diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 2754 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 5159 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1358 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 10219 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 33346 |
5 files changed, 26456 insertions, 26380 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index ca84745d..2a1ed37d 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2275580 . 3440300497) +(2277573 . 3440472337) (-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."))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\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(\\spad{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(\\spad{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| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|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(\\spad{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(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|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}."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . 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(\\spad{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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(\\spad{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| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|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(\\spad{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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(\\spad{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| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4380 . T) (-4378 . T) (-4377 . T) ((-4385 "*") . T) (-4376 . T) (-4381 . T) (-4375 . T)) +((-4387 . T) (-4385 . T) (-4384 . T) ((-4392 "*") . T) (-4383 . T) (-4388 . T) (-4382 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -3189) +(-32 R -3214) ((|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 -1028) (QUOTE (-558))))) +((|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (-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 -4383))) +((|HasAttribute| |#1| (QUOTE -4390))) (-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}."))) -((-4383 . T) (-4384 . T)) +((-4390 . T) (-4391 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,20 +82,20 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4377 . T) (-4378 . T) (-4380 . T)) +((-4384 . T) (-4385 . T) (-4387 . 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 -3189 UP UPUP -3142) +(-40 -3214 UP UPUP -2912) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4376 |has| (-406 |#2|) (-362)) (-4381 |has| (-406 |#2|) (-362)) (-4375 |has| (-406 |#2|) (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3994 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3994 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3994 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3994 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) -(-41 R -3189) +((-4383 |has| (-406 |#2|) (-362)) (-4388 |has| (-406 |#2|) (-362)) (-4382 |has| (-406 |#2|) (-362)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-4007 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-4007 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-4007 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -634) (QUOTE (-561)))) (-4007 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) +(-41 R -3214) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-306)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4380 |has| |#1| (-550)) (-4378 . T) (-4377 . T)) -((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4387 |has| |#1| (-553)) (-4385 . T) (-4384 . T)) +((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-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."))) -((-4383 . T) (-4384 . T)) -((-3994 (-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|))))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|))))))) +((-4390 . T) (-4391 . T)) +((-4007 (-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|))))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-362)))) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-362)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1028) (QUOTE (-558))))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| $ (QUOTE (-1042))) (|HasCategory| $ (LIST (QUOTE -1031) (QUOTE (-561))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4380 . T)) +((-4387 . 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 -3189) +(-54 |Base| R -3214) ((|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"))) -((-4383 . T) (-4384 . T)) +((-4390 . T) (-4391 . 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}"))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|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}."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-61 -3179) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-61 -3269) ((|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 -3179) +(-62 -3269) ((|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 -3179) +(-63 -3269) ((|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 -3179) +(-64 -3269) ((|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 -3179) +(-65 -3269) ((|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 -3179) +(-66 -3269) ((|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 -3179) +(-67 -3269) ((|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 -3179) +(-68 -3269) ((|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 -3179) +(-69 -3269) ((|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 -3179) +(-70 -3269) ((|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 -3179) +(-71 -3269) ((|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 -3179) +(-72 -3269) ((|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 -3179) +(-73 -3269) ((|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 -3179) +(-74 -3269) ((|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 -3179) +(-77 -3269) ((|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 -3179) +(-78 -3269) ((|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 -3179) +(-79 -3269) ((|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 -3179) +(-80 -3269) ((|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 -3179) +(-81 -3269) ((|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 -3179) +(-82 -3269) ((|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 -3179) +(-83 -3269) ((|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 -3179) +(-84 -3269) ((|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 -3179) +(-85 -3269) ((|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 -3179) +(-86 -3269) ((|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 -3179) +(-87 -3269) ((|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 -3179) +(-88 -3269) ((|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 -3179) +(-89 -3269) ((|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 (-362)))) (-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}."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-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\"."))) -((-4383 . T)) +((-4390 . 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."))) -((-4383 . T) ((-4385 "*") . T) (-4384 . T) (-4380 . T) (-4378 . T) (-4377 . T) (-4376 . T) (-4381 . T) (-4375 . T) (-4374 . T) (-4373 . T) (-4372 . T) (-4371 . T) (-4379 . T) (-4382 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4370 . T)) +((-4390 . T) ((-4392 "*") . T) (-4391 . T) (-4387 . T) (-4385 . T) (-4384 . T) (-4383 . T) (-4388 . T) (-4382 . T) (-4381 . T) (-4380 . T) (-4379 . T) (-4378 . T) (-4386 . T) (-4389 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4377 . 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}."))) -((-4380 . T)) +((-4387 . 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{\\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}."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-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 (-4385 "*")))) +((|HasAttribute| |#1| (QUOTE (-4392 "*")))) (-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"))) -((-4383 . T)) +((-4390 . 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."))) -((-4384 . T)) +((-4391 . 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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3994 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4007 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) (-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| (($ (|Symbol|) (|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| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4384 . T) (-4383 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1087))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-112) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-112) (QUOTE (-1087))) (|HasCategory| (-112) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4391 . T) (-4390 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1090))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-112) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-112) (QUOTE (-1090))) (|HasCategory| (-112) (LIST (QUOTE -608) (QUOTE (-856))))) (-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}"))) -((-4378 . T) (-4377 . T)) +((-4385 . T) (-4384 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) @@ -383,27 +383,27 @@ NIL (-113 A) ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op,{} foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op,{} [foo1,{}...,{}foon])} attaches [foo1,{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,{}...,{}fn]} then applying a derivation \\spad{D} to \\spad{op(a1,{}...,{}an)} returns \\spad{f1(a1,{}...,{}an) * D(a1) + ... + fn(a1,{}...,{}an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,{}...,{}an)} returns the result of \\spad{f(a1,{}...,{}an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op,{} [a1,{}...,{}an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,{}...,{}an)} is returned,{} and \"failed\" otherwise."))) NIL -((|HasCategory| |#1| (QUOTE (-841)))) +((|HasCategory| |#1| (QUOTE (-844)))) (-114) ((|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| (($ $ (|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| (((|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!| (($ $ (|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| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|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.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|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}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -3189 UP) +(-115 -3214 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 (-116 |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}."))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-117 |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}."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-899))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-116 |#1|) (QUOTE (-1012))) (|HasCategory| (-116 |#1|) (QUOTE (-811))) (-3994 (|HasCategory| (-116 |#1|) (QUOTE (-811))) (|HasCategory| (-116 |#1|) (QUOTE (-841)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-1138))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-306))) (|HasCategory| (-116 |#1|) (QUOTE (-543))) (|HasCategory| (-116 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-902))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-116 |#1|) (QUOTE (-1015))) (|HasCategory| (-116 |#1|) (QUOTE (-814))) (-4007 (|HasCategory| (-116 |#1|) (QUOTE (-814))) (|HasCategory| (-116 |#1|) (QUOTE (-844)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-116 |#1|) (QUOTE (-1141))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -512) (QUOTE (-1166)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-306))) (|HasCategory| (-116 |#1|) (QUOTE (-543))) (|HasCategory| (-116 |#1|) (QUOTE (-844))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-902)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))))) (-118 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4384))) +((|HasAttribute| |#1| (QUOTE -4391))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 @@ -414,15 +414,15 @@ NIL NIL (-121 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"))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,20 +430,20 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4383 . T) (-4384 . T)) +((-4390 . T) (-4391 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-127 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."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-128) ((|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.}")) (|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'.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#buf} returns the number of active elements in the buffer.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-3994 (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-129) (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087)))) (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| (-129) (QUOTE (-844))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-4007 (-12 (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-129) (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| (-129) (QUOTE (-844))) (|HasCategory| (-129) (QUOTE (-1090)))) (|HasCategory| (-129) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|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 @@ -462,13 +462,13 @@ NIL NIL (-133) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4385 "*") . T)) +(((-4392 "*") . T)) NIL -(-134 |minix| -1470 S T$) +(-134 |minix| -2164 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-135 |minix| -1470 R) +(-135 |minix| -2164 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 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 @@ -490,8 +490,8 @@ NIL NIL (-140) ((|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}."))) -((-4383 . T) (-4373 . T) (-4384 . T)) -((-3994 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-4390 . T) (-4380 . T) (-4391 . T)) +((-4007 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-141 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{\\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{\\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 @@ -506,7 +506,7 @@ NIL NIL (-144) ((|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."))) -((-4380 . T)) +((-4387 . T)) NIL (-145 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}."))) @@ -514,9 +514,9 @@ NIL NIL (-146) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4380 . T)) +((-4387 . T)) NIL -(-147 -3189 UP UPUP) +(-147 -3214 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 @@ -527,14 +527,14 @@ NIL (-149 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 -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasAttribute| |#1| (QUOTE -4383))) +((|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasAttribute| |#1| (QUOTE -4390))) (-150 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 (-151 |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."))) -((-4378 . T) (-4377 . T) (-4380 . T)) +((-4385 . T) (-4384 . T) (-4387 . T)) NIL (-152) ((|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."))) @@ -556,7 +556,7 @@ 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 -(-157 R -3189) +(-157 R -3214) ((|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 @@ -587,10 +587,10 @@ NIL (-164 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| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) NIL -((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-992))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasCategory| |#2| (QUOTE (-1048))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4379)) (|HasAttribute| |#2| (QUOTE -4382)) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-841)))) +((|HasCategory| |#2| (QUOTE (-902))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-995))) (|HasCategory| |#2| (QUOTE (-1190))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4386)) (|HasAttribute| |#2| (QUOTE -4389)) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-844)))) (-165 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| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) -((-4376 -3994 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4379 |has| |#1| (-6 -4379)) (-4382 |has| |#1| (-6 -4382)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 -4007 (|has| |#1| (-553)) (-12 (|has| |#1| (-306)) (|has| |#1| (-902)))) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4386 |has| |#1| (-6 -4386)) (-4389 |has| |#1| (-6 -4389)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-166 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."))) @@ -602,8 +602,8 @@ NIL NIL (-168 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}."))) -((-4376 -3994 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4379 |has| |#1| (-6 -4379)) (-4382 |has| |#1| (-6 -4382)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-819)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-841)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1012)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1185)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-899))))) (-3994 (-12 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T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| 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(QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-1051))) (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-362)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasAttribute| |#1| (QUOTE -4386)) (|HasAttribute| |#1| (QUOTE -4389)) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166))))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-348))))) (-169 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -614,7 +614,7 @@ NIL NIL (-171) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-172) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -622,7 +622,7 @@ NIL NIL (-173 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4385 "*") . T) (-4376 . T) (-4381 . T) (-4375 . T) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") . T) (-4383 . T) (-4388 . T) (-4382 . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-174) ((|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| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|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}."))) @@ -639,7 +639,7 @@ NIL (-177 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr,{} pat,{} res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-942 |#2|) (LIST (QUOTE -876) (|devaluate| |#1|)))) +((|HasCategory| (-945 |#2|) (LIST (QUOTE -879) (|devaluate| |#1|)))) (-178 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,{}r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,{}lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,{}lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,{}l)} \\undocumented{}"))) NIL @@ -676,7 +676,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors."))) NIL NIL -(-187 R -3189) +(-187 R -3214) ((|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 @@ -784,23 +784,23 @@ 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 -(-214 -3189 UP UPUP R) +(-214 -3214 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 -(-215 -3189 FP) +(-215 -3214 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 (-216) ((|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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3994 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4007 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) (-217) ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-218 R -3189) +(-218 R -3214) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -814,19 +814,19 @@ NIL NIL (-221 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-222 |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}."))) -((-4380 . T)) +((-4387 . T)) NIL -(-223 R -3189) +(-223 R -3214) ((|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 (-224) ((|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}."))) -((-1422 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-1417 . T) (-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-225) ((|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{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{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*\\%\\spad{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*\\%\\spad{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*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{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*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{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)}.}"))) @@ -834,23 +834,23 @@ NIL NIL (-226 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}"))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-553))) (|HasAttribute| |#1| (QUOTE (-4392 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-227 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 (-228 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."))) -((-4384 . T)) +((-4391 . T)) NIL (-229 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) +((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232)))) (-230 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4380 . T)) +((-4387 . T)) NIL (-231 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -858,36 +858,36 @@ NIL NIL (-232) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4380 . T)) +((-4387 . T)) NIL (-233 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4383))) +((|HasAttribute| |#1| (QUOTE -4390))) (-234 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}."))) -((-4384 . T)) +((-4391 . T)) NIL (-235) ((|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 -(-236 S -1470 R) +(-236 S -2164 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|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 (-362))) (|HasCategory| |#3| (QUOTE (-784))) (|HasCategory| |#3| (QUOTE (-839))) (|HasAttribute| |#3| (QUOTE -4380)) (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (QUOTE (-1087)))) -(-237 -1470 R) +((|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-787))) (|HasCategory| |#3| (QUOTE (-842))) (|HasAttribute| |#3| (QUOTE -4387)) (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-720))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (QUOTE (-1090)))) +(-237 -2164 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#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}.")) (|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"))) -((-4377 |has| |#2| (-1039)) (-4378 |has| |#2| (-1039)) (-4380 |has| |#2| (-6 -4380)) ((-4385 "*") |has| |#2| (-171)) (-4383 . T)) +((-4384 |has| |#2| (-1042)) (-4385 |has| |#2| (-1042)) (-4387 |has| |#2| (-6 -4387)) ((-4392 "*") |has| |#2| (-171)) (-4390 . T)) NIL -(-238 -1470 A B) +(-238 -2164 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 -(-239 -1470 R) +(-239 -2164 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."))) -((-4377 |has| |#2| (-1039)) (-4378 |has| |#2| (-1039)) (-4380 |has| |#2| (-6 -4380)) ((-4385 "*") |has| |#2| (-171)) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-839))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (-3994 (-12 (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-1087)))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (QUOTE (-1039)))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-362))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-1039)))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-362)))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-784))) (-3994 (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-839)))) (|HasCategory| |#2| (QUOTE (-839))) (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-171))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-1039)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (-3994 (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -898,7 +898,7 @@ NIL NIL (-242) ((|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}."))) -((-4376 . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-243 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."))) @@ -906,16 +906,16 @@ NIL NIL (-244 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}"))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-245 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 (-246 |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"))) -(((-4385 "*") |has| |#2| (-171)) (-4376 |has| |#2| (-550)) (-4381 |has| |#2| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) +(((-4392 "*") |has| |#2| (-171)) (-4383 |has| |#2| (-553)) (-4388 |has| |#2| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#2| (QUOTE (-902))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4388)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) (-247) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\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|) $) "\\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 @@ -926,23 +926,23 @@ NIL NIL (-249 |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((-4380 -3994 (-2157 (|has| |#4| (-1039)) (|has| |#4| (-232))) (-2157 (|has| |#4| (-1039)) (|has| |#4| (-890 (-1163)))) (|has| |#4| (-6 -4380)) (-2157 (|has| |#4| (-1039)) (|has| |#4| (-631 (-558))))) (-4377 |has| |#4| (-1039)) (-4378 |has| |#4| (-1039)) ((-4385 "*") |has| |#4| (-171)) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#4| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-232))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-717))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-784))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-839))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1039))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|))) 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(QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-1166)))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (-251 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 (-232)))) (-252 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."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) NIL (-253 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}."))) -((-4383 . T) (-4384 . T)) +((-4390 . T) (-4391 . T)) NIL (-254) ((|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."))) @@ -982,8 +982,8 @@ NIL NIL (-263 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"))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#3| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#3| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) (-264 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}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|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 @@ -1028,11 +1028,11 @@ 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 -(-275 R -3189) +(-275 R -3214) ((|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{\\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 -(-276 R -3189) +(-276 R -3214) ((|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{\\spad{ki}} was rewritten as \\spad{\\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 @@ -1051,10 +1051,10 @@ NIL (-280 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087)))) +((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090)))) (-281 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}."))) -((-4384 . T)) +((-4391 . T)) NIL (-282 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}."))) @@ -1075,18 +1075,18 @@ NIL (-286 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 -4384))) +((|HasAttribute| |#1| (QUOTE -4391))) (-287 |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 -(-288 S R |Mod| -2915 -3391 |exactQuo|) +(-288 S R |Mod| -3471 -1407 |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}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-289) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4376 . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-290) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1102,21 +1102,21 @@ NIL NIL (-293 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."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) (-295) ((|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 -(-296 -3189 S) +(-296 -3214 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 -(-297 E -3189) +(-297 E -3214) ((|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 @@ -1131,7 +1131,7 @@ NIL (-300 S) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1039)))) +((|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-1042)))) (-301) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL @@ -1154,7 +1154,7 @@ NIL NIL (-306) ((|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 \\spad{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|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-307 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1164,7 +1164,7 @@ 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 -(-309 -3189) +(-309 -3214) ((|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 @@ -1178,8 +1178,8 @@ NIL NIL (-312 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-1012))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-811))) (-3994 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-811))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-841)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-1138))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-232))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -308) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -285) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-306))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-543))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-841))) (-12 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| $ (QUOTE (-144)))) (-3994 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (-12 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| $ (QUOTE (-144)))))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-902))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-1015))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-814))) (-4007 (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-814))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-844)))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-1141))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-232))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -512) (QUOTE (-1166)) (LIST (QUOTE -1239) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -308) (LIST (QUOTE -1239) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (LIST (QUOTE -285) (LIST (QUOTE -1239) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1239) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-306))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-543))) (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (-12 (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-902))) (|HasCategory| $ (QUOTE (-144)))) (-4007 (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (-12 (|HasCategory| (-1239 |#1| |#2| |#3| |#4|) (QUOTE (-902))) (|HasCategory| $ (QUOTE (-144)))))) (-313 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1190,9 +1190,9 @@ NIL NIL (-315 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) 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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{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{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 @@ -1202,8 +1202,8 @@ NIL NIL (-318 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."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -1337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) (-319 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 @@ -1214,8 +1214,8 @@ NIL NIL (-321 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4378 . T) (-4377 . T)) -((|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-783)))) +((-4385 . T) (-4384 . T)) +((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-786)))) (-322 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{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| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL @@ -1223,26 +1223,26 @@ NIL (-323 S) ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The operation is commutative."))) NIL -((|HasCategory| (-762) (QUOTE (-783)))) +((|HasCategory| (-765) (QUOTE (-786)))) (-324 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL -((|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171)))) +((|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171)))) (-325 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-326 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."))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-327 S -3189) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-327 S -3214) ((|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 (-367)))) -(-328 -3189) +(-328 -3214) ((|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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-329) ((|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."))) @@ -1260,54 +1260,54 @@ 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 -(-333 S -3189 UP UPUP R) +(-333 S -3214 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 -(-334 -3189 UP UPUP R) +(-334 -3214 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 -(-335 -3189 UP UPUP R) +(-335 -3214 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL (-336 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|)))) (-337 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-338 |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{\\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.}"))) -((-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-378)))) (|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1028) (QUOTE (-558))))) +((-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-378)))) (|HasCategory| $ (QUOTE (-1042))) (|HasCategory| $ (LIST (QUOTE -1031) (QUOTE (-561))))) (-339 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 -(-340 S -3189 UP UPUP) +(-340 S -3214 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(\\spad{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 (-367))) (|HasCategory| |#2| (QUOTE (-362)))) -(-341 -3189 UP UPUP) +(-341 -3214 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(\\spad{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."))) -((-4376 |has| (-406 |#2|) (-362)) (-4381 |has| (-406 |#2|) (-362)) (-4375 |has| (-406 |#2|) (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 |has| (-406 |#2|) (-362)) (-4388 |has| (-406 |#2|) (-362)) (-4382 |has| (-406 |#2|) (-362)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-342 |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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3994 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4007 (|HasCategory| (-903 |#1|) (QUOTE (-144))) (|HasCategory| (-903 |#1|) (QUOTE (-367)))) (|HasCategory| (-903 |#1|) (QUOTE (-146))) (|HasCategory| (-903 |#1|) (QUOTE (-367))) (|HasCategory| (-903 |#1|) (QUOTE (-144)))) (-343 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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3994 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-344 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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3994 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-345 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 @@ -1322,33 +1322,33 @@ NIL NIL (-348) ((|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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-349 R UP -3189) +(-349 R UP -3214) ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-350 |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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3994 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4007 (|HasCategory| (-903 |#1|) (QUOTE (-144))) (|HasCategory| (-903 |#1|) (QUOTE (-367)))) (|HasCategory| (-903 |#1|) (QUOTE (-146))) (|HasCategory| (-903 |#1|) (QUOTE (-367))) (|HasCategory| (-903 |#1|) (QUOTE (-144)))) (-351 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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3994 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-352 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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3994 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-353 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3994 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4007 (|HasCategory| (-903 |#1|) (QUOTE (-144))) (|HasCategory| (-903 |#1|) (QUOTE (-367)))) (|HasCategory| (-903 |#1|) (QUOTE (-146))) (|HasCategory| (-903 |#1|) (QUOTE (-367))) (|HasCategory| (-903 |#1|) (QUOTE (-144)))) (-354 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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3994 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) -(-355 -3189 GF) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +(-355 -3214 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 @@ -1356,21 +1356,21 @@ 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 -(-357 -3189 FP FPP) +(-357 -3214 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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-358 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}."