-1176 2778159 2783025 2783636 "STREAM" 2784830 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1175 2777669 2777746 2777890 "STREAM3" 2778076 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1174 2776651 2776834 2777069 "STREAM2" 2777482 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1173 2776339 2776391 2776484 "STREAM1" 2776593 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1172 2775355 2775536 2775767 "STINPROD" 2776155 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1171 2774907 2775117 2775147 "STEP" 2775227 T STEP (NIL) -9 NIL 2775305 NIL) (-1170 2774094 2774396 2774544 "STEPAST" 2774781 T STEPAST (NIL) -8 NIL NIL NIL) (-1169 2767526 2773993 2774070 "STBL" 2774075 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1168 2762621 2766717 2766760 "STAGG" 2766913 NIL STAGG (NIL T) -9 NIL 2767002 NIL) (-1167 2760323 2760925 2761797 "STAGG-" 2761802 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1166 2758470 2760093 2760185 "STACK" 2760266 NIL STACK (NIL T) -8 NIL NIL NIL) (-1165 2751165 2756611 2757067 "SREGSET" 2758100 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1164 2743590 2744959 2746472 "SRDCMPK" 2749771 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1163 2736475 2741000 2741030 "SRAGG" 2742333 T SRAGG (NIL) -9 NIL 2742941 NIL) (-1162 2735492 2735747 2736126 "SRAGG-" 2736131 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1161 2729684 2734439 2734860 "SQMATRIX" 2735118 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1160 2723369 2726402 2727129 "SPLTREE" 2729029 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1159 2719332 2720025 2720671 "SPLNODE" 2722795 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1158 2718379 2718612 2718642 "SPFCAT" 2719086 T SPFCAT (NIL) -9 NIL NIL NIL) (-1157 2717116 2717326 2717590 "SPECOUT" 2718137 T SPECOUT (NIL) -7 NIL NIL NIL) (-1156 2708226 2710098 2710128 "SPADXPT" 2714804 T SPADXPT (NIL) -9 NIL 2716968 NIL) (-1155 2707987 2708027 2708096 "SPADPRSR" 2708179 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1154 2706036 2707942 2707973 "SPADAST" 2707978 T SPADAST (NIL) -8 NIL NIL NIL) (-1153 2697981 2699754 2699797 "SPACEC" 2704170 NIL SPACEC (NIL T) -9 NIL 2705986 NIL) (-1152 2696111 2697913 2697962 "SPACE3" 2697967 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1151 2694863 2695034 2695325 "SORTPAK" 2695916 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1150 2692955 2693258 2693670 "SOLVETRA" 2694527 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1149 2692005 2692227 2692488 "SOLVESER" 2692728 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1148 2687309 2688197 2689192 "SOLVERAD" 2691057 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1147 2683124 2683733 2684462 "SOLVEFOR" 2686676 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1146 2677394 2682473 2682570 "SNTSCAT" 2682575 NIL SNTSCAT (NIL T T T T) -9 NIL 2682645 NIL) (-1145 2671500 2675717 2676108 "SMTS" 2677084 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1144 2665917 2671388 2671465 "SMP" 2671470 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1143 2664076 2664377 2664775 "SMITH" 2665614 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1142 2656188 2660655 2660758 "SMATCAT" 2662109 NIL SMATCAT (NIL NIL T T T) -9 NIL 2662659 NIL) (-1141 2652402 2653439 2654873 "SMATCAT-" 2654878 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1140 2650068 2651638 2651681 "SKAGG" 2651942 NIL SKAGG (NIL T) -9 NIL 2652077 NIL) (-1139 2646266 2649541 2649725 "SINT" 2649877 T SINT (NIL) -8 NIL NIL 2650039) (-1138 2646038 2646076 2646142 "SIMPAN" 2646222 T SIMPAN (NIL) -7 NIL NIL NIL) (-1137 2645317 2645573 2645713 "SIG" 2645920 T SIG (NIL) -8 NIL NIL NIL) (-1136 2644155 2644376 2644651 "SIGNRF" 2645076 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1135 2642988 2643139 2643423 "SIGNEF" 2643984 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1134 2642294 2642571 2642695 "SIGAST" 2642886 T SIGAST (NIL) -8 NIL NIL NIL) (-1133 2639984 2640438 2640944 "SHP" 2641835 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1132 2633818 2639885 2639961 "SHDP" 2639966 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1131 2633391 2633583 2633613 "SGROUP" 2633706 T SGROUP (NIL) -9 NIL 2633768 NIL) (-1130 2633249 2633275 2633348 "SGROUP-" 2633353 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1129 2630040 2630738 2631461 "SGCF" 2632548 T SGCF (NIL) -7 NIL NIL NIL) (-1128 2624408 2629487 2629584 "SFRTCAT" 2629589 NIL SFRTCAT (NIL T T T T) -9 NIL 2629628 NIL) (-1127 2617829 2618847 2619983 "SFRGCD" 2623391 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1126 2610955 2612028 2613214 "SFQCMPK" 2616762 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1125 2610575 2610664 2610775 "SFORT" 2610896 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1124 2609693 2610415 2610536 "SEXOF" 2610541 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1123 2608800 2609574 2609642 "SEX" 2609647 T SEX (NIL) -8 NIL NIL NIL) (-1122 2604581 2605296 2605391 "SEXCAT" 2608013 NIL SEXCAT (NIL T T T T T) -9 NIL 2608573 NIL) (-1121 2601734 2604515 2604563 "SET" 2604568 NIL SET (NIL T) -8 NIL NIL NIL) (-1120 2599958 2600447 2600752 "SETMN" 2601475 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1119 2599454 2599606 2599636 "SETCAT" 2599812 T SETCAT (NIL) -9 NIL 2599922 NIL) (-1118 2599146 2599224 2599354 "SETCAT-" 2599359 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1117 2595507 2597607 2597650 "SETAGG" 2598520 NIL SETAGG (NIL T) -9 NIL 2598860 NIL) (-1116 2594965 2595081 2595318 "SETAGG-" 2595323 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1115 2594408 2594661 2594762 "SEQAST" 2594886 T SEQAST (NIL) -8 NIL NIL NIL) (-1114 2593607 2593901 2593962 "SEGXCAT" 2594248 NIL SEGXCAT (NIL T T) -9 NIL 2594368 NIL) (-1113 2592613 2593273 2593455 "SEG" 2593460 NIL SEG (NIL T) -8 NIL NIL NIL) (-1112 2591592 2591806 2591849 "SEGCAT" 2592371 NIL SEGCAT (NIL T) -9 NIL 2592592 NIL) (-1111 2590524 2590955 2591163 "SEGBIND" 2591419 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1110 2590145 2590204 2590317 "SEGBIND2" 2590459 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1109 2589718 2589946 2590023 "SEGAST" 2590090 T SEGAST (NIL) -8 NIL NIL NIL) (-1108 2588937 2589063 2589267 "SEG2" 2589562 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1107 2588308 2588872 2588919 "SDVAR" 2588924 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1106 2580567 2588078 2588208 "SDPOL" 2588213 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1105 2579160 2579426 2579745 "SCPKG" 2580282 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1104 2578324 2578496 2578688 "SCOPE" 2578990 T SCOPE (NIL) -8 NIL NIL NIL) (-1103 2577544 2577678 2577857 "SCACHE" 2578179 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1102 2577190 2577376 2577406 "SASTCAT" 2577411 T SASTCAT (NIL) -9 NIL 2577424 NIL) (-1101 2576677 2577025 2577101 "SAOS" 2577136 T SAOS (NIL) -8 NIL NIL NIL) (-1100 2576242 2576277 2576450 "SAERFFC" 2576636 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1099 2569913 2576139 2576219 "SAE" 2576224 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1098 2569506 2569541 2569700 "SAEFACT" 2569872 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1097 2567827 2568141 2568542 "RURPK" 2569172 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1096 2566464 2566770 2567075 "RULESET" 2567661 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1095 2563687 2564217 2564675 "RULE" 2566145 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1094 2563299 2563481 2563564 "RULECOLD" 2563639 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1093 2563089 2563117 2563188 "RTVALUE" 2563250 T RTVALUE (NIL) -8 NIL NIL NIL) (-1092 2562560 2562806 2562900 "RSTRCAST" 2563017 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1091 2557408 2558203 2559123 "RSETGCD" 2561759 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1090 2546638 2551717 2551814 "RSETCAT" 2555933 NIL RSETCAT (NIL T T T T) -9 NIL 2557030 NIL) (-1089 2544565 2545104 2545928 "RSETCAT-" 2545933 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1088 2536951 2538327 2539847 "RSDCMPK" 2543164 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1087 2534930 2535397 2535471 "RRCC" 2536557 NIL RRCC (NIL T T) -9 NIL 2536901 NIL) (-1086 2534281 2534455 2534734 "RRCC-" 2534739 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1085 2533724 2533977 2534078 "RPTAST" 2534202 T RPTAST (NIL) -8 NIL NIL NIL) (-1084 2507208 2516836 2516903 "RPOLCAT" 2527569 NIL RPOLCAT (NIL T T T) -9 NIL 2530729 NIL) (-1083 2498706 2501046 2504168 "RPOLCAT-" 2504173 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1082 2489637 2496917 2497399 "ROUTINE" 2498246 T ROUTINE (NIL) -8 NIL NIL NIL) (-1081 2486306 2489263 2489403 "ROMAN" 2489519 T ROMAN (NIL) -8 NIL NIL NIL) (-1080 2484550 2485166 2485426 "ROIRC" 2486111 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1079 2480782 2483066 2483096 "RNS" 2483400 T RNS (NIL) -9 NIL 2483674 NIL) (-1078 2479291 2479674 2480208 "RNS-" 2480283 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1077 2478694 2479102 2479132 "RNG" 2479137 T RNG (NIL) -9 NIL 2479158 NIL) (-1076 2477697 2478059 2478261 "RNGBIND" 2478545 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1075 2477096 2477484 2477527 "RMODULE" 2477532 NIL RMODULE (NIL T) -9 NIL 2477559 NIL) (-1074 2475932 2476026 2476362 "RMCAT2" 2476997 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1073 2472782 2475278 2475575 "RMATRIX" 2475694 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1072 2465609 2467869 2467984 "RMATCAT" 2471343 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2472325 NIL) (-1071 2464984 2465131 2465438 "RMATCAT-" 2465443 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1070 2464613 2464785 2464828 "RLINSET" 2464890 NIL RLINSET (NIL T) -9 NIL 2464934 NIL) (-1069 2464180 2464255 2464383 "RINTERP" 2464532 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1068 2463238 2463792 2463822 "RING" 2463878 T RING (NIL) -9 NIL 2463970 NIL) (-1067 2463030 2463074 2463171 "RING-" 2463176 NIL RING- (NIL T) -8 NIL NIL NIL) (-1066 2461871 2462108 2462366 "RIDIST" 2462794 T RIDIST (NIL) -7 NIL NIL NIL) (-1065 2453160 2461339 2461545 "RGCHAIN" 2461719 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1064 2452510 2452916 2452957 "RGBCSPC" 2453015 NIL RGBCSPC (NIL T) -9 NIL 2453067 NIL) (-1063 2451668 2452049 2452090 "RGBCMDL" 2452322 NIL RGBCMDL (NIL T) -9 NIL 2452436 NIL) (-1062 2448662 2449276 2449946 "RF" 2451032 NIL RF (NIL T) -7 NIL NIL NIL) (-1061 2448308 2448371 2448474 "RFFACTOR" 2448593 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1060 2448033 2448068 2448165 "RFFACT" 2448267 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1059 2446150 2446514 2446896 "RFDIST" 2447673 T RFDIST (NIL) -7 NIL NIL NIL) (-1058 2445603 2445695 2445858 "RETSOL" 2446052 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1057 2445239 2445319 2445362 "RETRACT" 2445495 NIL RETRACT (NIL T) -9 NIL 2445582 NIL) (-1056 2445088 2445113 2445200 "RETRACT-" 2445205 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1055 2444690 2444910 2444980 "RETAST" 2445040 T RETAST (NIL) -8 NIL NIL NIL) (-1054 2437428 2444343 2444470 "RESULT" 2444585 T RESULT (NIL) -8 NIL NIL NIL) (-1053 2436019 2436697 2436896 "RESRING" 2437331 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1052 2435655 2435704 2435802 "RESLATC" 2435956 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1051 2435360 2435395 2435502 "REPSQ" 2435614 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1050 2432782 2433362 2433964 "REP" 2434780 T REP (NIL) -7 NIL NIL NIL) (-1049 2432479 2432514 2432625 "REPDB" 2432741 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1048 2426379 2427768 2428991 "REP2" 2431291 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1047 2422756 2423437 2424245 "REP1" 2425606 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1046 2415452 2420897 2421353 "REGSET" 2422386 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1045 2414217 2414600 2414850 "REF" 2415237 NIL REF (NIL T) -8 NIL NIL NIL) (-1044 2413594 2413697 2413864 "REDORDER" 2414101 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1043 2409562 2412807 2413034 "RECLOS" 2413422 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1042 2408614 2408795 2409010 "REALSOLV" 2409369 T REALSOLV (NIL) -7 NIL NIL NIL) (-1041 2408460 2408501 2408531 "REAL" 2408536 T REAL (NIL) -9 NIL 2408571 NIL) (-1040 2404943 2405745 2406629 "REAL0Q" 2407625 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1039 2400544 2401532 2402593 "REAL0" 2403924 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1038 2400015 2400261 2400355 "RDUCEAST" 2400472 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1037 2399420 2399492 2399699 "RDIV" 2399937 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1036 2398488 2398662 2398875 "RDIST" 2399242 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1035 2397085 2397372 2397744 "RDETRS" 2398196 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1034 2394897 2395351 2395889 "RDETR" 2396627 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1033 2393522 2393800 2394197 "RDEEFS" 2394613 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1032 2392031 2392337 2392762 "RDEEF" 2393210 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1031 2386092 2389012 2389042 "RCFIELD" 2390337 T RCFIELD (NIL) -9 NIL 2391068 NIL) (-1030 2384156 2384660 2385356 "RCFIELD-" 2385431 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1029 2380425 2382257 2382300 "RCAGG" 2383384 NIL RCAGG (NIL T) -9 NIL 2383849 NIL) (-1028 2380053 2380147 2380310 "RCAGG-" 2380315 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1027 2379388 2379500 2379665 "RATRET" 2379937 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1026 2378941 2379008 2379129 "RATFACT" 2379316 