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3994 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-359 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 (-360 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4380 . T)) +((-4387 . T)) NIL (-361 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1378,7 +1378,7 @@ NIL NIL (-362) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-363 |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."))) @@ -1391,10 +1391,10 @@ NIL (-365 S R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\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| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-550)))) +((|HasCategory| |#2| (QUOTE (-553)))) (-366 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{\\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{\\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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4380 |has| |#1| (-550)) (-4378 . T) (-4377 . T)) +((-4387 |has| |#1| (-553)) (-4385 . T) (-4384 . T)) NIL (-367) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1406,7 +1406,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-362)))) (-369 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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4377 . T) (-4378 . T) (-4380 . T)) +((-4384 . T) (-4385 . T) (-4387 . T)) NIL (-370 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1415,14 +1415,14 @@ NIL (-371 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4384)) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087)))) +((|HasAttribute| |#1| (QUOTE -4391)) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090)))) (-372 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4383 . T)) +((-4390 . T)) NIL (-373 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4378 . T) (-4377 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4385 . T) (-4384 . T)) NIL (-374 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."))) @@ -1431,10 +1431,10 @@ NIL (-375 S R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) +((|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561))))) (-376 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) -((-4380 . T)) +((-4387 . T)) NIL (-377 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1442,7 +1442,7 @@ NIL NIL (-378) ((|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{\\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}."))) -((-4366 . T) (-4374 . T) (-1422 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4373 . T) (-4381 . T) (-1417 . T) (-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-379 |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}."))) @@ -1450,11 +1450,11 @@ NIL NIL (-380 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}"))) -((-4378 . T) (-4377 . T)) +((-4385 . T) (-4384 . T)) ((|HasCategory| |#1| (QUOTE (-171)))) (-381 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}."))) -((-4378 . T) (-4377 . T)) +((-4385 . T) (-4384 . T)) NIL (-382) ((|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}."))) @@ -1466,15 +1466,15 @@ NIL NIL (-384 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."))) -((-4378 . T) (-4377 . T)) +((-4385 . T) (-4384 . T)) ((|HasCategory| |#1| (QUOTE (-171)))) (-385 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL -((|HasCategory| |#1| (QUOTE (-841)))) +((|HasCategory| |#1| (QUOTE (-844)))) (-386) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-387) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1486,13 +1486,13 @@ NIL NIL (-389 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4378 . T) (-4377 . T)) +((-4385 . T) (-4384 . T)) NIL (-390) ((|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 -(-391 -3189 UP UPUP R) +(-391 -3214 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 @@ -1516,11 +1516,11 @@ 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 -(-397 -3179 |returnType| -2164 |symbols|) +(-397 -3269 |returnType| -2243 |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 -(-398 -3189 UP) +(-398 -3214 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 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.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1534,15 +1534,15 @@ NIL NIL (-401) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-402 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4366)) (|HasAttribute| |#1| (QUOTE -4374))) +((|HasAttribute| |#1| (QUOTE -4373)) (|HasAttribute| |#1| (QUOTE -4381))) (-403) ((|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\"."))) -((-1422 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-1417 . T) (-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-404 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."))) @@ -1554,20 +1554,20 @@ NIL NIL (-406 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."))) -((-4370 -12 (|has| |#1| (-6 -4381)) (|has| |#1| (-450)) (|has| |#1| (-6 -4370))) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-811))) (-3994 (|HasCategory| |#1| (QUOTE (-811))) (|HasCategory| |#1| (QUOTE (-841)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-543))) (-12 (|HasAttribute| |#1| (QUOTE -4381)) (|HasAttribute| |#1| (QUOTE -4370)) (|HasCategory| |#1| (QUOTE (-450)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((-4377 -12 (|has| |#1| (-6 -4388)) (|has| |#1| (-450)) (|has| |#1| (-6 -4377))) (-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-814))) (-4007 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#1| (QUOTE (-844)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822))))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-543))) (-12 (|HasAttribute| |#1| (QUOTE -4388)) (|HasAttribute| |#1| (QUOTE -4377)) (|HasCategory| |#1| (QUOTE (-450)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) (-407 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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 (-408 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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."))) -((-4377 . T) (-4378 . T) (-4380 . T)) +((-4384 . T) (-4385 . T) (-4387 . T)) NIL (-409 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) +((|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561))))) (-410 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL @@ -1576,14 +1576,14 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-412 R -3189 UP A) +(-412 R -3214 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)}."))) -((-4380 . T)) +((-4387 . T)) NIL -(-413 R -3189 UP A |ibasis|) +(-413 R -3214 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL -((|HasCategory| |#4| (LIST (QUOTE -1028) (|devaluate| |#2|)))) +((|HasCategory| |#4| (LIST (QUOTE -1031) (|devaluate| |#2|)))) (-414 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1594,12 +1594,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-416 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to 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{\\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."))) -((-4380 |has| |#1| (-550)) (-4378 . T) (-4377 . T)) +((-4387 |has| |#1| (-553)) (-4385 . T) (-4384 . T)) NIL (-417 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."))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1204))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-1204)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-450)))) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1209))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-450)))) (-418 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 @@ -1623,40 +1623,40 @@ NIL (-423 A S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) NIL -((|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-367)))) +((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-367)))) (-424 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4383 . T) (-4373 . T) (-4384 . T)) +((-4390 . T) (-4380 . T) (-4391 . T)) NIL -(-425 R -3189) +(-425 R -3214) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-426 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4370 -12 (|has| |#1| (-6 -4370)) (|has| |#2| (-6 -4370))) (-4377 . T) (-4378 . T) (-4380 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4370)) (|HasAttribute| |#2| (QUOTE -4370)))) -(-427 R -3189) +((-4377 -12 (|has| |#1| (-6 -4377)) (|has| |#2| (-6 -4377))) (-4384 . T) (-4385 . T) (-4387 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4377)) (|HasAttribute| |#2| (QUOTE -4377)))) +(-427 R -3214) ((|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 (-428 S R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) +((|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (-429 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| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|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}."))) -((-4380 -3994 (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) ((-4385 "*") |has| |#1| (-550)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-550)) (-4375 |has| |#1| (-550))) +((-4387 -4007 (|has| |#1| (-1042)) (|has| |#1| (-471))) (-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) ((-4392 "*") |has| |#1| (-553)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-553)) (-4382 |has| |#1| (-553))) NIL -(-430 R -3189) +(-430 R -3214) ((|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 -(-431 R -3189) +(-431 R -3214) ((|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{\\spad{ai} = \\spad{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{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-432 R -3189) +(-432 R -3214) ((|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 @@ -1664,10 +1664,10 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-434 R -3189 UP) +(-434 R -3214 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 -1028) (QUOTE (-48))))) +((|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-48))))) (-435) ((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) NIL @@ -1692,7 +1692,7 @@ 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 -(-441 R UP -3189) +(-441 R UP -3214) ((|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 @@ -1730,16 +1730,16 @@ NIL NIL (-450) ((|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}."))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-451 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"))) -((-4380 |has| (-406 (-942 |#1|)) (-550)) (-4378 . T) (-4377 . T)) -((|HasCategory| (-406 (-942 |#1|)) (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| (-406 (-942 |#1|)) (QUOTE (-550)))) +((-4387 |has| (-406 (-945 |#1|)) (-553)) (-4385 . T) (-4384 . T)) +((|HasCategory| (-406 (-945 |#1|)) (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| (-406 (-945 |#1|)) (QUOTE (-553)))) (-452 |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"))) -(((-4385 "*") |has| |#2| (-171)) (-4376 |has| |#2| (-550)) (-4381 |has| |#2| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) +(((-4392 "*") |has| |#2| (-171)) (-4383 |has| |#2| (-553)) (-4388 |has| |#2| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#2| (QUOTE (-902))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4388)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) (-453 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 @@ -1766,7 +1766,7 @@ NIL NIL (-459 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4378 . T) (-4377 . T)) +((-4385 . T) (-4384 . T)) NIL (-460 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1774,8 +1774,8 @@ NIL NIL (-461 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4384 . T) (-4383 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#4| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4391 . T) (-4390 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#4| (LIST (QUOTE -608) (QUOTE (-856))))) (-462 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL @@ -1804,7 +1804,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-469 |lv| -3189 R) +(-469 |lv| -3214 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1814,23 +1814,23 @@ NIL NIL (-471) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4380 . T)) +((-4387 . T)) NIL (-472 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|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."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -1337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) (-473 |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."))) -((-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087)))) +((-4391 . T)) +((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-844))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090)))) (-474 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)}"))) -((-4384 . T) (-4383 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4391 . T) (-4390 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -608) (QUOTE (-856))))) (-475) ((|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{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL (-476) ((|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'."))) @@ -1838,29 +1838,29 @@ NIL NIL (-477 |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."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) (-478) ((|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 (-479 |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"))) -(((-4385 "*") |has| |#2| (-171)) (-4376 |has| |#2| (-550)) (-4381 |has| |#2| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . 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(|parameters| (((|List| (|Identifier|)) $) "\\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| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL NIL (-482 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}."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-483 -3189 UP UPUP R) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-483 -3214 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 @@ -1870,12 +1870,12 @@ NIL NIL (-485) ((|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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3994 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4007 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) (-486 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 -4383)) (|HasAttribute| |#1| (QUOTE -4384)) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) +((|HasAttribute| |#1| (QUOTE -4390)) (|HasAttribute| |#1| (QUOTE -4391)) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (-487 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1896,34 +1896,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-492 -3189 UP |AlExt| |AlPol|) +(-492 -3214 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-493) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1028) (QUOTE (-558))))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| $ (QUOTE (-1042))) (|HasCategory| $ (LIST (QUOTE -1031) (QUOTE (-561))))) (-494 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-495 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."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-496 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 -(-497 R UP -3189) +(-497 R UP -3214) ((|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{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\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{\\spad{mi}} is given by \\spad{\\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{\\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{\\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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-498 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4384 . T) (-4383 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1087))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-112) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-112) (QUOTE (-1087))) (|HasCategory| (-112) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4391 . T) (-4390 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1090))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-112) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-112) (QUOTE (-1090))) (|HasCategory| (-112) (LIST (QUOTE -608) (QUOTE (-856))))) (-499 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL @@ -1936,10 +1936,10 @@ 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{\\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{\\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 -(-502 -3189 |Expon| |VarSet| |DPoly|) +(-502 -3214 |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 -606) (QUOTE (-1163))))) +((|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-1166))))) (-503 |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 @@ -1983,39 +1983,39 @@ NIL (-513 S E |un|) ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) NIL -((|HasCategory| |#2| (QUOTE (-783)))) +((|HasCategory| |#2| (QUOTE (-786)))) (-514 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}"))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-515) ((|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 (-516 |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}."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3994 (|HasCategory| (-575 |#1|) (QUOTE (-144))) (|HasCategory| (-575 |#1|) (QUOTE (-367)))) (|HasCategory| (-575 |#1|) (QUOTE (-146))) (|HasCategory| (-575 |#1|) (QUOTE (-367))) (|HasCategory| (-575 |#1|) (QUOTE (-144)))) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4007 (|HasCategory| (-578 |#1|) (QUOTE (-144))) (|HasCategory| (-578 |#1|) (QUOTE (-367)))) (|HasCategory| (-578 |#1|) (QUOTE (-146))) (|HasCategory| (-578 |#1|) (QUOTE (-367))) (|HasCategory| (-578 |#1|) (QUOTE (-144)))) (-517 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}."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-518 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."))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-519 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 -4384))) +((|HasAttribute| |#3| (QUOTE -4391))) (-520 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 -4384))) +((|HasAttribute| |#7| (QUOTE -4391))) (-521 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."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-553))) (|HasAttribute| |#1| (QUOTE (-4392 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-522) ((|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 @@ -2048,7 +2048,7 @@ 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 -(-530 K -3189 |Par|) +(-530 K -3214 |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 @@ -2072,7 +2072,7 @@ 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 -(-536 K -3189 |Par|) +(-536 K -3214 |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 @@ -2102,2931 +2102,2959 @@ NIL NIL (-543) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\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."))) -((-4381 . T) (-4382 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4388 . T) (-4389 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +NIL +(-544) +((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) +NIL +NIL +(-545) +((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) NIL -(-544 |Key| |Entry| |addDom|) +NIL +(-546) +((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) +NIL +NIL +(-547 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) -(-545 R -3189) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) +(-548 R -3214) ((|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 -(-546 R0 -3189 UP UPUP R) +(-549 R0 -3214 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 -(-547) +(-550) ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,{}m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,{}m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) NIL NIL -(-548 R) +(-551 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."))) -((-1422 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-1417 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-549 S) +(-552 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) NIL NIL -(-550) +(-553) ((|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."))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-551 R -3189) +(-554 R -3214) ((|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,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{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 -(-552 I) +(-555 I) ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra\\spad{'s} eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) NIL NIL -(-553) +(-556) ((|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 -(-554 R -3189 L) +(-557 R -3214 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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 -646) (|devaluate| |#2|)))) -(-555) +((|HasCategory| |#3| (LIST (QUOTE -649) (|devaluate| |#2|)))) +(-558) ((|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 -(-556 -3189 UP UPUP R) +(-559 -3214 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 -(-557 -3189 UP) +(-560 -3214 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 -(-558) +(-561) ((|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.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4365 . T) (-4371 . T) (-4375 . T) (-4370 . T) (-4381 . T) (-4382 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4372 . T) (-4378 . T) (-4382 . T) (-4377 . T) (-4388 . T) (-4389 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-559) +(-562) ((|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 -(-560 R -3189 L) +(-563 R -3214 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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 -646) (|devaluate| |#2|)))) -(-561 R -3189) +((|HasCategory| |#3| (LIST (QUOTE -649) (|devaluate| |#2|)))) +(-564 R -3214) ((|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 -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1126)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-621))))) -(-562 -3189 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-1129)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-624))))) +(-565 -3214 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,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{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 -(-563 S) +(-566 S) ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-564 -3189) +(-567 -3214) ((|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,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 -(-565 R) +(-568 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."))) -((-1422 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-1417 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-566) +(-569) ((|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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-567 R -3189) +(-570 R -3214) ((|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 -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-621))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-283)))) (|HasCategory| |#1| (QUOTE (-550)))) -(-568 -3189 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-624))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-283)))) (|HasCategory| |#1| (QUOTE (-553)))) +(-571 -3214 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' + +/[\\spad{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(+,{}[\\spad{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(+,{}[\\spad{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 -(-569 R -3189) +(-572 R -3214) ((|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 -(-570) +(-573) ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) NIL NIL -(-571) +(-574) ((|constructor| (NIL "\\indented{2}{This domain provides representation for binary files open} \\indented{2}{for input and output operations.} See Also: InputBinaryFile,{} OutputBinaryFile")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(f)} holds if \\spad{`f'} is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by \\spad{`f'} as a binary file."))) NIL NIL -(-572) +(-575) ((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|bothWays| (($) "`bothWays' indicates that an IO conduit is for both input and output.")) (|output| (($) "`output' indicates that an IO conduit is for output")) (|input| (($) "`input' indicates that an IO conduit is for input."))) NIL NIL -(-573) +(-576) ((|constructor| (NIL "This domain provides representation for ARPA Internet IP4 addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the IP4 address of host \\spad{`h'}.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address \\spad{`x'}.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'."))) NIL NIL -(-574 |p| |unBalanced?|) +(-577 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-575 |p|) +(-578 |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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) ((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367)))) -(-576) +(-579) ((|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 -(-577 R -3189) +(-580 R -3214) ((|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 -(-578 E -3189) +(-581 E -3214) ((|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 -(-579 -3189) +(-582 -3214) ((|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}."))) -((-4378 . T) (-4377 . T)) -((|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-1163))))) -(-580 I) +((-4385 . T) (-4384 . T)) +((|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-1166))))) +(-583 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL NIL -(-581 GF) +(-584 GF) ((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field."))) NIL NIL -(-582 R) +(-585 R) ((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL ((|HasCategory| |#1| (QUOTE (-146)))) -(-583) +(-586) ((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,{}2,{}...,{}n}} in Young\\spad{'s} natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,{}3,{}3,{}1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,{}listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young\\spad{'s} natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young\\spad{'s} natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,{}2,{}...,{}n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,{}\\spad{pi})} is the irreducible representation corresponding to partition {\\em lambda} in Young\\spad{'s} natural form of the permutation {\\em \\spad{pi}} in the symmetric group,{} whose elements permute {\\em {1,{}2,{}...,{}n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|Integer|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented."))) NIL NIL -(-584 R E V P TS) +(-587 R E V P TS) ((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,{}lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,{}univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial."))) NIL NIL -(-585) +(-588) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) NIL NIL -(-586 |mn|) +(-589 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-3994 (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) -(-587 E V R P) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-4007 (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090)))) (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +(-590 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 -(-588 |Coef|) +(-591 |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}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|)))) (|HasCategory| (-558) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) -(-589 |Coef|) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-561)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-561)) (|devaluate| |#1|)))) (|HasCategory| (-561) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-561)))))) +(-592 |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}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} 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.}"))) -((-4378 |has| |#1| (-550)) (-4377 |has| |#1| (-550)) ((-4385 "*") |has| |#1| (-550)) (-4376 |has| |#1| (-550)) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-550)))) -(-590 A B) +((-4385 |has| |#1| (-553)) (-4384 |has| |#1| (-553)) ((-4392 "*") |has| |#1| (-553)) (-4383 |has| |#1| (-553)) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-553)))) +(-593 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL NIL -(-591 A B C) +(-594 A B C) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) NIL NIL -(-592 R -3189 FG) +(-595 R -3214 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{\\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{\\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 -(-593 S) +(-596 S) ((|constructor| (NIL "\\indented{1}{This package implements 'infinite tuples' for the interpreter.} The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}s)} returns \\spad{[s,{}f(s),{}f(f(s)),{}...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}."))) NIL NIL -(-594 R |mn|) +(-597 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-595 S |Index| |Entry|) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#1| (QUOTE (-1042))) (-12 (|HasCategory| |#1| (QUOTE (-995))) (|HasCategory| |#1| (QUOTE (-1042)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-598 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 -4384)) (|HasCategory| |#2| (QUOTE (-841))) (|HasAttribute| |#1| (QUOTE -4383)) (|HasCategory| |#3| (QUOTE (-1087)))) -(-596 |Index| |Entry|) +((|HasAttribute| |#1| (QUOTE -4391)) (|HasCategory| |#2| (QUOTE (-844))) (|HasAttribute| |#1| (QUOTE -4390)) (|HasCategory| |#3| (QUOTE (-1090)))) +(-599 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL NIL -(-597) +(-600) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes."))) NIL NIL -(-598) +(-601) ((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join \\spad{`x'}.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'."))) NIL NIL -(-599 R A) +(-602 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)."))) -((-4380 -3994 (-2157 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4378 . T) (-4377 . T)) -((-3994 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) -(-600 |Entry|) +((-4387 -4007 (-2170 (|has| |#2| (-366 |#1|)) (|has| |#1| (-553))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-553)))) (-4385 . T) (-4384 . T)) +((-4007 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) +(-603 |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."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| (-1145) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (LIST (QUOTE -605) (QUOTE (-853))))) -(-601 S |Key| |Entry|) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (QUOTE (-1148))) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| (-1148) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -608) (QUOTE (-856))))) +(-604 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 -(-602 |Key| |Entry|) +(-605 |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}."))) -((-4384 . T)) +((-4391 . T)) NIL -(-603 R S) +(-606 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) NIL NIL -(-604 S) +(-607 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) -(-605 S) +((|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) +(-608 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-606 S) +(-609 S) ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-607 -3189 UP) +(-610 -3214 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 -(-608 S) +(-611 S) ((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms \\spad{`s'} into an element of `\\%'."))) NIL NIL -(-609) +(-612) ((|constructor| (NIL "This domain implements Kleene\\spad{'s} 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of \\spad{`x'} is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of \\spad{`x'} is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of \\spad{`x'} is `false'")) (|true| (($) "the definite truth value")) (|unknown| (($) "the indefinite `unknown'")) (|false| (($) "the definite falsehood value"))) NIL NIL -(-610 S) +(-613 S) ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms \\spad{`s'} into an element of `\\%'."))) NIL NIL -(-611 S R) +(-614 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) NIL NIL -(-612 R) +(-615 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."))) -((-4380 . T)) +((-4387 . T)) NIL -(-613 A R S) +(-616 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}."))) -((-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-839)))) -(-614 R -3189) +((-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-842)))) +(-617 R -3214) ((|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 -(-615 R UP) +(-618 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"))) -((-4378 . T) (-4377 . T) ((-4385 "*") . T) (-4376 . T) (-4380 . T)) -((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) -(-616 R E V P TS ST) +((-4385 . T) (-4384 . T) ((-4392 "*") . T) (-4383 . T) (-4387 . T)) +((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) +(-619 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 NIL -(-617 OV E Z P) +(-620 OV E Z P) ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \\spad{\"F\"}.")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,{}unilist,{}plead,{}vl,{}lvar,{}lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod,{} numFacts,{} evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) NIL NIL -(-618) +(-621) ((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'."))) NIL NIL -(-619 |VarSet| R |Order|) +(-622 |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}}."))) -((-4380 . T)) +((-4387 . T)) NIL -(-620 R |ls|) +(-623 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}}."))) NIL NIL -(-621) +(-624) ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-622 R -3189) +(-625 R -3214) ((|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{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\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 -(-623 |lv| -3189) +(-626 |lv| -3214) ((|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 -(-624) +(-627) ((|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}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|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."))) -((-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -1925) (QUOTE (-52))))))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1145) (QUOTE (-841))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (QUOTE (-1087)))) -(-625 S R) +((-4391 . T)) +((-12 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (QUOTE (-1148))) (LIST (QUOTE |:|) (QUOTE -2654) (QUOTE (-52))))))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-52) (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1148) (QUOTE (-844))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (QUOTE (-1090)))) +(-628 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-362)))) -(-626 R) +(-629 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4378 . T) (-4377 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4385 . T) (-4384 . T)) NIL -(-627 R A) +(-630 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4380 -3994 (-2157 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4378 . T) (-4377 . T)) -((-3994 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) -(-628 R FE) +((-4387 -4007 (-2170 (|has| |#2| (-366 |#1|)) (|has| |#1| (-553))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-553)))) (-4385 . T) (-4384 . T)) +((-4007 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) +(-631 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 NIL -(-629 R) +(-632 R) ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),{}x,{}a,{}\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) NIL NIL -(-630 S R) +(-633 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 -((-2143 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) -(-631 R) +((-2159 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) +(-634 R) ((|constructor| (NIL "An extension ring 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}."))) -((-4380 . T)) +((-4387 . T)) NIL -(-632 A B) +(-635 A B) ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) NIL NIL -(-633 A B) +(-636 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,{}u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,{}[1,{}2,{}3]) = [1,{}4,{}9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,{}[1,{}2,{}3],{}0) = fn(3,{}fn(2,{}fn(1,{}0)))} and \\spad{reduce(*,{}[2,{}3],{}1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,{}[1,{}2],{}0) = [fn(2,{}fn(1,{}0)),{}fn(1,{}0)]} and \\spad{scan(*,{}[2,{}3],{}1) = [2 * 1,{} 3 * (2 * 1)]}."))) NIL NIL -(-634 A B C) +(-637 A B C) ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,{}list1,{} u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,{}[1,{}2,{}3],{}[4,{}5,{}6]) = [1/4,{}2/4,{}1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) NIL NIL -(-635 S) +(-638 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()} returns the empty list."))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-636 T$) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-639 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL -(-637 S) +(-640 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-638 R) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-641 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL NIL -(-639 S E |un|) +(-642 S E |un|) ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,{}y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x,{} y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s,{} e,{} x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s,{} a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a,{} s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l,{} n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l,{} n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s,{} e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l,{} fop,{} fexp,{} unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a,{} b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a,{} n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) NIL NIL -(-640 A S) +(-643 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,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|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 -4384))) -(-641 S) +((|HasAttribute| |#1| (QUOTE -4391))) +(-644 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,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|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 -(-642 R -3189 L) +(-645 R -3214 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 -(-643 A) +(-646 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}}"))) -((-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) -(-644 A M) +((-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) +(-647 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) -(-645 S A) +((-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) +(-648 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL ((|HasCategory| |#2| (QUOTE (-362)))) -(-646 A) +(-649 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}."))) -((-4377 . T) (-4378 . T) (-4380 . T)) +((-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-647 -3189 UP) +(-650 -3214 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)))) -(-648 A -2511) +(-651 A -1558) ((|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}}"))) -((-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) -(-649 A L) +((-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) +(-652 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL NIL -(-650 S) +(-653 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-651) +(-654) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-652 M R S) +(-655 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}."))) -((-4378 . T) (-4377 . T)) -((|HasCategory| |#1| (QUOTE (-782)))) -(-653 R) +((-4385 . T) (-4384 . T)) +((|HasCategory| |#1| (QUOTE (-785)))) +(-656 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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) NIL NIL -(-654 |VarSet| R) +(-657 |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) (-4378 . T) (-4377 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4385 . T) (-4384 . T)) ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-171)))) -(-655 A S) +(-658 A S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) NIL NIL -(-656 S) +(-659 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}."))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL -(-657 -3189) +(-660 -3214) ((|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 -(-658 -3189 |Row| |Col| M) +(-661 -3214 |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 -(-659 R E OV P) +(-662 R E OV P) ((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,{}lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) NIL NIL -(-660 |n| R) +(-663 |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."))) -((-4380 . T) (-4383 . T) (-4377 . T) (-4378 . T)) -((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-550))) (-3994 (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) -(-661) +((-4387 . T) (-4390 . T) (-4384 . T) (-4385 . T)) +((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4392 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-553))) (-4007 (|HasAttribute| |#2| (QUOTE (-4392 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +(-664) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL NIL -(-662 |VarSet|) +(-665 |VarSet|) ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL NIL -(-663 A S) +(-666 A S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) NIL NIL -(-664 S) +(-667 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) NIL NIL -(-665 R) +(-668 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 -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-666) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-1042))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (QUOTE (-1042))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-669) ((|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 NIL -(-667 |VarSet|) +(-670 |VarSet|) ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL NIL -(-668 A) +(-671 A) ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,{}g,{}x)} is \\spad{g(n,{}g(n-1,{}..g(1,{}x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,{}n,{}x)} applies \\spad{f n} times to \\spad{x}."))) NIL NIL -(-669 A C) +(-672 A C) ((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,{}c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,{}c)} selects its first argument."))) NIL NIL -(-670 A B C) +(-673 A B C) ((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,{}g,{}x)} is \\spad{f(g x)}."))) NIL NIL -(-671) +(-674) ((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for \\spad{`s'}.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of \\spad{`s'}.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,{}t)} builds the mapping AST \\spad{s} \\spad{->} \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) NIL NIL -(-672 A) +(-675 A) ((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,{}x)= g(n,{}g(n-1,{}..g(1,{}x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,{}n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) NIL NIL -(-673 A C) +(-676 A C) ((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,{}a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) NIL NIL -(-674 A B C) +(-677 A B C) ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f(b,{}a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,{}b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,{}b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,{}b)}.}"))) NIL NIL -(-675 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +(-678 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-676 S R |Row| |Col|) +(-679 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| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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 (-4385 "*"))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-550)))) -(-677 R |Row| |Col|) +((|HasAttribute| |#2| (QUOTE (-4392 "*"))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-553)))) +(-680 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| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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"))) -((-4383 . T) (-4384 . T)) +((-4390 . T) (-4391 . T)) NIL -(-678 R |Row| |Col| M) +(-681 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."))) NIL -((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550)))) -(-679 R) +((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-553)))) +(-682 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."))) -((-4383 . T) (-4384 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-680 R) +((-4390 . T) (-4391 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-553))) (|HasAttribute| |#1| (QUOTE (-4392 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-683 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 NIL -(-681 T$) -((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "autoCoerce is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spad{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} 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|) "maybe(\\spad{x}) injects the value \\spad{`x'} into \\%."))) +(-684 T$) +((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\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 -(-682 S -3189 FLAF FLAS) +(-685 S -3214 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL -(-683 R Q) +(-686 R Q) ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) NIL NIL -(-684) +(-687) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4376 . T) (-4381 |has| (-689) (-362)) (-4375 |has| (-689) (-362)) (-4382 |has| (-689) (-6 -4382)) (-4379 |has| (-689) (-6 -4379)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-689) (QUOTE (-146))) (|HasCategory| (-689) (QUOTE (-144))) (|HasCategory| (-689) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-689) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-689) (QUOTE (-367))) (|HasCategory| (-689) (QUOTE (-362))) (-3994 (|HasCategory| (-689) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-689) (QUOTE (-362)))) (|HasCategory| (-689) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-689) (QUOTE (-232))) (-3994 (|HasCategory| (-689) (QUOTE (-362))) (|HasCategory| (-689) (QUOTE (-348)))) (|HasCategory| (-689) (QUOTE (-348))) (|HasCategory| (-689) (LIST (QUOTE -285) (QUOTE (-689)) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -308) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-689) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-689) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-689) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (-3994 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-362))) (|HasCategory| (-689) (QUOTE (-348)))) (|HasCategory| (-689) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-689) (QUOTE (-1012))) (|HasCategory| (-689) (QUOTE (-1185))) (-12 (|HasCategory| (-689) (QUOTE (-992))) (|HasCategory| (-689) (QUOTE (-1185)))) (-3994 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-362))) (-12 (|HasCategory| (-689) (QUOTE (-348))) (|HasCategory| (-689) (QUOTE (-899))))) (-3994 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (-12 (|HasCategory| (-689) (QUOTE (-362))) (|HasCategory| (-689) (QUOTE (-899)))) (-12 (|HasCategory| (-689) (QUOTE (-348))) (|HasCategory| (-689) (QUOTE (-899))))) (|HasCategory| (-689) (QUOTE (-543))) (-12 (|HasCategory| (-689) (QUOTE (-1048))) (|HasCategory| (-689) (QUOTE (-1185)))) (|HasCategory| (-689) (QUOTE (-1048))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899))) (-3994 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-362)))) (-3994 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-550)))) (-12 (|HasCategory| (-689) (QUOTE (-232))) (|HasCategory| (-689) (QUOTE (-362)))) (-12 (|HasCategory| (-689) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-689) (QUOTE (-362)))) (|HasCategory| (-689) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-689) (QUOTE (-841))) (|HasCategory| (-689) (QUOTE (-550))) (|HasAttribute| (-689) (QUOTE -4382)) (|HasAttribute| (-689) (QUOTE -4379)) (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-144)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-348))))) -(-685 S) +((-4383 . T) (-4388 |has| (-692) (-362)) (-4382 |has| (-692) (-362)) (-4389 |has| (-692) (-6 -4389)) (-4386 |has| (-692) (-6 -4386)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| (-692) (QUOTE (-146))) (|HasCategory| (-692) (QUOTE (-144))) (|HasCategory| (-692) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-692) (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| (-692) (QUOTE (-367))) (|HasCategory| (-692) (QUOTE (-362))) (-4007 (|HasCategory| (-692) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-692) (QUOTE (-362)))) (|HasCategory| (-692) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-692) (QUOTE (-232))) (-4007 (|HasCategory| (-692) (QUOTE (-362))) (|HasCategory| (-692) (QUOTE (-348)))) (|HasCategory| (-692) (QUOTE (-348))) (|HasCategory| (-692) (LIST (QUOTE -285) (QUOTE (-692)) (QUOTE (-692)))) (|HasCategory| (-692) (LIST (QUOTE -308) (QUOTE (-692)))) (|HasCategory| (-692) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-692)))) (|HasCategory| (-692) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-692) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-692) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-692) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (-4007 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-362))) (|HasCategory| (-692) (QUOTE (-348)))) (|HasCategory| (-692) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-692) (QUOTE (-1015))) (|HasCategory| (-692) (QUOTE (-1190))) (-12 (|HasCategory| (-692) (QUOTE (-995))) (|HasCategory| (-692) (QUOTE (-1190)))) (-4007 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-362))) (-12 (|HasCategory| (-692) (QUOTE (-348))) (|HasCategory| (-692) (QUOTE (-902))))) (-4007 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (-12 (|HasCategory| (-692) (QUOTE (-362))) (|HasCategory| (-692) (QUOTE (-902)))) (-12 (|HasCategory| (-692) (QUOTE (-348))) (|HasCategory| (-692) (QUOTE (-902))))) (|HasCategory| (-692) (QUOTE (-543))) (-12 (|HasCategory| (-692) (QUOTE (-1051))) (|HasCategory| (-692) (QUOTE (-1190)))) (|HasCategory| (-692) (QUOTE (-1051))) (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902))) (-4007 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-362)))) (-4007 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-553)))) (-12 (|HasCategory| (-692) (QUOTE (-232))) (|HasCategory| (-692) (QUOTE (-362)))) (-12 (|HasCategory| (-692) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-692) (QUOTE (-362)))) (|HasCategory| (-692) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-692) (QUOTE (-844))) (|HasCategory| (-692) (QUOTE (-553))) (|HasAttribute| (-692) (QUOTE -4389)) (|HasAttribute| (-692) (QUOTE -4386)) (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-144)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-348))))) +(-688 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}."))) -((-4384 . T)) +((-4391 . T)) NIL -(-686 U) +(-689 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}."))) NIL NIL -(-687) +(-690) ((|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 -(-688 OV E -3189 PG) +(-691 OV E -3214 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 -(-689) +(-692) ((|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}"))) -((-1422 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-1417 . T) (-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-690 R) +(-693 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) NIL NIL -(-691) +(-694) ((|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}"))) -((-4382 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4389 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-692 S D1 D2 I) +(-695 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,{}x,{}y)} returns a function \\spad{f: (D1,{} D2) -> I} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1,{} D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) NIL NIL -(-693 S) +(-696 S) ((|constructor| (NIL "MakeCachableSet(\\spad{S}) returns a cachable set which is equal to \\spad{S} as a set."))) NIL NIL -(-694 S) +(-697 S) ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x,{} y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) NIL NIL -(-695 S) +(-698 S) ((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e,{} foo,{} [x1,{}...,{}xn])} creates a function \\spad{foo(x1,{}...,{}xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x,{} y)} creates a function \\spad{foo(x,{} y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e,{} foo)} creates a function \\spad{foo() == e}."))) NIL NIL -(-696 S T$) +(-699 S T$) ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-697 S -3042 I) +(-700 S -3122 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 -(-698 E OV R P) +(-701 E OV R P) ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,{}lv,{}lu,{}lr,{}lp,{}lt,{}ln,{}t,{}r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,{}lv,{}lu,{}lr,{}lp,{}ln,{}r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,{}lv,{}lr,{}ln,{}lu,{}t,{}r)} \\undocumented"))) NIL NIL -(-699 R) +(-702 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)}.}"))) -((-4377 . T) (-4378 . T) (-4380 . T)) +((-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-700 R1 UP1 UPUP1 R2 UP2 UPUP2) +(-703 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f,{} p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) NIL NIL -(-701) +(-704) ((|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 -(-702 R |Mod| -2915 -3391 |exactQuo|) +(-705 R |Mod| -3471 -1407 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-703 R |Rep|) +(-706 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4379 |has| |#1| (-362)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) -(-704 IS E |ff|) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4386 |has| |#1| (-362)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +(-707 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL -(-705 R M) +(-708 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) (-4380 . T)) +((-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) (-4387 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146)))) -(-706 R |Mod| -2915 -3391 |exactQuo|) +(-709 R |Mod| -3471 -1407 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4380 . T)) +((-4387 . T)) NIL -(-707 S R) +(-710 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) NIL NIL -(-708 R) +(-711 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4378 . T) (-4377 . T)) +((-4385 . T) (-4384 . T)) NIL -(-709 -3189) +(-712 -3214) ((|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]]}."))) -((-4380 . T)) +((-4387 . T)) NIL -(-710 S) +(-713 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-711) +(-714) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-712 S) +(-715 S) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'t} a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\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 such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-713) +(-716) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'t} a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\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 such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-714 S R UP) +(-717 S R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) NIL ((|HasCategory| |#2| (QUOTE (-348))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-367)))) -(-715 R UP) +(-718 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."))) -((-4376 |has| |#1| (-362)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 |has| |#1| (-362)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-716 S) +(-719 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-717) +(-720) ((|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 -(-718 -3189 UP) +(-721 -3214 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 -(-719 |VarSet| E1 E2 R S PR PS) +(-722 |VarSet| E1 E2 R S PR PS) ((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (\\spad{PG})")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,{}p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,{}p)} \\undocumented"))) NIL NIL -(-720 |Vars1| |Vars2| E1 E2 R PR1 PR2) +(-723 |Vars1| |Vars2| E1 E2 R PR1 PR2) ((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-721 E OV R PPR) +(-724 E OV R PPR) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-722 |vl| R) +(-725 |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."))) -(((-4385 "*") |has| |#2| (-171)) (-4376 |has| |#2| (-550)) (-4381 |has| |#2| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) -(-723 E OV R PRF) +(((-4392 "*") |has| |#2| (-171)) (-4383 |has| |#2| (-553)) (-4388 |has| |#2| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#2| (QUOTE (-902))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4388)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) +(-726 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-724 E OV R P) +(-727 E OV R P) ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) NIL NIL -(-725 R S M) +(-728 R S M) ((|constructor| (NIL "MonoidRingFunctions2 implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,{}u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) NIL NIL -(-726 R M) +(-729 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) (-4380 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-841)))) -(-727 S) +((-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) (-4387 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-844)))) +(-730 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4373 . T) (-4384 . T)) +((-4380 . T) (-4391 . T)) NIL -(-728 S) +(-731 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}."))) -((-4383 . T) (-4373 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-729) +((-4390 . T) (-4380 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-732) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL NIL -(-730 S) +(-733 S) ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,{}l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) NIL NIL -(-731 |Coef| |Var|) +(-734 |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}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4378 . T) (-4377 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4385 . T) (-4384 . T) (-4387 . T)) NIL -(-732 OV E R P) +(-735 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) NIL NIL -(-733 E OV R P) +(-736 E OV R P) ((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) NIL NIL -(-734 S R) +(-737 S 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}."))) NIL NIL -(-735 R) +(-738 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}."))) -((-4378 . T) (-4377 . T)) +((-4385 . T) (-4384 . T)) NIL -(-736) +(-739) ((|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}."))) NIL NIL -(-737) +(-740) ((|constructor| (NIL "This package uses the NAG Library to calculate real zeros of continuous real functions of one or more variables. (Complex equations must be expressed in terms of the equivalent larger system of real equations.) See \\downlink{Manual Page}{manpageXXc05}.")) (|c05pbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN)))) "\\spad{c05pbf(n,{}ldfjac,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. The user must provide the Jacobian. See \\downlink{Manual Page}{manpageXXc05pbf}.")) (|c05nbf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN)))) "\\spad{c05nbf(n,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. See \\downlink{Manual Page}{manpageXXc05nbf}.")) (|c05adf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{c05adf(a,{}b,{}eps,{}eta,{}ifail,{}f)} locates a zero of a continuous function in a given interval by a combination of the methods of linear interpolation,{} extrapolation and bisection. See \\downlink{Manual Page}{manpageXXc05adf}."))) NIL NIL -(-738) +(-741) ((|constructor| (NIL "This package uses the NAG Library to calculate the discrete Fourier transform of a sequence of real or complex data values,{} and applies it to calculate convolutions and correlations. See \\downlink{Manual Page}{manpageXXc06}.")) (|c06gsf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gsf(m,{}n,{}x,{}ifail)} takes \\spad{m} Hermitian sequences,{} each containing \\spad{n} data values,{} and forms the real and imaginary parts of the \\spad{m} corresponding complex sequences. See \\downlink{Manual Page}{manpageXXc06gsf}.")) (|c06gqf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gqf(m,{}n,{}x,{}ifail)} forms the complex conjugates,{} each containing \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gqf}.")) (|c06gcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gcf(n,{}y,{}ifail)} forms the complex conjugate of a sequence of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gcf}.")) (|c06gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gbf(n,{}x,{}ifail)} forms the complex conjugate of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gbf}.")) (|c06fuf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fuf(m,{}n,{}init,{}x,{}y,{}trigm,{}trign,{}ifail)} computes the two-dimensional discrete Fourier transform of a bivariate sequence of complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fuf}.")) (|c06frf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06frf(m,{}n,{}init,{}x,{}y,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06frf}.")) (|c06fqf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fqf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} Hermitian sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fqf}.")) (|c06fpf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fpf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} real data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fpf}.")) (|c06ekf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ekf(job,{}n,{}x,{}y,{}ifail)} calculates the circular convolution of two real vectors of period \\spad{n}. No extra workspace is required. See \\downlink{Manual Page}{manpageXXc06ekf}.")) (|c06ecf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ecf(n,{}x,{}y,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ecf}.")) (|c06ebf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ebf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a Hermitian sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ebf}.")) (|c06eaf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06eaf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} real data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06eaf}."))) NIL NIL -(-739) +(-742) ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical value of definite integrals in one or more dimensions and to evaluate weights and abscissae of integration rules. See \\downlink{Manual Page}{manpageXXd01}.")) (|d01gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01gbf(ndim,{}a,{}b,{}maxcls,{}eps,{}lenwrk,{}mincls,{}wrkstr,{}ifail,{}functn)} returns an approximation to the integral of a function over a hyper-rectangular region,{} using a Monte Carlo method. An approximate relative error estimate is also returned. This routine is suitable for low accuracy work. See \\downlink{Manual Page}{manpageXXd01gbf}.")) (|d01gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|)) "\\spad{d01gaf(x,{}y,{}n,{}ifail)} integrates a function which is specified numerically at four or more points,{} over the whole of its specified range,{} using third-order finite-difference formulae with error estimates,{} according to a method due to Gill and Miller. See \\downlink{Manual Page}{manpageXXd01gaf}.")) (|d01fcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01fcf(ndim,{}a,{}b,{}maxpts,{}eps,{}lenwrk,{}minpts,{}ifail,{}functn)} attempts to evaluate a multi-dimensional integral (up to 15 dimensions),{} with constant and finite limits,{} to a specified relative accuracy,{} using an adaptive subdivision strategy. See \\downlink{Manual Page}{manpageXXd01fcf}.")) (|d01bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{d01bbf(a,{}b,{}itype,{}n,{}gtype,{}ifail)} returns the weight appropriate to a Gaussian quadrature. The formulae provided are Gauss-Legendre,{} Gauss-Rational,{} Gauss- Laguerre and Gauss-Hermite. See \\downlink{Manual Page}{manpageXXd01bbf}.")) (|d01asf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01asf(a,{}omega,{}key,{}epsabs,{}limlst,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}infty): See \\downlink{Manual Page}{manpageXXd01asf}.")) (|d01aqf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01aqf(a,{}b,{}c,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the Hilbert transform of a function \\spad{g}(\\spad{x}) over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01aqf}.")) (|d01apf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01apf(a,{}b,{}alfa,{}beta,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} is an adaptive integrator which calculates an approximation to the integral of a function \\spad{g}(\\spad{x})\\spad{w}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01apf}.")) (|d01anf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01anf(a,{}b,{}omega,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01anf}.")) (|d01amf| (((|Result|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01amf(bound,{}inf,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over an infinite or semi-infinite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01amf}.")) (|d01alf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01alf(a,{}b,{}npts,{}points,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01alf}.")) (|d01akf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01akf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is an adaptive integrator,{} especially suited to oscillating,{} non-singular integrands,{} which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01akf}.")) (|d01ajf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01ajf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general-purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01ajf}."))) NIL NIL -(-740) +(-743) ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical solution of ordinary differential equations. There are two main types of problem,{} those in which all boundary conditions are specified at one point (initial-value problems),{} and those in which the boundary conditions are distributed between two or more points (boundary- value problems and eigenvalue problems). Routines are available for initial-value problems,{} two-point boundary-value problems and Sturm-Liouville eigenvalue problems. See \\downlink{Manual Page}{manpageXXd02}.")) (|d02raf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp41| FCN JACOBF JACEPS))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp42| G JACOBG JACGEP)))) "\\spad{d02raf(n,{}mnp,{}numbeg,{}nummix,{}tol,{}init,{}iy,{}ijac,{}lwork,{}liwork,{}np,{}x,{}y,{}deleps,{}ifail,{}fcn,{}g)} solves the two-point boundary-value problem with general boundary conditions for a system of ordinary differential equations,{} using a deferred correction technique and Newton iteration. See \\downlink{Manual Page}{manpageXXd02raf}.")) (|d02kef| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL))) (|FileName|) (|FileName|)) "\\spad{d02kef(xpoint,{}m,{}k,{}tol,{}maxfun,{}match,{}elam,{}delam,{}hmax,{}maxit,{}ifail,{}coeffn,{}bdyval,{}monit,{}report)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. Files \\spad{monit} and \\spad{report} will be used to define the subroutines for the MONIT and REPORT arguments. See \\downlink{Manual Page}{manpageXXd02gbf}.") (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL)))) "\\spad{d02kef(xpoint,{}m,{}k,{}tol,{}maxfun,{}match,{}elam,{}delam,{}hmax,{}maxit,{}ifail,{}coeffn,{}bdyval)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. ASP domains Asp12 and Asp33 are used to supply default subroutines for the MONIT and REPORT arguments via their \\axiomOp{outputAsFortran} operation.")) (|d02gbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp77| FCNF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp78| FCNG)))) "\\spad{d02gbf(a,{}b,{}n,{}tol,{}mnp,{}lw,{}liw,{}c,{}d,{}gam,{}x,{}np,{}ifail,{}fcnf,{}fcng)} solves a general linear two-point boundary value problem for a system of ordinary differential equations using a deferred correction technique. See \\downlink{Manual Page}{manpageXXd02gbf}.")) (|d02gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02gaf(u,{}v,{}n,{}a,{}b,{}tol,{}mnp,{}lw,{}liw,{}x,{}np,{}ifail,{}fcn)} solves the two-point boundary-value problem with assigned boundary values for a system of ordinary differential equations,{} using a deferred correction technique and a Newton iteration. See \\downlink{Manual Page}{manpageXXd02gaf}.")) (|d02ejf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp31| PEDERV))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02ejf(xend,{}m,{}n,{}relabs,{}iw,{}x,{}y,{}tol,{}ifail,{}g,{}fcn,{}pederv,{}output)} integrates a stiff system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a variable-order,{} variable-step method implementing the Backward Differentiation Formulae (\\spad{BDF}),{} until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02ejf}.")) (|d02cjf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|String|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02cjf(xend,{}m,{}n,{}tol,{}relabs,{}x,{}y,{}ifail,{}g,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over a range with suitable initial conditions,{} using a variable-order,{} variable-step Adams method until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02cjf}.")) (|d02bhf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02bhf(xend,{}n,{}irelab,{}hmax,{}x,{}y,{}tol,{}ifail,{}g,{}fcn)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} until a user-specified function of the solution is zero. See \\downlink{Manual Page}{manpageXXd02bhf}.")) (|d02bbf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02bbf(xend,{}m,{}n,{}irelab,{}x,{}y,{}tol,{}ifail,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} and returns the solution at points specified by the user. See \\downlink{Manual Page}{manpageXXd02bbf}."))) NIL NIL -(-741) +(-744) ((|constructor| (NIL "This package uses the NAG Library to solve partial differential equations. See \\downlink{Manual Page}{manpageXXd03}.")) (|d03faf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|ThreeDimensionalMatrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03faf(xs,{}xf,{}l,{}lbdcnd,{}bdxs,{}bdxf,{}ys,{}yf,{}m,{}mbdcnd,{}bdys,{}bdyf,{}zs,{}zf,{}n,{}nbdcnd,{}bdzs,{}bdzf,{}lambda,{}ldimf,{}mdimf,{}lwrk,{}f,{}ifail)} solves the Helmholtz equation in Cartesian co-ordinates in three dimensions using the standard seven-point finite difference approximation. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXd03faf}.")) (|d03eef| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp73| PDEF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp74| BNDY)))) "\\spad{d03eef(xmin,{}xmax,{}ymin,{}ymax,{}ngx,{}ngy,{}lda,{}scheme,{}ifail,{}pdef,{}bndy)} discretizes a second order elliptic partial differential equation (PDE) on a rectangular region. See \\downlink{Manual Page}{manpageXXd03eef}.")) (|d03edf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03edf(ngx,{}ngy,{}lda,{}maxit,{}acc,{}iout,{}a,{}rhs,{}ub,{}ifail)} solves seven-diagonal systems of linear equations which arise from the discretization of an elliptic partial differential equation on a rectangular region. This routine uses a multigrid technique. See \\downlink{Manual Page}{manpageXXd03edf}."))) NIL NIL -(-742) +(-745) ((|constructor| (NIL "This package uses the NAG Library to calculate the interpolation of a function of one or two variables. When provided with the value of the function (and possibly one or more of its lowest-order derivatives) at each of a number of values of the variable(\\spad{s}),{} the routines provide either an interpolating function or an interpolated value. For some of the interpolating functions,{} there are supporting routines to evaluate,{} differentiate or integrate them. See \\downlink{Manual Page}{manpageXXe01}.")) (|e01sff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sff(m,{}x,{}y,{}f,{}rnw,{}fnodes,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolating function computed by E01SEF. See \\downlink{Manual Page}{manpageXXe01sff}.")) (|e01sef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sef(m,{}x,{}y,{}f,{}nw,{}nq,{}rnw,{}rnq,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using a modified Shepard method. See \\downlink{Manual Page}{manpageXXe01sef}.")) (|e01sbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sbf(m,{}x,{}y,{}f,{}triang,{}grads,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolant function computed by E01SAF. See \\downlink{Manual Page}{manpageXXe01sbf}.")) (|e01saf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01saf(m,{}x,{}y,{}f,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using the method of Renka and Cline. See \\downlink{Manual Page}{manpageXXe01saf}.")) (|e01daf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01daf(mx,{}my,{}x,{}y,{}f,{}ifail)} computes a bicubic spline interpolating surface through a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. See \\downlink{Manual Page}{manpageXXe01daf}.")) (|e01bhf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01bhf(n,{}x,{}f,{}d,{}a,{}b,{}ifail)} evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval [a,{}\\spad{b}]. See \\downlink{Manual Page}{manpageXXe01bhf}.")) (|e01bgf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bgf(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points. See \\downlink{Manual Page}{manpageXXe01bgf}.")) (|e01bff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bff(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant at a set of points. See \\downlink{Manual Page}{manpageXXe01bff}.")) (|e01bef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bef(n,{}x,{}f,{}ifail)} computes a monotonicity-preserving piecewise cubic Hermite interpolant to a set of data points. See \\downlink{Manual Page}{manpageXXe01bef}.")) (|e01baf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e01baf(m,{}x,{}y,{}lck,{}lwrk,{}ifail)} determines a cubic spline to a given set of data. See \\downlink{Manual Page}{manpageXXe01baf}."))) NIL NIL -(-743) +(-746) ((|constructor| (NIL "This package uses the NAG Library to find a function which approximates a set of data points. Typically the data contain random errors,{} as of experimental measurement,{} which need to be smoothed out. To seek an approximation to the data,{} it is first necessary to specify for the approximating function a mathematical form (a polynomial,{} for example) which contains a number of unspecified coefficients: the appropriate fitting routine then derives for the coefficients the values which provide the best fit of that particular form. The package deals mainly with curve and surface fitting (\\spadignore{i.e.