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1025 2378249 2378369 2378521 "RANDSRC" 2378811 T RANDSRC (NIL) -7 NIL NIL NIL) (-1024 2377983 2378027 2378100 "RADUTIL" 2378198 T RADUTIL (NIL) -7 NIL NIL NIL) (-1023 2370819 2376814 2377125 "RADIX" 2377706 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1022 2361287 2370661 2370791 "RADFF" 2370796 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1021 2360934 2361009 2361039 "RADCAT" 2361199 T RADCAT (NIL) -9 NIL NIL NIL) (-1020 2360716 2360764 2360864 "RADCAT-" 2360869 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1019 2358814 2360486 2360578 "QUEUE" 2360659 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1018 2355083 2358747 2358795 "QUAT" 2358800 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1017 2354714 2354757 2354888 "QUATCT2" 2355034 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1016 2347548 2351164 2351206 "QUATCAT" 2351997 NIL QUATCAT (NIL T) -9 NIL 2352763 NIL) (-1015 2343687 2344724 2346114 "QUATCAT-" 2346210 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1014 2341152 2342763 2342806 "QUAGG" 2343187 NIL QUAGG (NIL T) -9 NIL 2343362 NIL) (-1013 2340754 2340974 2341044 "QQUTAST" 2341104 T QQUTAST (NIL) -8 NIL NIL NIL) (-1012 2339767 2340267 2340432 "QFORM" 2340635 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1011 2330162 2335669 2335711 "QFCAT" 2336379 NIL QFCAT (NIL T) -9 NIL 2337380 NIL) (-1010 2325003 2326418 2328268 "QFCAT-" 2328364 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1009 2324634 2324677 2324808 "QFCAT2" 2324954 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1008 2324089 2324199 2324331 "QEQUAT" 2324524 T QEQUAT (NIL) -8 NIL NIL NIL) (-1007 2317215 2318288 2319474 "QCMPACK" 2323022 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1006 2314753 2315201 2315631 "QALGSET" 2316870 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1005 2313988 2314164 2314400 "QALGSET2" 2314571 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1004 2312673 2312897 2313216 "PWFFINTB" 2313761 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1003 2310848 2311016 2311372 "PUSHVAR" 2312487 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1002 2306737 2307791 2307834 "PTRANFN" 2309745 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1001 2305128 2305419 2305743 "PTPACK" 2306448 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1000 2304757 2304814 2304925 "PTFUNC2" 2305065 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-999 2299202 2303599 2303640 "PTCAT" 2303936 NIL PTCAT (NIL T) -9 NIL 2304089 NIL) (-998 2298860 2298895 2299019 "PSQFR" 2299161 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-997 2297455 2297753 2298087 "PSEUDLIN" 2298558 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-996 2284218 2286589 2288913 "PSETPK" 2295215 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-995 2277236 2279976 2280072 "PSETCAT" 2283093 NIL PSETCAT (NIL T T T T) -9 NIL 2283907 NIL) (-994 2275072 2275706 2276527 "PSETCAT-" 2276532 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-993 2274421 2274586 2274614 "PSCURVE" 2274882 T PSCURVE (NIL) -9 NIL 2275049 NIL) (-992 2270419 2271935 2272000 "PSCAT" 2272844 NIL PSCAT (NIL T T T) -9 NIL 2273084 NIL) (-991 2269482 2269698 2270098 "PSCAT-" 2270103 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-990 2267841 2268551 2268814 "PRTITION" 2269239 T PRTITION (NIL) -8 NIL NIL NIL) (-989 2267316 2267562 2267654 "PRTDAST" 2267769 T PRTDAST (NIL) -8 NIL NIL NIL) (-988 2256406 2258620 2260808 "PRS" 2265178 NIL PRS (NIL T T) -7 NIL NIL NIL) (-987 2254217 2255756 2255796 "PRQAGG" 2255979 NIL PRQAGG (NIL T) -9 NIL 2256081 NIL) (-986 2253553 2253858 2253886 "PROPLOG" 2254025 T PROPLOG (NIL) -9 NIL 2254140 NIL) (-985 2253157 2253214 2253337 "PROPFUN2" 2253476 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-984 2252472 2252593 2252765 "PROPFUN1" 2253018 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-983 2250653 2251219 2251516 "PROPFRML" 2252208 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-982 2250122 2250229 2250357 "PROPERTY" 2250545 T PROPERTY (NIL) -8 NIL NIL NIL) (-981 2244180 2248288 2249108 "PRODUCT" 2249348 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-980 2241458 2243638 2243872 "PR" 2243991 NIL PR (NIL T T) -8 NIL NIL NIL) (-979 2241254 2241286 2241345 "PRINT" 2241419 T PRINT (NIL) -7 NIL NIL NIL) (-978 2240594 2240711 2240863 "PRIMES" 2241134 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-977 2238659 2239060 2239526 "PRIMELT" 2240173 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-976 2238388 2238437 2238465 "PRIMCAT" 2238589 T PRIMCAT (NIL) -9 NIL NIL NIL) (-975 2234503 2238326 2238371 "PRIMARR" 2238376 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-974 2233510 2233688 2233916 "PRIMARR2" 2234321 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-973 2233153 2233209 2233320 "PREASSOC" 2233448 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-972 2232628 2232761 2232789 "PPCURVE" 2232994 T PPCURVE (NIL) -9 NIL 2233130 NIL) (-971 2232223 2232423 2232506 "PORTNUM" 2232565 T PORTNUM (NIL) -8 NIL NIL NIL) (-970 2229582 2229981 2230573 "POLYROOT" 2231804 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-969 2223496 2229186 2229346 "POLY" 2229455 NIL POLY (NIL T) -8 NIL NIL NIL) (-968 2222879 2222937 2223171 "POLYLIFT" 2223432 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-967 2219154 2219603 2220232 "POLYCATQ" 2222424 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-966 2205504 2210901 2210966 "POLYCAT" 2214480 NIL POLYCAT (NIL T T T) -9 NIL 2216358 NIL) (-965 2198227 2200303 2202943 "POLYCAT-" 2202948 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-964 2197814 2197882 2198002 "POLY2UP" 2198153 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-963 2197446 2197503 2197612 "POLY2" 2197751 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-962 2196131 2196370 2196646 "POLUTIL" 2197220 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-961 2194486 2194763 2195094 "POLTOPOL" 2195853 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-960 2189951 2194422 2194468 "POINT" 2194473 NIL POINT (NIL T) -8 NIL NIL NIL) (-959 2188138 2188495 2188870 "PNTHEORY" 2189596 T PNTHEORY (NIL) -7 NIL NIL NIL) (-958 2186596 2186893 2187292 "PMTOOLS" 2187836 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-957 2186189 2186267 2186384 "PMSYM" 2186512 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-956 2185697 2185766 2185941 "PMQFCAT" 2186114 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-955 2185052 2185162 2185318 "PMPRED" 2185574 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-954 2184445 2184531 2184693 "PMPREDFS" 2184953 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-953 2183109 2183317 2183695 "PMPLCAT" 2184207 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-952 2182641 2182720 2182872 "PMLSAGG" 2183024 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-951 2182114 2182190 2182372 "PMKERNEL" 2182559 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-950 2181731 2181806 2181919 "PMINS" 2182033 NIL PMINS (NIL T) -7 NIL NIL NIL) (-949 2181173 2181242 2181451 "PMFS" 2181656 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-948 2180401 2180519 2180724 "PMDOWN" 2181050 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-947 2179568 2179726 2179907 "PMASS" 2180240 T PMASS (NIL) -7 NIL NIL NIL) (-946 2178841 2178951 2179114 "PMASSFS" 2179455 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-945 2178496 2178564 2178658 "PLOTTOOL" 2178767 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-944 2173103 2174307 2175455 "PLOT" 2177368 T PLOT (NIL) -8 NIL NIL NIL) (-943 2168907 2169951 2170872 "PLOT3D" 2172202 T PLOT3D (NIL) -8 NIL NIL NIL) (-942 2167819 2167996 2168231 "PLOT1" 2168711 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-941 2143210 2147885 2152736 "PLEQN" 2163085 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-940 2142528 2142650 2142830 "PINTERP" 2143075 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-939 2142221 2142268 2142371 "PINTERPA" 2142475 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-938 2141437 2141985 2142072 "PI" 2142112 T PI (NIL) -8 NIL NIL 2142179) (-937 2139734 2140709 2140737 "PID" 2140919 T PID (NIL) -9 NIL 2141053 NIL) (-936 2139485 2139522 2139597 "PICOERCE" 2139691 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-935 2138805 2138944 2139120 "PGROEB" 2139341 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-934 2134392 2135206 2136111 "PGE" 2137920 T PGE (NIL) -7 NIL NIL NIL) (-933 2132515 2132762 2133128 "PGCD" 2134109 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-932 2131853 2131956 2132117 "PFRPAC" 2132399 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-931 2128493 2130401 2130754 "PFR" 2131532 NIL PFR (NIL T) -8 NIL NIL NIL) (-930 2126882 2127126 2127451 "PFOTOOLS" 2128240 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-929 2125415 2125654 2126005 "PFOQ" 2126639 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-928 2123916 2124128 2124484 "PFO" 2125199 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-927 2120469 2123805 2123874 "PF" 2123879 NIL PF (NIL NIL) -8 NIL NIL NIL) (-926 2117803 2119074 2119102 "PFECAT" 2119687 T PFECAT (NIL) -9 NIL 2120071 NIL) (-925 2117248 2117402 2117616 "PFECAT-" 2117621 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-924 2115851 2116103 2116404 "PFBRU" 2116997 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-923 2113717 2114069 2114501 "PFBR" 2115502 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-922 2109763 2111229 2111876 "PERM" 2113103 NIL PERM (NIL T) -8 NIL NIL NIL) (-921 2104997 2105970 2106840 "PERMGRP" 2108926 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-920 2103116 2104076 2104117 "PERMCAT" 2104517 NIL PERMCAT (NIL T) -9 NIL 2104815 NIL) (-919 2102769 2102810 2102934 "PERMAN" 2103069 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-918 2100257 2102434 2102556 "PENDTREE" 2102680 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-917 2099186 2099401 2099442 "PDSPC" 2099975 NIL PDSPC (NIL T) -9 NIL 2100220 NIL) (-916 2098289 2098507 2098869 "PDSPC-" 2098874 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-915 2097171 2097939 2097980 "PDRING" 2097985 NIL PDRING (NIL T) -9 NIL 2098013 NIL) (-914 2096058 2096676 2096730 "PDMOD" 2096735 NIL PDMOD (NIL T T) -9 NIL 2096839 NIL) (-913 2093273 2094051 2094719 "PDEPROB" 2095410 T PDEPROB (NIL) -8 NIL NIL NIL) (-912 2090818 2091322 2091877 "PDEPACK" 2092738 T PDEPACK (NIL) -7 NIL NIL NIL) (-911 2089730 2089920 2090171 "PDECOMP" 2090617 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-910 2087309 2088152 2088180 "PDECAT" 2088967 T PDECAT (NIL) -9 NIL 2089680 NIL) (-909 2086938 2086993 2087047 "PDDOM" 2087212 NIL PDDOM (NIL T T) -9 NIL 2087292 NIL) (-908 2086757 2086787 2086894 "PDDOM-" 2086899 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-907 2086508 2086541 2086631 "PCOMP" 2086718 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-906 2084686 2085309 2085606 "PBWLB" 2086237 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-905 2077159 2078759 2080097 "PATTERN" 2083369 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-904 2076791 2076848 2076957 "PATTERN2" 2077096 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-903 2074548 2074936 2075393 "PATTERN1" 2076380 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-902 2071916 2072497 2072978 "PATRES" 2074113 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-901 2071480 2071547 2071679 "PATRES2" 2071843 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-900 2069363 2069768 2070175 "PATMATCH" 2071147 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-899 2068873 2069082 2069123 "PATMAB" 2069230 NIL PATMAB (NIL T) -9 NIL 2069313 NIL) (-898 2067391 2067727 2067985 "PATLRES" 2068678 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-897 2066937 2067060 2067101 "PATAB" 2067106 NIL PATAB (NIL T) -9 NIL 2067278 NIL) (-896 2065119 2065514 2065937 "PARTPERM" 2066534 T PARTPERM (NIL) -7 NIL NIL NIL) (-895 2064740 2064803 2064905 "PARSURF" 2065050 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-894 2064372 2064429 2064538 "PARSU2" 2064677 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-893 2064136 2064176 2064243 "PARSER" 2064325 T PARSER (NIL) -7 NIL NIL NIL) (-892 2063757 2063820 2063922 "PARSCURV" 2064067 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-891 2063389 2063446 2063555 "PARSC2" 2063694 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-890 2063028 2063086 2063183 "PARPCURV" 2063325 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-889 2062660 2062717 2062826 "PARPC2" 2062965 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-888 2061721 2062033 2062215 "PARAMAST" 2062498 T PARAMAST (NIL) -8 NIL NIL NIL) (-887 2061241 2061327 2061446 "PAN2EXPR" 2061622 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-886 2060018 2060362 2060590 "PALETTE" 2061033 T PALETTE (NIL) -8 NIL NIL NIL) (-885 2058411 2059023 2059383 "PAIR" 2059704 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-884 2052011 2057668 2057863 "PADICRC" 2058265 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-883 2044935 2051355 2051540 "PADICRAT" 2051858 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-882 2043250 2044872 2044917 "PADIC" 2044922 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-881 2040360 2041924 2041964 "PADICCT" 2042545 NIL PADICCT (NIL NIL) -9 NIL 2042827 NIL) (-880 2039317 2039517 2039785 "PADEPAC" 2040147 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-879 2038529 2038662 2038868 "PADE" 2039179 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-878 2036916 2037737 2038017 "OWP" 2038333 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-877 2036409 2036622 2036719 "OVERSET" 2036839 T OVERSET (NIL) -8 NIL NIL NIL) (-876 2035455 2036014 2036186 "OVAR" 2036277 