} fitting with functions of one and of two variables) when a polynomial or a cubic spline is used as the fitting function,{} since these cover the most common needs. However,{} fitting with other functions and/or more variables can be undertaken by means of general linear or nonlinear routines (some of which are contained in other packages) depending on whether the coefficients in the function occur linearly or nonlinearly. Cases where a graph rather than a set of data points is given can be treated simply by first reading a suitable set of points from the graph. The package also contains routines for evaluating,{} differentiating and integrating polynomial and spline curves and surfaces,{} once the numerical values of their coefficients have been determined. See \\downlink{Manual Page}{manpageXXe02}.")) (|e02zaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02zaf(px,{}py,{}lamda,{}mu,{}m,{}x,{}y,{}npoint,{}nadres,{}ifail)} sorts two-dimensional data into rectangular panels. See \\downlink{Manual Page}{manpageXXe02zaf}.")) (|e02gaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02gaf(m,{}la,{}nplus2,{}toler,{}a,{}b,{}ifail)} calculates an \\spad{l} solution to an over-determined system of \\indented{22}{1} linear equations. See \\downlink{Manual Page}{manpageXXe02gaf}.")) (|e02dff| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02dff(mx,{}my,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}lwrk,{}liwrk,{}ifail)} calculates values of a bicubic spline representation. The spline is evaluated at all points on a rectangular grid. See \\downlink{Manual Page}{manpageXXe02dff}.")) (|e02def| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02def(m,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}ifail)} calculates values of a bicubic spline representation. See \\downlink{Manual Page}{manpageXXe02def}.")) (|e02ddf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02ddf(start,{}m,{}x,{}y,{}f,{}w,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{}lamda,{}ny,{}mu,{}wrk,{}ifail)} computes a bicubic spline approximation to a set of scattered data are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02ddf}.")) (|e02dcf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{e02dcf(start,{}mx,{}x,{}my,{}y,{}f,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{}lamda,{}ny,{}mu,{}wrk,{}iwrk,{}ifail)} computes a bicubic spline approximation to a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. The knots of the spline are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02dcf}.")) (|e02daf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02daf(m,{}px,{}py,{}x,{}y,{}f,{}w,{}mu,{}point,{}npoint,{}nc,{}nws,{}eps,{}lamda,{}ifail)} forms a minimal,{} weighted least-squares bicubic spline surface fit with prescribed knots to a given set of data points. See \\downlink{Manual Page}{manpageXXe02daf}.")) (|e02bef| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|))) "\\spad{e02bef(start,{}m,{}x,{}y,{}w,{}s,{}nest,{}lwrk,{}n,{}lamda,{}ifail,{}wrk,{}iwrk)} computes a cubic spline approximation to an arbitrary set of data points. The knot are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02bef}.")) (|e02bdf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02bdf(ncap7,{}lamda,{}c,{}ifail)} computes the definite integral from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bdf}.")) (|e02bcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|)) "\\spad{e02bcf(ncap7,{}lamda,{}c,{}x,{}left,{}ifail)} evaluates a cubic spline and its first three derivatives from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bcf}.")) (|e02bbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02bbf(ncap7,{}lamda,{}c,{}x,{}ifail)} evaluates a cubic spline representation. See \\downlink{Manual Page}{manpageXXe02bbf}.")) (|e02baf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02baf(m,{}ncap7,{}x,{}y,{}w,{}lamda,{}ifail)} computes a weighted least-squares approximation to an arbitrary set of data points by a cubic splines prescribed by the user. Cubic spline can also be carried out. See \\downlink{Manual Page}{manpageXXe02baf}.")) (|e02akf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|)) "\\spad{e02akf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}x,{}ifail)} evaluates a polynomial from its Chebyshev-series representation,{} allowing an arbitrary index increment for accessing the array of coefficients. See \\downlink{Manual Page}{manpageXXe02akf}.")) (|e02ajf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ajf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}qatm1,{}iaint1,{}laint,{}ifail)} determines the coefficients in the Chebyshev-series representation of the indefinite integral of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ajf}.")) (|e02ahf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ahf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}iadif1,{}ladif,{}ifail)} determines the coefficients in the Chebyshev-series representation of the derivative of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ahf}.")) (|e02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02agf(m,{}kplus1,{}nrows,{}xmin,{}xmax,{}x,{}y,{}w,{}mf,{}xf,{}yf,{}lyf,{}ip,{}lwrk,{}liwrk,{}ifail)} computes constrained weighted least-squares polynomial approximations in Chebyshev-series form to an arbitrary set of data points. The values of the approximations and any number of their derivatives can be specified at selected points. See \\downlink{Manual Page}{manpageXXe02agf}.")) (|e02aef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02aef(nplus1,{}a,{}xcap,{}ifail)} evaluates a polynomial from its Chebyshev-series representation. See \\downlink{Manual Page}{manpageXXe02aef}.")) (|e02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02adf(m,{}kplus1,{}nrows,{}x,{}y,{}w,{}ifail)} computes weighted least-squares polynomial approximations to an arbitrary set of data points. See \\downlink{Manual Page}{manpageXXe02adf}."))) NIL NIL -(-744) +(-747) ((|constructor| (NIL "This package uses the NAG Library to perform optimization. An optimization problem involves minimizing a function (called the objective function) of several variables,{} possibly subject to restrictions on the values of the variables defined by a set of constraint functions. The routines in the NAG Foundation Library are concerned with function minimization only,{} since the problem of maximizing a given function can be transformed into a minimization problem simply by multiplying the function by \\spad{-1}. See \\downlink{Manual Page}{manpageXXe04}.")) (|e04ycf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04ycf(job,{}m,{}n,{}fsumsq,{}s,{}lv,{}v,{}ifail)} returns estimates of elements of the variance matrix of the estimated regression coefficients for a nonlinear least squares problem. The estimates are derived from the Jacobian of the function \\spad{f}(\\spad{x}) at the solution. See \\downlink{Manual Page}{manpageXXe04ycf}.")) (|e04ucf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Boolean|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp55| CONFUN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04ucf(n,{}nclin,{}ncnln,{}nrowa,{}nrowj,{}nrowr,{}a,{}bl,{}bu,{}liwork,{}lwork,{}sta,{}cra,{}der,{}fea,{}fun,{}hes,{}infb,{}infs,{}linf,{}lint,{}list,{}maji,{}majp,{}mini,{}minp,{}mon,{}nonf,{}opt,{}ste,{}stao,{}stac,{}stoo,{}stoc,{}ve,{}istate,{}cjac,{}clamda,{}r,{}x,{}ifail,{}confun,{}objfun)} is designed to minimize an arbitrary smooth function subject to constraints on the variables,{} linear constraints. (E04UCF may be used for unconstrained,{} bound-constrained and linearly constrained optimization.) The user must provide subroutines that define the objective and constraint functions and as many of their first partial derivatives as possible. Unspecified derivatives are approximated by finite differences. All matrices are treated as dense,{} and hence E04UCF is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04ucf}.")) (|e04naf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Boolean|) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp20| QPHESS)))) "\\spad{e04naf(itmax,{}msglvl,{}n,{}nclin,{}nctotl,{}nrowa,{}nrowh,{}ncolh,{}bigbnd,{}a,{}bl,{}bu,{}cvec,{}featol,{}hess,{}cold,{}lpp,{}orthog,{}liwork,{}lwork,{}x,{}istate,{}ifail,{}qphess)} is a comprehensive programming (\\spad{QP}) or linear programming (\\spad{LP}) problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04naf}.")) (|e04mbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04mbf(itmax,{}msglvl,{}n,{}nclin,{}nctotl,{}nrowa,{}a,{}bl,{}bu,{}cvec,{}linobj,{}liwork,{}lwork,{}x,{}ifail)} is an easy-to-use routine for solving linear programming problems,{} or for finding a feasible point for such problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04mbf}.")) (|e04jaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp24| FUNCT1)))) "\\spad{e04jaf(n,{}ibound,{}liw,{}lw,{}bl,{}bu,{}x,{}ifail,{}funct1)} is an easy-to-use quasi-Newton algorithm for finding a minimum of a function \\spad{F}(\\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ),{} subject to fixed upper and \\indented{25}{1\\space{2}2\\space{6}\\spad{n}} lower bounds of the independent variables \\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ,{} using \\indented{43}{1\\space{2}2\\space{6}\\spad{n}} function values only. See \\downlink{Manual Page}{manpageXXe04jaf}.")) (|e04gcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp19| LSFUN2)))) "\\spad{e04gcf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun2)} is an easy-to-use quasi-Newton algorithm for finding an unconstrained minimum of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). First derivatives are required. See \\downlink{Manual Page}{manpageXXe04gcf}.")) (|e04fdf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp50| LSFUN1)))) "\\spad{e04fdf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun1)} is an easy-to-use algorithm for finding an unconstrained minimum of a sum of squares of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). No derivatives are required. See \\downlink{Manual Page}{manpageXXe04fdf}.")) (|e04dgf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04dgf(n,{}es,{}fu,{}it,{}lin,{}list,{}ma,{}op,{}pr,{}sta,{}sto,{}ve,{}x,{}ifail,{}objfun)} minimizes an unconstrained nonlinear function of several variables using a pre-conditioned,{} limited memory quasi-Newton conjugate gradient method. First derivatives are required. The routine is intended for use on large scale problems. See \\downlink{Manual Page}{manpageXXe04dgf}."))) NIL NIL -(-745) +(-748) ((|constructor| (NIL "This package uses the NAG Library to provide facilities for matrix factorizations and associated transformations. See \\downlink{Manual Page}{manpageXXf01}.")) (|f01ref| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01ref(wheret,{}m,{}n,{}ncolq,{}lda,{}theta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the complex \\spad{m} by \\spad{m} unitary matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01ref}.")) (|f01rdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}theta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01rdf}.")) (|f01rcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the complex \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01rcf}.")) (|f01qef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qef(wheret,{}m,{}n,{}ncolq,{}lda,{}zeta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the real \\spad{m} by \\spad{m} orthogonal matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01qef}.")) (|f01qdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}zeta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01qdf}.")) (|f01qcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the real \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01qcf}.")) (|f01mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01mcf(n,{}avals,{}lal,{}nrow,{}ifail)} computes the Cholesky factorization of a real symmetric positive-definite variable-bandwidth matrix. See \\downlink{Manual Page}{manpageXXf01mcf}.")) (|f01maf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{f01maf(n,{}nz,{}licn,{}lirn,{}abort,{}avals,{}irn,{}icn,{}droptl,{}densw,{}ifail)} computes an incomplete Cholesky factorization of a real sparse symmetric positive-definite matrix A. See \\downlink{Manual Page}{manpageXXf01maf}.")) (|f01bsf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Boolean|) (|DoubleFloat|) (|Boolean|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01bsf(n,{}nz,{}licn,{}ivect,{}jvect,{}icn,{}ikeep,{}grow,{}eta,{}abort,{}idisp,{}avals,{}ifail)} factorizes a real sparse matrix using the pivotal sequence previously obtained by F01BRF when a matrix of the same sparsity pattern was factorized. See \\downlink{Manual Page}{manpageXXf01bsf}.")) (|f01brf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Boolean|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01brf(n,{}nz,{}licn,{}lirn,{}pivot,{}lblock,{}grow,{}abort,{}a,{}irn,{}icn,{}ifail)} factorizes a real sparse matrix. The routine either forms the LU factorization of a permutation of the entire matrix,{} or,{} optionally,{} first permutes the matrix to block lower triangular form and then only factorizes the diagonal blocks. See \\downlink{Manual Page}{manpageXXf01brf}."))) NIL NIL -(-746) +(-749) ((|constructor| (NIL "This package uses the NAG Library to compute \\begin{items} \\item eigenvalues and eigenvectors of a matrix \\item eigenvalues and eigenvectors of generalized matrix eigenvalue problems \\item singular values and singular vectors of a matrix. \\end{items} See \\downlink{Manual Page}{manpageXXf02}.")) (|f02xef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f02xef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldph,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general complex matrix. See \\downlink{Manual Page}{manpageXXf02xef}.")) (|f02wef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02wef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldpt,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general real matrix. See \\downlink{Manual Page}{manpageXXf02wef}.")) (|f02fjf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE))) (|FileName|)) "\\spad{f02fjf(n,{}k,{}tol,{}novecs,{}nrx,{}lwork,{}lrwork,{}liwork,{}m,{}noits,{}x,{}ifail,{}dot,{}image,{}monit)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.") (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE)))) "\\spad{f02fjf(n,{}k,{}tol,{}novecs,{}nrx,{}lwork,{}lrwork,{}liwork,{}m,{}noits,{}x,{}ifail,{}dot,{}image)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.")) (|f02bjf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bjf(n,{}ia,{}ib,{}eps1,{}matv,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues and,{} if required,{} all the eigenvectors of the generalized eigenproblem Ax=(lambda)\\spad{Bx} where A and \\spad{B} are real,{} square matrices,{} using the \\spad{QZ} algorithm. See \\downlink{Manual Page}{manpageXXf02bjf}.")) (|f02bbf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bbf(ia,{}n,{}alb,{}ub,{}m,{}iv,{}a,{}ifail)} calculates selected eigenvalues of a real symmetric matrix by reduction to tridiagonal form,{} bisection and inverse iteration,{} where the selected eigenvalues lie within a given interval. See \\downlink{Manual Page}{manpageXXf02bbf}.")) (|f02axf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02axf(ar,{}iar,{}\\spad{ai},{}iai,{}n,{}ivr,{}ivi,{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02axf}.")) (|f02awf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02awf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02awf}.")) (|f02akf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02akf(iar,{}iai,{}n,{}ivr,{}ivi,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex matrix. See \\downlink{Manual Page}{manpageXXf02akf}.")) (|f02ajf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02ajf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02ajf}.")) (|f02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02agf(ia,{}n,{}ivr,{}ivi,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02agf}.")) (|f02aff| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aff(ia,{}n,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02aff}.")) (|f02aef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aef(ia,{}ib,{}n,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf02aef}.")) (|f02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02adf(ia,{}ib,{}n,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive- definite matrix. See \\downlink{Manual Page}{manpageXXf02adf}.")) (|f02abf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02abf(a,{}ia,{}n,{}iv,{}ifail)} calculates all the eigenvalues of a real symmetric matrix. See \\downlink{Manual Page}{manpageXXf02abf}.")) (|f02aaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aaf(ia,{}n,{}a,{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02aaf}."))) NIL NIL -(-747) +(-750) ((|constructor| (NIL "This package uses the NAG Library to solve the matrix equation \\axiom{AX=B},{} where \\axiom{\\spad{B}} may be a single vector or a matrix of multiple right-hand sides. The matrix \\axiom{A} may be real,{} complex,{} symmetric,{} Hermitian positive- definite,{} or sparse. It may also be rectangular,{} in which case a least-squares solution is obtained. See \\downlink{Manual Page}{manpageXXf04}.")) (|f04qaf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp30| APROD)))) "\\spad{f04qaf(m,{}n,{}damp,{}atol,{}btol,{}conlim,{}itnlim,{}msglvl,{}lrwork,{}liwork,{}b,{}ifail,{}aprod)} solves sparse unsymmetric equations,{} sparse linear least- squares problems and sparse damped linear least-squares problems,{} using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04qaf}.")) (|f04mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04mcf(n,{}al,{}lal,{}d,{}nrow,{}ir,{}b,{}nrb,{}iselct,{}nrx,{}ifail)} computes the approximate solution of a system of real linear equations with multiple right-hand sides,{} AX=B,{} where A is a symmetric positive-definite variable-bandwidth matrix,{} which has previously been factorized by F01MCF. Related systems may also be solved. See \\downlink{Manual Page}{manpageXXf04mcf}.")) (|f04mbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| APROD))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp34| MSOLVE)))) "\\spad{f04mbf(n,{}b,{}precon,{}shift,{}itnlim,{}msglvl,{}lrwork,{}liwork,{}rtol,{}ifail,{}aprod,{}msolve)} solves a system of real sparse symmetric linear equations using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04mbf}.")) (|f04maf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f04maf(n,{}nz,{}avals,{}licn,{}irn,{}lirn,{}icn,{}wkeep,{}ikeep,{}inform,{}b,{}acc,{}noits,{}ifail)} \\spad{e} a sparse symmetric positive-definite system of linear equations,{} Ax=b,{} using a pre-conditioned conjugate gradient method,{} where A has been factorized by F01MAF. See \\downlink{Manual Page}{manpageXXf04maf}.")) (|f04jgf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04jgf(m,{}n,{}nra,{}tol,{}lwork,{}a,{}b,{}ifail)} finds the solution of a linear least-squares problem,{} Ax=b ,{} where A is a real \\spad{m} by \\spad{n} (m>=n) matrix and \\spad{b} is an \\spad{m} element vector. If the matrix of observations is not of full rank,{} then the minimal least-squares solution is returned. See \\downlink{Manual Page}{manpageXXf04jgf}.")) (|f04faf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04faf(job,{}n,{}d,{}e,{}b,{}ifail)} calculates the approximate solution of a set of real symmetric positive-definite tridiagonal linear equations. See \\downlink{Manual Page}{manpageXXf04faf}.")) (|f04axf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|))) "\\spad{f04axf(n,{}a,{}licn,{}icn,{}ikeep,{}mtype,{}idisp,{}rhs)} calculates the approximate solution of a set of real sparse linear equations with a single right-hand side,{} Ax=b or \\indented{1}{\\spad{T}} A \\spad{x=b},{} where A has been factorized by F01BRF or F01BSF. See \\downlink{Manual Page}{manpageXXf04axf}.")) (|f04atf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04atf(a,{}ia,{}b,{}n,{}iaa,{}ifail)} calculates the accurate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting,{} and iterative refinement. See \\downlink{Manual Page}{manpageXXf04atf}.")) (|f04asf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04asf(ia,{}b,{}n,{}a,{}ifail)} calculates the accurate solution of a set of real symmetric positive-definite linear equations with a single right- hand side,{} Ax=b,{} using a Cholesky factorization and iterative refinement. See \\downlink{Manual Page}{manpageXXf04asf}.")) (|f04arf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04arf(ia,{}b,{}n,{}a,{}ifail)} calculates the approximate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04arf}.")) (|f04adf| (((|Result|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f04adf(ia,{}b,{}ib,{}n,{}m,{}ic,{}a,{}ifail)} calculates the approximate solution of a set of complex linear equations with multiple right-hand sides,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04adf}."))) NIL NIL -(-748) +(-751) ((|constructor| (NIL "This package uses the NAG Library to compute matrix factorizations,{} and to solve systems of linear equations following the matrix factorizations. See \\downlink{Manual Page}{manpageXXf07}.")) (|f07fef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fef(uplo,{}n,{}nrhs,{}a,{}lda,{}ldb,{}b)} (DPOTRS) solves a real symmetric positive-definite system of linear equations with multiple right-hand sides,{} AX=B,{} where A has been factorized by F07FDF (DPOTRF). See \\downlink{Manual Page}{manpageXXf07fef}.")) (|f07fdf| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fdf(uplo,{}n,{}lda,{}a)} (DPOTRF) computes the Cholesky factorization of a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf07fdf}.")) (|f07aef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07aef(trans,{}n,{}nrhs,{}a,{}lda,{}ipiv,{}ldb,{}b)} (DGETRS) solves a real system of linear equations with \\indented{36}{\\spad{T}} multiple right-hand sides,{} AX=B or A \\spad{X=B},{} where A has been factorized by F07ADF (DGETRF). See \\downlink{Manual Page}{manpageXXf07aef}.")) (|f07adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07adf(m,{}n,{}lda,{}a)} (DGETRF) computes the LU factorization of a real \\spad{m} by \\spad{n} matrix. See \\downlink{Manual Page}{manpageXXf07adf}."))) NIL NIL -(-749) +(-752) ((|constructor| (NIL "This package uses the NAG Library to compute some commonly occurring physical and mathematical functions. See \\downlink{Manual Page}{manpageXXs}.")) (|s21bdf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bdf(x,{}y,{}z,{}r,{}ifail)} returns a value of the symmetrised elliptic integral of the third kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bdf}.")) (|s21bcf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bcf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the second kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bcf}.")) (|s21bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bbf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bbf}.")) (|s21baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21baf(x,{}y,{}ifail)} returns a value of an elementary integral,{} which occurs as a degenerate case of an elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21baf}.")) (|s20adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20adf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{C}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20adf}.")) (|s20acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20acf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{S}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20acf}.")) (|s19adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19adf(x,{}ifail)} returns a value for the Kelvin function kei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19adf}.")) (|s19acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19acf(x,{}ifail)} returns a value for the Kelvin function ker(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs19acf}.")) (|s19abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19abf(x,{}ifail)} returns a value for the Kelvin function bei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19abf}.")) (|s19aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19aaf(x,{}ifail)} returns a value for the Kelvin function ber(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19aaf}.")) (|s18def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{I}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18def}.")) (|s18dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{K}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18dcf}.")) (|s18aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aff(x,{}ifail)} returns a value for the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18aff}.")) (|s18aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aef(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18aef}.")) (|s18adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18adf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18adf}.")) (|s18acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18acf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18acf}.")) (|s17dlf| (((|Result|) (|Integer|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dlf(m,{}fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Hankel functions \\indented{2}{(1)\\space{11}(2)} \\indented{1}{\\spad{H}\\space{6}(\\spad{z}) or \\spad{H}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}\\space{8}(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dlf}.")) (|s17dhf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dhf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Bi}(\\spad{z}) or its derivative Bi'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dhf}.")) (|s17dgf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dgf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Ai}(\\spad{z}) or its derivative Ai'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dgf}.")) (|s17def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{J}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17def}.")) (|s17dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{Y}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dcf}.")) (|s17akf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17akf(x,{}ifail)} returns a value for the derivative of the Airy function \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17akf}.")) (|s17ajf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ajf(x,{}ifail)} returns a value of the derivative of the Airy function \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ajf}.")) (|s17ahf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ahf(x,{}ifail)} returns a value of the Airy function,{} \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ahf}.")) (|s17agf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17agf(x,{}ifail)} returns a value for the Airy function,{} \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17agf}.")) (|s17aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aff(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17aff}.")) (|s17aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aef(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17aef}.")) (|s17adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17adf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17adf}.")) (|s17acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17acf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17acf}.")) (|s15aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15aef(x,{}ifail)} returns the value of the error function erf(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15aef}.")) (|s15adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15adf(x,{}ifail)} returns the value of the complementary error function,{} erfc(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15adf}.")) (|s14baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s14baf(a,{}x,{}tol,{}ifail)} computes values for the incomplete gamma functions \\spad{P}(a,{}\\spad{x}) and \\spad{Q}(a,{}\\spad{x}). See \\downlink{Manual Page}{manpageXXs14baf}.")) (|s14abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14abf(x,{}ifail)} returns a value for the log,{} \\spad{ln}(Gamma(\\spad{x})),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14abf}.")) (|s14aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14aaf(x,{}ifail)} returns the value of the Gamma function (Gamma)(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14aaf}.")) (|s13adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13adf(x,{}ifail)} returns the value of the sine integral See \\downlink{Manual Page}{manpageXXs13adf}.")) (|s13acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13acf(x,{}ifail)} returns the value of the cosine integral See \\downlink{Manual Page}{manpageXXs13acf}.")) (|s13aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13aaf(x,{}ifail)} returns the value of the exponential integral \\indented{1}{\\spad{E} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs13aaf}.")) (|s01eaf| (((|Result|) (|Complex| (|DoubleFloat|)) (|Integer|)) "\\spad{s01eaf(z,{}ifail)} S01EAF evaluates the exponential function exp(\\spad{z}) ,{} for complex \\spad{z}. See \\downlink{Manual Page}{manpageXXs01eaf}."))) NIL NIL -(-750) +(-753) ((|constructor| (NIL "Support functions for the NAG Library Link functions")) (|restorePrecision| (((|Void|)) "\\spad{restorePrecision()} \\undocumented{}")) (|checkPrecision| (((|Boolean|)) "\\spad{checkPrecision()} \\undocumented{}")) (|dimensionsOf| (((|SExpression|) (|Symbol|) (|Matrix| (|Integer|))) "\\spad{dimensionsOf(s,{}m)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|Matrix| (|DoubleFloat|))) "\\spad{dimensionsOf(s,{}m)} \\undocumented{}")) (|aspFilename| (((|String|) (|String|)) "\\spad{aspFilename(\"f\")} returns a String consisting of \\spad{\"f\"} suffixed with \\indented{1}{an extension identifying the current AXIOM session.}")) (|fortranLinkerArgs| (((|String|)) "\\spad{fortranLinkerArgs()} returns the current linker arguments")) (|fortranCompilerName| (((|String|)) "\\spad{fortranCompilerName()} returns the name of the currently selected \\indented{1}{Fortran compiler}"))) NIL NIL -(-751 S) +(-754 S) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-752) +(-755) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-753 S) +(-756 S) ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-754) +(-757) ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-755 |Par|) +(-758 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-756 -3189) +(-759 -3214) ((|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 -(-757 P -3189) +(-760 P -3214) ((|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 -(-758 T$) +(-761 T$) NIL NIL NIL -(-759 UP -3189) +(-762 UP -3214) ((|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{\\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{\\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{\\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{\\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{\\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{\\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 -(-760) +(-763) ((|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-761 R) +(-764 R) ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,{}lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-762) +(-765) ((|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."))) -(((-4385 "*") . T)) +(((-4392 "*") . T)) NIL -(-763 R -3189) +(-766 R -3214) ((|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 -(-764 S) +(-767 S) ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) NIL NIL -(-765) +(-768) ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) NIL NIL -(-766 R |PolR| E |PolE|) +(-769 R |PolR| E |PolE|) ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) NIL NIL -(-767 R E V P TS) +(-770 R E V P TS) ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\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 -(-768 -3189 |ExtF| |SUEx| |ExtP| |n|) +(-771 -3214 |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 -(-769 BP E OV R P) +(-772 BP E OV R P) ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) NIL NIL -(-770 |Par|) +(-773 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,{}eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with variable \\spad{x}. Fraction \\spad{P} \\spad{RN}.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with a new symbol as variable."))) NIL NIL -(-771 R |VarSet|) +(-774 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."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163))))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163)))) (-2143 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163)))))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163)))) (-2143 (|HasCategory| |#1| (QUOTE (-543)))) (-2143 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163)))) (-2143 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-558))))) (-2143 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163)))) (-2143 (|HasCategory| |#1| (LIST (QUOTE -982) (QUOTE (-558))))))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) -(-772 R S) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . 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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 -(-773 R) +(-776 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4379 |has| |#1| (-362)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . 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T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +(-777 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) -(-775 R E V P) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) +(-778 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.}"))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL -(-776 S) +(-779 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-171)))) -(-777) +((-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-1042))) (|HasCategory| |#1| (QUOTE (-171)))) +(-780) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL NIL -(-778) +(-781) ((|numericalIntegration| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|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.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|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 -(-779) +(-782) ((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,{}y,{}x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})\\spad{**}(-1/5)}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try ,{} did ,{} next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is the same as \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation\\spad{'s} right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) NIL NIL -(-780) +(-783) ((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) NIL NIL -(-781 |Curve|) +(-784 |Curve|) ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,{}r,{}n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) NIL NIL -(-782) +(-785) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering."))) NIL NIL -(-783) +(-786) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-784) +(-787) ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,{}y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) NIL NIL -(-785) +(-788) ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) NIL NIL -(-786) +(-789) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-787 S R) +(-790 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-1048))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-367)))) -(-788 R) +((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-367)))) +(-791 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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,{}\\spad{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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4377 . T) (-4378 . T) (-4380 . T)) +((-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-789 -3994 R OS S) +(-792 -4007 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL -(-790 R) +(-793 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-3994 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3994 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) -(-791) +((-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-4007 (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4007 (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) +(-794) ((|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 -(-792 R -3189 L) +(-795 R -3214 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{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-793 R -3189) +(-796 R -3214) ((|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 -(-794) +(-797) ((|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 -(-795 R -3189) +(-798 R -3214) ((|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 -(-796) +(-799) ((|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 -(-797 -3189 UP UPUP R) +(-800 -3214 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 -(-798 -3189 UP L LQ) +(-801 -3214 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 -(-799) +(-802) ((|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 -(-800 -3189 UP L LQ) +(-803 -3214 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^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{\\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{\\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 \\spad{ai}}} is \\spad{\\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 -(-801 -3189 UP) +(-804 -3214 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 -(-802 -3189 L UP A LO) +(-805 -3214 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 -(-803 -3189 UP) +(-806 -3214 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{\\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 \\spad{ai}}} is \\spad{\\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)))) -(-804 -3189 LO) +(-807 -3214 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) 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(((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-805 -3189 LODO) +(-808 -3214 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(\\spad{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(\\spad{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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(|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166))))) (-4007 (|HasCategory| |#2| (QUOTE (-1042))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasAttribute| |#2| (QUOTE -4387)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))))) +(-810 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. 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T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) -(-808 |Kernels| R |var|) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +(-811 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4385 "*") |has| |#2| (-362)) (-4376 |has| |#2| (-362)) (-4381 |has| |#2| (-362)) (-4375 |has| |#2| (-362)) (-4380 . T) (-4378 . T) (-4377 . T)) +(((-4392 "*") |has| |#2| (-362)) (-4383 |has| |#2| (-362)) (-4388 |has| |#2| (-362)) (-4382 |has| |#2| (-362)) (-4387 . T) (-4385 . T) (-4384 . T)) ((|HasCategory| |#2| (QUOTE (-362)))) -(-809 S) +(-812 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) NIL NIL -(-810 S) +(-813 S) ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the \\spad{n-th} monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the \\spad{n-th} monomial of \\spad{x}.")) (|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} and \\spad{y = m * r} hold and such that \\spad{l} and \\spad{r} have no overlap,{} that is \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l,{} r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x,{} s)} returns the exact right quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} that is \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x,{} s)} returns the exact left quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} \\indented{1}{by \\spad{y} that is \\spad{q} such that \\spad{x = y * q},{}} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,{}y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}.")) (** (($ |#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."))) NIL NIL -(-811) +(-814) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-812) +(-815) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) NIL NIL -(-813) +(-816) ((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,{}cd,{}s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,{}i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,{}i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,{}i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,{}i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,{}enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,{}mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,{}mode,{}enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) NIL NIL -(-814) +(-817) ((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) NIL NIL -(-815) +(-818) ((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) NIL NIL -(-816) +(-819) ((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,{}l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) NIL NIL -(-817 R) +(-820 R) ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) NIL NIL -(-818 P R) +(-821 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) -((-4377 . T) (-4378 . T) (-4380 . T)) +((-4384 . T) (-4385 . T) (-4387 . T)) ((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-232)))) -(-819) +(-822) ((|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."))) NIL NIL -(-820) +(-823) ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,{}cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,{}cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the \\spad{CDs} supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) NIL NIL -(-821 S) +(-824 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4383 . T) (-4373 . T) (-4384 . T)) +((-4390 . T) (-4380 . T) (-4391 . T)) NIL -(-822) +(-825) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) NIL NIL -(-823 R S) +(-826 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f,{} r,{} i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL -(-824 R) +(-827 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."))) -((-4380 |has| |#1| (-839))) -((|HasCategory| |#1| (QUOTE (-839))) (-3994 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3994 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) -(-825 A S) +((-4387 |has| |#1| (-842))) +((|HasCategory| |#1| (QUOTE (-842))) (-4007 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4007 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) +(-828 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.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL NIL -(-826 S) +(-829 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.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL NIL -(-827 R) +(-830 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) (-4380 . T)) +((-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) (-4387 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146)))) -(-828) +(-831) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) NIL NIL -(-829) +(-832) ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,{}sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of \\spad{`x'}."))) NIL NIL -(-830) +(-833) ((|numericalOptimization| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-831) +(-834) ((|goodnessOfFit| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{goodnessOfFit(lf,{}start)} is a top level ANNA function to check to goodness of fit of a least squares model \\spadignore{i.e.} the minimization of a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation. goodnessOfFit(\\spad{lf},{}\\spad{start}) is a top level function to iterate over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then checks the goodness of fit of the least squares model.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{goodnessOfFit(prob)} is a top level ANNA function to check to goodness of fit of a least squares model as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation.")) (|optimize| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{optimize(lf,{}start)} is a top level ANNA function to minimize a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints \\spadignore{i.e.} a least-squares problem. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|))) "\\spad{optimize(f,{}start)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with simple constraints. The bounds on the variables are defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|Expression| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}cons,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with the given constraints. \\blankline These constraints may be simple constraints on the variables in which case \\axiom{\\spad{cons}} would be an empty list and the bounds on those variables defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}},{} or a mixture of simple,{} linear and non-linear constraints,{} where \\axiom{\\spad{cons}} contains the linear and non-linear constraints and the bounds on these are added to \\axiom{\\spad{upper}} and \\axiom{\\spad{lower}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{optimize(prob)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{optimize(prob,{}routines)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} listed in \\axiom{\\spad{routines}} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information."))) NIL NIL -(-832) +(-835) ((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-833 R S) +(-836 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f,{} r,{} p,{} m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL -(-834 R) +(-837 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4380 |has| |#1| (-839))) -((|HasCategory| |#1| (QUOTE (-839))) (-3994 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3994 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) -(-835) +((-4387 |has| |#1| (-842))) +((|HasCategory| |#1| (QUOTE (-842))) (-4007 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4007 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) +(-838) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-836 -1470 S) +(-839 -2164 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL -(-837) +(-840) ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) NIL NIL -(-838 S) +(-841 S) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) NIL NIL -(-839) +(-842) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4380 . T)) +((-4387 . T)) NIL -(-840 S) +(-843 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) NIL NIL -(-841) +(-844) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) NIL NIL -(-842 S R) +(-845 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) NIL -((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171)))) -(-843 R) +((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171)))) +(-846 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4377 . T) (-4378 . T) (-4380 . T)) +((-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-844 R C) +(-847 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 (-362))) (|HasCategory| |#1| (QUOTE (-550)))) -(-845 R |sigma| -3691) +((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) +(-848 R |sigma| -3790) ((|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."))) -((-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) -(-846 |x| R |sigma| -3691) +((-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) +(-849 |x| R |sigma| -3790) ((|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}."))) -((-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-362)))) -(-847 R) +((-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-362)))) +(-850 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) -(-848) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) +(-851) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL NIL -(-849) +(-852) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-850 S) +(-853 S) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-851) +(-854) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-852) +(-855) ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) NIL NIL -(-853) +(-856) ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL -(-854) +(-857) ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-855 |VariableList|) +(-858 |VariableList|) ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) NIL NIL -(-856 R |vl| |wl| |wtlevel|) +(-859 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)"))) -((-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) (-4380 . T)) +((-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) (-4387 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362)))) -(-857 R PS UP) +(-860 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-858 R |x| |pt|) +(-861 R |x| |pt|) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-859 |p|) +(-862 |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}."))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-860 |p|) +(-863 |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)."))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-861 |p|) +(-864 |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)."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-860 |#1|) (QUOTE (-899))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-146))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-860 |#1|) (QUOTE (-1012))) (|HasCategory| (-860 |#1|) (QUOTE (-811))) (-3994 (|HasCategory| (-860 |#1|) (QUOTE (-811))) (|HasCategory| (-860 |#1|) (QUOTE (-841)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-1138))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-232))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -860) (|devaluate| |#1|)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (QUOTE (-306))) (|HasCategory| (-860 |#1|) (QUOTE (-543))) (|HasCategory| (-860 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))))) -(-862 |p| PADIC) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| (-863 |#1|) (QUOTE (-902))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-863 |#1|) (QUOTE (-144))) (|HasCategory| (-863 |#1|) (QUOTE (-146))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-863 |#1|) (QUOTE (-1015))) (|HasCategory| (-863 |#1|) (QUOTE (-814))) (-4007 (|HasCategory| (-863 |#1|) (QUOTE (-814))) (|HasCategory| (-863 |#1|) (QUOTE (-844)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-863 |#1|) (QUOTE (-1141))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| (-863 |#1|) (QUOTE (-232))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -512) (QUOTE (-1166)) (LIST (QUOTE -863) (|devaluate| |#1|)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -863) (|devaluate| |#1|)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -863) (|devaluate| |#1|)) (LIST (QUOTE -863) (|devaluate| |#1|)))) (|HasCategory| (-863 |#1|) (QUOTE (-306))) (|HasCategory| (-863 |#1|) (QUOTE (-543))) (|HasCategory| (-863 |#1|) (QUOTE (-844))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-863 |#1|) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-863 |#1|) (QUOTE (-902)))) (|HasCategory| (-863 |#1|) (QUOTE (-144))))) +(-865 |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)}."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-811))) (-3994 (|HasCategory| |#2| (QUOTE (-811))) (|HasCategory| |#2| (QUOTE (-841)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1138))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) -(-863 S T$) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#2| (QUOTE (-902))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-814))) (-4007 (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-1141))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-844))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) +(-866 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 (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) -(-864) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))))) +(-867) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL NIL -(-865) +(-868) ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) NIL NIL -(-866 CF1 CF2) +(-869 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-867 |ComponentFunction|) +(-870 |ComponentFunction|) ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,{}c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) NIL NIL -(-868 CF1 CF2) +(-871 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-869 |ComponentFunction|) +(-872 |ComponentFunction|) ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,{}c2,{}c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-870) +(-873) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) NIL NIL -(-871 CF1 CF2) +(-874 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-872 |ComponentFunction|) +(-875 |ComponentFunction|) ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,{}i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,{}c2,{}c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-873) +(-876) ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,{}2,{}3,{}...,{}n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,{}l1,{}l2,{}..,{}ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'s}.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,{}l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,{}2,{}4],{}[2,{}3,{}5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}\\spad{'s},{} and 4 \\spad{5}\\spad{'s}.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,{}st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,{}l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|Integer|)) (|List| (|Integer|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}.")) (|partitions| (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l)} is the stream of all \\indented{1}{partitions whose number of} \\indented{1}{parts and largest part are no greater than \\spad{p} and \\spad{l}.}") (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{partitions(n)} is the stream of all partitions of \\spad{n}.") (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l,{}n)} is the stream of partitions \\indented{1}{of \\spad{n} whose number of parts is no greater than \\spad{p}} \\indented{1}{and whose largest part is no greater than \\spad{l}.}"))) NIL NIL -(-874 R) +(-877 R) ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) NIL NIL -(-875 R S L) +(-878 R S L) ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,{}r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-876 S) +(-879 S) ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) NIL NIL -(-877 |Base| |Subject| |Pat|) +(-880 |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 (-2143 (|HasCategory| |#2| (QUOTE (-1039)))) (-2143 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (-2143 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163))))) -(-878 R A B) +((-12 (-2159 (|HasCategory| |#2| (QUOTE (-1042)))) (-2159 (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166)))))) (-12 (|HasCategory| |#2| (QUOTE (-1042))) (-2159 (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166))))) +(-881 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL NIL -(-879 R S) +(-882 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-880 R -3042) +(-883 R -3122) ((|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 -(-881 R S) +(-884 R S) ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f,{} p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL -(-882 R) +(-885 R) ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-883 |VarSet|) +(-886 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2,{} .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1,{} l2,{} .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL NIL -(-884 UP R) +(-887 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,{}q)} \\undocumented"))) NIL NIL -(-885) +(-888) ((|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 -(-886 UP -3189) +(-889 UP -3214) ((|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 -(-887) +(-890) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st,{}tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,{}routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}"))) NIL NIL -(-888) +(-891) ((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-889 A S) +(-892 A S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|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}-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)}.") (($ $ |#2|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-890 S) +(-893 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4380 . T)) +((-4387 . T)) NIL -(-891 S) +(-894 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 (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-892 |n| R) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-895 |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 -(-893 S) +(-896 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}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under 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."))) -((-4380 . T)) +((-4387 . T)) NIL -(-894 S) +(-897 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}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-895 S) +(-898 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|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."))) -((-4380 . T)) -((-3994 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) -(-896 R E |VarSet| S) +((-4387 . T)) +((-4007 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-844)))) +(-899 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 \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-897 R S) +(-900 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-898 S) +(-901 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-144)))) -(-899) +(-902) ((|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 \\spad{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}."))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-900 |p|) +(-903 |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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) ((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367)))) -(-901 R0 -3189 UP UPUP R) +(-904 R0 -3214 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 -(-902 UP UPUP R) +(-905 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) NIL NIL -(-903 UP UPUP) +(-906 UP UPUP) ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) NIL NIL -(-904 R) +(-907 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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-905 R) +(-908 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num,{} facdenom,{} var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf,{} var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) NIL NIL -(-906 E OV R P) +(-909 E OV R P) ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}."))) NIL NIL -(-907) +(-910) ((|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(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{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 \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{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(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{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 -(-908 -3189) +(-911 -3214) ((|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 -(-909 R) +(-912 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL NIL -(-910) +(-913) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-911) +(-914) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4385 "*") . T)) +(((-4392 "*") . T)) NIL -(-912 -3189 P) +(-915 -3214 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-913 |xx| -3189) +(-916 |xx| -3214) ((|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 -(-914 R |Var| |Expon| GR) +(-917 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{~=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-915 S) +(-918 S) ((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-916) +(-919) ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL -(-917) +(-920) ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}."))) NIL NIL -(-918) +(-921) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-919 R -3189) +(-922 R -3214) ((|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| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL -(-920) +(-923) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-921 S A B) +(-924 S A B) ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-922 S R -3189) +(-925 S R -3214) ((|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 -(-923 I) +(-926 I) ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n,{} pat,{} res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-924 S E) +(-927 S E) ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,{}...,{}en),{} pat,{} res)} matches the pattern \\spad{pat} to \\spad{f(e1,{}...,{}en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-925 S R L) +(-928 S R L) ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l,{} pat,{} res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-926 S E V R P) +(-929 S E V R P) ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -876) (|devaluate| |#1|)))) -(-927 R -3189 -3042) +((|HasCategory| |#3| (LIST (QUOTE -879) (|devaluate| |#1|)))) +(-930 R -3214 -3122) ((|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 -(-928 -3042) +(-931 -3122) ((|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 -(-929 S R Q) +(-932 S R Q) ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b,{} pat,{} res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-930 S) +(-933 S) ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) NIL NIL -(-931 S R P) +(-934 S R P) ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj,{} lpat,{} res,{} match)} matches the product of patterns \\spad{reduce(*,{}lpat)} to the product of subjects \\spad{reduce(*,{}lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj,{} lpat,{} op,{} res,{} match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) NIL NIL -(-932) +(-935) ((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n,{} n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!,{} n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,{}[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,{}x)} computed by solving the differential equation \\spad{differentiate(E(n,{}x),{}x) = n E(n-1,{}x)} where \\spad{E(0,{}x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,{}1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,{}x)} computed by solving the differential equation \\spad{differentiate(B(n,{}x),{}x) = n B(n-1,{}x)} where \\spad{B(0,{}x) = 1} and initial condition comes from \\spad{B(n) = B(n,{}0)}."))) NIL NIL -(-933 R) +(-936 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-934 |lv| R) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#1| (QUOTE (-1042))) (-12 (|HasCategory| |#1| (QUOTE (-995))) (|HasCategory| |#1| (QUOTE (-1042)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-937 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL NIL -(-935 |TheField| |ThePols|) +(-938 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL -((|HasCategory| |#1| (QUOTE (-839)))) -(-936 R S) +((|HasCategory| |#1| (QUOTE (-842)))) +(-939 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f,{} p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-937 |x| R) +(-940 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p,{} x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,{}Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-938 S R E |VarSet|) +(-941 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 (-899))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#4| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#4| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#4| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-841)))) -(-939 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-902))) (|HasAttribute| |#2| (QUOTE -4388)) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#4| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#4| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#4| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-844)))) +(-942 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}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) NIL -(-940 E V R P -3189) +(-943 E V R P -3214) ((|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 -(-941 E |Vars| R P S) +(-944 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap,{} coefmap,{} p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-942 R) +(-945 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}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) -(-943 E V R P -3189) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +(-946 E V R P -3214) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-450)))) -(-944) +(-947) ((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}."))) NIL NIL -(-945) +(-948) ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-946 R L) +(-949 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op,{} m)} returns the matrix A such that \\spad{A w = (W',{}W'',{}...,{}W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L),{} m}."))) NIL NIL -(-947 A B) +(-950 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) NIL NIL -(-948 S) +(-951 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"))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-949) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-952) ((|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 -(-950 -3189) +(-953 -3214) ((|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{\\spad{ai} = \\spad{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{\\spad{ai} = \\spad{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 -(-951 I) +(-954 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,{}b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-952) +(-955) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL -(-953 R E) +(-956 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}"))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4381))) -(-954 A B) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4388))) +(-957 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"))) -((-4380 -12 (|has| |#2| (-471)) (|has| |#1| (-471)))) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE 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(|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) -(-955) +((-4387 -12 (|has| |#2| (-471)) (|has| |#1| (-471)))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#2| (QUOTE (-787)))) (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-844))))) (-12 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#2| (QUOTE (-787)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#2| (QUOTE (-787))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#2| (QUOTE (-787))))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#2| (QUOTE (-720))))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#2| (QUOTE (-720)))) (-12 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#2| (QUOTE (-787))))) (-12 (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#2| (QUOTE (-720)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-844))))) +(-958) ((|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| (($ (|Symbol|) (|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| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-956 T$) +(-959 T$) ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|equivOperands| (((|Pair| $ $) $) "\\spad{equivOperands p} extracts the operands to the logical equivalence; otherwise errors.")) (|equiv?| (((|Boolean|) $) "\\spad{equiv? p} is \\spad{true} when \\spad{`p'} is a logical equivalence.")) (|impliesOperands| (((|Pair| $ $) $) "\\spad{impliesOperands p} extracts the operands to the logical implication; otherwise errors.")) (|implies?| (((|Boolean|) $) "\\spad{implies? p} is \\spad{true} when \\spad{`p'} is a logical implication.")) (|orOperands| (((|Pair| $ $) $) "\\spad{orOperands p} extracts the operands to the logical disjunction; otherwise errors.")) (|or?| (((|Boolean|) $) "\\spad{or? p} is \\spad{true} when \\spad{`p'} is a logical disjunction.")) (|andOperands| (((|Pair| $ $) $) "\\spad{andOperands p} extracts the operands of the logical conjunction; otherwise errors.")) (|and?| (((|Boolean|) $) "\\spad{and? p} is \\spad{true} when \\spad{`p'} is a logical conjunction.")) (|notOperand| (($ $) "\\spad{notOperand returns} the operand to the logical `not' operator; otherwise errors.")) (|not?| (((|Boolean|) $) "\\spad{not? p} is \\spad{true} when \\spad{`p'} is a logical negation")) (|variable| (((|Symbol|) $) "\\spad{variable p} extracts the variable name from \\spad{`p'}; otherwise errors.")) (|variable?| (((|Boolean|) $) "variables? \\spad{p} returns \\spad{true} when \\spad{`p'} really is a variable.")) (|term| ((|#1| $) "\\spad{term p} extracts the term value from \\spad{`p'}; otherwise errors.")) (|term?| (((|Boolean|) $) "\\spad{term? p} returns \\spad{true} when \\spad{`p'} really is a term")) (|variables| (((|Set| (|Symbol|)) $) "\\spad{variables(p)} returns the set of propositional variables appearing in the proposition \\spad{`p'}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional variable.") (($ |#1|) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional formula"))) NIL NIL -(-957) +(-960) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,{}q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,{}q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}."))) NIL NIL -(-958 S) +(-961 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4383 . T) (-4384 . T)) +((-4390 . T) (-4391 . T)) NIL -(-959 R |polR|) +(-962 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) NIL ((|HasCategory| |#1| (QUOTE (-450)))) -(-960) +(-963) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-961) +(-964) ((|constructor| (NIL "\\indented{1}{Partition is an OrderedCancellationAbelianMonoid which is used} as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(\\spad{li})} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(\\spad{li})} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-962 S |Coef| |Expon| |Var|) +(-965 S |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) NIL NIL -(-963 |Coef| |Expon| |Var|) +(-966 |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}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-964) +(-967) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-965 S R E |VarSet| P) +(-968 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL -((|HasCategory| |#2| (QUOTE (-550)))) -(-966 R E |VarSet| P) +((|HasCategory| |#2| (QUOTE (-553)))) +(-969 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."))) -((-4383 . T)) +((-4390 . T)) NIL -(-967 R E V P) +(-970 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-306)))) (|HasCategory| |#1| (QUOTE (-450)))) -(-968 K) +(-971 K) ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m,{} v)} returns \\spad{[[C_1,{} g_1],{}...,{}[C_k,{} g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,{}...,{}C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M,{} A,{} sig,{} der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M,{} sig,{} der)} returns \\spad{[R,{} A,{} A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) NIL NIL -(-969 |VarSet| E RC P) +(-972 |VarSet| E RC P) ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{gcd} domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) NIL NIL -(-970 R) +(-973 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}."))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL -(-971 R1 R2) +(-974 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) NIL NIL -(-972 R) +(-975 R) ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) NIL NIL -(-973 K) +(-976 K) ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns \\spad{csc}(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,{}n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) NIL NIL -(-974 R E OV PPR) +(-977 R E OV PPR) ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-975 K R UP -3189) +(-978 K R UP -3214) ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL -(-976 |vl| |nv|) +(-979 |vl| |nv|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) NIL NIL -(-977 R |Var| |Expon| |Dpoly|) +(-980 R |Var| |Expon| |Dpoly|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-306))))) -(-978 R E V P TS) +(-981 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-979) +(-982) ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,{}\"a\")} creates a new equation."))) NIL NIL -(-980 A B R S) +(-983 A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) NIL NIL -(-981 A S) +(-984 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 (-899))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-811))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1138)))) -(-982 S) +((|HasCategory| |#2| (QUOTE (-902))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-1141)))) +(-985 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}."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-983 |n| K) +(-986 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) NIL NIL -(-984) +(-987) ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) NIL NIL -(-985 S) +(-988 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."))) -((-4383 . T) (-4384 . T)) +((-4390 . T) (-4391 . T)) NIL -(-986 S R) +(-989 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-1048))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-289)))) -(-987 R) +((|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-289)))) +(-990 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}."))) -((-4376 |has| |#1| (-289)) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 |has| |#1| (-289)) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-988 QR R QS S) +(-991 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL -(-989 R) +(-992 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.}"))) -((-4376 |has| |#1| (-289)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543)))) -(-990 S) +((-4383 |has| |#1| (-289)) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-543)))) +(-993 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}."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-991 S) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-994 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-992) +(-995) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-993 -3189 UP UPUP |radicnd| |n|) +(-996 -3214 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4376 |has| (-406 |#2|) (-362)) (-4381 |has| (-406 |#2|) (-362)) (-4375 |has| (-406 |#2|) (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3994 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3994 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3994 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3994 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) -(-994 |bb|) +((-4383 |has| (-406 |#2|) (-362)) (-4388 |has| (-406 |#2|) (-362)) (-4382 |has| (-406 |#2|) (-362)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-4007 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-4007 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-4007 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -634) (QUOTE (-561)))) (-4007 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) +(-997 |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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3994 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) -(-995) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4007 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) +(-998) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL NIL -(-996) +(-999) ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) NIL NIL -(-997 RP) +(-1000 RP) ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) NIL NIL -(-998 S) +(-1001 S) ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) NIL NIL -(-999 A S) +(-1002 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 -4384)) (|HasCategory| |#2| (QUOTE (-1087)))) -(-1000 S) +((|HasAttribute| |#1| (QUOTE -4391)) (|HasCategory| |#2| (QUOTE (-1090)))) +(-1003 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL NIL -(-1001 S) +(-1004 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) NIL NIL -(-1002) +(-1005) ((|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}}"))) -((-4376 . T) (-4381 . T) (-4375 . T) (-4378 . T) (-4377 . T) ((-4385 "*") . T) (-4380 . T)) +((-4383 . T) (-4388 . T) (-4382 . T) (-4385 . T) (-4384 . T) ((-4392 "*") . T) (-4387 . T)) NIL -(-1003 R -3189) +(-1006 R -3214) ((|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 -(-1004 R -3189) +(-1007 R -3214) ((|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 -(-1005 -3189 UP) +(-1008 -3214 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 -(-1006 -3189 UP) +(-1009 -3214 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 -(-1007 S) +(-1010 S) ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,{}u,{}n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-1008 F1 UP UPUP R F2) +(-1011 F1 UP UPUP R F2) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,{}u,{}g)} \\undocumented"))) NIL NIL -(-1009) +(-1012) ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) NIL NIL -(-1010 |Pol|) +(-1013 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-1011 |Pol|) +(-1014 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-1012) +(-1015) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-1013) +(-1016) ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,{}lv,{}eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) NIL NIL -(-1014 |TheField|) +(-1017 |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"))) -((-4376 . T) (-4381 . T) (-4375 . T) (-4378 . T) (-4377 . T) ((-4385 "*") . T) (-4380 . T)) -((-3994 (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558))))) -(-1015 -3189 L) +((-4383 . T) (-4388 . T) (-4382 . T) (-4385 . T) (-4384 . T) ((-4392 "*") . T) (-4387 . T)) +((-4007 (|HasCategory| (-406 (-561)) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-406 (-561)) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 (-561)) (LIST (QUOTE -1031) (QUOTE (-561))))) +(-1018 -3214 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{\\spad{fi}} must satisfy \\spad{op \\spad{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 -(-1016 S) +(-1019 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,{}m)} same as \\spad{setelt(n,{}m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,{}m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) NIL -((|HasCategory| |#1| (QUOTE (-1087)))) -(-1017 R E V P) +((|HasCategory| |#1| (QUOTE (-1090)))) +(-1020 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."))) -((-4384 . T) (-4383 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -605) (QUOTE (-853))))) -(-1018 R) +((-4391 . T) (-4390 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -608) (QUOTE (-856))))) +(-1021 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(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{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 \\spad{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 \\spad{ai}} and {\\em \\spad{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 (-4385 "*")))) -(-1019 R) +((|HasAttribute| |#1| (QUOTE (-4392 "*")))) +(-1022 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-306)))) -(-1020 S) +(-1023 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i,{} r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-1021) +(-1024) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) NIL NIL -(-1022 S) +(-1025 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r,{} i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL NIL -(-1023 S) +(-1026 S) ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1024 -3189 |Expon| |VarSet| |FPol| |LFPol|) +(-1027 -3214 |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"))) -(((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1025) +(-1028) ((|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.