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-875 2034719 2034840 2035001 "OUT" 2035314 T OUT (NIL) -7 NIL NIL NIL) (-874 2023591 2025828 2028028 "OUTFORM" 2032539 T OUTFORM (NIL) -8 NIL NIL NIL) (-873 2022927 2023188 2023315 "OUTBFILE" 2023484 T OUTBFILE (NIL) -8 NIL NIL NIL) (-872 2022234 2022399 2022427 "OUTBCON" 2022745 T OUTBCON (NIL) -9 NIL 2022911 NIL) (-871 2021835 2021947 2022104 "OUTBCON-" 2022109 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-870 2021215 2021564 2021653 "OSI" 2021766 T OSI (NIL) -8 NIL NIL NIL) (-869 2020745 2021083 2021111 "OSGROUP" 2021116 T OSGROUP (NIL) -9 NIL 2021138 NIL) (-868 2019490 2019717 2020002 "ORTHPOL" 2020492 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-867 2017041 2019325 2019446 "OREUP" 2019451 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-866 2014444 2016732 2016859 "ORESUP" 2016983 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-865 2011972 2012472 2013033 "OREPCTO" 2013933 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-864 2005658 2007859 2007900 "OREPCAT" 2010248 NIL OREPCAT (NIL T) -9 NIL 2011352 NIL) (-863 2002805 2003587 2004645 "OREPCAT-" 2004650 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-862 2001956 2002254 2002282 "ORDSET" 2002591 T ORDSET (NIL) -9 NIL 2002755 NIL) (-861 2001387 2001535 2001759 "ORDSET-" 2001764 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-860 1999952 2000743 2000771 "ORDRING" 2000973 T ORDRING (NIL) -9 NIL 2001098 NIL) (-859 1999597 1999691 1999835 "ORDRING-" 1999840 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 1998977 1999440 1999468 "ORDMON" 1999473 T ORDMON (NIL) -9 NIL 1999494 NIL) (-857 1998139 1998286 1998481 "ORDFUNS" 1998826 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1997477 1997896 1997924 "ORDFIN" 1997989 T ORDFIN (NIL) -9 NIL 1998063 NIL) (-855 1994036 1996063 1996472 "ORDCOMP" 1997101 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1993302 1993429 1993615 "ORDCOMP2" 1993896 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1989883 1990793 1991607 "OPTPROB" 1992508 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1986685 1987324 1988028 "OPTPACK" 1989199 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1984372 1985138 1985166 "OPTCAT" 1985985 T OPTCAT (NIL) -9 NIL 1986635 NIL) (-850 1983756 1984049 1984154 "OPSIG" 1984287 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1983524 1983563 1983629 "OPQUERY" 1983710 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1980655 1981835 1982339 "OP" 1983053 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1980029 1980255 1980296 "OPERCAT" 1980508 NIL OPERCAT (NIL T) -9 NIL 1980605 NIL) (-846 1979784 1979840 1979957 "OPERCAT-" 1979962 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1976597 1978581 1978950 "ONECOMP" 1979448 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1975902 1976017 1976191 "ONECOMP2" 1976469 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1975321 1975427 1975557 "OMSERVER" 1975792 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1972183 1974761 1974801 "OMSAGG" 1974862 NIL OMSAGG (NIL T) -9 NIL 1974926 NIL) (-841 1970806 1971069 1971351 "OMPKG" 1971921 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1970236 1970339 1970367 "OM" 1970666 T OM (NIL) -9 NIL NIL NIL) (-839 1968783 1969785 1969954 "OMLO" 1970117 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1967743 1967890 1968110 "OMEXPR" 1968609 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1967034 1967289 1967425 "OMERR" 1967627 T OMERR (NIL) -8 NIL NIL NIL) (-836 1966185 1966455 1966615 "OMERRK" 1966894 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1965636 1965862 1965970 "OMENC" 1966097 T OMENC (NIL) -8 NIL NIL NIL) (-834 1959531 1960716 1961887 "OMDEV" 1964485 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1958600 1958771 1958965 "OMCONN" 1959357 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1957121 1958097 1958125 "OINTDOM" 1958130 T OINTDOM (NIL) -9 NIL 1958151 NIL) (-831 1954459 1955809 1956146 "OFMONOID" 1956816 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1953831 1954396 1954441 "ODVAR" 1954446 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1951254 1953576 1953731 "ODR" 1953736 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1943567 1951030 1951156 "ODPOL" 1951161 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1937371 1943439 1943544 "ODP" 1943549 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1936137 1936352 1936627 "ODETOOLS" 1937145 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1933104 1933762 1934478 "ODESYS" 1935470 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1927986 1928894 1929919 "ODERTRIC" 1932179 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1927412 1927494 1927688 "ODERED" 1927898 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1924300 1924848 1925525 "ODERAT" 1926835 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1921259 1921724 1922321 "ODEPRRIC" 1923829 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1919202 1919798 1920284 "ODEPROB" 1920793 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1915722 1916207 1916854 "ODEPRIM" 1918681 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1914971 1915073 1915333 "ODEPAL" 1915614 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1911133 1911924 1912788 "ODEPACK" 1914127 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1910194 1910301 1910523 "ODEINT" 1911022 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1904295 1905720 1907167 "ODEIFTBL" 1908767 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1899693 1900479 1901431 "ODEEF" 1903454 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1899042 1899131 1899354 "ODECONST" 1899598 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1897167 1897828 1897856 "ODECAT" 1898461 T ODECAT (NIL) -9 NIL 1898992 NIL) (-811 1894022 1896872 1896994 "OCT" 1897077 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1893660 1893703 1893830 "OCTCT2" 1893973 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1888271 1890706 1890746 "OC" 1891843 NIL OC (NIL T) -9 NIL 1892701 NIL) (-808 1885498 1886246 1887236 "OC-" 1887330 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1884850 1885318 1885346 "OCAMON" 1885351 T OCAMON (NIL) -9 NIL 1885372 NIL) (-806 1884381 1884722 1884750 "OASGP" 1884755 T OASGP (NIL) -9 NIL 1884775 NIL) (-805 1883642 1884131 1884159 "OAMONS" 1884199 T OAMONS (NIL) -9 NIL 1884242 NIL) (-804 1883056 1883489 1883517 "OAMON" 1883522 T OAMON (NIL) -9 NIL 1883542 NIL) (-803 1882314 1882832 1882860 "OAGROUP" 1882865 T OAGROUP (NIL) -9 NIL 1882885 NIL) (-802 1882004 1882054 1882142 "NUMTUBE" 1882258 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1875577 1877095 1878631 "NUMQUAD" 1880488 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1871333 1872321 1873346 "NUMODE" 1874572 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1868688 1869568 1869596 "NUMINT" 1870519 T NUMINT (NIL) -9 NIL 1871283 NIL) (-798 1867636 1867833 1868051 "NUMFMT" 1868490 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1853995 1856940 1859472 "NUMERIC" 1865143 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1848365 1853444 1853539 "NTSCAT" 1853544 NIL NTSCAT (NIL T T T T) -9 NIL 1853583 NIL) (-795 1847559 1847724 1847917 "NTPOLFN" 1848204 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1835368 1844384 1845196 "NSUP" 1846780 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1835000 1835057 1835166 "NSUP2" 1835305 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1824958 1834774 1834907 "NSMP" 1834912 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1823390 1823691 1824048 "NREP" 1824646 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1821981 1822233 1822591 "NPCOEF" 1823133 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1821047 1821162 1821378 "NORMRETR" 1821862 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1819088 1819378 1819787 "NORMPK" 1820755 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1818773 1818801 1818925 "NORMMA" 1819054 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1818573 1818730 1818759 "NONE" 1818764 T NONE (NIL) -8 NIL NIL NIL) (-785 1818362 1818391 1818460 "NONE1" 1818537 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1817859 1817921 1818100 "NODE1" 1818294 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1816140 1816991 1817246 "NNI" 1817593 T NNI (NIL) -8 NIL NIL 1817828) (-782 1814560 1814873 1815237 "NLINSOL" 1815808 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1810801 1811796 1812695 "NIPROB" 1813681 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1809558 1809792 1810094 "NFINTBAS" 1810563 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1808732 1809208 1809249 "NETCLT" 1809421 NIL NETCLT (NIL T) -9 NIL 1809503 NIL) (-778 1807440 1807671 1807952 "NCODIV" 1808500 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1807202 1807239 1807314 "NCNTFRAC" 1807397 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1805382 1805746 1806166 "NCEP" 1806827 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1804233 1805006 1805034 "NASRING" 1805144 T NASRING (NIL) -9 NIL 1805224 NIL) (-774 1804028 1804072 1804166 "NASRING-" 1804171 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1803135 1803660 1803688 "NARNG" 1803805 T NARNG (NIL) -9 NIL 1803896 NIL) (-772 1802827 1802894 1803028 "NARNG-" 1803033 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1801706 1801913 1802148 "NAGSP" 1802612 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1792978 1794662 1796335 "NAGS" 1800053 T NAGS (NIL) -7 NIL NIL NIL) (-769 1791526 1791834 1792165 "NAGF07" 1792667 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1786064 1787355 1788662 "NAGF04" 1790239 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1779032 1780646 1782279 "NAGF02" 1784451 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1774256 1775356 1776473 "NAGF01" 1777935 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1767884 1769450 1771035 "NAGE04" 1772691 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1759053 1761174 1763304 "NAGE02" 1765774 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1755006 1755953 1756917 "NAGE01" 1758109 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1752801 1753335 1753893 "NAGD03" 1754468 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1744551 1746479 1748433 "NAGD02" 1750867 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1738362 1739787 1741227 "NAGD01" 1743131 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1734571 1735393 1736230 "NAGC06" 1737545 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1733036 1733368 1733724 "NAGC05" 1734235 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1732412 1732531 1732675 "NAGC02" 1732912 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1731371 1731954 1731994 "NAALG" 1732073 NIL NAALG (NIL T) -9 NIL 1732134 NIL) (-755 1731206 1731235 1731325 "NAALG-" 1731330 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1725156 1726264 1727451 "MULTSQFR" 1730102 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1724475 1724550 1724734 "MULTFACT" 1725068 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1717146 1721060 1721113 "MTSCAT" 1722183 NIL MTSCAT (NIL T T) -9 NIL 1722698 NIL) (-751 1716858 1716912 1717004 "MTHING" 1717086 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1716650 1716683 1716743 "MSYSCMD" 1716818 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1712732 1715405 1715725 "MSET" 1716363 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1709801 1712293 1712334 "MSETAGG" 1712339 NIL MSETAGG (NIL T) -9 NIL 1712373 NIL) (-747 1705643 1707180 1707925 "MRING" 1709101 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1705209 1705276 1705407 "MRF2" 1705570 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1704827 1704862 1705006 "MRATFAC" 1705168 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1702439 1702734 1703165 "MPRFF" 1704532 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1696468 1702293 1702390 "MPOLY" 1702395 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1695958 1695993 1696201 "MPCPF" 1696427 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1695472 1695515 1695699 "MPC3" 1695909 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1694667 1694748 1694969 "MPC2" 1695387 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1692968 1693305 1693695 "MONOTOOL" 1694327 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1692193 1692510 1692538 "MONOID" 1692757 T MONOID (NIL) -9 NIL 1692904 NIL) (-737 1691739 1691858 1692039 "MONOID-" 1692044 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1681295 1687517 1687576 "MONOGEN" 1688250 NIL MONOGEN (NIL T T) -9 NIL 1688706 NIL) (-735 1678513 1679248 1680248 "MONOGEN-" 1680367 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1677346 1677792 1677820 "MONADWU" 1678212 T MONADWU (NIL) -9 NIL 1678450 NIL) (-733 1676718 1676877 1677125 "MONADWU-" 1677130 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1676077 1676321 1676349 "MONAD" 1676556 T MONAD (NIL) -9 NIL 1676668 NIL) (-731 1675762 1675840 1675972 "MONAD-" 1675977 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1674051 1674675 1674954 "MOEBIUS" 1675515 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1673329 1673733 1673773 "MODULE" 1673778 NIL MODULE (NIL T) -9 NIL 1673817 NIL) (-728 1672897 1672993 1673183 "MODULE-" 1673188 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1670577 1671261 1671588 "MODRING" 1672721 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1667521 1668682 1669203 "MODOP" 1670106 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1666109 1666588 1666865 "MODMONOM" 1667384 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1655885 1664400 1664814 "MODMON" 1665746 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1653041 1654729 1655005 "MODFIELD" 1655760 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1652018 1652322 1652512 "MMLFORM" 1652871 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1651544 1651587 1651766 "MMAP" 1651969 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1649623 1650390 1650431 "MLO" 1650854 NIL MLO (NIL T) -9 NIL 1651096 NIL) (-719 1646989 1647505 1648107 "MLIFT" 1649104 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1646380 1646464 1646618 "MKUCFUNC" 1646900 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1645979 1646049 1646172 "MKRECORD" 1646303 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1645026 1645188 1645416 "MKFUNC" 1645790 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1644414 1644518 1644674 "MKFLCFN" 1644909 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1643691 1643793 1643978 "MKBCFUNC" 1644307 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1640288 1643245 1643381 "MINT" 1643575 T MINT (NIL) -8 NIL NIL NIL) (-712 1639100 1639343 1639620 "MHROWRED" 1640043 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1634480 1637635 1638040 "MFLOAT" 1638715 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1633837 1633913 1634084 "MFINFACT" 1634392 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1630152 1631000 1631884 "MESH" 1632973 T MESH (NIL) -7 NIL NIL NIL) (-708 1628542 1628854 1629207 "MDDFACT" 1629839 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1625337 1627701 1627742 "MDAGG" 1627997 NIL MDAGG (NIL T) -9 NIL 1628140 NIL) (-706 1614039 1624630 1624837 "MCMPLX" 1625150 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1613176 1613322 1613523 "MCDEN" 1613888 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1611066 1611336 1611716 "MCALCFN" 1612906 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1609991 1610231 1610464 "MAYBE" 1610872 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1607603 1608126 1608688 "MATSTOR" 1609462 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1603560 1606975 1607223 "MATRIX" 1607388 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1599326 1600033 1600769 "MATLIN" 1602917 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1589432 1592618 1592695 "MATCAT" 1597575 NIL MATCAT (NIL T T T) -9 NIL 1598992 NIL) (-698 1585788 1586809 1588165 "MATCAT-" 1588170 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1584382 1584535 1584868 "MATCAT2" 1585623 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1582494 1582818 1583202 "MAPPKG3" 1584057 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1581475 1581648 1581870 "MAPPKG2" 1582318 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1579974 1580258 1580585 "MAPPKG1" 1581181 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1579053 1579380 1579557 "MAPPAST" 1579817 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1578664 1578722 1578845 "MAPHACK3" 1578989 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1578256 1578317 1578431 "MAPHACK2" 1578596 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1577694 1577797 1577939 "MAPHACK1" 1578147 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1575773 1576394 1576698 "MAGMA" 1577422 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1575252 1575497 1575588 "MACROAST" 1575702 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1571670 1573491 1573952 "M3D" 1574824 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1565745 1570009 1570050 "LZSTAGG" 1570832 NIL LZSTAGG (NIL T) -9 NIL 1571127 NIL) (-685 1561703 1562876 1564333 "LZSTAGG-" 1564338 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1558790 1559594 1560081 "LWORD" 1561248 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1558366 1558594 1558669 "LSTAST" 1558735 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1551264 1558137 1558271 "LSQM" 1558276 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1550488 1550627 1550855 "LSPP" 1551119 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1548300 1548601 1549057 "LSMP" 1550177 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1545079 1545753 1546483 "LSMP1" 1547602 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1538925 1544216 1544257 "LSAGG" 1544319 NIL LSAGG (NIL T) -9 NIL 1544397 NIL) (-677 1535620 1536544 1537757 "LSAGG-" 1537762 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1533219 1534764 1535013 "LPOLY" 1535415 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1532801 1532886 1533009 "LPEFRAC" 1533128 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1531122 1531895 1532148 "LO" 1532633 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1530774 1530886 1530914 "LOGIC" 1531025 T LOGIC (NIL) -9 NIL 1531106 NIL) (-672 1530636 1530659 1530730 "LOGIC-" 1530735 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1529829 1529969 1530162 "LODOOPS" 1530492 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1527252 1529745 1529811 "LODO" 1529816 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1525790 1526025 1526378 "LODOF" 1526999 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1521994 1524425 1524466 "LODOCAT" 1524904 NIL LODOCAT (NIL T) -9 NIL 1525115 NIL) (-667 1521727 1521785 1521912 "LODOCAT-" 1521917 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1519047 1521568 1521686 "LODO2" 1521691 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1516482 1518984 1519029 "LODO1" 1519034 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1515363 1515528 1515833 "LODEEF" 1516305 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1510666 1513557 1513598 "LNAGG" 1514460 NIL LNAGG (NIL T) -9 NIL 1514895 NIL) (-662 1509813 1510027 1510369 "LNAGG-" 1510374 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1505949 1506738 1507377 "LMOPS" 1509228 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1505352 1505740 1505781 "LMODULE" 1505786 NIL LMODULE (NIL T) -9 NIL 1505812 NIL) (-659 1502550 1504997 1505120 "LMDICT" 1505262 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1502182 1502354 1502395 "LLINSET" 1502456 NIL LLINSET (NIL T) -9 NIL 1502500 NIL) (-657 1501881 1502090 1502150 "LITERAL" 1502155 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1495044 1500815 1501119 "LIST" 1501610 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1494569 1494643 1494782 "LIST3" 1494964 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1493576 1493754 1493982 "LIST2" 1494387 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1491710 1492022 1492421 "LIST2MAP" 1493223 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1491355 1491543 1491584 "LINSET" 1491589 NIL LINSET (NIL T) -9 NIL 1491623 NIL) (-651 1489790 1490396 1490437 "LINEXP" 1490927 NIL LINEXP (NIL T) -9 NIL 1491200 NIL) (-650 1488367 1488627 1488938 "LINDEP" 1489542 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1485134 1485853 1486630 "LIMITRF" 1487622 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1483437 1483733 1484142 "LIMITPS" 1484829 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1477865 1482948 1483176 "LIE" 1483258 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1476813 1477282 1477322 "LIECAT" 1477462 NIL LIECAT (NIL T) -9 NIL 1477613 NIL) (-645 1476654 1476681 1476769 "LIECAT-" 1476774 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1469241 1476194 1476350 "LIB" 1476518 T LIB (NIL) -8 NIL NIL NIL) (-643 1464876 1465759 1466694 "LGROBP" 1468358 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1462874 1463148 1463498 "LF" 1464597 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1461714 1462406 1462434 "LFCAT" 1462641 T LFCAT (NIL) -9 NIL 1462780 NIL) (-640 1458616 1459246 1459934 "LEXTRIPK" 1461078 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1455360 1456186 1456689 "LEXP" 1458196 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1454836 1455081 1455173 "LETAST" 1455288 T LETAST (NIL) -8 NIL NIL NIL) (-637 1453234 1453547 1453948 "LEADCDET" 1454518 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1452424 1452498 1452727 "LAZM3PK" 1453155 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1447341 1450501 1451039 "LAUPOL" 1451936 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1446920 1446964 1447125 "LAPLACE" 1447291 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1444859 1446021 1446272 "LA" 1446753 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1443853 1444437 1444478 "LALG" 1444540 NIL LALG (NIL T) -9 NIL 1444599 NIL) (-631 1443567 1443626 1443762 "LALG-" 1443767 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1443402 1443426 1443467 "KVTFROM" 1443529 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1442325 1442769 1442954 "KTVLOGIC" 1443237 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1442160 1442184 1442225 "KRCFROM" 1442287 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1441064 1441251 1441550 "KOVACIC" 1441960 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1440899 1440923 1440964 "KONVERT" 1441026 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1440734 1440758 1440799 "KOERCE" 1440861 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1438565 1439327 1439704 "KERNEL" 1440390 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1438061 1438142 1438274 "KERNEL2" 1438479 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1431831 1436600 1436654 "KDAGG" 1437031 NIL KDAGG (NIL T T) -9 NIL 1437237 NIL) (-621 1431360 1431484 1431689 "KDAGG-" 1431694 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1424508 1431021 1431176 "KAFILE" 1431238 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1418936 1424019 1424247 "JORDAN" 1424329 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1418315 1418585 1418706 "JOINAST" 1418835 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1418161 1418220 1418275 "JAVACODE" 1418280 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1414413 1416366 1416420 "IXAGG" 1417349 NIL IXAGG (NIL T T) -9 NIL 1417808 NIL) (-615 1413332 1413638 1414057 "IXAGG-" 1414062 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1408862 1413254 1413313 "IVECTOR" 1413318 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1407628 1407865 1408131 "ITUPLE" 1408629 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1406130 1406307 1406602 "ITRIGMNP" 1407450 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1404875 1405079 1405362 "ITFUN3" 1405906 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1404507 1404564 1404673 "ITFUN2" 1404812 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1403666 1403987 1404161 "ITFORM" 1404353 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1401627 1402686 1402964 "ITAYLOR" 1403421 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1390572 1395764 1396927 "ISUPS" 1400497 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1389676 1389816 1390052 "ISUMP" 1390419 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1385051 1389621 1389662 "ISTRING" 1389667 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1384527 1384772 1384864 "ISAST" 1384979 T ISAST (NIL) -8 NIL NIL NIL) (-603 1383736 1383818 1384034 "IRURPK" 1384441 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1382672 1382873 1383113 "IRSN" 1383516 T IRSN (NIL) -7 NIL NIL NIL) (-601 1380743 1381098 1381527 "IRRF2F" 1382310 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1380490 1380528 1380604 "IRREDFFX" 1380699 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1379105 1379364 1379663 "IROOT" 1380223 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1375709 1376789 1377481 "IR" 1378445 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1374914 1375202 1375353 "IRFORM" 1375578 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1372527 1373022 1373588 "IR2" 1374392 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1371627 1371740 1371954 "IR2F" 1372410 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1371418 1371452 1371512 "IPRNTPK" 1371587 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1367999 1371307 1371376 "IPF" 1371381 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1366326 1367924 1367981 "IPADIC" 1367986 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1365638 1365886 1366016 "IP4ADDR" 1366216 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1365012 1365267 1365399 "IOMODE" 1365526 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1364085 1364609 1364736 "IOBFILE" 1364905 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1363573 1363989 1364017 "IOBCON" 1364022 T IOBCON (NIL) -9 NIL 1364043 NIL) (-587 1363084 1363142 1363325 "INVLAPLA" 1363509 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1352732 1355086 1357472 "INTTR" 1360748 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1349067 1349809 1350674 "INTTOOLS" 1351917 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1348653 1348744 1348861 "INTSLPE" 1348970 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1346606 1348576 1348635 "INTRVL" 1348640 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1344208 1344720 1345295 "INTRF" 1346091 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1343619 1343716 1343858 "INTRET" 1344106 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1341616 1342005 1342475 "INTRAT" 1343227 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1338879 1339462 1340081 "INTPM" 1341101 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1335624 1336223 1336961 "INTPAF" 1338265 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1330803 1331765 1332816 "INTPACK" 1334593 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1327623 1330600 1330709 "INT" 1330714 T INT (NIL) -8 NIL NIL NIL) (-575 1326875 1327027 1327235 "INTHERTR" 1327465 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1326314 1326394 1326582 "INTHERAL" 1326789 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1324160 1324603 1325060 "INTHEORY" 1325877 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1315566 1317187 1318959 "INTG0" 1322512 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1296139 