}"))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -1925) (QUOTE (-52))))))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) -(-1026) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (QUOTE (-1166))) (LIST (QUOTE |:|) (QUOTE -2654) (QUOTE (-52))))))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-52) (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-1166) (QUOTE (-844))) (|HasCategory| (-52) (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856))))) +(-1029) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-1027 A S) +(-1030 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-1028 S) +(-1031 S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-1029 Q R) +(-1032 Q R) ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-1030) +(-1033) ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,{}m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,{}m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,{}g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,{}g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-1031 UP) +(-1034 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1032 R) +(-1035 R) ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) NIL NIL -(-1033 R) +(-1036 R) ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-1034 T$) +(-1037 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of \\spad{`c'}.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of \\spad{`c'}.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) NIL NIL -(-1035 T$) +(-1038 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) NIL NIL -(-1036 R |ls|) +(-1039 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}."))) -((-4384 . T) (-4383 . T)) -((-12 (|HasCategory| (-771 |#1| (-855 |#2|)) (QUOTE (-1087))) (|HasCategory| (-771 |#1| (-855 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -771) (|devaluate| |#1|) (LIST (QUOTE -855) (|devaluate| |#2|)))))) (|HasCategory| (-771 |#1| (-855 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-771 |#1| (-855 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| (-855 |#2|) (QUOTE (-367))) (|HasCategory| (-771 |#1| (-855 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) -(-1037) +((-4391 . T) (-4390 . T)) +((-12 (|HasCategory| (-774 |#1| (-858 |#2|)) (QUOTE (-1090))) (|HasCategory| (-774 |#1| (-858 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -774) (|devaluate| |#1|) (LIST (QUOTE -858) (|devaluate| |#2|)))))) (|HasCategory| (-774 |#1| (-858 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-774 |#1| (-858 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| (-858 |#2|) (QUOTE (-367))) (|HasCategory| (-774 |#1| (-858 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) +(-1040) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-1038 S) +(-1041 S) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) NIL NIL -(-1039) +(-1042) ((|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."))) -((-4380 . T)) +((-4387 . T)) NIL -(-1040 |xx| -3189) +(-1043 |xx| -3214) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-1041 S |m| |n| R |Row| |Col|) +(-1044 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) NIL -((|HasCategory| |#4| (QUOTE (-306))) (|HasCategory| |#4| (QUOTE (-362))) (|HasCategory| |#4| (QUOTE (-550))) (|HasCategory| |#4| (QUOTE (-171)))) -(-1042 |m| |n| R |Row| |Col|) +((|HasCategory| |#4| (QUOTE (-306))) (|HasCategory| |#4| (QUOTE (-362))) (|HasCategory| |#4| (QUOTE (-553))) (|HasCategory| |#4| (QUOTE (-171)))) +(-1045 |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"))) -((-4383 . T) (-4378 . T) (-4377 . T)) +((-4390 . T) (-4385 . T) (-4384 . T)) NIL -(-1043 |m| |n| R) +(-1046 |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}."))) -((-4383 . T) (-4378 . T) (-4377 . T)) -((-3994 (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853))))) -(-1044 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4390 . T) (-4385 . T) (-4384 . T)) +((-4007 (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-553))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -608) (QUOTE (-856))))) +(-1047 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-1045 R) +(-1048 R) ((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ $ |#1|) "\\spad{x*r} returns the right multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL NIL -(-1046) +(-1049) ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline"))) NIL NIL -(-1047 S) +(-1050 S) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-1048) +(-1051) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1049 |TheField| |ThePolDom|) +(-1052 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1050) +(-1053) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4371 . T) (-4375 . T) (-4370 . T) (-4381 . T) (-4382 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4378 . T) (-4382 . T) (-4377 . T) (-4388 . T) (-4389 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1051) +(-1054) ((|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}"))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -1925) (QUOTE (-52))))))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) -(-1052 S R E V) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (QUOTE (-1166))) (LIST (QUOTE |:|) (QUOTE -2654) (QUOTE (-52))))))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-52) (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-1166) (QUOTE (-844))) (|HasCategory| (-52) (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856))))) +(-1055 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -982) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-1163))))) -(-1053 R E V) +((|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -985) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-1166))))) +(-1056 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) NIL -(-1054) +(-1057) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) NIL NIL -(-1055 S |TheField| |ThePols|) +(-1058 S |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1056 |TheField| |ThePols|) +(-1059 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1057 R E V P TS) +(-1060 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{gcd} need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1058 S R E V P) +(-1061 S R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{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,{}...,{}\\spad{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(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#5| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) NIL NIL -(-1059 R E V P) +(-1062 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,{}...,{}\\spad{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,{}...,{}\\spad{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(\\spad{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}."))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL -(-1060 R E V P TS) +(-1063 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1061) +(-1064) ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-1062 |f|) +(-1065 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1063 |Base| R -3189) +(-1066 |Base| R -3214) ((|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 -(-1064 |Base| R -3189) +(-1067 |Base| R -3214) ((|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 -(-1065 R |ls|) +(-1068 R |ls|) ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,{}univ?,{}check?)} returns the same as \\spad{rur(lp,{}true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,{}true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,{}univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,{}univ?)} returns a list of items \\spad{[u,{}lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,{}lc]} in \\spad{rur(lp,{}univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-1066 UP SAE UPA) +(-1069 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1067 R UP M) +(-1070 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."))) -((-4376 |has| |#1| (-362)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))))) -(-1068 UP SAE UPA) +((-4383 |has| |#1| (-362)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))))) +(-1071 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1069) +(-1072) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1070) +(-1073) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-1071 S) +(-1074 S) ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(x,{} y)} to determine whether \\spad{x < y (f(x,{}y) < 0),{} x = y (f(x,{}y) = 0)},{} or \\spad{x > y (f(x,{}y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) NIL NIL -(-1072) +(-1075) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,{}s)} pushs a new contour with sole binding \\spad{`b'}.")) (|findBinding| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(n,{}s)} returns the first binding of \\spad{`n'} in \\spad{`s'}; otherwise `failed'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) NIL NIL -(-1073 R) +(-1076 R) ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) NIL NIL -(-1074 R) +(-1077 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"))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) -(-1075 S) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +(-1078 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL NIL -(-1076 R S) +(-1079 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l),{} f(l+k),{}...,{} f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL -((|HasCategory| |#1| (QUOTE (-839)))) -(-1077) +((|HasCategory| |#1| (QUOTE (-842)))) +(-1080) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1078 R S) +(-1081 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1079 S) +(-1082 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions.")) (|segment| (((|Segment| |#1|) $) "\\spad{segment(segb)} returns the segment from the right hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{segment(segb)} returns \\spad{a..b}.")) (|variable| (((|Symbol|) $) "\\spad{variable(segb)} returns the variable from the left hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{variable(segb)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) (|Segment| |#1|)) "\\spad{equation(v,{}a..b)} creates a segment binding value with variable \\spad{v} and segment \\spad{a..b}. Note that the interpreter parses \\spad{v=a..b} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1087)))) -(-1080 S) +((|HasCategory| |#1| (QUOTE (-1090)))) +(-1083 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) NIL NIL -(-1081 S) +(-1084 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (QUOTE (-1087)))) -(-1082 S L) +((|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) +(-1085 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l),{} f(l+k),{} ...,{} f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l,{} l+k,{} ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,{}3,{}5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) NIL NIL -(-1083) +(-1086) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1084 A S) +(-1087 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1085 S) +(-1088 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4373 . T)) +((-4380 . T)) NIL -(-1086 S) +(-1089 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1087) +(-1090) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1088 |m| |n|) +(-1091 |m| |n|) ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1089 S) +(-1092 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)}}"))) -((-4383 . T) (-4373 . T) (-4384 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-1090 |Str| |Sym| |Int| |Flt| |Expr|) +((-4390 . T) (-4380 . T) (-4391 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-1093 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|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|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL NIL -(-1091) +(-1094) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1092 |Str| |Sym| |Int| |Flt| |Expr|) +(-1095 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1093 R FS) +(-1096 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,{}ftype,{}body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program."))) NIL NIL -(-1094 R E V P TS) +(-1097 R E V P TS) ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(\\spad{ts},{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1095 R E V P TS) +(-1098 R E V P TS) ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1096 R E V P) +(-1099 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.}"))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL -(-1097) +(-1100) ((|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| (|Integer|)) (|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| (|Integer|)) (|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| (|Integer|))) "\\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 \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{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,{}\\spad{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 \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL -(-1098 S) +(-1101 S) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1099) +(-1102) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1100 |dimtot| |dim1| S) +(-1103 |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. 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(-12 (|HasCategory| |#3| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#3| (QUOTE (-1090))))) (-4007 (-12 (|HasCategory| |#3| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-720))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-787))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-842))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#3| (QUOTE (-1042))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561)))))) (-4007 (-12 (|HasCategory| |#3| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-720))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-787))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-842))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561)))))) (|HasCategory| (-561) (QUOTE (-844))) (-12 (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1042)))) (-12 (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-1166))))) (-4007 (|HasCategory| |#3| (QUOTE (-1042))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561)))))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#3| (QUOTE (-1090)))) (|HasAttribute| |#3| (QUOTE -4387)) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) +(-1104 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 ((|HasCategory| |#1| (QUOTE (-450)))) -(-1102) +(-1105) ((|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 -(-1103 R -3189) +(-1106 R -3214) ((|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 -(-1104 R) +(-1107 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1105) +(-1108) ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,{}t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) NIL NIL -(-1106) +(-1109) ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) NIL NIL -(-1107) +(-1110) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|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."))) -((-4371 . T) (-4375 . T) (-4370 . T) (-4381 . T) (-4382 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4378 . T) (-4382 . T) (-4377 . T) (-4388 . T) (-4389 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1108 S) +(-1111 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4383 . T) (-4384 . T)) +((-4390 . T) (-4391 . T)) NIL -(-1109 S |ndim| R |Row| |Col|) +(-1112 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-362))) (|HasAttribute| |#3| (QUOTE (-4385 "*"))) (|HasCategory| |#3| (QUOTE (-171)))) -(-1110 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-362))) (|HasAttribute| |#3| (QUOTE (-4392 "*"))) (|HasCategory| |#3| (QUOTE (-171)))) +(-1113 |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."))) -((-4383 . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4390 . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1111 R |Row| |Col| M) +(-1114 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,{}B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) NIL NIL -(-1112 R |VarSet|) +(-1115 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) -(-1113 |Coef| |Var| SMP) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +(-1116 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) -(-1114 R E V P) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-362)))) +(-1117 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}"))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL -(-1115 UP -3189) +(-1118 UP -3214) ((|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 -(-1116 R) +(-1119 R) ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,{}lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,{}x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) NIL NIL -(-1117 R) +(-1120 R) ((|constructor| (NIL "This package finds the function func3 where func1 and func2 \\indented{1}{are given and\\space{2}func1 = func3(func2) .\\space{2}If there is no solution then} \\indented{1}{function func1 will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect,{} var,{} n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1,{} func2,{} newvar)} returns a function func3 where \\spad{func1} = func3(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) NIL NIL -(-1118 R) +(-1121 R) ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs,{} lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,{}x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,{}x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) NIL NIL -(-1119 S A) +(-1122 S A) ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,{}f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,{}f)} \\undocumented"))) NIL -((|HasCategory| |#1| (QUOTE (-841)))) -(-1120 R) +((|HasCategory| |#1| (QUOTE (-844)))) +(-1123 R) ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) NIL NIL -(-1121 R) +(-1124 R) ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} creates a surface defined over a list of curves,{} \\spad{p0} through \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); close2 set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through \\spad{pn},{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if close2 is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and close2 indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument close2 equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} [props],{} prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{}[props],{}prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,{}p1,{}...,{}pn])} creates a polygon defined by a list of points,{} \\spad{p0} through \\spad{pn},{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,{}[[r0],{}[r1],{}...,{}[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,{}[p0,{}p1,{}...,{}pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,{}R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,{}[[lr0],{}[lr1],{}...,{}[lrn],{}[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,{}[p0,{}p1,{}...,{}pn,{}p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,{}p1,{}p2,{}...,{}pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,{}[[p0],{}[p1],{}...,{}[pn]])} adds a space curve which is a list of points \\spad{p0} through \\spad{pn} defined by lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,{}[p0,{}p1,{}...,{}pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,{}i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,{}[x,{}y,{}z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,{}p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,{}i,{}p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,{}[p0,{}p1,{}...,{}pn])} adds a list of points from \\spad{p0} through \\spad{pn} to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,{}s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1122) +(-1125) ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) NIL NIL -(-1123) +(-1126) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) NIL NIL -(-1124) +(-1127) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) NIL NIL -(-1125) +(-1128) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,{}o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) NIL NIL -(-1126) +(-1129) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,{}z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,{}z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,{}z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,{}z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,{}x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,{}x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,{}x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) NIL NIL -(-1127 V C) +(-1130 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}o2)} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}o1,{}o2)} returns \\spad{true} iff \\axiom{o1(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{vt}.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) NIL NIL -(-1128 V C) +(-1131 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))) (-3994 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))))) (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853))))) -(-1129 |ndim| R) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1130) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1130 |#1| |#2|) (QUOTE (-1090)))) (|HasCategory| (-1130 |#1| |#2|) (QUOTE (-1090))) (-4007 (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1130) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1130 |#1| |#2|) (QUOTE (-1090))))) (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -608) (QUOTE (-856))))) +(-1132 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4380 . T) (-4372 |has| |#2| (-6 (-4385 "*"))) (-4383 . T) (-4377 . T) (-4378 . T)) -((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (-3994 (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) -(-1130 S) +((-4387 . T) (-4379 |has| |#2| (-6 (-4392 "*"))) (-4390 . T) (-4384 . T) (-4385 . T)) +((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4392 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-362))) (-4007 (|HasAttribute| |#2| (QUOTE (-4392 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +(-1133 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1131) +(-1134) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL -(-1132 R E V P TS) +(-1135 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1133 R E V P) +(-1136 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."))) -((-4384 . T) (-4383 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -605) (QUOTE (-853))))) -(-1134 S) +((-4391 . T) (-4390 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -608) (QUOTE (-856))))) +(-1137 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}."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-1135 A S) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-1138 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1136 S) +(-1139 S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1137 |Key| |Ent| |dent|) +(-1140 |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."))) -((-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087)))) -(-1138) +((-4391 . T)) +((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-844))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090)))) +(-1141) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL NIL -(-1139 |Coef|) +(-1142 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-1140 S) +(-1143 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,{}u)}."))) NIL NIL -(-1141 A B) +(-1144 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,{}f,{}u)},{} where \\spad{u} is a finite stream \\spad{[x0,{}x1,{}...,{}xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,{}b),{} r1 = f(x1,{}r0),{}...,{} r(n) = f(xn,{}r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,{}h,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[y0,{}y1,{}y2,{}...]},{} where \\spad{y0 = h(x0,{}b)},{} \\spad{y1 = h(x1,{}y0)},{}\\spad{...} \\spad{yn = h(xn,{}y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,{}s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}...]) = [f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL NIL -(-1142 A B C) +(-1145 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}st1,{}st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}..],{}[y0,{}y1,{}y2,{}..]) = [f(x0,{}y0),{}f(x1,{}y1),{}..]}."))) NIL NIL -(-1143 S) +(-1146 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."))) -((-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-1144) +((-4391 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-1147) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL -(-1145) +(-1148) NIL -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) -(-1146 |Entry|) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +(-1149 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#1|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (QUOTE (-1087))) (|HasCategory| (-1145) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (LIST (QUOTE -605) (QUOTE (-853))))) -(-1147 A) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (QUOTE (-1148))) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| (-1148) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -608) (QUOTE (-856))))) +(-1150 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 1.")) (|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,{}\\spad{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 (-362))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) -(-1148 |Coef|) +((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) +(-1151 |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 -(-1149 |Coef|) +(-1152 |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 -(-1150 R UP) +(-1153 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 (-306)))) -(-1151 |n| R) +(-1154 |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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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 -(-1152 S1 S2) +(-1155 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 -(-1153) +(-1156) ((|constructor| (NIL "This domain represents the filter iterator syntax.")) 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(|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 -(-1164 R) +(-1167 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{\\spad{ri}'s}: \\spad{[r1 + ... + rn,{} r1 r2 + ... + r(n-1) rn,{} ...,{} r1 r2 ... rn]}."))) NIL NIL -(-1165 R) +(-1168 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| (-961) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasAttribute| |#1| (QUOTE -4381))) -(-1166) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| (-964) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasAttribute| |#1| (QUOTE -4388))) +(-1169) ((|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 -(-1167) +(-1170) ((|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 -(-1168) +(-1171) ((|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}{symbols,{} 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: Integer,{} DoubleFloat,{} Symbol,{} String,{} SExpression. See Also: SExpression. 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|) $ (|[\|\|]| (|Symbol|))) "\\spad{x case Symbol} is \\spad{true} if \\spad{`x'} really is a Symbol") (((|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|) (|Symbol|) (|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| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Symbol|) (|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.") (((|Symbol|) $) "\\spad{autoCoerce(s)} forcibly extracts a symbo 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'}.") (((|Symbol|) $) "\\spad{coerce(s)} extracts a symbol 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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1169 R) +(-1172 N) +((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files."))) +NIL +NIL +(-1173 N) +((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample()} returns 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 +(-1174 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 -(-1170) +(-1175) ((|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()} returns a string representation of a filename extension for native modules.")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform()} returns 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 -(-1171 S) +(-1176 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 -(-1172 S) +(-1177 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 -(-1173 |Key| |Entry|) +(-1178 |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}"))) -((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) -(-1174 R) +((-4390 . T) (-4391 . T)) +((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) +(-1179 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{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL NIL -(-1175 S |Key| |Entry|) +(-1180 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 -(-1176 |Key| |Entry|) +(-1181 |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})}."))) -((-4384 . T)) +((-4391 . T)) NIL -(-1177 |Key| |Entry|) +(-1182 |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 -(-1178) +(-1183) ((|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 -(-1179 S) +(-1184 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 -(-1180) +(-1185) ((|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 -(-1181) +(-1186) ((|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 -(-1182 R) +(-1187 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 -(-1183) +(-1188) ((|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 -(-1184 S) +(-1189 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1185) +(-1190) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1186 S) +(-1191 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4384 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-1187 S) +((-4391 . T) (-4390 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-1192 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1188) +(-1193) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1189 R -3189) +(-1194 R -3214) ((|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 -(-1190 R |Row| |Col| M) +(-1195 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 -(-1191 R -3189) +(-1196 R -3214) ((|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 -606) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -876) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -876) (|devaluate| |#1|))))) -(-1192 S R E V P) +((-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -879) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -879) (|devaluate| |#1|))))) +(-1197 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 (-367)))) -(-1193 R E V P) +(-1198 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL -(-1194 |Coef|) +(-1199 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) -(-1195 |Curve|) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-362)))) +(-1200 |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 -(-1196) +(-1201) ((|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 -(-1197 S) +(-1202 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 (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-1198 -3189) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-1203 -3214) ((|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 -(-1199) +(-1204) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1200) +(-1205) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1201 S) +(-1206 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 < \\spad{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 < \\spad{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 (-841)))) -(-1202) +((|HasCategory| |#1| (QUOTE (-844)))) +(-1207) ((|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 -(-1203 S) +(-1208 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 -(-1204) +(-1209) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +NIL +(-1210) +((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) +NIL +NIL +(-1211) +((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL -(-1205 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +NIL +(-1212 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1206 |Coef|) +(-1213 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1207 S |Coef| UTS) +(-1214 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 (-362)))) -(-1208 |Coef| UTS) +(-1215 |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)}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1209 |Coef| UTS) +(-1216 |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)}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-811)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-841)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-899)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-1012)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-1138)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-3994 (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-144))))) (-3994 (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-146))))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|))))) (|HasCategory| (-558) (QUOTE 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for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1212 R S) +(-1219 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) 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(SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) NIL -((|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (QUOTE (-1087)))) -(-1214 |x| R |y| S) +((|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) +(-1221 |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 -(-1215 R Q UP) +(-1222 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 -(-1216 R UP) +(-1223 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 -(-1217 R UP) +(-1224 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 -(-1218 R U) +(-1225 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 -(-1219 |x| R) +(-1226 |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}"))) -(((-4385 "*") |has| |#2| (-171)) (-4376 |has| |#2| (-550)) (-4379 |has| |#2| (-362)) (-4381 |has| |#2| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-1138))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) -(-1220 R PR S PS) +(((-4392 "*") |has| |#2| (-171)) (-4383 |has| |#2| (-553)) (-4386 |has| |#2| (-362)) (-4388 |has| |#2| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#2| (QUOTE (-902))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-1141))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE -4388)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) +(-1227 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1221 S R) +(-1228 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 -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-1138)))) -(-1222 R) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-1141)))) +(-1229 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}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4379 |has| |#1| (-362)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4386 |has| |#1| (-362)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) NIL -(-1223 S |Coef| |Expon|) +(-1230 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}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|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 -890) (QUOTE (-1163)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1099))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3940) (LIST (|devaluate| |#2|) (QUOTE (-1163)))))) -(-1224 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1102))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4022) (LIST (|devaluate| |#2|) (QUOTE (-1166)))))) +(-1231 |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}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1225 RC P) +(-1232 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1226 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1233 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1227 |Coef|) +(-1234 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1228 S |Coef| ULS) +(-1235 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 -(-1229 |Coef| ULS) +(-1236 |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)}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1230 |Coef| ULS) +(-1237 |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)}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -1337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) -(-1231 |Coef| |var| |cen|) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) +(-1238 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -1337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) -(-1232 R FE |var| |cen|) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) +(-1239 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))}."))) -(((-4385 "*") |has| (-1231 |#2| |#3| |#4|) (-171)) (-4376 |has| (-1231 |#2| |#3| |#4|) (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-171))) (-3994 (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-362))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-450))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-550)))) -(-1233 A S) +(((-4392 "*") |has| (-1238 |#2| |#3| |#4|) (-171)) (-4383 |has| (-1238 |#2| |#3| |#4|) (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| (-1238 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-171))) (-4007 (|HasCategory| (-1238 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-1238 |#2| |#3| |#4|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| (-1238 |#2| |#3| |#4|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-1238 |#2| |#3| |#4|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-362))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-450))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-553)))) +(-1240 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4384))) -(-1234 S) +((|HasAttribute| |#1| (QUOTE -4391))) +(-1241 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1235 |Coef1| |Coef2| UTS1 UTS2) +(-1242 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1236 S |Coef|) +(-1243 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-558)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasSignature| |#2| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1337) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1163))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362)))) -(-1237 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-952))) (|HasCategory| |#2| (QUOTE (-1190))) (|HasSignature| |#2| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1842) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1166))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362)))) +(-1244 |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."