1300929 1305739 "INTFTBL" 1310776 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1295388 1295526 1295699 "INTFACT" 1295998 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1292815 1293261 1293818 "INTEF" 1294942 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1291182 1291921 1291949 "INTDOM" 1292250 T INTDOM (NIL) -9 NIL 1292457 NIL) (-567 1290551 1290725 1290967 "INTDOM-" 1290972 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1286939 1288867 1288921 "INTCAT" 1289720 NIL INTCAT (NIL T) -9 NIL 1290041 NIL) (-565 1286411 1286514 1286642 "INTBIT" 1286831 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1285110 1285264 1285571 "INTALG" 1286256 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1284593 1284683 1284840 "INTAF" 1285014 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1277936 1284403 1284543 "INTABL" 1284548 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1277269 1277735 1277800 "INT8" 1277834 T INT8 (NIL) -8 NIL NIL 1277879) (-560 1276601 1277067 1277132 "INT64" 1277166 T INT64 (NIL) -8 NIL NIL 1277211) (-559 1275933 1276399 1276464 "INT32" 1276498 T INT32 (NIL) -8 NIL NIL 1276543) (-558 1275265 1275731 1275796 "INT16" 1275830 T INT16 (NIL) -8 NIL NIL 1275875) (-557 1269982 1272826 1272854 "INS" 1273788 T INS (NIL) -9 NIL 1274453 NIL) (-556 1267222 1267993 1268967 "INS-" 1269040 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1265997 1266224 1266522 "INPSIGN" 1266975 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1265115 1265232 1265429 "INPRODPF" 1265877 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1264009 1264126 1264363 "INPRODFF" 1264995 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1263009 1263161 1263421 "INNMFACT" 1263845 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1262206 1262303 1262491 "INMODGCD" 1262908 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1260714 1260959 1261283 "INFSP" 1261951 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1259898 1260015 1260198 "INFPROD0" 1260594 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1256753 1257963 1258478 "INFORM" 1259391 T INFORM (NIL) -8 NIL NIL NIL) (-547 1256363 1256423 1256521 "INFORM1" 1256688 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1255886 1255975 1256089 "INFINITY" 1256269 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1255062 1255606 1255707 "INETCLTS" 1255805 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1253678 1253928 1254249 "INEP" 1254810 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1252927 1253575 1253640 "INDE" 1253645 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1252491 1252559 1252676 "INCRMAPS" 1252854 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1251309 1251760 1251966 "INBFILE" 1252305 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1246608 1247545 1248489 "INBFF" 1250397 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1245516 1245785 1245813 "INBCON" 1246326 T INBCON (NIL) -9 NIL 1246592 NIL) (-538 1244768 1244991 1245267 "INBCON-" 1245272 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1244247 1244492 1244583 "INAST" 1244697 T INAST (NIL) -8 NIL NIL NIL) (-536 1243674 1243926 1244032 "IMPTAST" 1244161 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1240120 1243518 1243622 "IMATRIX" 1243627 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1238828 1238951 1239267 "IMATQF" 1239976 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1237048 1237275 1237612 "IMATLIN" 1238584 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1231626 1236972 1237030 "ILIST" 1237035 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1229531 1231486 1231599 "IIARRAY2" 1231604 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1224929 1229442 1229506 "IFF" 1229511 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1224276 1224546 1224662 "IFAST" 1224833 T IFAST (NIL) -8 NIL NIL NIL) (-528 1219271 1223568 1223756 "IFARRAY" 1224133 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1218451 1219175 1219248 "IFAMON" 1219253 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1218035 1218100 1218154 "IEVALAB" 1218361 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1217710 1217778 1217938 "IEVALAB-" 1217943 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1217341 1217624 1217687 "IDPO" 1217692 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1216591 1217230 1217305 "IDPOAMS" 1217310 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1215898 1216480 1216555 "IDPOAM" 1216560 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214957 1215233 1215286 "IDPC" 1215699 NIL IDPC (NIL T T) -9 NIL 1215848 NIL) (-520 1214426 1214849 1214922 "IDPAM" 1214927 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1213802 1214318 1214391 "IDPAG" 1214396 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1213447 1213638 1213713 "IDENT" 1213747 T IDENT (NIL) -8 NIL NIL NIL) (-517 1209702 1210550 1211445 "IDECOMP" 1212604 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1202539 1203625 1204672 "IDEAL" 1208738 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1201699 1201811 1202011 "ICDEN" 1202423 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1200770 1201179 1201326 "ICARD" 1201572 T ICARD (NIL) -8 NIL NIL NIL) (-513 1198830 1199143 1199548 "IBPTOOLS" 1200447 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1194437 1198450 1198563 "IBITS" 1198749 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1191160 1191736 1192431 "IBATOOL" 1193854 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1188939 1189401 1189934 "IBACHIN" 1190695 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1186768 1188785 1188888 "IARRAY2" 1188893 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1182874 1186694 1186751 "IARRAY1" 1186756 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1176742 1181286 1181767 "IAN" 1182413 T IAN (NIL) -8 NIL NIL NIL) (-506 1176253 1176310 1176483 "IALGFACT" 1176679 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1175781 1175894 1175922 "HYPCAT" 1176129 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1175319 1175436 1175622 "HYPCAT-" 1175627 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1174914 1175114 1175197 "HOSTNAME" 1175256 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1174759 1174796 1174837 "HOMOTOP" 1174842 NIL HOMOTOP (NIL T) -9 NIL 1174875 NIL) (-501 1171391 1172769 1172810 "HOAGG" 1173791 NIL HOAGG (NIL T) -9 NIL 1174470 NIL) (-500 1169985 1170384 1170910 "HOAGG-" 1170915 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1163709 1169578 1169728 "HEXADEC" 1169855 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1162457 1162679 1162942 "HEUGCD" 1163486 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1161533 1162294 1162424 "HELLFDIV" 1162429 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1159712 1161310 1161398 "HEAP" 1161477 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1158975 1159264 1159398 "HEADAST" 1159598 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1152823 1158890 1158952 "HDP" 1158957 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1146543 1152458 1152610 "HDMP" 1152724 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1145867 1146007 1146171 "HB" 1146399 T HB (NIL) -7 NIL NIL NIL) (-491 1139253 1145713 1145817 "HASHTBL" 1145822 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1138729 1138974 1139066 "HASAST" 1139181 T HASAST (NIL) -8 NIL NIL NIL) (-489 1136507 1138351 1138533 "HACKPI" 1138567 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1132175 1136360 1136473 "GTSET" 1136478 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1125590 1132053 1132151 "GSTBL" 1132156 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1117977 1124755 1125011 "GSERIES" 1125390 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1117118 1117535 1117563 "GROUP" 1117766 T GROUP (NIL) -9 NIL 1117900 NIL) (-484 1116484 1116643 1116894 "GROUP-" 1116899 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1114851 1115172 1115559 "GROEBSOL" 1116161 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1113765 1114053 1114104 "GRMOD" 1114633 NIL GRMOD (NIL T T) -9 NIL 1114801 NIL) (-481 1113533 1113569 1113697 "GRMOD-" 1113702 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1108823 1109887 1110887 "GRIMAGE" 1112553 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1107289 1107550 1107874 "GRDEF" 1108519 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1106733 1106849 1106990 "GRAY" 1107168 T GRAY (NIL) -7 NIL NIL NIL) (-477 1105920 1106326 1106377 "GRALG" 1106530 NIL GRALG (NIL T T) -9 NIL 1106623 NIL) (-476 1105581 1105654 1105817 "GRALG-" 1105822 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1102358 1105166 1105344 "GPOLSET" 1105488 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1101712 1101769 1102027 "GOSPER" 1102295 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1097444 1098150 1098676 "GMODPOL" 1101411 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1096449 1096633 1096871 "GHENSEL" 1097256 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1090605 1091448 1092468 "GENUPS" 1095533 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1090302 1090353 1090442 "GENUFACT" 1090548 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1089714 1089791 1089956 "GENPGCD" 1090220 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1089188 1089223 1089436 "GENMFACT" 1089673 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1087754 1088011 1088318 "GENEEZ" 1088931 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1081634 1087365 1087527 "GDMP" 1087677 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1070977 1075405 1076511 "GCNAALG" 1080617 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1069304 1070166 1070194 "GCDDOM" 1070449 T GCDDOM (NIL) -9 NIL 1070606 NIL) (-463 1068774 1068901 1069116 "GCDDOM-" 1069121 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1067446 1067631 1067935 "GB" 1068553 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1056062 1058392 1060784 "GBINTERN" 1065137 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1053899 1054191 1054612 "GBF" 1055737 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1052680 1052845 1053112 "GBEUCLID" 1053715 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1052029 1052154 1052303 "GAUSSFAC" 1052551 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1050396 1050698 1051012 "GALUTIL" 1051748 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1048704 1048978 1049302 "GALPOLYU" 1050123 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1046069 1046359 1046766 "GALFACTU" 1048401 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1037875 1039374 1040982 "GALFACT" 1044501 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1035263 1035921 1035949 "FVFUN" 1037105 T FVFUN (NIL) -9 NIL 1037825 NIL) (-452 1034529 1034711 1034739 "FVC" 1035030 T FVC (NIL) -9 NIL 1035213 NIL) (-451 1034172 1034354 1034422 "FUNDESC" 1034481 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1033787 1033969 1034050 "FUNCTION" 1034124 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1031531 1032109 1032575 "FT" 1033341 T FT (NIL) -8 NIL NIL NIL) (-448 1030322 1030832 1031035 "FTEM" 1031348 T FTEM (NIL) -8 NIL NIL NIL) (-447 1028613 1028902 1029299 "FSUPFACT" 1030013 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1027010 1027299 1027631 "FST" 1028301 T FST (NIL) -8 NIL NIL NIL) (-445 1026209 1026315 1026503 "FSRED" 1026892 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1024908 1025164 1025511 "FSPRMELT" 1025924 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1022214 1022652 1023138 "FSPECF" 1024471 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1003287 1011988 1012029 "FS" 1015913 NIL FS (NIL T) -9 NIL 1018202 NIL) (-441 991930 994923 998980 "FS-" 999280 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 991458 991512 991682 "FSINT" 991871 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 989750 990451 990754 "FSERIES" 991237 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 988792 988908 989132 "FSCINT" 989630 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 985000 987736 987777 "FSAGG" 988147 NIL FSAGG (NIL T) -9 NIL 988406 NIL) (-436 982762 983363 984159 "FSAGG-" 984254 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 981804 981947 982174 "FSAGG2" 982615 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 979482 979762 980310 "FS2UPS" 981522 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 979116 979159 979288 "FS2" 979433 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 977994 978165 978467 "FS2EXPXP" 978941 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 977420 977535 977687 "FRUTIL" 977874 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 968833 972915 974273 "FR" 976094 NIL FR (NIL T) -8 NIL NIL NIL) (-429 963847 966522 966562 "FRNAALG" 967882 NIL FRNAALG (NIL T) -9 NIL 968480 NIL) (-428 959520 960596 961871 "FRNAALG-" 962621 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 959158 959201 959328 "FRNAAF2" 959471 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 957533 958007 958303 "FRMOD" 958970 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 955276 955908 956226 "FRIDEAL" 957324 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 954467 954554 954845 "FRIDEAL2" 955183 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 953600 954014 954055 "FRETRCT" 954060 NIL FRETRCT (NIL T) -9 NIL 954236 NIL) (-422 952712 952943 953294 "FRETRCT-" 953299 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 949800 951010 951069 "FRAMALG" 951951 NIL FRAMALG (NIL T T) -9 NIL 952243 NIL) (-420 947934 948389 949019 "FRAMALG-" 949242 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 941585 947407 947684 "FRAC" 947689 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 941221 941278 941385 "FRAC2" 941522 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 940857 940914 941021 "FR2" 941158 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 935370 938263 938291 "FPS" 939410 T FPS (NIL) -9 NIL 939967 NIL) (-415 934819 934928 935092 "FPS-" 935238 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 932121 933790 933818 "FPC" 934043 T FPC (NIL) -9 NIL 934185 NIL) (-413 931914 931954 932051 "FPC-" 932056 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 930704 931402 931443 "FPATMAB" 931448 NIL FPATMAB (NIL T) -9 NIL 931600 NIL) (-411 928943 929446 929793 "FPARFRAC" 930420 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 924337 924835 925517 "FORTRAN" 928375 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 922053 922553 923092 "FORT" 923818 T FORT (NIL) -7 NIL NIL NIL) (-408 919729 920291 920319 "FORTFN" 921379 T FORTFN (NIL) -9 NIL 922003 NIL) (-407 919493 919543 919571 "FORTCAT" 919630 T FORTCAT (NIL) -9 NIL 919692 NIL) (-406 917599 918109 918499 "FORMULA" 919123 T FORMULA (NIL) -8 NIL NIL NIL) (-405 917387 917417 917486 "FORMULA1" 917563 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 916910 916962 917135 "FORDER" 917329 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 916006 916170 916363 "FOP" 916737 T FOP (NIL) -7 NIL NIL NIL) (-402 914587 915286 915460 "FNLA" 915888 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 913316 913731 913759 "FNCAT" 914219 T FNCAT (NIL) -9 NIL 914479 NIL) (-400 912855 913275 913303 "FNAME" 913308 T FNAME (NIL) -8 NIL NIL NIL) (-399 911418 912381 912409 "FMTC" 912414 T FMTC (NIL) -9 NIL 912450 NIL) (-398 910164 911354 911400 "FMONOID" 911405 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 906992 908160 908201 "FMONCAT" 909418 NIL FMONCAT (NIL T) -9 NIL 910023 NIL) (-396 906184 906734 906883 "FM" 906888 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 903608 904254 904282 "FMFUN" 905426 T FMFUN (NIL) -9 NIL 906134 NIL) (-394 902877 903058 903086 "FMC" 903376 T FMC (NIL) -9 NIL 903558 NIL) (-393 899956 900816 900870 "FMCAT" 902065 NIL FMCAT (NIL T T) -9 NIL 902560 NIL) (-392 898822 899722 899822 "FM1" 899901 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 896596 897012 897506 "FLOATRP" 898373 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 890174 894325 894946 "FLOAT" 895995 T FLOAT (NIL) -8 NIL NIL NIL) (-389 887612 888112 888690 "FLOATCP" 889641 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 886282 887218 887259 "FLINEXP" 887264 NIL FLINEXP (NIL T) -9 NIL 887357 NIL) (-387 884710 885159 885743 "FLINEXP-" 885748 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883786 883930 884154 "FLASORT" 884562 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880902 881770 881822 "FLALG" 883049 NIL FLALG (NIL T T) -9 NIL 883516 NIL) (-384 874606 878358 878399 "FLAGG" 879661 NIL FLAGG (NIL T) -9 NIL 880313 NIL) (-383 873332 873671 874161 "FLAGG-" 874166 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 872374 872517 872744 "FLAGG2" 873185 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 869225 870233 870292 "FINRALG" 871420 NIL FINRALG (NIL T T) -9 NIL 871928 NIL) (-380 868385 868614 868953 "FINRALG-" 868958 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867765 868004 868032 "FINITE" 868228 T FINITE (NIL) -9 NIL 868335 NIL) (-378 860122 862309 862349 "FINAALG" 866016 NIL FINAALG (NIL T) -9 NIL 867469 NIL) (-377 855454 856504 857648 "FINAALG-" 859027 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854822 855209 855312 "FILE" 855384 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 853480 853818 853872 "FILECAT" 854556 NIL FILECAT (NIL T T) -9 NIL 854772 NIL) (-374 851196 852724 852752 "FIELD" 852792 T FIELD (NIL) -9 NIL 852872 NIL) (-373 849816 850201 850712 "FIELD-" 850717 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 847666 848451 848798 "FGROUP" 849502 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846756 846920 847140 "FGLMICPK" 847498 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 842588 846681 846738 "FFX" 846743 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 842189 842250 842385 "FFSLPE" 842521 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 838179 838961 839757 "FFPOLY" 841425 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837683 837719 837928 "FFPOLY2" 838137 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 833529 837602 837665 "FFP" 837670 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828927 833440 833504 "FF" 833509 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 824053 828270 828460 "FFNBX" 828781 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818981 823188 823446 "FFNBP" 823907 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 813614 818265 818476 "FFNB" 818814 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 812446 812644 812959 "FFINTBAS" 813411 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 808472 810693 810721 "FFIELDC" 811341 T FFIELDC (NIL) -9 NIL 811717 NIL) (-359 807134 807505 808002 "FFIELDC-" 808007 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806703 806749 806873 "FFHOM" 807076 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 804398 804885 805402 "FFF" 806218 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 800016 804140 804241 "FFCGX" 804341 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 795638 799748 799855 "FFCGP" 799959 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790821 795365 795473 "FFCG" 795574 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 770302 780497 780583 "FFCAT" 785748 NIL FFCAT (NIL T T T) -9 NIL 787199 NIL) (-352 765499 766547 767861 "FFCAT-" 769091 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764910 764953 765188 "FFCAT2" 765450 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 754233 757882 759102 "FEXPR" 763762 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 753195 753630 753671 "FEVALAB" 753755 NIL FEVALAB (NIL T) -9 NIL 754016 NIL) (-348 752354 752564 752902 "FEVALAB-" 752907 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750920 751737 751940 "FDIV" 752253 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747940 748681 748796 "FDIVCAT" 750364 NIL FDIVCAT (NIL T T T T) -9 NIL 750801 NIL) (-345 747702 747729 747899 "FDIVCAT-" 747904 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746922 747009 747286 "FDIV2" 747609 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745896 746217 746419 "FCTRDATA" 746740 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 744582 744841 745130 "FCPAK1" 745627 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743681 744082 744223 "FCOMP" 744473 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 727386 730831 734369 "FC" 740163 T FC (NIL) -8 NIL NIL NIL) (-339 719665 723693 723733 "FAXF" 725535 NIL FAXF (NIL T) -9 NIL 726227 NIL) (-338 716942 717599 718424 "FAXF-" 718889 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711994 716318 716494 "FARRAY" 716799 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706888 708955 709008 "FAMR" 710031 NIL FAMR (NIL T T) -9 NIL 710491 NIL) (-335 705778 706080 706515 "FAMR-" 706520 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704947 705700 705753 "FAMONOID" 705758 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702733 703443 703496 "FAMONC" 704437 NIL FAMONC (NIL T T) -9 NIL 704823 NIL) (-332 701397 702487 702624 "FAGROUP" 702629 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 699192 699511 699914 "FACUTIL" 701078 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 698291 698476 698698 "FACTFUNC" 699002 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690713 697594 697793 "EXPUPXS" 698147 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 688196 688736 689322 "EXPRTUBE" 690147 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 684467 685059 685789 "EXPRODE" 687535 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669959 683116 683545 "EXPR" 684071 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 664513 665100 665906 "EXPR2UPS" 669257 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 664145 664202 664311 "EXPR2" 664450 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 655150 663296 663587 "EXPEXPAN" 663981 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654950 655107 655136 "EXIT" 655141 T EXIT (NIL) -8 NIL NIL NIL) (-321 654430 654674 654765 "EXITAST" 654879 T EXITAST (NIL) -8 NIL NIL NIL) (-320 654057 654119 654232 "EVALCYC" 654362 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 653598 653716 653757 "EVALAB" 653927 NIL EVALAB (NIL T) -9 NIL 654031 NIL) (-318 653079 653201 653422 "EVALAB-" 653427 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 650447 651749 651777 "EUCDOM" 652332 T EUCDOM (NIL) -9 NIL 652682 NIL) (-316 648852 649294 649884 "EUCDOM-" 649889 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 636391 639150 641900 "ESTOOLS" 646122 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 636023 636080 636189 "ESTOOLS2" 636328 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635774 635816 635896 "ESTOOLS1" 635975 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629811 631419 631447 "ES" 634215 T ES (NIL) -9 NIL 635625 NIL) (-311 624758 626045 627862 "ES-" 628026 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 621132 621893 622673 "ESCONT" 623998 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620877 620909 620991 "ESCONT1" 621094 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 620552 620602 620702 "ES2" 620821 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 620182 620240 620349 "ES1" 620488 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 619398 619527 619703 "ERROR" 620026 T ERROR (NIL) -7 NIL NIL NIL) (-305 612790 619257 619348 "EQTBL" 619353 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 605293 608104 609553 "EQ" 611374 NIL -2149 (NIL T) -8 NIL NIL NIL) (-303 604925 604982 605091 "EQ2" 605230 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 600216 601263 602356 "EP" 603864 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598816 599107 599413 "ENV" 599930 T ENV (NIL) -8 NIL NIL NIL) (-300 597910 598464 598492 "ENTIRER" 598497 T ENTIRER (NIL) -9 NIL 598543 NIL) (-299 594604 596092 596453 "EMR" 597718 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593734 593919 593973 "ELTAGG" 594353 NIL ELTAGG (NIL T T) -9 NIL 594564 NIL) (-297 593453 593515 593656 "ELTAGG-" 593661 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 593217 593246 593300 "ELTAB" 593384 NIL ELTAB (NIL T T) -9 NIL 593436 NIL) (-295 592343 592489 592688 "ELFUTS" 593068 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 592085 592141 592169 "ELEMFUN" 592274 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591955 591976 592044 "ELEMFUN-" 592049 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586769 590025 590066 "ELAGG" 591006 NIL ELAGG (NIL T) -9 NIL 591469 NIL) (-291 585054 585488 586151 "ELAGG-" 586156 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 584366 584503 584659 "ELABOR" 584918 T ELABOR (NIL) -8 NIL NIL NIL) (-289 583027 583306 583600 "ELABEXPR" 584092 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575861 577664 578493 "EFUPXS" 582302 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 569309 571110 571921 "EFULS" 575136 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566794 567152 567624 "EFSTRUC" 568941 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 556585 558151 559699 "EF" 565309 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 555659 556070 556219 "EAB" 556456 T EAB (NIL) -8 NIL NIL NIL) (-283 554841 555618 555646 "E04UCFA" 555651 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 554023 554800 554828 "E04NAFA" 554833 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 553205 553982 554010 "E04MBFA" 554015 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 552387 553164 553192 "E04JAFA" 553197 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 551571 552346 552374 "E04GCFA" 552379 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550755 551530 551558 "E04FDFA" 551563 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549937 550714 550742 "E04DGFA" 550747 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 544110 545462 546826 "E04AGNT" 548593 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542881 543424 543464 "DVARCAT" 543805 NIL DVARCAT (NIL T) -9 NIL 543968 NIL) (-274 542085 542297 542611 "DVARCAT-" 542616 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534954 541884 542013 "DSMP" 542018 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 533377 534096 534137 "DSEXT" 534500 NIL DSEXT (NIL T) -9 NIL 534794 NIL) (-271 531662 532090 532756 "DSEXT-" 532761 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 526443 527607 528675 "DROPT" 530614 T DROPT (NIL) -8 NIL NIL NIL) (-269 526108 526167 526265 "DROPT1" 526378 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 521223 522349 523486 "DROPT0" 524991 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 519568 519893 520279 "DRAWPT" 520857 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 514155 515078 516157 "DRAW" 518542 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513788 513841 513959 "DRAWHACK" 514096 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 512519 512788 513079 "DRAWCX" 513517 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 512034 512103 512254 "DRAWCURV" 512445 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 502502 504464 506579 "DRAWCFUN" 509939 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 499266 501195 501236 "DQAGG" 501865 NIL DQAGG (NIL T) -9 NIL 502139 NIL) (-260 486739 493477 493560 "DPOLCAT" 495412 NIL DPOLCAT (NIL T T T T) -9 NIL 495957 NIL) (-259 481576 482924 484882 "DPOLCAT-" 484887 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474931 481437 481535 "DPMO" 481540 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 468189 474711 474878 "DPMM" 474883 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 467759 467973 468062 "DOMTMPLT" 468120 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 467192 467561 467641 "DOMCTOR" 467699 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 466404 466672 466823 "DOMAIN" 467061 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 460124 466039 466191 "DMP" 466305 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 458069 459191 459232 "DMEXT" 459237 NIL DMEXT (NIL T) -9 NIL 459413 NIL) (-251 457669 457725 457869 "DLP" 458007 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 451491 456996 457186 "DLIST" 457511 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 448288 450344 450385 "DLAGG" 450935 NIL DLAGG (NIL T) -9 NIL 451165 NIL) (-248 446964 447628 447656 "DIVRING" 447748 T DIVRING (NIL) -9 NIL 447831 NIL) (-247 446201 446391 446691 "DIVRING-" 446696 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 444303 444660 445066 "DISPLAY" 445815 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 438171 444217 444280 "DIRPROD" 444285 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 437019 437222 437487 "DIRPROD2" 437964 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 425774 431805 431858 "DIRPCAT" 432116 NIL DIRPCAT (NIL NIL T) -9 NIL 432991 NIL) (-242 422374 423230 424367 "DIRPCAT-" 424704 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421661 421821 422007 "DIOSP" 422208 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418316 420573 420614 "DIOPS" 421048 NIL DIOPS (NIL T) -9 NIL 421277 NIL) (-239 417865 417979 418170 "DIOPS-" 418175 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 416916 417544 417572 "DIFRING" 417577 T DIFRING (NIL) -9 NIL 417599 NIL) (-237 416588 416662 416690 "DIFFSPC" 416809 T DIFFSPC (NIL) -9 NIL 416884 NIL) (-236 416233 416311 416463 "DIFFSPC-" 416468 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415289 415767 415808 "DIFFMOD" 415813 NIL DIFFMOD (NIL T) -9 NIL 415911 NIL) (-234 414997 415042 415083 "DIFFDOM" 415204 NIL DIFFDOM (NIL T) -9 NIL 415272 NIL) (-233 414850 414874 414958 "DIFFDOM-" 414963 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412782 414054 414095 "DIFEXT" 414100 NIL DIFEXT (NIL T) -9 NIL 414253 NIL) (-231 410057 412314 412355 "DIAGG" 412360 NIL DIAGG (NIL T) -9 NIL 412380 NIL) (-230 409441 409598 409850 "DIAGG-" 409855 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404858 408400 408677 "DHMATRIX" 409210 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400470 401379 402389 "DFSFUN" 403868 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395548 399401 399713 "DFLOAT" 400178 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393811 394092 394481 "DFINTTLS" 395256 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390840 391832 392232 "DERHAM" 393477 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388641 390615 390704 "DEQUEUE" 390784 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 387895 388028 388211 "DEGRED" 388503 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384325 385070 385916 "DEFINTRF" 387123 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 381880 382349 382941 "DEFINTEF" 383844 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 381230 381500 381615 "DEFAST" 381785 T DEFAST (NIL) -8 NIL NIL NIL) (-219 374954 380823 380973 "DECIMAL" 381100 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372466 372924 373430 "DDFACT" 374498 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 372062 372105 372256 "DBLRESP" 372417 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 369930 370292 370653 "DBASE" 371828 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 369172 369410 369556 "DATAARY" 369829 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368278 369131 369159 "D03FAFA" 369164 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367385 368237 368265 "D03EEFA" 368270 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365335 365801 366290 "D03AGNT" 366916 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364624 365294 365322 "D02EJFA" 365327 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 363913 364583 364611 "D02CJFA" 364616 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 363202 363872 363900 "D02BHFA" 363905 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362491 363161 363189 "D02BBFA" 363194 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355688 357277 358883 "D02AGNT" 360905 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353456 353979 354525 "D01WGTS" 355162 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352523 353415 353443 "D01TRNS" 353448 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351591 352482 352510 "D01GBFA" 352515 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350659 351550 351578 "D01FCFA" 351583 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349727 350618 350646 "D01ASFA" 350651 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348795 349686 349714 "D01AQFA" 349719 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347863 348754 348782 "D01APFA" 348787 T D01APFA (NIL) -8 NIL NIL NIL) (-199 346931 347822 347850 "D01ANFA" 347855 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 345999 346890 346918 "D01AMFA" 346923 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 345067 345958 345986 "D01ALFA" 345991 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 344135 345026 345054 "D01AKFA" 345059 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 343203 344094 344122 "D01AJFA" 344127 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336498 338051 339612 "D01AGNT" 341662 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335835 335963 336115 "CYCLOTOM" 336366 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332568 333283 334010 "CYCLES" 335128 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331880 332014 332185 "CVMP" 332429 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329721 329979 330348 "CTRIGMNP" 331608 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 329157 329515 329588 "CTOR" 329668 T CTOR (NIL) -8 NIL NIL NIL) (-188 328666 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NIL NIL) (-163 267311 267506 267593 "COMM" 267688 T COMM (NIL) -8 NIL NIL NIL) (-162 266887 267115 267190 "COMMAAST" 267256 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266136 266330 266358 "COMBOPC" 266696 T COMBOPC (NIL) -9 NIL 266871 NIL) (-160 265032 265242 265484 "COMBINAT" 265926 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 261489 262063 262690 "COMBF" 264454 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 260247 260605 260840 "COLOR" 261274 T COLOR (NIL) -8 NIL NIL NIL) (-157 259723 259968 260060 "COLONAST" 260175 T COLONAST (NIL) -8 NIL NIL NIL) (-156 259363 259410 259535 "CMPLXRT" 259670 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 258811 259063 259162 "CLLCTAST" 259284 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 254313 255341 256421 "CLIP" 257751 T CLIP (NIL) -7 NIL NIL NIL) (-153 252654 253414 253654 "CLIF" 254140 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 248829 250800 250841 "CLAGG" 251770 NIL CLAGG (NIL T) -9 NIL 252306 NIL) (-151 247251 247708 248291 "CLAGG-" 248296 NIL CLAGG- (NIL T T) 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NIL) (-137 228009 229028 229772 "CARTEN" 232183 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227117 227265 227486 "CARTEN2" 227856 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 225433 226267 226524 "CARD" 226880 T CARD (NIL) -8 NIL NIL NIL) (-134 225009 225237 225312 "CAPSLAST" 225378 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 224513 224721 224749 "CACHSET" 224881 T CACHSET (NIL) -9 NIL 224959 NIL) (-132 223983 224305 224333 "CABMON" 224383 T CABMON (NIL) -9 NIL 224439 NIL) (-131 223456 223687 223797 "BYTEORD" 223893 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 222433 222985 223127 "BYTE" 223290 T BYTE (NIL) -8 NIL NIL 223412) (-129 217783 221938 222110 "BYTEBUF" 222281 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 215292 217475 217582 "BTREE" 217709 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 212741 214940 215062 "BTOURN" 215202 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210111 212211 212252 "BTCAT" 212320 NIL BTCAT (NIL T) -9 NIL 212397 NIL) (-125 209778 209858 210007 "BTCAT-" 210012 NIL BTCAT- 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T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 177712 178116 178170 "BMODULE" 178175 NIL BMODULE (NIL T T) -9 NIL 178240 NIL) (-110 173513 177510 177583 "BITS" 177659 T BITS (NIL) -8 NIL NIL NIL) (-109 172934 173053 173193 "BINDING" 173393 T BINDING (NIL) -8 NIL NIL NIL) (-108 166661 172529 172678 "BINARY" 172805 T BINARY (NIL) -8 NIL NIL NIL) (-107 164441 165916 165957 "BGAGG" 166217 NIL BGAGG (NIL T) -9 NIL 166354 NIL) (-106 164272 164304 164395 "BGAGG-" 164400 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 163343 163656 163861 "BFUNCT" 164087 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 162033 162211 162499 "BEZOUT" 163167 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 158502 160885 161215 "BBTREE" 161736 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158236 158289 158317 "BASTYPE" 158436 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 158088 158117 158190 "BASTYPE-" 158195 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 157522 157598 157750 "BALFACT" 157999 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156378 156937 157123 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94662 "AMR" 95410 NIL AMR (NIL T T) -9 NIL 96010 NIL) (-46 92335 92556 92919 "AMR-" 92924 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 76774 92252 92313 "ALIST" 92318 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73579 76368 76537 "ALGSC" 76692 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70135 70689 71296 "ALGPKG" 73019 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69412 69513 69697 "ALGMFACT" 70021 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65447 66026 66620 "ALGMANIP" 68996 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55666 65073 65223 "ALGFF" 65380 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54862 54993 55172 "ALGFACT" 55524 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53803 54403 54441 "ALGEBRA" 54446 NIL ALGEBRA (NIL T) -9 NIL 54487 NIL) (-37 53521 53580 53712 "ALGEBRA-" 53717 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35584 51493 51545 "ALAGG" 51681 NIL ALAGG (NIL T T) -9 NIL 51842 NIL) (-35 35120 35233 35259 "AHYP" 35460 T AHYP (NIL) -9 NIL NIL NIL) (-34 34051 34299 34325 "AGG" 34824 T AGG (NIL) -9 NIL 35103 NIL) (-33 33485 33647 33861 "AGG-" 33866 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31291 31714 32119 "AF" 33127 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30771 31016 31106 "ADDAST" 31219 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30039 30298 30454 "ACPLOT" 30633 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18670 26971 27009 "ACFS" 27616 NIL ACFS (NIL T) -9 NIL 27855 NIL) (-28 16697 17187 17949 "ACFS-" 17954 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12815 14744 14770 "ACF" 15649 T ACF (NIL) -9 NIL 16062 NIL) (-26 11519 11853 12346 "ACF-" 12351 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11091 11286 11312 "ABELSG" 11404 T ABELSG (NIL) -9 NIL 11469 NIL) (-24 10958 10983 11049 "ABELSG-" 11054 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10301 10588 10614 "ABELMON" 10784 T ABELMON (NIL) -9 NIL 10896 NIL) (-22 9965 10049 10187 "ABELMON-" 10192 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9313 9685 9711 "ABELGRP" 9783 T ABELGRP (NIL) -9 NIL 9858 NIL) (-20 8776 8905 9121 "ABELGRP-" 9126 NIL ABELGRP- 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(-439 *3 *4)) (-4 *3 (-13 (-174) (-38 (-419 (-576))))))) @@ -2006,52 +4871,52 @@ (-12 (-5 *2 (-1144 *3 (-624 *1))) (-4 *3 (-1068)) (-4 *3 (-1119)) (-4 *1 (-442 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-1123)) (-5 *1 (-446)))) - ((*1 *2 *1) (-12 (-5 *2 (-1196)) (-5 *1 (-446)))) - ((*1 *1 *2) (-12 (-5 *2 (-1196)) (-5 *1 (-446)))) - ((*1 *1 *2) (-12 (-5 *2 (-1178)) (-5 *1 (-446)))) + ((*1 *2 *1) (-12 (-5 *2 (-1195)) (-5 *1 (-446)))) + ((*1 *1 *2) (-12 (-5 *2 (-1195)) (-5 *1 (-446)))) + ((*1 *1 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-446)) (-5 *1 (-449)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1200)) (|:| -3424 (-656 (-340))))) + (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -2401 (-656 (-340))))) (-4 *1 (-452)))) ((*1 *1 *2) (-12 (-5 *2 (-340)) (-4 *1 (-452)))) ((*1 *1 *2) (-12 (-5 *2 (-656 (-340))) (-4 *1 (-452)))) - ((*1 *1 *2) (-12 (-5 *2 (-1287 (-711))) (-4 *1 (-452)))) + ((*1 *1 *2) (-12 (-5 *2 (-1286 (-711))) (-4 *1 (-452)))) ((*1 *1 *2) (-12 - (-5 *2 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*5)) (-4 *3 (-862)) + (-12 (-5 *2 (-1306 *3 *4)) (-5 *1 (-639 *3 *4 *5)) (-4 *3 (-862)) (-4 *4 (-13 (-174) (-729 (-419 (-576))))) (-14 *5 (-938)))) ((*1 *2 *1) - (-12 (-5 *2 (-1302 *3 *4)) (-5 *1 (-639 *3 *4 *5)) (-4 *3 (-862)) + (-12 (-5 *2 (-1301 *3 *4)) (-5 *1 (-639 *3 *4 *5)) (-4 *3 (-862)) (-4 *4 (-13 (-174) (-729 (-419 (-576))))) (-14 *5 (-938)))) ((*1 *1 *2) (-12 (-4 *3 (-174)) (-5 *1 (-647 *3 *2)) (-4 *2 (-756 *3)))) @@ -2078,7 +4943,7 @@ ((*1 *2 *1) (-12 (-5 *2 (-390)) (-5 *1 (-711)))) ((*1 *2 *3) (-12 (-5 *3 (-326 (-576))) (-5 *2 (-326 (-713))) (-5 *1 (-713)))) - ((*1 *2 *3) (-12 (-5 *3 (-874)) (-5 *2 (-1178)) (-5 *1 (-722)))) + ((*1 *2 *3) (-12 (-5 *3 (-874)) (-5 *2 (-1177)) (-5 *1 (-722)))) ((*1 *2 *1) (-12 (-4 *2 (-174)) (-5 *1 (-723 *2 *3 *4 *5 *6)) (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) @@ -2088,7 +4953,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-656 (-2 (|:| -1856 *3) (|:| -1585 *4)))) + (-12 (-5 *2 (-656 (-2 (|:| -1706 *3) (|:| -3605 *4)))) (-4 *3 (-1068)) (-4 *4 (-738)) (-5 *1 (-747 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-576)) (-4 *1 (-775)))) ((*1 *1 *2) @@ -2096,60 +4961,60 @@ (-5 *2 (-3 (|:| |nia| - (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) - (|:| -2920 