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1238 |Coef| |var| |cen|) +(-1245 |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|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|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| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{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}."))) -(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -1337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) -(-1239 |Coef| UTS) +(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-765)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-765)) (|devaluate| |#1|)))) (|HasCategory| (-765) (QUOTE (-1102))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-765))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-765))))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) +(-1246 |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 -(-1240 -3189 UP L UTS) +(-1247 -3214 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 (-550)))) -(-1241) +((|HasCategory| |#1| (QUOTE (-553)))) +(-1248) ((|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 -(-1242 |sym|) +(-1249 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1243 S R) +(-1250 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 (-992))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1244 R) +((|HasCategory| |#2| (QUOTE (-995))) (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (QUOTE (-720))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1251 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4384 . T) (-4383 . T)) +((-4391 . T) (-4390 . T)) NIL -(-1245 A B) +(-1252 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1246 R) +(-1253 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4384 . T) (-4383 . T)) -((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-1247) +((-4391 . T) (-4390 . T)) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#1| (QUOTE (-1042))) (-12 (|HasCategory| |#1| (QUOTE (-995))) (|HasCategory| |#1| (QUOTE (-1042)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-1254) ((|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,{}\\spad{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{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\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(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\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 -(-1248) +(-1255) ((|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 -(-1249) +(-1256) ((|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 -(-1250) +(-1257) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{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 -(-1251) +(-1258) ((|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| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1252 A S) +(-1259 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1253 S) +(-1260 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}."))) -((-4378 . T) (-4377 . T)) +((-4385 . T) (-4384 . T)) NIL -(-1254 R) +(-1261 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 -(-1255 K R UP -3189) +(-1262 K R UP -3214) ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL -(-1256) +(-1263) ((|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 -(-1257) +(-1264) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1258 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1265 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)"))) -((-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) (-4380 . T)) +((-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) (-4387 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362)))) -(-1259 R E V P) +(-1266 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}}."))) -((-4384 . T) (-4383 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -605) (QUOTE (-853))))) -(-1260 R) +((-4391 . T) (-4390 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -608) (QUOTE (-856))))) +(-1267 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})"))) -((-4377 . T) (-4378 . T) (-4380 . T)) +((-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1261 |vl| R) +(-1268 |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."))) -((-4380 . T) (-4376 |has| |#2| (-6 -4376)) (-4378 . T) (-4377 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4376))) -(-1262 R |VarSet| XPOLY) +((-4387 . T) (-4383 |has| |#2| (-6 -4383)) (-4385 . T) (-4384 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4383))) +(-1269 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 -(-1263 |vl| R) +(-1270 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4376 |has| |#2| (-6 -4376)) (-4378 . T) (-4377 . T) (-4380 . T)) +((-4383 |has| |#2| (-6 -4383)) (-4385 . T) (-4384 . T) (-4387 . T)) NIL -(-1264 S -3189) +(-1271 S -3214) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146)))) -(-1265 -3189) +(-1272 -3214) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL -(-1266 |VarSet| R) +(-1273 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4376 |has| |#2| (-6 -4376)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -708) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasAttribute| |#2| (QUOTE -4376))) -(-1267 |vl| R) +((-4383 |has| |#2| (-6 -4383)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -711) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasAttribute| |#2| (QUOTE -4383))) +(-1274 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4376 |has| |#2| (-6 -4376)) (-4378 . T) (-4377 . T) (-4380 . T)) +((-4383 |has| |#2| (-6 -4383)) (-4385 . T) (-4384 . T) (-4387 . T)) NIL -(-1268 R) +(-1275 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4376 |has| |#1| (-6 -4376)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasAttribute| |#1| (QUOTE -4376))) -(-1269 R E) +((-4383 |has| |#1| (-6 -4383)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasAttribute| |#1| (QUOTE -4383))) +(-1276 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4380 . T) (-4381 |has| |#1| (-6 -4381)) (-4376 |has| |#1| (-6 -4376)) (-4378 . T) (-4377 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasAttribute| |#1| (QUOTE -4381)) (|HasAttribute| |#1| (QUOTE -4376))) -(-1270 |VarSet| R) +((-4387 . T) (-4388 |has| |#1| (-6 -4388)) (-4383 |has| |#1| (-6 -4383)) (-4385 . T) (-4384 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4387)) (|HasAttribute| |#1| (QUOTE -4388)) (|HasAttribute| |#1| (QUOTE -4383))) +(-1277 |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."))) -((-4376 |has| |#2| (-6 -4376)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4376))) -(-1271 A) +((-4383 |has| |#2| (-6 -4383)) (-4385 . T) (-4384 . T) (-4387 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4383))) +(-1278 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 -(-1272 R |ls| |ls2|) +(-1279 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 -(-1273 R) +(-1280 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 -(-1274 |p|) +(-1281 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +(((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) NIL NIL NIL @@ -5044,4 +5072,4 @@ NIL NIL NIL NIL -((-3 NIL 2275560 2275565 2275570 2275575) (-2 NIL 2275540 2275545 2275550 2275555) (-1 NIL 2275520 2275525 2275530 2275535) (0 NIL 2275500 2275505 2275510 2275515) (-1274 "ZMOD.spad" 2275309 2275322 2275438 2275495) (-1273 "ZLINDEP.spad" 2274353 2274364 2275299 2275304) (-1272 "ZDSOLVE.spad" 2264202 2264224 2274343 2274348) (-1271 "YSTREAM.spad" 2263695 2263706 2264192 2264197) (-1270 "XRPOLY.spad" 2262915 2262935 2263551 2263620) (-1269 "XPR.spad" 2260706 2260719 2262633 2262732) (-1268 "XPOLY.spad" 2260261 2260272 2260562 2260631) (-1267 "XPOLYC.spad" 2259578 2259594 2260187 2260256) (-1266 "XPBWPOLY.spad" 2258015 2258035 2259358 2259427) (-1265 "XF.spad" 2256476 2256491 2257917 2258010) (-1264 "XF.spad" 2254917 2254934 2256360 2256365) (-1263 "XFALG.spad" 2251941 2251957 2254843 2254912) (-1262 "XEXPPKG.spad" 2251192 2251218 2251931 2251936) (-1261 "XDPOLY.spad" 2250806 2250822 2251048 2251117) (-1260 "XALG.spad" 2250466 2250477 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1992306) (-1148 "STTFNC.spad" 1984878 1984894 1988400 1988405) (-1147 "STTAYLOR.spad" 1977276 1977287 1984759 1984764) (-1146 "STRTBL.spad" 1975781 1975798 1975930 1975957) (-1145 "STRING.spad" 1975190 1975199 1975204 1975231) (-1144 "STRICAT.spad" 1974978 1974987 1975158 1975185) (-1143 "STREAM.spad" 1971836 1971847 1974503 1974518) (-1142 "STREAM3.spad" 1971381 1971396 1971826 1971831) (-1141 "STREAM2.spad" 1970449 1970462 1971371 1971376) (-1140 "STREAM1.spad" 1970153 1970164 1970439 1970444) (-1139 "STINPROD.spad" 1969059 1969075 1970143 1970148) (-1138 "STEP.spad" 1968260 1968269 1969049 1969054) (-1137 "STBL.spad" 1966786 1966814 1966953 1966968) (-1136 "STAGG.spad" 1965861 1965872 1966776 1966781) (-1135 "STAGG.spad" 1964934 1964947 1965851 1965856) (-1134 "STACK.spad" 1964285 1964296 1964541 1964568) (-1133 "SREGSET.spad" 1961989 1962006 1963931 1963958) (-1132 "SRDCMPK.spad" 1960534 1960554 1961979 1961984) (-1131 "SRAGG.spad" 1955631 1955640 1960502 1960529) (-1130 "SRAGG.spad" 1950748 1950759 1955621 1955626) (-1129 "SQMATRIX.spad" 1948364 1948382 1949280 1949367) (-1128 "SPLTREE.spad" 1942916 1942929 1947800 1947827) (-1127 "SPLNODE.spad" 1939504 1939517 1942906 1942911) (-1126 "SPFCAT.spad" 1938281 1938290 1939494 1939499) (-1125 "SPECOUT.spad" 1936831 1936840 1938271 1938276) (-1124 "SPADXPT.spad" 1928970 1928979 1936821 1936826) (-1123 "spad-parser.spad" 1928435 1928444 1928960 1928965) (-1122 "SPADAST.spad" 1928136 1928145 1928425 1928430) (-1121 "SPACEC.spad" 1912149 1912160 1928126 1928131) (-1120 "SPACE3.spad" 1911925 1911936 1912139 1912144) (-1119 "SORTPAK.spad" 1911470 1911483 1911881 1911886) (-1118 "SOLVETRA.spad" 1909227 1909238 1911460 1911465) (-1117 "SOLVESER.spad" 1907747 1907758 1909217 1909222) (-1116 "SOLVERAD.spad" 1903757 1903768 1907737 1907742) (-1115 "SOLVEFOR.spad" 1902177 1902195 1903747 1903752) (-1114 "SNTSCAT.spad" 1901777 1901794 1902145 1902172) (-1113 "SMTS.spad" 1900037 1900063 1901342 1901439) (-1112 "SMP.spad" 1897476 1897496 1897866 1897993) (-1111 "SMITH.spad" 1896319 1896344 1897466 1897471) (-1110 "SMATCAT.spad" 1894429 1894459 1896263 1896314) (-1109 "SMATCAT.spad" 1892471 1892503 1894307 1894312) (-1108 "SKAGG.spad" 1891432 1891443 1892439 1892466) (-1107 "SINT.spad" 1890258 1890267 1891298 1891427) (-1106 "SIMPAN.spad" 1889986 1889995 1890248 1890253) (-1105 "SIG.spad" 1889314 1889323 1889976 1889981) (-1104 "SIGNRF.spad" 1888422 1888433 1889304 1889309) (-1103 "SIGNEF.spad" 1887691 1887708 1888412 1888417) (-1102 "SIGAST.spad" 1887072 1887081 1887681 1887686) (-1101 "SHP.spad" 1884990 1885005 1887028 1887033) (-1100 "SHDP.spad" 1874701 1874728 1875210 1875341) (-1099 "SGROUP.spad" 1874309 1874318 1874691 1874696) (-1098 "SGROUP.spad" 1873915 1873926 1874299 1874304) (-1097 "SGCF.spad" 1866796 1866805 1873905 1873910) (-1096 "SFRTCAT.spad" 1865724 1865741 1866764 1866791) (-1095 "SFRGCD.spad" 1864787 1864807 1865714 1865719) (-1094 "SFQCMPK.spad" 1859424 1859444 1864777 1864782) (-1093 "SFORT.spad" 1858859 1858873 1859414 1859419) (-1092 "SEXOF.spad" 1858702 1858742 1858849 1858854) (-1091 "SEX.spad" 1858594 1858603 1858692 1858697) (-1090 "SEXCAT.spad" 1856145 1856185 1858584 1858589) (-1089 "SET.spad" 1854445 1854456 1855566 1855605) (-1088 "SETMN.spad" 1852879 1852896 1854435 1854440) (-1087 "SETCAT.spad" 1852364 1852373 1852869 1852874) (-1086 "SETCAT.spad" 1851847 1851858 1852354 1852359) (-1085 "SETAGG.spad" 1848368 1848379 1851827 1851842) (-1084 "SETAGG.spad" 1844897 1844910 1848358 1848363) (-1083 "SEQAST.spad" 1844600 1844609 1844887 1844892) (-1082 "SEGXCAT.spad" 1843722 1843735 1844590 1844595) (-1081 "SEG.spad" 1843535 1843546 1843641 1843646) (-1080 "SEGCAT.spad" 1842442 1842453 1843525 1843530) (-1079 "SEGBIND.spad" 1841514 1841525 1842397 1842402) (-1078 "SEGBIND2.spad" 1841210 1841223 1841504 1841509) (-1077 "SEGAST.spad" 1840924 1840933 1841200 1841205) (-1076 "SEG2.spad" 1840349 1840362 1840880 1840885) (-1075 "SDVAR.spad" 1839625 1839636 1840339 1840344) (-1074 "SDPOL.spad" 1837015 1837026 1837306 1837433) (-1073 "SCPKG.spad" 1835094 1835105 1837005 1837010) (-1072 "SCOPE.spad" 1834239 1834248 1835084 1835089) (-1071 "SCACHE.spad" 1832921 1832932 1834229 1834234) (-1070 "SASTCAT.spad" 1832830 1832839 1832911 1832916) (-1069 "SAOS.spad" 1832702 1832711 1832820 1832825) (-1068 "SAERFFC.spad" 1832415 1832435 1832692 1832697) (-1067 "SAE.spad" 1830590 1830606 1831201 1831336) (-1066 "SAEFACT.spad" 1830291 1830311 1830580 1830585) (-1065 "RURPK.spad" 1827932 1827948 1830281 1830286) (-1064 "RULESET.spad" 1827373 1827397 1827922 1827927) (-1063 "RULE.spad" 1825577 1825601 1827363 1827368) (-1062 "RULECOLD.spad" 1825429 1825442 1825567 1825572) (-1061 "RSTRCAST.spad" 1825146 1825155 1825419 1825424) (-1060 "RSETGCD.spad" 1821524 1821544 1825136 1825141) (-1059 "RSETCAT.spad" 1811308 1811325 1821492 1821519) (-1058 "RSETCAT.spad" 1801112 1801131 1811298 1811303) (-1057 "RSDCMPK.spad" 1799564 1799584 1801102 1801107) (-1056 "RRCC.spad" 1797948 1797978 1799554 1799559) (-1055 "RRCC.spad" 1796330 1796362 1797938 1797943) (-1054 "RPTAST.spad" 1796032 1796041 1796320 1796325) (-1053 "RPOLCAT.spad" 1775392 1775407 1795900 1796027) (-1052 "RPOLCAT.spad" 1754466 1754483 1774976 1774981) (-1051 "ROUTINE.spad" 1750329 1750338 1753113 1753140) (-1050 "ROMAN.spad" 1749657 1749666 1750195 1750324) (-1049 "ROIRC.spad" 1748737 1748769 1749647 1749652) (-1048 "RNS.spad" 1747640 1747649 1748639 1748732) (-1047 "RNS.spad" 1746629 1746640 1747630 1747635) (-1046 "RNG.spad" 1746364 1746373 1746619 1746624) (-1045 "RMODULE.spad" 1746002 1746013 1746354 1746359) (-1044 "RMCAT2.spad" 1745410 1745467 1745992 1745997) (-1043 "RMATRIX.spad" 1744234 1744253 1744577 1744616) (-1042 "RMATCAT.spad" 1739767 1739798 1744190 1744229) (-1041 "RMATCAT.spad" 1735190 1735223 1739615 1739620) (-1040 "RINTERP.spad" 1735078 1735098 1735180 1735185) (-1039 "RING.spad" 1734548 1734557 1735058 1735073) (-1038 "RING.spad" 1734026 1734037 1734538 1734543) (-1037 "RIDIST.spad" 1733410 1733419 1734016 1734021) (-1036 "RGCHAIN.spad" 1731989 1732005 1732895 1732922) (-1035 "RGBCSPC.spad" 1731770 1731782 1731979 1731984) (-1034 "RGBCMDL.spad" 1731300 1731312 1731760 1731765) (-1033 "RF.spad" 1728914 1728925 1731290 1731295) (-1032 "RFFACTOR.spad" 1728376 1728387 1728904 1728909) (-1031 "RFFACT.spad" 1728111 1728123 1728366 1728371) (-1030 "RFDIST.spad" 1727099 1727108 1728101 1728106) (-1029 "RETSOL.spad" 1726516 1726529 1727089 1727094) (-1028 "RETRACT.spad" 1725944 1725955 1726506 1726511) (-1027 "RETRACT.spad" 1725370 1725383 1725934 1725939) (-1026 "RETAST.spad" 1725182 1725191 1725360 1725365) (-1025 "RESULT.spad" 1723242 1723251 1723829 1723856) (-1024 "RESRING.spad" 1722589 1722636 1723180 1723237) (-1023 "RESLATC.spad" 1721913 1721924 1722579 1722584) (-1022 "REPSQ.spad" 1721642 1721653 1721903 1721908) (-1021 "REP.spad" 1719194 1719203 1721632 1721637) (-1020 "REPDB.spad" 1718899 1718910 1719184 1719189) (-1019 "REP2.spad" 1708471 1708482 1718741 1718746) (-1018 "REP1.spad" 1702461 1702472 1708421 1708426) (-1017 "REGSET.spad" 1700258 1700275 1702107 1702134) (-1016 "REF.spad" 1699587 1699598 1700213 1700218) (-1015 "REDORDER.spad" 1698763 1698780 1699577 1699582) (-1014 "RECLOS.spad" 1697546 1697566 1698250 1698343) (-1013 "REALSOLV.spad" 1696678 1696687 1697536 1697541) (-1012 "REAL.spad" 1696550 1696559 1696668 1696673) (-1011 "REAL0Q.spad" 1693832 1693847 1696540 1696545) (-1010 "REAL0.spad" 1690660 1690675 1693822 1693827) (-1009 "RDUCEAST.spad" 1690381 1690390 1690650 1690655) (-1008 "RDIV.spad" 1690032 1690057 1690371 1690376) (-1007 "RDIST.spad" 1689595 1689606 1690022 1690027) (-1006 "RDETRS.spad" 1688391 1688409 1689585 1689590) (-1005 "RDETR.spad" 1686498 1686516 1688381 1688386) (-1004 "RDEEFS.spad" 1685571 1685588 1686488 1686493) (-1003 "RDEEF.spad" 1684567 1684584 1685561 1685566) (-1002 "RCFIELD.spad" 1681753 1681762 1684469 1684562) (-1001 "RCFIELD.spad" 1679025 1679036 1681743 1681748) (-1000 "RCAGG.spad" 1676937 1676948 1679015 1679020) (-999 "RCAGG.spad" 1674777 1674789 1676856 1676861) (-998 "RATRET.spad" 1674138 1674148 1674767 1674772) (-997 "RATFACT.spad" 1673831 1673842 1674128 1674133) (-996 "RANDSRC.spad" 1673151 1673159 1673821 1673826) (-995 "RADUTIL.spad" 1672906 1672914 1673141 1673146) (-994 "RADIX.spad" 1669808 1669821 1671373 1671466) (-993 "RADFF.spad" 1668222 1668258 1668340 1668496) (-992 "RADCAT.spad" 1667816 1667824 1668212 1668217) (-991 "RADCAT.spad" 1667408 1667418 1667806 1667811) (-990 "QUEUE.spad" 1666751 1666761 1667015 1667042) (-989 "QUAT.spad" 1665333 1665343 1665675 1665740) (-988 "QUATCT2.spad" 1664952 1664970 1665323 1665328) (-987 "QUATCAT.spad" 1663117 1663127 1664882 1664947) (-986 "QUATCAT.spad" 1661033 1661045 1662800 1662805) (-985 "QUAGG.spad" 1659859 1659869 1661001 1661028) (-984 "QQUTAST.spad" 1659628 1659636 1659849 1659854) (-983 "QFORM.spad" 1659091 1659105 1659618 1659623) (-982 "QFCAT.spad" 1657794 1657804 1658993 1659086) (-981 "QFCAT.spad" 1656088 1656100 1657289 1657294) (-980 "QFCAT2.spad" 1655779 1655795 1656078 1656083) (-979 "QEQUAT.spad" 1655336 1655344 1655769 1655774) (-978 "QCMPACK.spad" 1650083 1650102 1655326 1655331) (-977 "QALGSET.spad" 1646158 1646190 1649997 1650002) (-976 "QALGSET2.spad" 1644154 1644172 1646148 1646153) (-975 "PWFFINTB.spad" 1641464 1641485 1644144 1644149) (-974 "PUSHVAR.spad" 1640793 1640812 1641454 1641459) (-973 "PTRANFN.spad" 1636919 1636929 1640783 1640788) (-972 "PTPACK.spad" 1634007 1634017 1636909 1636914) (-971 "PTFUNC2.spad" 1633828 1633842 1633997 1634002) (-970 "PTCAT.spad" 1633077 1633087 1633796 1633823) (-969 "PSQFR.spad" 1632384 1632408 1633067 1633072) (-968 "PSEUDLIN.spad" 1631242 1631252 1632374 1632379) (-967 "PSETPK.spad" 1616675 1616691 1631120 1631125) (-966 "PSETCAT.spad" 1610595 1610618 1616655 1616670) (-965 "PSETCAT.spad" 1604489 1604514 1610551 1610556) (-964 "PSCURVE.spad" 1603472 1603480 1604479 1604484) (-963 "PSCAT.spad" 1602239 1602268 1603370 1603467) (-962 "PSCAT.spad" 1601096 1601127 1602229 1602234) (-961 "PRTITION.spad" 1600041 1600049 1601086 1601091) (-960 "PRTDAST.spad" 1599760 1599768 1600031 1600036) (-959 "PRS.spad" 1589322 1589339 1599716 1599721) (-958 "PRQAGG.spad" 1588753 1588763 1589290 1589317) (-957 "PROPLOG.spad" 1588156 1588164 1588743 1588748) (-956 "PROPFRML.spad" 1586074 1586085 1588146 1588151) (-955 "PROPERTY.spad" 1585568 1585576 1586064 1586069) (-954 "PRODUCT.spad" 1583248 1583260 1583534 1583589) (-953 "PR.spad" 1581634 1581646 1582339 1582466) (-952 "PRINT.spad" 1581386 1581394 1581624 1581629) (-951 "PRIMES.spad" 1579637 1579647 1581376 1581381) (-950 "PRIMELT.spad" 1577618 1577632 1579627 1579632) (-949 "PRIMCAT.spad" 1577241 1577249 1577608 1577613) (-948 "PRIMARR.spad" 1576246 1576256 1576424 1576451) (-947 "PRIMARR2.spad" 1574969 1574981 1576236 1576241) (-946 "PREASSOC.spad" 1574341 1574353 1574959 1574964) (-945 "PPCURVE.spad" 1573478 1573486 1574331 1574336) (-944 "PORTNUM.spad" 1573253 1573261 1573468 1573473) (-943 "POLYROOT.spad" 1572082 1572104 1573209 1573214) (-942 "POLY.spad" 1569379 1569389 1569896 1570023) (-941 "POLYLIFT.spad" 1568640 1568663 1569369 1569374) (-940 "POLYCATQ.spad" 1566742 1566764 1568630 1568635) (-939 "POLYCAT.spad" 1560148 1560169 1566610 1566737) (-938 "POLYCAT.spad" 1552856 1552879 1559320 1559325) (-937 "POLY2UP.spad" 1552304 1552318 1552846 1552851) (-936 "POLY2.spad" 1551899 1551911 1552294 1552299) (-935 "POLUTIL.spad" 1550840 1550869 1551855 1551860) (-934 "POLTOPOL.spad" 1549588 1549603 1550830 1550835) (-933 "POINT.spad" 1548427 1548437 1548514 1548541) (-932 "PNTHEORY.spad" 1545093 1545101 1548417 1548422) (-931 "PMTOOLS.spad" 1543850 1543864 1545083 1545088) (-930 "PMSYM.spad" 1543395 1543405 1543840 1543845) (-929 "PMQFCAT.spad" 1542982 1542996 1543385 1543390) (-928 "PMPRED.spad" 1542451 1542465 1542972 1542977) (-927 "PMPREDFS.spad" 1541895 1541917 1542441 1542446) (-926 "PMPLCAT.spad" 1540965 1540983 1541827 1541832) (-925 "PMLSAGG.spad" 1540546 1540560 1540955 1540960) (-924 "PMKERNEL.spad" 1540113 1540125 1540536 1540541) (-923 "PMINS.spad" 1539689 1539699 1540103 1540108) (-922 "PMFS.spad" 1539262 1539280 1539679 1539684) (-921 "PMDOWN.spad" 1538548 1538562 1539252 1539257) (-920 "PMASS.spad" 1537560 1537568 1538538 1538543) (-919 "PMASSFS.spad" 1536529 1536545 1537550 1537555) (-918 "PLOTTOOL.spad" 1536309 1536317 1536519 1536524) (-917 "PLOT.spad" 1531140 1531148 1536299 1536304) (-916 "PLOT3D.spad" 1527560 1527568 1531130 1531135) (-915 "PLOT1.spad" 1526701 1526711 1527550 1527555) (-914 "PLEQN.spad" 1513917 1513944 1526691 1526696) (-913 "PINTERP.spad" 1513533 1513552 1513907 1513912) (-912 "PINTERPA.spad" 1513315 1513331 1513523 1513528) (-911 "PI.spad" 1512922 1512930 1513289 1513310) (-910 "PID.spad" 1511878 1511886 1512848 1512917) (-909 "PICOERCE.spad" 1511535 1511545 1511868 1511873) (-908 "PGROEB.spad" 1510132 1510146 1511525 1511530) (-907 "PGE.spad" 1501385 1501393 1510122 1510127) (-906 "PGCD.spad" 1500267 1500284 1501375 1501380) (-905 "PFRPAC.spad" 1499410 1499420 1500257 1500262) (-904 "PFR.spad" 1496067 1496077 1499312 1499405) (-903 "PFOTOOLS.spad" 1495325 1495341 1496057 1496062) (-902 "PFOQ.spad" 1494695 1494713 1495315 1495320) (-901 "PFO.spad" 1494114 1494141 1494685 1494690) (-900 "PF.spad" 1493688 1493700 1493919 1494012) (-899 "PFECAT.spad" 1491354 1491362 1493614 1493683) (-898 "PFECAT.spad" 1489048 1489058 1491310 1491315) (-897 "PFBRU.spad" 1486918 1486930 1489038 1489043) (-896 "PFBR.spad" 1484456 1484479 1486908 1486913) (-895 "PERM.spad" 1480137 1480147 1484286 1484301) (-894 "PERMGRP.spad" 1474873 1474883 1480127 1480132) (-893 "PERMCAT.spad" 1473425 1473435 1474853 1474868) (-892 "PERMAN.spad" 1471957 1471971 1473415 1473420) (-891 "PENDTREE.spad" 1471296 1471306 1471586 1471591) (-890 "PDRING.spad" 1469787 1469797 1471276 1471291) (-889 "PDRING.spad" 1468286 1468298 1469777 1469782) (-888 "PDEPROB.spad" 1467301 1467309 1468276 1468281) (-887 "PDEPACK.spad" 1461303 1461311 1467291 1467296) (-886 "PDECOMP.spad" 1460765 1460782 1461293 1461298) (-885 "PDECAT.spad" 1459119 1459127 1460755 1460760) (-884 "PCOMP.spad" 1458970 1458983 1459109 1459114) (-883 "PBWLB.spad" 1457552 1457569 1458960 1458965) (-882 "PATTERN.spad" 1451983 1451993 1457542 1457547) (-881 "PATTERN2.spad" 1451719 1451731 1451973 1451978) (-880 "PATTERN1.spad" 1450021 1450037 1451709 1451714) (-879 "PATRES.spad" 1447568 1447580 1450011 1450016) (-878 "PATRES2.spad" 1447230 1447244 1447558 1447563) (-877 "PATMATCH.spad" 1445387 1445418 1446938 1446943) (-876 "PATMAB.spad" 1444812 1444822 1445377 1445382) (-875 "PATLRES.spad" 1443896 1443910 1444802 1444807) (-874 "PATAB.spad" 1443660 1443670 1443886 1443891) (-873 "PARTPERM.spad" 1441022 1441030 1443650 1443655) (-872 "PARSURF.spad" 1440450 1440478 1441012 1441017) (-871 "PARSU2.spad" 1440245 1440261 1440440 1440445) (-870 "script-parser.spad" 1439765 1439773 1440235 1440240) (-869 "PARSCURV.spad" 1439193 1439221 1439755 1439760) (-868 "PARSC2.spad" 1438982 1438998 1439183 1439188) (-867 "PARPCURV.spad" 1438440 1438468 1438972 1438977) (-866 "PARPC2.spad" 1438229 1438245 1438430 1438435) (-865 "PAN2EXPR.spad" 1437641 1437649 1438219 1438224) (-864 "PALETTE.spad" 1436611 1436619 1437631 1437636) (-863 "PAIR.spad" 1435594 1435607 1436199 1436204) (-862 "PADICRC.spad" 1432924 1432942 1434099 1434192) (-861 "PADICRAT.spad" 1430939 1430951 1431160 1431253) (-860 "PADIC.spad" 1430634 1430646 1430865 1430934) (-859 "PADICCT.spad" 1429175 1429187 1430560 1430629) (-858 "PADEPAC.spad" 1427854 1427873 1429165 1429170) (-857 "PADE.spad" 1426594 1426610 1427844 1427849) (-856 "OWP.spad" 1425834 1425864 1426452 1426519) (-855 "OVAR.spad" 1425615 1425638 1425824 1425829) (-854 "OUT.spad" 1424699 1424707 1425605 1425610) (-853 "OUTFORM.spad" 1413995 1414003 1424689 1424694) (-852 "OUTBFILE.spad" 1413413 1413421 1413985 1413990) (-851 "OUTBCON.spad" 1412888 1412896 1413403 1413408) (-850 "OUTBCON.spad" 1412361 1412371 1412878 1412883) (-849 "OSI.spad" 1411836 1411844 1412351 1412356) (-848 "OSGROUP.spad" 1411754 1411762 1411826 1411831) (-847 "ORTHPOL.spad" 1410215 1410225 1411671 1411676) (-846 "OREUP.spad" 1409668 1409696 1409895 1409934) (-845 "ORESUP.spad" 1408967 1408991 1409348 1409387) (-844 "OREPCTO.spad" 1406786 1406798 1408887 1408892) (-843 "OREPCAT.spad" 1400843 1400853 1406742 1406781) (-842 "OREPCAT.spad" 1394790 1394802 1400691 1400696) (-841 "ORDSET.spad" 1393956 1393964 1394780 1394785) (-840 "ORDSET.spad" 1393120 1393130 1393946 1393951) (-839 "ORDRING.spad" 1392510 1392518 1393100 1393115) (-838 "ORDRING.spad" 1391908 1391918 1392500 1392505) (-837 "ORDMON.spad" 1391763 1391771 1391898 1391903) (-836 "ORDFUNS.spad" 1390889 1390905 1391753 1391758) (-835 "ORDFIN.spad" 1390709 1390717 1390879 1390884) (-834 "ORDCOMP.spad" 1389174 1389184 1390256 1390285) (-833 "ORDCOMP2.spad" 1388459 1388471 1389164 1389169) (-832 "OPTPROB.spad" 1387097 1387105 1388449 1388454) (-831 "OPTPACK.spad" 1379482 1379490 1387087 1387092) (-830 "OPTCAT.spad" 1377157 1377165 1379472 1379477) (-829 "OPSIG.spad" 1376809 1376817 1377147 1377152) (-828 "OPQUERY.spad" 1376358 1376366 1376799 1376804) (-827 "OP.spad" 1376100 1376110 1376180 1376247) (-826 "OPERCAT.spad" 1375688 1375698 1376090 1376095) (-825 "OPERCAT.spad" 1375274 1375286 1375678 1375683) (-824 "ONECOMP.spad" 1374019 1374029 1374821 1374850) (-823 "ONECOMP2.spad" 1373437 1373449 1374009 1374014) (-822 "OMSERVER.spad" 1372439 1372447 1373427 1373432) (-821 "OMSAGG.spad" 1372227 1372237 1372395 1372434) (-820 "OMPKG.spad" 1370839 1370847 1372217 1372222) (-819 "OM.spad" 1369804 1369812 1370829 1370834) (-818 "OMLO.spad" 1369229 1369241 1369690 1369729) (-817 "OMEXPR.spad" 1369063 1369073 1369219 1369224) (-816 "OMERR.spad" 1368606 1368614 1369053 1369058) (-815 "OMERRK.spad" 1367640 1367648 1368596 1368601) (-814 "OMENC.spad" 1366984 1366992 1367630 1367635) 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"DECIMAL.spad" 248096 248104 248457 248550) (-215 "DDFACT.spad" 245895 245912 248086 248091) (-214 "DBLRESP.spad" 245493 245517 245885 245890) (-213 "DBASE.spad" 244147 244157 245483 245488) (-212 "DATAARY.spad" 243609 243622 244137 244142) (-211 "D03FAFA.spad" 243437 243445 243599 243604) (-210 "D03EEFA.spad" 243257 243265 243427 243432) (-209 "D03AGNT.spad" 242337 242345 243247 243252) (-208 "D02EJFA.spad" 241799 241807 242327 242332) (-207 "D02CJFA.spad" 241277 241285 241789 241794) (-206 "D02BHFA.spad" 240767 240775 241267 241272) (-205 "D02BBFA.spad" 240257 240265 240757 240762) (-204 "D02AGNT.spad" 235061 235069 240247 240252) (-203 "D01WGTS.spad" 233380 233388 235051 235056) (-202 "D01TRNS.spad" 233357 233365 233370 233375) (-201 "D01GBFA.spad" 232879 232887 233347 233352) (-200 "D01FCFA.spad" 232401 232409 232869 232874) (-199 "D01ASFA.spad" 231869 231877 232391 232396) (-198 "D01AQFA.spad" 231315 231323 231859 231864) (-197 "D01APFA.spad" 230739 230747 231305 231310) (-196 "D01ANFA.spad" 230233 230241 230729 230734) (-195 "D01AMFA.spad" 229743 229751 230223 230228) (-194 "D01ALFA.spad" 229283 229291 229733 229738) (-193 "D01AKFA.spad" 228809 228817 229273 229278) (-192 "D01AJFA.spad" 228332 228340 228799 228804) (-191 "D01AGNT.spad" 224391 224399 228322 228327) (-190 "CYCLOTOM.spad" 223897 223905 224381 224386) (-189 "CYCLES.spad" 220729 220737 223887 223892) (-188 "CVMP.spad" 220146 220156 220719 220724) (-187 "CTRIGMNP.spad" 218636 218652 220136 220141) (-186 "CTOR.spad" 218536 218544 218626 218631) (-185 "CTORKIND.spad" 218139 218147 218526 218531) (-184 "CTORCAT.spad" 217594 217602 218129 218134) (-183 "CTORCAT.spad" 217047 217057 217584 217589) (-182 "CTORCALL.spad" 216627 216635 217037 217042) (-181 "CSTTOOLS.spad" 215870 215883 216617 216622) (-180 "CRFP.spad" 209574 209587 215860 215865) (-179 "CRCEAST.spad" 209294 209302 209564 209569) (-178 "CRAPACK.spad" 208337 208347 209284 209289) (-177 "CPMATCH.spad" 207837 207852 208262 208267) (-176 "CPIMA.spad" 207542 207561 207827 207832) (-175 "COORDSYS.spad" 202435 202445 207532 207537) (-174 "CONTOUR.spad" 201837 201845 202425 202430) (-173 "CONTFRAC.spad" 197449 197459 201739 201832) (-172 "CONDUIT.spad" 197207 197215 197439 197444) (-171 "COMRING.spad" 196881 196889 197145 197202) (-170 "COMPPROP.spad" 196395 196403 196871 196876) (-169 "COMPLPAT.spad" 196162 196177 196385 196390) (-168 "COMPLEX.spad" 190198 190208 190442 190691) (-167 "COMPLEX2.spad" 189911 189923 190188 190193) (-166 "COMPFACT.spad" 189513 189527 189901 189906) (-165 "COMPCAT.spad" 187651 187661 189259 189508) (-164 "COMPCAT.spad" 185470 185482 187080 187085) (-163 "COMMUPC.spad" 185216 185234 185460 185465) (-162 "COMMONOP.spad" 184749 184757 185206 185211) (-161 "COMM.spad" 184558 184566 184739 184744) (-160 "COMMAAST.spad" 184321 184329 184548 184553) (-159 "COMBOPC.spad" 183226 183234 184311 184316) (-158 "COMBINAT.spad" 181971 181981 183216 183221) (-157 "COMBF.spad" 179339 179355 181961 181966) (-156 "COLOR.spad" 178176 178184 179329 179334) (-155 "COLONAST.spad" 177842 177850 178166 178171) (-154 "CMPLXRT.spad" 177551 177568 177832 177837) (-153 "CLLCTAST.spad" 177213 177221 177541 177546) (-152 "CLIP.spad" 173305 173313 177203 177208) (-151 "CLIF.spad" 171944 171960 173261 173300) (-150 "CLAGG.spad" 168429 168439 171934 171939) (-149 "CLAGG.spad" 164785 164797 168292 168297) (-148 "CINTSLPE.spad" 164110 164123 164775 164780) (-147 "CHVAR.spad" 162188 162210 164100 164105) (-146 "CHARZ.spad" 162103 162111 162168 162183) (-145 "CHARPOL.spad" 161611 161621 162093 162098) (-144 "CHARNZ.spad" 161364 161372 161591 161606) (-143 "CHAR.spad" 159232 159240 161354 161359) (-142 "CFCAT.spad" 158548 158556 159222 159227) (-141 "CDEN.spad" 157706 157720 158538 158543) (-140 "CCLASS.spad" 155855 155863 157117 157156) (-139 "CATEGORY.spad" 154945 154953 155845 155850) (-138 "CATCTOR.spad" 154836 154844 154935 154940) (-137 "CATAST.spad" 154463 154471 154826 154831) (-136 "CASEAST.spad" 154177 154185 154453 154458) (-135 "CARTEN.spad" 149280 149304 154167 154172) (-134 "CARTEN2.spad" 148666 148693 149270 149275) (-133 "CARD.spad" 145955 145963 148640 148661) (-132 "CAPSLAST.spad" 145729 145737 145945 145950) (-131 "CACHSET.spad" 145351 145359 145719 145724) (-130 "CABMON.spad" 144904 144912 145341 145346) (-129 "BYTE.spad" 144325 144333 144894 144899) (-128 "BYTEBUF.spad" 142157 142165 143494 143521) (-127 "BTREE.spad" 141226 141236 141764 141791) (-126 "BTOURN.spad" 140229 140239 140833 140860) (-125 "BTCAT.spad" 139617 139627 140197 140224) (-124 "BTCAT.spad" 139025 139037 139607 139612) (-123 "BTAGG.spad" 138147 138155 138993 139020) (-122 "BTAGG.spad" 137289 137299 138137 138142) (-121 "BSTREE.spad" 136024 136034 136896 136923) (-120 "BRILL.spad" 134219 134230 136014 136019) (-119 "BRAGG.spad" 133143 133153 134209 134214) (-118 "BRAGG.spad" 132031 132043 133099 133104) (-117 "BPADICRT.spad" 130012 130024 130267 130360) (-116 "BPADIC.spad" 129676 129688 129938 130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP.spad" 124796 124804 129322 129327) (-113 "BOP1.spad" 122182 122192 124752 124757) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP8.spad" 97774 97787 98721 98726) (-87 "ASP80.spad" 97096 97109 97764 97769) (-86 "ASP7.spad" 96256 96269 97086 97091) (-85 "ASP78.spad" 95707 95720 96246 96251) (-84 "ASP77.spad" 95076 95089 95697 95702) (-83 "ASP74.spad" 94168 94181 95066 95071) (-82 "ASP73.spad" 93439 93452 94158 94163) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP4.spad" 87927 87940 88622 88627) (-77 "ASP49.spad" 86926 86939 87917 87922) (-76 "ASP42.spad" 85333 85372 86916 86921) (-75 "ASP41.spad" 83912 83951 85323 85328) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP1.spad" 67361 67374 67970 67975) (-63 "ASP19.spad" 62047 62060 67351 67356) (-62 "ASP12.spad" 61461 61474 62037 62042) (-61 "ASP10.spad" 60732 60745 61451 61456) (-60 "ARRAY2.spad" 60092 60101 60339 60366) (-59 "ARRAY1.spad" 58927 58936 59275 59302) (-58 "ARRAY12.spad" 57596 57607 58917 58922) (-57 "ARR2CAT.spad" 53258 53279 57564 57591) (-56 "ARR2CAT.spad" 48940 48963 53248 53253) (-55 "ARITY.spad" 48508 48515 48930 48935) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY.spad" 45709 45716 47357 47362) (-51 "ANY1.spad" 44780 44789 45699 45704) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2277553 2277558 2277563 2277568) (-2 NIL 2277533 2277538 2277543 2277548) (-1 NIL 2277513 2277518 2277523 2277528) (0 NIL 2277493 2277498 2277503 2277508) (-1281 "ZMOD.spad" 2277302 2277315 2277431 2277488) (-1280 "ZLINDEP.spad" 2276346 2276357 2277292 2277297) (-1279 "ZDSOLVE.spad" 2266195 2266217 2276336 2276341) (-1278 "YSTREAM.spad" 2265688 2265699 2266185 2266190) (-1277 "XRPOLY.spad" 2264908 2264928 2265544 2265613) (-1276 "XPR.spad" 2262699 2262712 2264626 2264725) (-1275 "XPOLY.spad" 2262254 2262265 2262555 2262624) (-1274 "XPOLYC.spad" 2261571 2261587 2262180 2262249) (-1273 "XPBWPOLY.spad" 2260008 2260028 2261351 2261420) (-1272 "XF.spad" 2258469 2258484 2259910 2260003) (-1271 "XF.spad" 2256910 2256927 2258353 2258358) (-1270 "XFALG.spad" 2253934 2253950 2256836 2256905) (-1269 "XEXPPKG.spad" 2253185 2253211 2253924 2253929) (-1268 "XDPOLY.spad" 2252799 2252815 2253041 2253110) (-1267 "XALG.spad" 2252459 2252470 2252755 2252794) (-1266 "WUTSET.spad" 2248298 2248315 2252105 2252132) (-1265 "WP.spad" 2247497 2247541 2248156 2248223) (-1264 "WHILEAST.spad" 2247295 2247304 2247487 2247492) (-1263 "WHEREAST.spad" 2246966 2246975 2247285 2247290) (-1262 "WFFINTBS.spad" 2244529 2244551 2246956 2246961) (-1261 "WEIER.spad" 2242743 2242754 2244519 2244524) (-1260 "VSPACE.spad" 2242416 2242427 2242711 2242738) (-1259 "VSPACE.spad" 2242109 2242122 2242406 2242411) (-1258 "VOID.spad" 2241786 2241795 2242099 2242104) (-1257 "VIEW.spad" 2239408 2239417 2241776 2241781) (-1256 "VIEWDEF.spad" 2234605 2234614 2239398 2239403) (-1255 "VIEW3D.spad" 2218440 2218449 2234595 2234600) (-1254 "VIEW2D.spad" 2206177 2206186 2218430 2218435) (-1253 "VECTOR.spad" 2204852 2204863 2205103 2205130) (-1252 "VECTOR2.spad" 2203479 2203492 2204842 2204847) (-1251 "VECTCAT.spad" 2201379 2201390 2203447 2203474) (-1250 "VECTCAT.spad" 2199087 2199100 2201157 2201162) (-1249 "VARIABLE.spad" 2198867 2198882 2199077 2199082) (-1248 "UTYPE.spad" 2198511 2198520 2198857 2198862) (-1247 "UTSODETL.spad" 2197804 2197828 2198467 2198472) (-1246 "UTSODE.spad" 2195992 2196012 2197794 2197799) (-1245 "UTS.spad" 2190781 2190809 2194459 2194556) (-1244 "UTSCAT.spad" 2188232 2188248 2190679 2190776) (-1243 "UTSCAT.spad" 2185327 2185345 2187776 2187781) (-1242 "UTS2.spad" 2184920 2184955 2185317 2185322) (-1241 "URAGG.spad" 2179552 2179563 2184910 2184915) (-1240 "URAGG.spad" 2174148 2174161 2179508 2179513) (-1239 "UPXSSING.spad" 2171791 2171817 2173229 2173362) (-1238 "UPXS.spad" 2168939 2168967 2169923 2170072) (-1237 "UPXSCONS.spad" 2166696 2166716 2167071 2167220) (-1236 "UPXSCCA.spad" 2165261 2165281 2166542 2166691) (-1235 "UPXSCCA.spad" 2163968 2163990 2165251 2165256) (-1234 "UPXSCAT.spad" 2162549 2162565 2163814 2163963) (-1233 "UPXS2.spad" 2162090 2162143 2162539 2162544) (-1232 "UPSQFREE.spad" 2160502 2160516 2162080 2162085) (-1231 "UPSCAT.spad" 2158095 2158119 2160400 2160497) (-1230 "UPSCAT.spad" 2155394 2155420 2157701 2157706) (-1229 "UPOLYC.spad" 2150372 2150383 2155236 2155389) (-1228 "UPOLYC.spad" 2145242 2145255 2150108 2150113) (-1227 "UPOLYC2.spad" 2144711 2144730 2145232 2145237) (-1226 "UP.spad" 2141868 2141883 2142261 2142414) (-1225 "UPMP.spad" 2140758 2140771 2141858 2141863) (-1224 "UPDIVP.spad" 2140321 2140335 2140748 2140753) (-1223 "UPDECOMP.spad" 2138558 2138572 2140311 2140316) (-1222 "UPCDEN.spad" 2137765 2137781 2138548 2138553) (-1221 "UP2.spad" 2137127 2137148 2137755 2137760) (-1220 "UNISEG.spad" 2136480 2136491 2137046 2137051) (-1219 "UNISEG2.spad" 2135973 2135986 2136436 2136441) (-1218 "UNIFACT.spad" 2135074 2135086 2135963 2135968) (-1217 "ULS.spad" 2125626 2125654 2126719 2127148) (-1216 "ULSCONS.spad" 2118020 2118040 2118392 2118541) (-1215 "ULSCCAT.spad" 2115749 2115769 2117866 2118015) (-1214 "ULSCCAT.spad" 2113586 2113608 2115705 2115710) (-1213 "ULSCAT.spad" 2111802 2111818 2113432 2113581) (-1212 "ULS2.spad" 2111314 2111367 2111792 2111797) (-1211 "UINT32.spad" 2111190 2111199 2111304 2111309) (-1210 "UINT16.spad" 2111066 2111075 2111180 2111185) (-1209 "UFD.spad" 2110131 2110140 2110992 2111061) (-1208 "UFD.spad" 2109258 2109269 2110121 