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) + (|:| -2691 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-227))) - (|:| -2920 (-656 (-1113 (-855 (-227))))) + (|:| -2691 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-781)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-326 (-227))) - (|:| -2920 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) + (|:| -2691 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-781)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) - (|:| -2920 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) + (|:| -2691 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-781)))) - ((*1 *2 *3) (-12 (-5 *2 (-786)) (-5 *1 (-785 *3)) (-4 *3 (-1237)))) + ((*1 *2 *3) (-12 (-5 *2 (-786)) (-5 *1 (-785 *3)) (-4 *3 (-1236)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) - (|:| |fn| (-1287 (-326 (-227)))) (|:| |yinit| (-656 (-227))) + (|:| |fn| (-1286 (-326 (-227)))) (|:| |yinit| (-656 (-227))) (|:| |intvals| (-656 (-227))) (|:| |g| (-326 (-227))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-820)))) - ((*1 *1 *2) (-12 (-5 *2 (-1196)) (-5 *1 (-836)))) + ((*1 *1 *2) (-12 (-5 *2 (-1195)) (-5 *1 (-836)))) ((*1 *1 *2) (-12 (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-227))) (|:| -3503 (-656 (-227))) + (-2 (|:| |fn| (-326 (-227))) (|:| -1538 (-656 (-227))) (|:| |lb| (-656 (-855 (-227)))) (|:| |cf| (-656 (-326 (-227)))) (|:| |ub| (-656 (-855 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-656 (-326 (-227)))) - (|:| -3503 (-656 (-227))))))) + (|:| -1538 (-656 (-227))))))) (-5 *1 (-853)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-656 (-326 (-227)))) (|:| -3503 (-656 (-227))))) + (-2 (|:| |lfn| (-656 (-326 (-227)))) (|:| -1538 (-656 (-227))))) (-5 *1 (-853)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-326 (-227))) (|:| -3503 (-656 (-227))) + (-2 (|:| |fn| (-326 (-227))) (|:| -1538 (-656 (-227))) (|:| |lb| (-656 (-855 (-227)))) (|:| |cf| (-656 (-326 (-227)))) (|:| |ub| (-656 (-855 (-227)))))) (-5 *1 (-853)))) @@ -2171,7 +5036,7 @@ (-2 (|:| |start| (-227)) (|:| |finish| (-227)) (|:| |grid| (-783)) (|:| |boundaryType| (-576)) (|:| |dStart| (-701 (-227))) (|:| |dFinish| (-701 (-227)))))) - (|:| |f| (-656 (-656 (-326 (-227))))) (|:| |st| (-1178)) + (|:| |f| (-656 (-656 (-326 (-227))))) (|:| |st| (-1177)) (|:| |tol| (-227)))) (-5 *1 (-913)))) ((*1 *1 *2) @@ -2187,8 +5052,8 @@ ((*1 *2 *3) (-12 (-5 *3 (-489)) (-5 *2 (-326 *4)) (-5 *1 (-936 *4)) (-4 *4 (-568)))) - ((*1 *2 *3) (-12 (-5 *2 (-1292)) (-5 *1 (-1052 *3)) (-4 *3 (-1237)))) - ((*1 *2 *3) (-12 (-5 *3 (-322)) (-5 *1 (-1052 *2)) (-4 *2 (-1237)))) + ((*1 *2 *3) (-12 (-5 *2 (-1291)) (-5 *1 (-1052 *3)) (-4 *3 (-1236)))) + ((*1 *2 *3) (-12 (-5 *3 (-322)) (-5 *1 (-1052 *2)) (-4 *2 (-1236)))) ((*1 *1 *2) (-12 (-4 *3 (-374)) (-4 *4 (-805)) (-4 *5 (-862)) (-5 *1 (-1053 *3 *4 *5 *2 *6)) (-4 *2 (-966 *3 *4 *5)) @@ -2204,114 +5069,1612 @@ ((*1 *2 *1) (-12 (-4 *1 (-1153 *3)) (-4 *3 (-1068)) (-5 *2 (-874)))) ((*1 *1 *2) (-12 (-5 *2 (-145)) (-4 *1 (-1163)))) ((*1 *2 *3) - (-12 (-5 *2 (-1176 *3)) (-5 *1 (-1180 *3)) (-4 *3 (-1068)))) + (-12 (-5 *2 (-1176 *3)) (-5 *1 (-1179 *3)) (-4 *3 (-1068)))) ((*1 *1 *2) - (-12 (-5 *2 (-1283 *4)) (-14 *4 (-1196)) (-5 *1 (-1187 *3 *4 *5)) + (-12 (-5 *2 (-1282 *4)) (-14 *4 (-1195)) (-5 *1 (-1186 *3 *4 *5)) (-4 *3 (-1068)) (-14 *5 *3))) ((*1 *1 *2) - (-12 (-5 *2 (-1283 *4)) (-14 *4 (-1196)) (-5 *1 (-1194 *3 *4 *5)) + (-12 (-5 *2 (-1282 *4)) (-14 *4 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(-4 *1 (-25)) (-5 *2 (-938)))) ((*1 *1 *1 *1) @@ -3239,12 +8211,12 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-227)) (-5 *1 (-158)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-938)) (-5 *1 (-158)))) ((*1 *2 *1 *2) - (-12 (-5 *2 (-960 *3)) (-4 *3 (-13 (-374) (-1222))) + (-12 (-5 *2 (-960 *3)) (-4 *3 (-13 (-374) (-1221))) (-5 *1 (-229 *3)))) ((*1 *1 *2 *1) - (-12 (-5 *1 (-304 *2)) (-4 *2 (-1131)) (-4 *2 (-1237)))) + (-12 (-5 *1 (-304 *2)) (-4 *2 (-1131)) (-4 *2 (-1236)))) ((*1 *1 *1 *2) - (-12 (-5 *1 (-304 *2)) (-4 *2 (-1131)) (-4 *2 (-1237)))) + (-12 (-5 *1 (-304 *2)) (-4 *2 (-1131)) (-4 *2 (-1236)))) ((*1 *1 *2 *3) (-12 (-4 *1 (-333 *3 *2)) (-4 *3 (-1119)) (-4 *2 (-132)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-372 *2)) (-4 *2 (-1119)))) @@ -3256,11 +8228,11 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-397 *2)) (-4 *2 (-1119)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-397 *2)) (-4 *2 (-1119)))) ((*1 *1 *2 *1) - (-12 (-14 *3 (-656 (-1196))) (-4 *4 (-174)) - (-4 *6 (-243 (-2048 *3) (-783))) + (-12 (-14 *3 (-656 (-1195))) (-4 *4 (-174)) + (-4 *6 (-243 (-3485 *3) (-783))) (-14 *7 - (-1 (-112) (-2 (|:| -2550 *5) (|:| -3175 *6)) - (-2 (|:| -2550 *5) (|:| -3175 *6)))) + (-1 (-112) (-2 (|:| -3257 *5) (|:| -4274 *6)) + (-2 (|:| -3257 *5) (|:| -4274 *6)))) (-5 *1 (-473 *3 *4 *5 *6 *7 *2)) (-4 *5 (-862)) (-4 *2 (-966 *4 *6 (-876 *3))))) ((*1 *1 *1 *2) @@ -3271,7 +8243,7 @@ (-12 (-4 *2 (-374)) (-4 *3 (-805)) (-4 *4 (-862)) (-5 *1 (-516 *2 *3 *4 *5)) (-4 *5 (-966 *2 *3 *4)))) ((*1 *2 *2 *2) - (-12 (-5 *2 (-1287 *3)) (-4 *3 (-360)) (-5 *1 (-540 *3)))) + (-12 (-5 *2 (-1286 *3)) (-4 *3 (-360)) (-5 *1 (-540 *3)))) ((*1 *1 *1 *1) (-5 *1 (-548))) ((*1 *1 *1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-608 *3)) (-4 *3 (-1068)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-658 *2)) (-4 *2 (-1131)))) @@ -3301,7 +8273,7 @@ ((*1 *1 *1 *1) (-4 *1 (-732))) ((*1 *1 *1 *1) (-5 *1 (-874))) ((*1 *1 *1 *1) (-12 (-5 *1 (-905 *2)) (-4 *2 (-1119)))) ((*1 *2 *3 *2) - (-12 (-5 *2 (-1287 *4)) (-4 *4 (-1263 *3)) (-4 *3 (-568)) + (-12 (-5 *2 (-1286 *4)) (-4 *4 (-1262 *3)) (-4 *3 (-568)) 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(-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1237)) + (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1236)) (-4 *4 (-384 *3)) (-4 *5 (-384 *3)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-59 *5)) (-4 *5 (-1237)) - (-4 *6 (-1237)) (-5 *2 (-59 *6)) (-5 *1 (-58 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-59 *5)) (-4 *5 (-1236)) + (-4 *6 (-1236)) (-5 *2 (-59 *6)) (-5 *1 (-58 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *8 *7)) (-5 *4 (-137 *5 *6 *7)) (-14 *5 (-576)) (-14 *6 (-783)) (-4 *7 (-174)) (-4 *8 (-174)) @@ -10372,19 +15522,19 @@ (-4 *6 (-174)) (-5 *2 (-171 *6)) (-5 *1 (-170 *5 *6)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-326 *3) (-326 *3))) (-4 *3 (-13 (-1068) (-862))) - (-5 *1 (-225 *3 *4)) (-14 *4 (-656 (-1196))))) + (-5 *1 (-225 *3 *4)) (-14 *4 (-656 (-1195))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) - (-4 *6 (-1237)) (-4 *7 (-1237)) (-5 *2 (-245 *5 *7)) + (-4 *6 (-1236)) (-4 *7 (-1236)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-304 *5)) (-4 *5 (-1237)) - (-4 *6 (-1237)) (-5 *2 (-304 *6)) (-5 *1 (-303 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-304 *5)) (-4 *5 (-1236)) + (-4 *6 (-1236)) (-5 *2 (-304 *6)) (-5 *1 (-303 *5 *6)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1237)) (-5 *1 (-304 *3)))) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1236)) (-5 *1 (-304 *3)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1178)) (-5 *5 (-624 *6)) - (-4 *6 (-312)) (-4 *2 (-1237)) (-5 *1 (-307 *6 *2)))) + (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1177)) (-5 *5 (-624 *6)) + (-4 *6 (-312)) (-4 *2 (-1236)) (-5 *1 (-307 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *2 *5)) (-5 *4 (-624 *5)) (-4 *5 (-312)) (-4 *2 (-312)) (-5 *1 (-308 *5 *2)))) @@ -10398,20 +15548,20 @@ (-4 *6 (-1119)) (-5 *2 (-326 *6)) (-5 *1 (-324 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-347 *5 *6 *7 *8)) (-4 *5 (-374)) - (-4 *6 (-1263 *5)) (-4 *7 (-1263 (-419 *6))) (-4 *8 (-353 *5 *6 *7)) - (-4 *9 (-374)) (-4 *10 (-1263 *9)) (-4 *11 (-1263 (-419 *10))) + (-4 *6 (-1262 *5)) (-4 *7 (-1262 (-419 *6))) (-4 *8 (-353 *5 *6 *7)) + (-4 *9 (-374)) (-4 *10 (-1262 *9)) (-4 *11 (-1262 (-419 *10))) (-5 *2 (-347 *9 *10 *11 *12)) (-5 *1 (-344 *5 *6 *7 *8 *9 *10 *11 *12)) (-4 *12 (-353 *9 *10 *11)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-349 *3)) (-4 *3 (-1119)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1241)) (-4 *8 (-1241)) - (-4 *6 (-1263 *5)) (-4 *7 (-1263 (-419 *6))) (-4 *9 (-1263 *8)) + (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1240)) (-4 *8 (-1240)) + (-4 *6 (-1262 *5)) (-4 *7 (-1262 (-419 *6))) (-4 *9 (-1262 *8)) (-4 *2 (-353 *8 *9 *10)) (-5 *1 (-351 *5 *6 *7 *4 *8 *9 *10 *2)) - (-4 *4 (-353 *5 *6 *7)) (-4 *10 (-1263 (-419 *9))))) + (-4 *4 (-353 *5 *6 *7)) (-4 *10 (-1262 (-419 *9))))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1237)) (-4 *6 (-1237)) + (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1236)) (-4 *6 (-1236)) (-4 *2 (-384 *6)) (-5 *1 (-382 *5 *4 *6 *2)) (-4 *4 (-384 *5)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-393 *3 *4)) (-4 *3 (-1068)) @@ -10424,9 +15574,9 @@ (-4 *6 (-568)) (-5 *2 (-419 *6)) (-5 *1 (-418 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-425 *5 *6 *7 *8)) (-4 *5 (-317)) - (-4 *6 (-1011 *5)) (-4 *7 (-1263 *6)) + (-4 *6 (-1011 *5)) (-4 *7 (-1262 *6)) (-4 *8 (-13 (-421 *6 *7) (-1057 *6))) (-4 *9 (-317)) - (-4 *10 (-1011 *9)) (-4 *11 (-1263 *10)) + (-4 *10 (-1011 *9)) (-4 *11 (-1262 *10)) (-5 *2 (-425 *9 *10 *11 *12)) (-5 *1 (-424 *5 *6 *7 *8 *9 *10 *11 *12)) (-4 *12 (-13 (-421 *10 *11) (-1057 *10))))) @@ -10442,7 +15592,7 @@ (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1119)) (-4 *6 (-1119)) (-4 *2 (-437 *6)) (-5 *1 (-435 *5 *4 *6 *2)) (-4 *4 (-437 *5)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-501 *3)) (-4 *3 (-1237)))) + (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-501 *3)) (-4 *3 (-1236)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-521 *3 *4)) (-4 *3 (-1119)) (-4 *4 (-862)))) @@ -10451,9 +15601,9 @@ (-4 *6 (-374)) (-5 *2 (-598 *6)) (-5 *1 (-596 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -4015 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -3116 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-374)) (-4 *6 (-374)) - (-5 *2 (-2 (|:| -4015 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -3116 *6) (|:| |coeff| *6))) (-5 *1 (-596 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -10473,31 +15623,31 @@ (-656 (-2 (|:| |coeff| *6) (|:| |logand| *6)))))) (-5 *1 (-596 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-613 *5)) (-4 *5 (-1237)) - (-4 *6 (-1237)) (-5 *2 (-613 *6)) (-5 *1 (-610 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-613 *5)) (-4 *5 (-1236)) + (-4 *6 (-1236)) (-5 *2 (-613 *6)) (-5 *1 (-610 *5 *6)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-613 *6)) (-5 *5 (-613 *7)) - (-4 *6 (-1237)) (-4 *7 (-1237)) (-4 *8 (-1237)) (-5 *2 (-613 *8)) + (-4 *6 (-1236)) (-4 *7 (-1236)) (-4 *8 (-1236)) (-5 *2 (-613 *8)) (-5 *1 (-611 *6 *7 *8)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-1176 *6)) (-5 *5 (-613 *7)) - (-4 *6 (-1237)) (-4 *7 (-1237)) (-4 *8 (-1237)) (-5 *2 (-1176 *8)) + (-4 *6 (-1236)) (-4 *7 (-1236)) (-4 *8 (-1236)) (-5 *2 (-1176 *8)) (-5 *1 (-611 *6 *7 *8)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-613 *6)) (-5 *5 (-1176 *7)) - (-4 *6 (-1237)) (-4 *7 (-1237)) (-4 *8 (-1237)) (-5 *2 (-1176 *8)) + (-4 *6 (-1236)) (-4 *7 (-1236)) (-4 *8 (-1236)) (-5 *2 (-1176 *8)) (-5 *1 (-611 *6 *7 *8)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1237)) (-5 *1 (-613 *3)))) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1236)) (-5 *1 (-613 *3)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-656 *5)) (-4 *5 (-1237)) - (-4 *6 (-1237)) (-5 *2 (-656 *6)) (-5 *1 (-654 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-656 *5)) (-4 *5 (-1236)) + (-4 *6 (-1236)) (-5 *2 (-656 *6)) (-5 *1 (-654 *5 *6)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-656 *6)) (-5 *5 (-656 *7)) - (-4 *6 (-1237)) (-4 *7 (-1237)) (-4 *8 (-1237)) (-5 *2 (-656 *8)) + (-4 *6 (-1236)) (-4 *7 (-1236)) (-4 *8 (-1236)) (-5 *2 (-656 *8)) (-5 *1 (-655 *6 *7 *8)))) ((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-663 *3)) (-4 *3 (-1237)))) + (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-663 *3)) (-4 *3 (-1236)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1068)) (-4 *8 (-1068)) (-4 *6 (-384 *5)) (-4 *7 (-384 *5)) (-4 *2 (-699 *8 *9 *10)) @@ -10510,9 +15660,9 @@ (-4 *4 (-699 *5 *6 *7)) (-4 *9 (-384 *8)) (-4 *10 (-384 *8)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-568)) (-4 *7 (-568)) - (-4 *6 (-1263 *5)) (-4 *2 (-1263 (-419 *8))) - (-5 *1 (-721 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1263 (-419 *6))) - (-4 *8 (-1263 *7)))) + (-4 *6 (-1262 *5)) (-4 *2 (-1262 (-419 *8))) + (-5 *1 (-721 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1262 (-419 *6))) + (-4 *8 (-1262 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *8)) (-4 *8 (-1068)) (-4 *9 (-1068)) (-4 *5 (-862)) (-4 *6 (-805)) (-4 *2 (-966 *9 *7 *5)) @@ -10549,14 +15699,14 @@ (-12 (-5 *2 (-855 *6)) (-5 *3 (-1 *6 *5)) (-5 *4 (-855 *5)) (-4 *5 (-1119)) (-4 *6 (-1119)) (-5 *1 (-854 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-890 *5)) (-4 *5 (-1237)) - (-4 *6 (-1237)) (-5 *2 (-890 *6)) (-5 *1 (-889 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-890 *5)) (-4 *5 (-1236)) + (-4 *6 (-1236)) (-5 *2 (-890 *6)) (-5 *1 (-889 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-892 *5)) (-4 *5 (-1237)) - (-4 *6 (-1237)) (-5 *2 (-892 *6)) (-5 *1 (-891 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-892 *5)) (-4 *5 (-1236)) + (-4 *6 (-1236)) (-5 *2 (-892 *6)) (-5 *1 (-891 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-895 *5)) (-4 *5 (-1237)) - (-4 *6 (-1237)) (-5 *2 (-895 *6)) (-5 *1 (-894 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-895 *5)) (-4 *5 (-1236)) + (-4 *6 (-1236)) (-5 *2 (-895 *6)) (-5 *1 (-894 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-902 *5 *6)) (-4 *5 (-1119)) (-4 *6 (-1119)) (-4 *7 (-1119)) (-5 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