2110126) (-1207 "UDVO.spad" 2108105 2108114 2109248 2109253) (-1206 "UDPO.spad" 2105532 2105543 2108061 2108066) (-1205 "TYPE.spad" 2105464 2105473 2105522 2105527) (-1204 "TYPEAST.spad" 2105383 2105392 2105454 2105459) (-1203 "TWOFACT.spad" 2104033 2104048 2105373 2105378) (-1202 "TUPLE.spad" 2103517 2103528 2103932 2103937) (-1201 "TUBETOOL.spad" 2100354 2100363 2103507 2103512) (-1200 "TUBE.spad" 2098995 2099012 2100344 2100349) (-1199 "TS.spad" 2097584 2097600 2098560 2098657) (-1198 "TSETCAT.spad" 2084711 2084728 2097552 2097579) (-1197 "TSETCAT.spad" 2071824 2071843 2084667 2084672) (-1196 "TRMANIP.spad" 2066190 2066207 2071530 2071535) (-1195 "TRIMAT.spad" 2065149 2065174 2066180 2066185) (-1194 "TRIGMNIP.spad" 2063666 2063683 2065139 2065144) (-1193 "TRIGCAT.spad" 2063178 2063187 2063656 2063661) (-1192 "TRIGCAT.spad" 2062688 2062699 2063168 2063173) (-1191 "TREE.spad" 2061259 2061270 2062295 2062322) (-1190 "TRANFUN.spad" 2061090 2061099 2061249 2061254) (-1189 "TRANFUN.spad" 2060919 2060930 2061080 2061085) (-1188 "TOPSP.spad" 2060593 2060602 2060909 2060914) (-1187 "TOOLSIGN.spad" 2060256 2060267 2060583 2060588) (-1186 "TEXTFILE.spad" 2058813 2058822 2060246 2060251) (-1185 "TEX.spad" 2055945 2055954 2058803 2058808) (-1184 "TEX1.spad" 2055501 2055512 2055935 2055940) (-1183 "TEMUTL.spad" 2055056 2055065 2055491 2055496) (-1182 "TBCMPPK.spad" 2053149 2053172 2055046 2055051) (-1181 "TBAGG.spad" 2052185 2052208 2053129 2053144) (-1180 "TBAGG.spad" 2051229 2051254 2052175 2052180) (-1179 "TANEXP.spad" 2050605 2050616 2051219 2051224) (-1178 "TABLE.spad" 2049016 2049039 2049286 2049313) (-1177 "TABLEAU.spad" 2048497 2048508 2049006 2049011) (-1176 "TABLBUMP.spad" 2045280 2045291 2048487 2048492) (-1175 "SYSTEM.spad" 2044554 2044563 2045270 2045275) (-1174 "SYSSOLP.spad" 2042027 2042038 2044544 2044549) (-1173 "SYSNNI.spad" 2041203 2041214 2042017 2042022) (-1172 "SYSINT.spad" 2040676 2040687 2041193 2041198) (-1171 "SYNTAX.spad" 2036946 2036955 2040666 2040671) (-1170 "SYMTAB.spad" 2035002 2035011 2036936 2036941) (-1169 "SYMS.spad" 2030987 2030996 2034992 2034997) (-1168 "SYMPOLY.spad" 2029994 2030005 2030076 2030203) (-1167 "SYMFUNC.spad" 2029469 2029480 2029984 2029989) (-1166 "SYMBOL.spad" 2026896 2026905 2029459 2029464) (-1165 "SWITCH.spad" 2023653 2023662 2026886 2026891) (-1164 "SUTS.spad" 2020552 2020580 2022120 2022217) (-1163 "SUPXS.spad" 2017687 2017715 2018684 2018833) (-1162 "SUP.spad" 2014456 2014467 2015237 2015390) (-1161 "SUPFRACF.spad" 2013561 2013579 2014446 2014451) (-1160 "SUP2.spad" 2012951 2012964 2013551 2013556) (-1159 "SUMRF.spad" 2011917 2011928 2012941 2012946) (-1158 "SUMFS.spad" 2011550 2011567 2011907 2011912) (-1157 "SULS.spad" 2002089 2002117 2003195 2003624) (-1156 "SUCHTAST.spad" 2001858 2001867 2002079 2002084) (-1155 "SUCH.spad" 2001538 2001553 2001848 2001853) (-1154 "SUBSPACE.spad" 1993545 1993560 2001528 2001533) (-1153 "SUBRESP.spad" 1992705 1992719 1993501 1993506) (-1152 "STTF.spad" 1988804 1988820 1992695 1992700) (-1151 "STTFNC.spad" 1985272 1985288 1988794 1988799) (-1150 "STTAYLOR.spad" 1977670 1977681 1985153 1985158) (-1149 "STRTBL.spad" 1976175 1976192 1976324 1976351) (-1148 "STRING.spad" 1975584 1975593 1975598 1975625) (-1147 "STRICAT.spad" 1975372 1975381 1975552 1975579) (-1146 "STREAM.spad" 1972230 1972241 1974897 1974912) (-1145 "STREAM3.spad" 1971775 1971790 1972220 1972225) (-1144 "STREAM2.spad" 1970843 1970856 1971765 1971770) (-1143 "STREAM1.spad" 1970547 1970558 1970833 1970838) (-1142 "STINPROD.spad" 1969453 1969469 1970537 1970542) (-1141 "STEP.spad" 1968654 1968663 1969443 1969448) (-1140 "STBL.spad" 1967180 1967208 1967347 1967362) (-1139 "STAGG.spad" 1966255 1966266 1967170 1967175) (-1138 "STAGG.spad" 1965328 1965341 1966245 1966250) (-1137 "STACK.spad" 1964679 1964690 1964935 1964962) (-1136 "SREGSET.spad" 1962383 1962400 1964325 1964352) (-1135 "SRDCMPK.spad" 1960928 1960948 1962373 1962378) (-1134 "SRAGG.spad" 1956025 1956034 1960896 1960923) (-1133 "SRAGG.spad" 1951142 1951153 1956015 1956020) (-1132 "SQMATRIX.spad" 1948758 1948776 1949674 1949761) (-1131 "SPLTREE.spad" 1943310 1943323 1948194 1948221) (-1130 "SPLNODE.spad" 1939898 1939911 1943300 1943305) (-1129 "SPFCAT.spad" 1938675 1938684 1939888 1939893) (-1128 "SPECOUT.spad" 1937225 1937234 1938665 1938670) (-1127 "SPADXPT.spad" 1929364 1929373 1937215 1937220) (-1126 "spad-parser.spad" 1928829 1928838 1929354 1929359) (-1125 "SPADAST.spad" 1928530 1928539 1928819 1928824) (-1124 "SPACEC.spad" 1912543 1912554 1928520 1928525) (-1123 "SPACE3.spad" 1912319 1912330 1912533 1912538) (-1122 "SORTPAK.spad" 1911864 1911877 1912275 1912280) (-1121 "SOLVETRA.spad" 1909621 1909632 1911854 1911859) (-1120 "SOLVESER.spad" 1908141 1908152 1909611 1909616) (-1119 "SOLVERAD.spad" 1904151 1904162 1908131 1908136) (-1118 "SOLVEFOR.spad" 1902571 1902589 1904141 1904146) (-1117 "SNTSCAT.spad" 1902171 1902188 1902539 1902566) (-1116 "SMTS.spad" 1900431 1900457 1901736 1901833) (-1115 "SMP.spad" 1897870 1897890 1898260 1898387) (-1114 "SMITH.spad" 1896713 1896738 1897860 1897865) (-1113 "SMATCAT.spad" 1894823 1894853 1896657 1896708) (-1112 "SMATCAT.spad" 1892865 1892897 1894701 1894706) (-1111 "SKAGG.spad" 1891826 1891837 1892833 1892860) (-1110 "SINT.spad" 1890652 1890661 1891692 1891821) (-1109 "SIMPAN.spad" 1890380 1890389 1890642 1890647) (-1108 "SIG.spad" 1889708 1889717 1890370 1890375) (-1107 "SIGNRF.spad" 1888816 1888827 1889698 1889703) (-1106 "SIGNEF.spad" 1888085 1888102 1888806 1888811) (-1105 "SIGAST.spad" 1887466 1887475 1888075 1888080) (-1104 "SHP.spad" 1885384 1885399 1887422 1887427) (-1103 "SHDP.spad" 1875095 1875122 1875604 1875735) (-1102 "SGROUP.spad" 1874703 1874712 1875085 1875090) (-1101 "SGROUP.spad" 1874309 1874320 1874693 1874698) (-1100 "SGCF.spad" 1867190 1867199 1874299 1874304) (-1099 "SFRTCAT.spad" 1866118 1866135 1867158 1867185) (-1098 "SFRGCD.spad" 1865181 1865201 1866108 1866113) (-1097 "SFQCMPK.spad" 1859818 1859838 1865171 1865176) (-1096 "SFORT.spad" 1859253 1859267 1859808 1859813) (-1095 "SEXOF.spad" 1859096 1859136 1859243 1859248) (-1094 "SEX.spad" 1858988 1858997 1859086 1859091) (-1093 "SEXCAT.spad" 1856539 1856579 1858978 1858983) (-1092 "SET.spad" 1854839 1854850 1855960 1855999) (-1091 "SETMN.spad" 1853273 1853290 1854829 1854834) (-1090 "SETCAT.spad" 1852758 1852767 1853263 1853268) (-1089 "SETCAT.spad" 1852241 1852252 1852748 1852753) (-1088 "SETAGG.spad" 1848762 1848773 1852221 1852236) (-1087 "SETAGG.spad" 1845291 1845304 1848752 1848757) (-1086 "SEQAST.spad" 1844994 1845003 1845281 1845286) (-1085 "SEGXCAT.spad" 1844116 1844129 1844984 1844989) (-1084 "SEG.spad" 1843929 1843940 1844035 1844040) (-1083 "SEGCAT.spad" 1842836 1842847 1843919 1843924) (-1082 "SEGBIND.spad" 1841908 1841919 1842791 1842796) (-1081 "SEGBIND2.spad" 1841604 1841617 1841898 1841903) (-1080 "SEGAST.spad" 1841318 1841327 1841594 1841599) (-1079 "SEG2.spad" 1840743 1840756 1841274 1841279) (-1078 "SDVAR.spad" 1840019 1840030 1840733 1840738) (-1077 "SDPOL.spad" 1837409 1837420 1837700 1837827) (-1076 "SCPKG.spad" 1835488 1835499 1837399 1837404) (-1075 "SCOPE.spad" 1834633 1834642 1835478 1835483) (-1074 "SCACHE.spad" 1833315 1833326 1834623 1834628) (-1073 "SASTCAT.spad" 1833224 1833233 1833305 1833310) (-1072 "SAOS.spad" 1833096 1833105 1833214 1833219) (-1071 "SAERFFC.spad" 1832809 1832829 1833086 1833091) (-1070 "SAE.spad" 1830984 1831000 1831595 1831730) (-1069 "SAEFACT.spad" 1830685 1830705 1830974 1830979) (-1068 "RURPK.spad" 1828326 1828342 1830675 1830680) (-1067 "RULESET.spad" 1827767 1827791 1828316 1828321) (-1066 "RULE.spad" 1825971 1825995 1827757 1827762) (-1065 "RULECOLD.spad" 1825823 1825836 1825961 1825966) (-1064 "RSTRCAST.spad" 1825540 1825549 1825813 1825818) (-1063 "RSETGCD.spad" 1821918 1821938 1825530 1825535) (-1062 "RSETCAT.spad" 1811702 1811719 1821886 1821913) (-1061 "RSETCAT.spad" 1801506 1801525 1811692 1811697) (-1060 "RSDCMPK.spad" 1799958 1799978 1801496 1801501) (-1059 "RRCC.spad" 1798342 1798372 1799948 1799953) (-1058 "RRCC.spad" 1796724 1796756 1798332 1798337) (-1057 "RPTAST.spad" 1796426 1796435 1796714 1796719) (-1056 "RPOLCAT.spad" 1775786 1775801 1796294 1796421) (-1055 "RPOLCAT.spad" 1754860 1754877 1775370 1775375) (-1054 "ROUTINE.spad" 1750723 1750732 1753507 1753534) (-1053 "ROMAN.spad" 1750051 1750060 1750589 1750718) (-1052 "ROIRC.spad" 1749131 1749163 1750041 1750046) (-1051 "RNS.spad" 1748034 1748043 1749033 1749126) (-1050 "RNS.spad" 1747023 1747034 1748024 1748029) (-1049 "RNG.spad" 1746758 1746767 1747013 1747018) (-1048 "RMODULE.spad" 1746396 1746407 1746748 1746753) (-1047 "RMCAT2.spad" 1745804 1745861 1746386 1746391) (-1046 "RMATRIX.spad" 1744628 1744647 1744971 1745010) (-1045 "RMATCAT.spad" 1740161 1740192 1744584 1744623) (-1044 "RMATCAT.spad" 1735584 1735617 1740009 1740014) (-1043 "RINTERP.spad" 1735472 1735492 1735574 1735579) (-1042 "RING.spad" 1734942 1734951 1735452 1735467) (-1041 "RING.spad" 1734420 1734431 1734932 1734937) (-1040 "RIDIST.spad" 1733804 1733813 1734410 1734415) (-1039 "RGCHAIN.spad" 1732383 1732399 1733289 1733316) (-1038 "RGBCSPC.spad" 1732164 1732176 1732373 1732378) (-1037 "RGBCMDL.spad" 1731694 1731706 1732154 1732159) (-1036 "RF.spad" 1729308 1729319 1731684 1731689) (-1035 "RFFACTOR.spad" 1728770 1728781 1729298 1729303) (-1034 "RFFACT.spad" 1728505 1728517 1728760 1728765) (-1033 "RFDIST.spad" 1727493 1727502 1728495 1728500) (-1032 "RETSOL.spad" 1726910 1726923 1727483 1727488) (-1031 "RETRACT.spad" 1726338 1726349 1726900 1726905) (-1030 "RETRACT.spad" 1725764 1725777 1726328 1726333) (-1029 "RETAST.spad" 1725576 1725585 1725754 1725759) (-1028 "RESULT.spad" 1723636 1723645 1724223 1724250) (-1027 "RESRING.spad" 1722983 1723030 1723574 1723631) (-1026 "RESLATC.spad" 1722307 1722318 1722973 1722978) (-1025 "REPSQ.spad" 1722036 1722047 1722297 1722302) (-1024 "REP.spad" 1719588 1719597 1722026 1722031) (-1023 "REPDB.spad" 1719293 1719304 1719578 1719583) (-1022 "REP2.spad" 1708865 1708876 1719135 1719140) (-1021 "REP1.spad" 1702855 1702866 1708815 1708820) (-1020 "REGSET.spad" 1700652 1700669 1702501 1702528) (-1019 "REF.spad" 1699981 1699992 1700607 1700612) (-1018 "REDORDER.spad" 1699157 1699174 1699971 1699976) (-1017 "RECLOS.spad" 1697940 1697960 1698644 1698737) (-1016 "REALSOLV.spad" 1697072 1697081 1697930 1697935) (-1015 "REAL.spad" 1696944 1696953 1697062 1697067) (-1014 "REAL0Q.spad" 1694226 1694241 1696934 1696939) (-1013 "REAL0.spad" 1691054 1691069 1694216 1694221) (-1012 "RDUCEAST.spad" 1690775 1690784 1691044 1691049) (-1011 "RDIV.spad" 1690426 1690451 1690765 1690770) (-1010 "RDIST.spad" 1689989 1690000 1690416 1690421) (-1009 "RDETRS.spad" 1688785 1688803 1689979 1689984) (-1008 "RDETR.spad" 1686892 1686910 1688775 1688780) (-1007 "RDEEFS.spad" 1685965 1685982 1686882 1686887) (-1006 "RDEEF.spad" 1684961 1684978 1685955 1685960) (-1005 "RCFIELD.spad" 1682147 1682156 1684863 1684956) (-1004 "RCFIELD.spad" 1679419 1679430 1682137 1682142) (-1003 "RCAGG.spad" 1677331 1677342 1679409 1679414) (-1002 "RCAGG.spad" 1675170 1675183 1677250 1677255) (-1001 "RATRET.spad" 1674530 1674541 1675160 1675165) (-1000 "RATFACT.spad" 1674222 1674234 1674520 1674525) (-999 "RANDSRC.spad" 1673542 1673550 1674212 1674217) (-998 "RADUTIL.spad" 1673297 1673305 1673532 1673537) (-997 "RADIX.spad" 1670199 1670212 1671764 1671857) (-996 "RADFF.spad" 1668613 1668649 1668731 1668887) (-995 "RADCAT.spad" 1668207 1668215 1668603 1668608) (-994 "RADCAT.spad" 1667799 1667809 1668197 1668202) (-993 "QUEUE.spad" 1667142 1667152 1667406 1667433) (-992 "QUAT.spad" 1665724 1665734 1666066 1666131) (-991 "QUATCT2.spad" 1665343 1665361 1665714 1665719) (-990 "QUATCAT.spad" 1663508 1663518 1665273 1665338) (-989 "QUATCAT.spad" 1661424 1661436 1663191 1663196) (-988 "QUAGG.spad" 1660250 1660260 1661392 1661419) (-987 "QQUTAST.spad" 1660019 1660027 1660240 1660245) (-986 "QFORM.spad" 1659482 1659496 1660009 1660014) (-985 "QFCAT.spad" 1658185 1658195 1659384 1659477) (-984 "QFCAT.spad" 1656479 1656491 1657680 1657685) (-983 "QFCAT2.spad" 1656170 1656186 1656469 1656474) (-982 "QEQUAT.spad" 1655727 1655735 1656160 1656165) (-981 "QCMPACK.spad" 1650474 1650493 1655717 1655722) (-980 "QALGSET.spad" 1646549 1646581 1650388 1650393) (-979 "QALGSET2.spad" 1644545 1644563 1646539 1646544) (-978 "PWFFINTB.spad" 1641855 1641876 1644535 1644540) (-977 "PUSHVAR.spad" 1641184 1641203 1641845 1641850) (-976 "PTRANFN.spad" 1637310 1637320 1641174 1641179) (-975 "PTPACK.spad" 1634398 1634408 1637300 1637305) (-974 "PTFUNC2.spad" 1634219 1634233 1634388 1634393) (-973 "PTCAT.spad" 1633468 1633478 1634187 1634214) (-972 "PSQFR.spad" 1632775 1632799 1633458 1633463) (-971 "PSEUDLIN.spad" 1631633 1631643 1632765 1632770) (-970 "PSETPK.spad" 1617066 1617082 1631511 1631516) (-969 "PSETCAT.spad" 1610986 1611009 1617046 1617061) (-968 "PSETCAT.spad" 1604880 1604905 1610942 1610947) (-967 "PSCURVE.spad" 1603863 1603871 1604870 1604875) (-966 "PSCAT.spad" 1602630 1602659 1603761 1603858) (-965 "PSCAT.spad" 1601487 1601518 1602620 1602625) (-964 "PRTITION.spad" 1600432 1600440 1601477 1601482) (-963 "PRTDAST.spad" 1600151 1600159 1600422 1600427) (-962 "PRS.spad" 1589713 1589730 1600107 1600112) (-961 "PRQAGG.spad" 1589144 1589154 1589681 1589708) (-960 "PROPLOG.spad" 1588547 1588555 1589134 1589139) (-959 "PROPFRML.spad" 1586465 1586476 1588537 1588542) (-958 "PROPERTY.spad" 1585959 1585967 1586455 1586460) (-957 "PRODUCT.spad" 1583639 1583651 1583925 1583980) (-956 "PR.spad" 1582025 1582037 1582730 1582857) (-955 "PRINT.spad" 1581777 1581785 1582015 1582020) (-954 "PRIMES.spad" 1580028 1580038 1581767 1581772) (-953 "PRIMELT.spad" 1578009 1578023 1580018 1580023) (-952 "PRIMCAT.spad" 1577632 1577640 1577999 1578004) (-951 "PRIMARR.spad" 1576637 1576647 1576815 1576842) (-950 "PRIMARR2.spad" 1575360 1575372 1576627 1576632) (-949 "PREASSOC.spad" 1574732 1574744 1575350 1575355) (-948 "PPCURVE.spad" 1573869 1573877 1574722 1574727) (-947 "PORTNUM.spad" 1573644 1573652 1573859 1573864) (-946 "POLYROOT.spad" 1572473 1572495 1573600 1573605) (-945 "POLY.spad" 1569770 1569780 1570287 1570414) (-944 "POLYLIFT.spad" 1569031 1569054 1569760 1569765) (-943 "POLYCATQ.spad" 1567133 1567155 1569021 1569026) (-942 "POLYCAT.spad" 1560539 1560560 1567001 1567128) (-941 "POLYCAT.spad" 1553247 1553270 1559711 1559716) (-940 "POLY2UP.spad" 1552695 1552709 1553237 1553242) (-939 "POLY2.spad" 1552290 1552302 1552685 1552690) (-938 "POLUTIL.spad" 1551231 1551260 1552246 1552251) (-937 "POLTOPOL.spad" 1549979 1549994 1551221 1551226) (-936 "POINT.spad" 1548818 1548828 1548905 1548932) (-935 "PNTHEORY.spad" 1545484 1545492 1548808 1548813) (-934 "PMTOOLS.spad" 1544241 1544255 1545474 1545479) (-933 "PMSYM.spad" 1543786 1543796 1544231 1544236) (-932 "PMQFCAT.spad" 1543373 1543387 1543776 1543781) (-931 "PMPRED.spad" 1542842 1542856 1543363 1543368) (-930 "PMPREDFS.spad" 1542286 1542308 1542832 1542837) (-929 "PMPLCAT.spad" 1541356 1541374 1542218 1542223) (-928 "PMLSAGG.spad" 1540937 1540951 1541346 1541351) (-927 "PMKERNEL.spad" 1540504 1540516 1540927 1540932) (-926 "PMINS.spad" 1540080 1540090 1540494 1540499) (-925 "PMFS.spad" 1539653 1539671 1540070 1540075) (-924 "PMDOWN.spad" 1538939 1538953 1539643 1539648) (-923 "PMASS.spad" 1537951 1537959 1538929 1538934) (-922 "PMASSFS.spad" 1536920 1536936 1537941 1537946) (-921 "PLOTTOOL.spad" 1536700 1536708 1536910 1536915) (-920 "PLOT.spad" 1531531 1531539 1536690 1536695) (-919 "PLOT3D.spad" 1527951 1527959 1531521 1531526) (-918 "PLOT1.spad" 1527092 1527102 1527941 1527946) (-917 "PLEQN.spad" 1514308 1514335 1527082 1527087) (-916 "PINTERP.spad" 1513924 1513943 1514298 1514303) (-915 "PINTERPA.spad" 1513706 1513722 1513914 1513919) (-914 "PI.spad" 1513313 1513321 1513680 1513701) (-913 "PID.spad" 1512269 1512277 1513239 1513308) (-912 "PICOERCE.spad" 1511926 1511936 1512259 1512264) (-911 "PGROEB.spad" 1510523 1510537 1511916 1511921) (-910 "PGE.spad" 1501776 1501784 1510513 1510518) (-909 "PGCD.spad" 1500658 1500675 1501766 1501771) (-908 "PFRPAC.spad" 1499801 1499811 1500648 1500653) (-907 "PFR.spad" 1496458 1496468 1499703 1499796) (-906 "PFOTOOLS.spad" 1495716 1495732 1496448 1496453) (-905 "PFOQ.spad" 1495086 1495104 1495706 1495711) (-904 "PFO.spad" 1494505 1494532 1495076 1495081) (-903 "PF.spad" 1494079 1494091 1494310 1494403) (-902 "PFECAT.spad" 1491745 1491753 1494005 1494074) (-901 "PFECAT.spad" 1489439 1489449 1491701 1491706) (-900 "PFBRU.spad" 1487309 1487321 1489429 1489434) (-899 "PFBR.spad" 1484847 1484870 1487299 1487304) (-898 "PERM.spad" 1480528 1480538 1484677 1484692) (-897 "PERMGRP.spad" 1475264 1475274 1480518 1480523) (-896 "PERMCAT.spad" 1473816 1473826 1475244 1475259) (-895 "PERMAN.spad" 1472348 1472362 1473806 1473811) (-894 "PENDTREE.spad" 1471687 1471697 1471977 1471982) (-893 "PDRING.spad" 1470178 1470188 1471667 1471682) (-892 "PDRING.spad" 1468677 1468689 1470168 1470173) (-891 "PDEPROB.spad" 1467692 1467700 1468667 1468672) (-890 "PDEPACK.spad" 1461694 1461702 1467682 1467687) (-889 "PDECOMP.spad" 1461156 1461173 1461684 1461689) (-888 "PDECAT.spad" 1459510 1459518 1461146 1461151) (-887 "PCOMP.spad" 1459361 1459374 1459500 1459505) (-886 "PBWLB.spad" 1457943 1457960 1459351 1459356) (-885 "PATTERN.spad" 1452374 1452384 1457933 1457938) (-884 "PATTERN2.spad" 1452110 1452122 1452364 1452369) (-883 "PATTERN1.spad" 1450412 1450428 1452100 1452105) (-882 "PATRES.spad" 1447959 1447971 1450402 1450407) (-881 "PATRES2.spad" 1447621 1447635 1447949 1447954) (-880 "PATMATCH.spad" 1445778 1445809 1447329 1447334) (-879 "PATMAB.spad" 1445203 1445213 1445768 1445773) (-878 "PATLRES.spad" 1444287 1444301 1445193 1445198) (-877 "PATAB.spad" 1444051 1444061 1444277 1444282) (-876 "PARTPERM.spad" 1441413 1441421 1444041 1444046) (-875 "PARSURF.spad" 1440841 1440869 1441403 1441408) (-874 "PARSU2.spad" 1440636 1440652 1440831 1440836) (-873 "script-parser.spad" 1440156 1440164 1440626 1440631) (-872 "PARSCURV.spad" 1439584 1439612 1440146 1440151) (-871 "PARSC2.spad" 1439373 1439389 1439574 1439579) (-870 "PARPCURV.spad" 1438831 1438859 1439363 1439368) (-869 "PARPC2.spad" 1438620 1438636 1438821 1438826) (-868 "PAN2EXPR.spad" 1438032 1438040 1438610 1438615) (-867 "PALETTE.spad" 1437002 1437010 1438022 1438027) (-866 "PAIR.spad" 1435985 1435998 1436590 1436595) (-865 "PADICRC.spad" 1433315 1433333 1434490 1434583) (-864 "PADICRAT.spad" 1431330 1431342 1431551 1431644) (-863 "PADIC.spad" 1431025 1431037 1431256 1431325) (-862 "PADICCT.spad" 1429566 1429578 1430951 1431020) (-861 "PADEPAC.spad" 1428245 1428264 1429556 1429561) (-860 "PADE.spad" 1426985 1427001 1428235 1428240) (-859 "OWP.spad" 1426225 1426255 1426843 1426910) (-858 "OVAR.spad" 1426006 1426029 1426215 1426220) (-857 "OUT.spad" 1425090 1425098 1425996 1426001) (-856 "OUTFORM.spad" 1414386 1414394 1425080 1425085) (-855 "OUTBFILE.spad" 1413804 1413812 1414376 1414381) (-854 "OUTBCON.spad" 1413279 1413287 1413794 1413799) (-853 "OUTBCON.spad" 1412752 1412762 1413269 1413274) (-852 "OSI.spad" 1412227 1412235 1412742 1412747) (-851 "OSGROUP.spad" 1412145 1412153 1412217 1412222) (-850 "ORTHPOL.spad" 1410606 1410616 1412062 1412067) (-849 "OREUP.spad" 1410059 1410087 1410286 1410325) (-848 "ORESUP.spad" 1409358 1409382 1409739 1409778) (-847 "OREPCTO.spad" 1407177 1407189 1409278 1409283) (-846 "OREPCAT.spad" 1401234 1401244 1407133 1407172) (-845 "OREPCAT.spad" 1395181 1395193 1401082 1401087) (-844 "ORDSET.spad" 1394347 1394355 1395171 1395176) (-843 "ORDSET.spad" 1393511 1393521 1394337 1394342) (-842 "ORDRING.spad" 1392901 1392909 1393491 1393506) (-841 "ORDRING.spad" 1392299 1392309 1392891 1392896) (-840 "ORDMON.spad" 1392154 1392162 1392289 1392294) (-839 "ORDFUNS.spad" 1391280 1391296 1392144 1392149) (-838 "ORDFIN.spad" 1391100 1391108 1391270 1391275) (-837 "ORDCOMP.spad" 1389565 1389575 1390647 1390676) (-836 "ORDCOMP2.spad" 1388850 1388862 1389555 1389560) (-835 "OPTPROB.spad" 1387488 1387496 1388840 1388845) (-834 "OPTPACK.spad" 1379873 1379881 1387478 1387483) (-833 "OPTCAT.spad" 1377548 1377556 1379863 1379868) (-832 "OPSIG.spad" 1377200 1377208 1377538 1377543) (-831 "OPQUERY.spad" 1376749 1376757 1377190 1377195) (-830 "OP.spad" 1376491 1376501 1376571 1376638) (-829 "OPERCAT.spad" 1376079 1376089 1376481 1376486) (-828 "OPERCAT.spad" 1375665 1375677 1376069 1376074) (-827 "ONECOMP.spad" 1374410 1374420 1375212 1375241) (-826 "ONECOMP2.spad" 1373828 1373840 1374400 1374405) (-825 "OMSERVER.spad" 1372830 1372838 1373818 1373823) (-824 "OMSAGG.spad" 1372618 1372628 1372786 1372825) (-823 "OMPKG.spad" 1371230 1371238 1372608 1372613) (-822 "OM.spad" 1370195 1370203 1371220 1371225) (-821 "OMLO.spad" 1369620 1369632 1370081 1370120) (-820 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(-801 "ODEPRIM.spad" 1325655 1325677 1328371 1328376) (-800 "ODEPAL.spad" 1325031 1325055 1325645 1325650) (-799 "ODEPACK.spad" 1311633 1311641 1325021 1325026) (-798 "ODEINT.spad" 1311064 1311080 1311623 1311628) (-797 "ODEIFTBL.spad" 1308459 1308467 1311054 1311059) (-796 "ODEEF.spad" 1303826 1303842 1308449 1308454) (-795 "ODECONST.spad" 1303345 1303363 1303816 1303821) (-794 "ODECAT.spad" 1301941 1301949 1303335 1303340) (-793 "OCT.spad" 1300079 1300089 1300795 1300834) (-792 "OCTCT2.spad" 1299723 1299744 1300069 1300074) (-791 "OC.spad" 1297497 1297507 1299679 1299718) (-790 "OC.spad" 1294996 1295008 1297180 1297185) (-789 "OCAMON.spad" 1294844 1294852 1294986 1294991) (-788 "OASGP.spad" 1294659 1294667 1294834 1294839) (-787 "OAMONS.spad" 1294179 1294187 1294649 1294654) (-786 "OAMON.spad" 1294040 1294048 1294169 1294174) (-785 "OAGROUP.spad" 1293902 1293910 1294030 1294035) (-784 "NUMTUBE.spad" 1293489 1293505 1293892 1293897) (-783 "NUMQUAD.spad" 1281351 1281359 1293479 1293484) (-782 "NUMODE.spad" 1272487 1272495 1281341 1281346) (-781 "NUMINT.spad" 1270045 1270053 1272477 1272482) (-780 "NUMFMT.spad" 1268885 1268893 1270035 1270040) (-779 "NUMERIC.spad" 1260957 1260967 1268690 1268695) (-778 "NTSCAT.spad" 1259459 1259475 1260925 1260952) (-777 "NTPOLFN.spad" 1259004 1259014 1259376 1259381) (-776 "NSUP.spad" 1252014 1252024 1256554 1256707) (-775 "NSUP2.spad" 1251406 1251418 1252004 1252009) (-774 "NSMP.spad" 1247601 1247620 1247909 1248036) (-773 "NREP.spad" 1245973 1245987 1247591 1247596) (-772 "NPCOEF.spad" 1245219 1245239 1245963 1245968) (-771 "NORMRETR.spad" 1244817 1244856 1245209 1245214) (-770 "NORMPK.spad" 1242719 1242738 1244807 1244812) (-769 "NORMMA.spad" 1242407 1242433 1242709 1242714) (-768 "NONE.spad" 1242148 1242156 1242397 1242402) (-767 "NONE1.spad" 1241824 1241834 1242138 1242143) (-766 "NODE1.spad" 1241293 1241309 1241814 1241819) (-765 "NNI.spad" 1240180 1240188 1241267 1241288) (-764 "NLINSOL.spad" 1238802 1238812 1240170 1240175) (-763 "NIPROB.spad" 1237343 1237351 1238792 1238797) (-762 "NFINTBAS.spad" 1234803 1234820 1237333 1237338) (-761 "NETCLT.spad" 1234777 1234788 1234793 1234798) (-760 "NCODIV.spad" 1232975 1232991 1234767 1234772) (-759 "NCNTFRAC.spad" 1232617 1232631 1232965 1232970) (-758 "NCEP.spad" 1230777 1230791 1232607 1232612) (-757 "NASRING.spad" 1230373 1230381 1230767 1230772) (-756 "NASRING.spad" 1229967 1229977 1230363 1230368) (-755 "NARNG.spad" 1229311 1229319 1229957 1229962) (-754 "NARNG.spad" 1228653 1228663 1229301 1229306) (-753 "NAGSP.spad" 1227726 1227734 1228643 1228648) (-752 "NAGS.spad" 1217251 1217259 1227716 1227721) (-751 "NAGF07.spad" 1215644 1215652 1217241 1217246) (-750 "NAGF04.spad" 1209876 1209884 1215634 1215639) (-749 "NAGF02.spad" 1203685 1203693 1209866 1209871) (-748 "NAGF01.spad" 1199288 1199296 1203675 1203680) (-747 "NAGE04.spad" 1192748 1192756 1199278 1199283) (-746 "NAGE02.spad" 1183090 1183098 1192738 1192743) (-745 "NAGE01.spad" 1178974 1178982 1183080 1183085) (-744 "NAGD03.spad" 1176894 1176902 1178964 1178969) (-743 "NAGD02.spad" 1169425 1169433 1176884 1176889) (-742 "NAGD01.spad" 1163538 1163546 1169415 1169420) (-741 "NAGC06.spad" 1159325 1159333 1163528 1163533) (-740 "NAGC05.spad" 1157794 1157802 1159315 1159320) (-739 "NAGC02.spad" 1157049 1157057 1157784 1157789) (-738 "NAALG.spad" 1156584 1156594 1157017 1157044) (-737 "NAALG.spad" 1156139 1156151 1156574 1156579) (-736 "MULTSQFR.spad" 1153097 1153114 1156129 1156134) (-735 "MULTFACT.spad" 1152480 1152497 1153087 1153092) (-734 "MTSCAT.spad" 1150514 1150535 1152378 1152475) (-733 "MTHING.spad" 1150171 1150181 1150504 1150509) (-732 "MSYSCMD.spad" 1149605 1149613 1150161 1150166) (-731 "MSET.spad" 1147547 1147557 1149311 1149350) (-730 "MSETAGG.spad" 1147392 1147402 1147515 1147542) (-729 "MRING.spad" 1144363 1144375 1147100 1147167) (-728 "MRF2.spad" 1143931 1143945 1144353 1144358) (-727 "MRATFAC.spad" 1143477 1143494 1143921 1143926) (-726 "MPRFF.spad" 1141507 1141526 1143467 1143472) (-725 "MPOLY.spad" 1138942 1138957 1139301 1139428) (-724 "MPCPF.spad" 1138206 1138225 1138932 1138937) (-723 "MPC3.spad" 1138021 1138061 1138196 1138201) (-722 "MPC2.spad" 1137663 1137696 1138011 1138016) (-721 "MONOTOOL.spad" 1135998 1136015 1137653 1137658) (-720 "MONOID.spad" 1135317 1135325 1135988 1135993) (-719 "MONOID.spad" 1134634 1134644 1135307 1135312) (-718 "MONOGEN.spad" 1133380 1133393 1134494 1134629) (-717 "MONOGEN.spad" 1132148 1132163 1133264 1133269) (-716 "MONADWU.spad" 1130162 1130170 1132138 1132143) (-715 "MONADWU.spad" 1128174 1128184 1130152 1130157) (-714 "MONAD.spad" 1127318 1127326 1128164 1128169) (-713 "MONAD.spad" 1126460 1126470 1127308 1127313) (-712 "MOEBIUS.spad" 1125146 1125160 1126440 1126455) (-711 "MODULE.spad" 1125016 1125026 1125114 1125141) (-710 "MODULE.spad" 1124906 1124918 1125006 1125011) (-709 "MODRING.spad" 1124237 1124276 1124886 1124901) (-708 "MODOP.spad" 1122896 1122908 1124059 1124126) (-707 "MODMONOM.spad" 1122625 1122643 1122886 1122891) (-706 "MODMON.spad" 1119384 1119400 1120103 1120256) (-705 "MODFIELD.spad" 1118742 1118781 1119286 1119379) (-704 "MMLFORM.spad" 1117602 1117610 1118732 1118737) (-703 "MMAP.spad" 1117342 1117376 1117592 1117597) (-702 "MLO.spad" 1115769 1115779 1117298 1117337) (-701 "MLIFT.spad" 1114341 1114358 1115759 1115764) (-700 "MKUCFUNC.spad" 1113874 1113892 1114331 1114336) (-699 "MKRECORD.spad" 1113476 1113489 1113864 1113869) (-698 "MKFUNC.spad" 1112857 1112867 1113466 1113471) (-697 "MKFLCFN.spad" 1111813 1111823 1112847 1112852) (-696 "MKCHSET.spad" 1111678 1111688 1111803 1111808) (-695 "MKBCFUNC.spad" 1111163 1111181 1111668 1111673) (-694 "MINT.spad" 1110602 1110610 1111065 1111158) (-693 "MHROWRED.spad" 1109103 1109113 1110592 1110597) (-692 "MFLOAT.spad" 1107619 1107627 1108993 1109098) (-691 "MFINFACT.spad" 1107019 1107041 1107609 1107614) (-690 "MESH.spad" 1104751 1104759 1107009 1107014) (-689 "MDDFACT.spad" 1102944 1102954 1104741 1104746) (-688 "MDAGG.spad" 1102231 1102241 1102924 1102939) (-687 "MCMPLX.spad" 1098217 1098225 1098831 1099020) (-686 "MCDEN.spad" 1097425 1097437 1098207 1098212) (-685 "MCALCFN.spad" 1094527 1094553 1097415 1097420) (-684 "MAYBE.spad" 1093811 1093822 1094517 1094522) (-683 "MATSTOR.spad" 1091087 1091097 1093801 1093806) (-682 "MATRIX.spad" 1089791 1089801 1090275 1090302) (-681 "MATLIN.spad" 1087117 1087141 1089675 1089680) (-680 "MATCAT.spad" 1078702 1078724 1087085 1087112) (-679 "MATCAT.spad" 1070159 1070183 1078544 1078549) (-678 "MATCAT2.spad" 1069427 1069475 1070149 1070154) (-677 "MAPPKG3.spad" 1068326 1068340 1069417 1069422) (-676 "MAPPKG2.spad" 1067660 1067672 1068316 1068321) (-675 "MAPPKG1.spad" 1066478 1066488 1067650 1067655) (-674 "MAPPAST.spad" 1065791 1065799 1066468 1066473) (-673 "MAPHACK3.spad" 1065599 1065613 1065781 1065786) (-672 "MAPHACK2.spad" 1065364 1065376 1065589 1065594) (-671 "MAPHACK1.spad" 1064994 1065004 1065354 1065359) (-670 "MAGMA.spad" 1062784 1062801 1064984 1064989) (-669 "MACROAST.spad" 1062363 1062371 1062774 1062779) (-668 "M3D.spad" 1060059 1060069 1061741 1061746) (-667 "LZSTAGG.spad" 1057287 1057297 1060049 1060054) (-666 "LZSTAGG.spad" 1054513 1054525 1057277 1057282) (-665 "LWORD.spad" 1051218 1051235 1054503 1054508) (-664 "LSTAST.spad" 1051002 1051010 1051208 1051213) (-663 "LSQM.spad" 1049228 1049242 1049626 1049677) (-662 "LSPP.spad" 1048761 1048778 1049218 1049223) (-661 "LSMP.spad" 1047601 1047629 1048751 1048756) (-660 "LSMP1.spad" 1045405 1045419 1047591 1047596) (-659 "LSAGG.spad" 1045074 1045084 1045373 1045400) (-658 "LSAGG.spad" 1044763 1044775 1045064 1045069) (-657 "LPOLY.spad" 1043717 1043736 1044619 1044688) (-656 "LPEFRAC.spad" 1042974 1042984 1043707 1043712) (-655 "LO.spad" 1042375 1042389 1042908 1042935) (-654 "LOGIC.spad" 1041977 1041985 1042365 1042370) (-653 "LOGIC.spad" 1041577 1041587 1041967 1041972) (-652 "LODOOPS.spad" 1040495 1040507 1041567 1041572) (-651 "LODO.spad" 1039879 1039895 1040175 1040214) (-650 "LODOF.spad" 1038923 1038940 1039836 1039841) (-649 "LODOCAT.spad" 1037581 1037591 1038879 1038918) (-648 "LODOCAT.spad" 1036237 1036249 1037537 1037542) (-647 "LODO2.spad" 1035510 1035522 1035917 1035956) (-646 "LODO1.spad" 1034910 1034920 1035190 1035229) (-645 "LODEEF.spad" 1033682 1033700 1034900 1034905) (-644 "LNAGG.spad" 1029484 1029494 1033672 1033677) (-643 "LNAGG.spad" 1025250 1025262 1029440 1029445) (-642 "LMOPS.spad" 1021986 1022003 1025240 1025245) (-641 "LMODULE.spad" 1021628 1021638 1021976 1021981) (-640 "LMDICT.spad" 1020911 1020921 1021179 1021206) (-639 "LITERAL.spad" 1020817 1020828 1020901 1020906) (-638 "LIST.spad" 1018535 1018545 1019964 1019991) (-637 "LIST3.spad" 1017826 1017840 1018525 1018530) (-636 "LIST2.spad" 1016466 1016478 1017816 1017821) (-635 "LIST2MAP.spad" 1013343 1013355 1016456 1016461) (-634 "LINEXP.spad" 1012775 1012785 1013323 1013338) (-633 "LINDEP.spad" 1011552 1011564 1012687 1012692) (-632 "LIMITRF.spad" 1009466 1009476 1011542 1011547) (-631 "LIMITPS.spad" 1008349 1008362 1009456 1009461) (-630 "LIE.spad" 1006363 1006375 1007639 1007784) (-629 "LIECAT.spad" 1005839 1005849 1006289 1006358) (-628 "LIECAT.spad" 1005343 1005355 1005795 1005800) (-627 "LIB.spad" 1003391 1003399 1004002 1004017) (-626 "LGROBP.spad" 1000744 1000763 1003381 1003386) (-625 "LF.spad" 999663 999679 1000734 1000739) (-624 "LFCAT.spad" 998682 998690 999653 999658) (-623 "LEXTRIPK.spad" 994185 994200 998672 998677) (-622 "LEXP.spad" 992188 992215 994165 994180) (-621 "LETAST.spad" 991887 991895 992178 992183) (-620 "LEADCDET.spad" 990271 990288 991877 991882) (-619 "LAZM3PK.spad" 988975 988997 990261 990266) (-618 "LAUPOL.spad" 987664 987677 988568 988637) (-617 "LAPLACE.spad" 987237 987253 987654 987659) (-616 "LA.spad" 986677 986691 987159 987198) (-615 "LALG.spad" 986453 986463 986657 986672) (-614 "LALG.spad" 986237 986249 986443 986448) (-613 "KVTFROM.spad" 985972 985982 986227 986232) (-612 "KTVLOGIC.spad" 985395 985403 985962 985967) (-611 "KRCFROM.spad" 985133 985143 985385 985390) (-610 "KOVACIC.spad" 983846 983863 985123 985128) (-609 "KONVERT.spad" 983568 983578 983836 983841) (-608 "KOERCE.spad" 983305 983315 983558 983563) (-607 "KERNEL.spad" 981840 981850 983089 983094) (-606 "KERNEL2.spad" 981543 981555 981830 981835) (-605 "KDAGG.spad" 980646 980668 981523 981538) (-604 "KDAGG.spad" 979757 979781 980636 980641) (-603 "KAFILE.spad" 978720 978736 978955 978982) (-602 "JORDAN.spad" 976547 976559 978010 978155) (-601 "JOINAST.spad" 976241 976249 976537 976542) (-600 "JAVACODE.spad" 976107 976115 976231 976236) (-599 "IXAGG.spad" 974230 974254 976097 976102) (-598 "IXAGG.spad" 972208 972234 974077 974082) (-597 "IVECTOR.spad" 970979 970994 971134 971161) (-596 "ITUPLE.spad" 970124 970134 970969 970974) (-595 "ITRIGMNP.spad" 968935 968954 970114 970119) (-594 "ITFUN3.spad" 968429 968443 968925 968930) (-593 "ITFUN2.spad" 968159 968171 968419 968424) (-592 "ITAYLOR.spad" 965951 965966 967995 968120) (-591 "ISUPS.spad" 958362 958377 964925 965022) (-590 "ISUMP.spad" 957859 957875 958352 958357) (-589 "ISTRING.spad" 956862 956875 957028 957055) (-588 "ISAST.spad" 956581 956589 956852 956857) (-587 "IRURPK.spad" 955294 955313 956571 956576) (-586 "IRSN.spad" 953254 953262 955284 955289) (-585 "IRRF2F.spad" 951729 951739 953210 953215) (-584 "IRREDFFX.spad" 951330 951341 951719 951724) (-583 "IROOT.spad" 949661 949671 951320 951325) (-582 "IR.spad" 947450 947464 949516 949543) (-581 "IR2.spad" 946470 946486 947440 947445) (-580 "IR2F.spad" 945670 945686 946460 946465) (-579 "IPRNTPK.spad" 945430 945438 945660 945665) (-578 "IPF.spad" 944995 945007 945235 945328) (-577 "IPADIC.spad" 944756 944782 944921 944990) (-576 "IP4ADDR.spad" 944313 944321 944746 944751) (-575 "IOMODE.spad" 943934 943942 944303 944308) (-574 "IOBFILE.spad" 943295 943303 943924 943929) (-573 "IOBCON.spad" 943160 943168 943285 943290) (-572 "INVLAPLA.spad" 942805 942821 943150 943155) (-571 "INTTR.spad" 936051 936068 942795 942800) (-570 "INTTOOLS.spad" 933762 933778 935625 935630) (-569 "INTSLPE.spad" 933068 933076 933752 933757) (-568 "INTRVL.spad" 932634 932644 932982 933063) (-567 "INTRF.spad" 930998 931012 932624 932629) (-566 "INTRET.spad" 930430 930440 930988 930993) (-565 "INTRAT.spad" 929105 929122 930420 930425) (-564 "INTPM.spad" 927468 927484 928748 928753) (-563 "INTPAF.spad" 925236 925254 927400 927405) (-562 "INTPACK.spad" 915546 915554 925226 925231) (-561 "INT.spad" 914907 914915 915400 915541) (-560 "INTHERTR.spad" 914173 914190 914897 914902) (-559 "INTHERAL.spad" 913839 913863 914163 914168) (-558 "INTHEORY.spad" 910252 910260 913829 913834) (-557 "INTG0.spad" 903715 903733 910184 910189) (-556 "INTFTBL.spad" 897744 897752 903705 903710) (-555 "INTFACT.spad" 896803 896813 897734 897739) (-554 "INTEF.spad" 895118 895134 896793 896798) (-553 "INTDOM.spad" 893733 893741 895044 895113) (-552 "INTDOM.spad" 892410 892420 893723 893728) (-551 "INTCAT.spad" 890663 890673 892324 892405) 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-608) 149621) ((-342 . -1046) T) ((-636 . -488) 149602) ((-140 . -102) T) ((-44 . -130) T) ((-288 . -1099) T) ((-671 . -93) T) ((-666 . -93) T) ((-654 . -605) 149584) ((-636 . -605) 149537) ((-476 . -93) T) ((-354 . -605) 149519) ((-351 . -605) 149501) ((-343 . -605) 149483) ((-263 . -606) 149231) ((-263 . -605) 149213) ((-246 . -605) 149195) ((-246 . -606) 149056) ((-132 . -93) T) ((-137 . -93) T) ((-136 . -93) T) ((-1210 . -1028) 149022) ((-1194 . -512) 148989) ((-1128 . -605) 148971) ((-810 . -848) T) ((-810 . -717) T) ((-594 . -287) 148948) ((-575 . -708) 148913) ((-477 . -606) NIL) ((-477 . -605) 148895) ((-516 . -708) 148840) ((-315 . -102) T) ((-312 . -102) T) ((-288 . -23) T) ((-151 . -130) T) ((-900 . -605) 148822) ((-385 . -717) T) ((-862 . -1045) 148774) ((-900 . -606) 148756) ((-862 . -111) 148694) ((-705 . -1039) T) ((-703 . -1222) 148678) ((-138 . -102) T) ((-135 . -102) T) ((-114 . -102) T) ((-684 . -348) NIL) ((-517 . -605) 148610) ((-378 . -786) T) ((-222 . -1087) T) 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146764) ((-1230 . -1045) 146599) ((-1210 . -890) 146432) ((-1209 . -1045) 146240) ((-1194 . -289) 146219) ((-1133 . -150) 146203) ((-1107 . -102) T) ((-1105 . -1087) T) ((-1067 . -23) T) ((-1062 . -102) T) ((-917 . -945) T) ((-728 . -308) 146141) ((-75 . -1200) T) ((-30 . -945) T) ((-168 . -899) 146094) ((-654 . -381) 146066) ((-112 . -835) T) ((-1 . -605) 146048) ((-1067 . -1099) T) ((-128 . -641) 146030) ((-50 . -612) 146014) ((-993 . -408) 145986) ((-588 . -890) 145899) ((-437 . -102) T) ((-140 . -308) NIL) ((-128 . -372) 145881) ((-862 . -1039) T) ((-824 . -841) 145860) ((-81 . -1200) T) ((-702 . -289) T) ((-40 . -1046) T) ((-575 . -171) T) ((-516 . -171) T) ((-509 . -605) 145842) ((-168 . -638) 145752) ((-505 . -605) 145734) ((-350 . -146) 145716) ((-350 . -144) T) ((-358 . -1099) T) ((-352 . -1099) T) ((-344 . -1099) T) ((-994 . -306) T) ((-904 . -306) T) ((-862 . -242) T) ((-108 . -1099) T) ((-862 . -232) 145695) ((-1230 . -111) 145516) ((-1209 . -111) 145305) ((-244 . -1234) 145289) ((-558 . -839) T) ((-358 . -23) T) ((-353 . -348) T) ((-315 . -308) 145276) ((-312 . -308) 145217) ((-352 . -23) T) ((-318 . -130) T) ((-344 . -23) T) ((-994 . -1012) T) ((-31 . -608) 145198) ((-108 . -23) T) ((-244 . -596) 145175) ((-1232 . -38) 145067) ((-1219 . -899) 145046) ((-112 . -1087) T) ((-1025 . -102) T) ((-1219 . -638) 144971) ((-861 . -785) NIL) ((-846 . -638) 144945) ((-861 . -782) NIL) ((-807 . -876) NIL) ((-861 . -717) T) ((-1074 . -512) 144818) ((-773 . -512) 144765) ((-771 . -512) 144717) ((-565 . -638) 144704) ((-807 . -1028) 144532) ((-452 . -512) 144475) ((-387 . -388) T) ((-1230 . -608) 144288) ((-1209 . -608) 144036) ((-60 . -1200) T) ((-613 . -841) 144015) ((-498 . -651) T) ((-1133 . -966) 143984) ((-993 . -450) T) ((-689 . -839) T) ((-508 . -783) T) ((-472 . -1045) 143819) ((-342 . -1087) T) ((-312 . -1138) NIL) ((-288 . -130) T) ((-393 . -1087) T) ((-684 . -369) 143786) ((-860 . -1046) T) ((-222 . -612) 143763) ((-326 . -285) 143740) ((-472 . -111) 143561) ((-1230 . -1039) T) ((-1209 . -1039) T) ((-807 . -376) 143545) ((-168 . -717) T) ((-644 . -102) T) ((-1230 . -242) 143524) ((-1230 . -232) 143476) ((-1209 . -232) 143381) ((-1209 . -242) 143360) ((-993 . -401) NIL) ((-660 . -631) 143308) ((-315 . -38) 143218) ((-312 . -38) 143147) ((-69 . -605) 143129) ((-318 . -491) 143095) ((-1173 . -287) 143074) ((-1100 . -1099) 142984) ((-83 . -1200) T) ((-61 . -605) 142966) ((-477 . -287) 142945) ((-1261 . -1028) 142922) ((-1151 . -1087) T) ((-1100 . -23) 142792) ((-807 . -890) 142728) ((-1219 . -717) T) ((-1089 . -1200) T) ((-472 . -608) 142554) ((-1074 . -289) 142485) ((-956 . -1087) T) ((-883 . -102) T) ((-773 . -289) 142396) ((-326 . -19) 142380) ((-59 . -287) 142357) ((-771 . -289) 142288) ((-846 . -717) T) ((-117 . -839) NIL) ((-514 . -287) 142265) ((-326 . -596) 142242) ((-494 . -287) 142219) ((-452 . -289) 142150) ((-1025 . -308) 142001) ((-671 . -488) 141982) ((-565 . -717) T) ((-666 . -488) 141963) ((-671 . -605) 141913) ((-666 . -605) 141879) ((-652 . -605) 141861) ((-476 . -488) 141842) ((-476 . -605) 141808) ((-244 . -606) 141769) ((-244 . -488) 141746) ((-137 . -488) 141727) ((-136 . -488) 141708) ((-132 . -488) 141689) ((-244 . -605) 141581) ((-212 . -102) T) ((-137 . -605) 141547) ((-136 . -605) 141513) ((-132 . -605) 141479) ((-1134 . -34) T) ((-933 . -1200) T) ((-342 . -708) 141424) ((-660 . -25) T) ((-660 . -21) T) ((-1163 . -608) 141405) ((-472 . -1039) T) ((-627 . -416) 141370) ((-599 . -416) 141335) ((-1107 . -1138) T) ((-575 . -289) T) ((-516 . -289) T) ((-1231 . -306) 141314) ((-472 . -232) 141266) ((-472 . -242) 141245) ((-1210 . -306) 141224) ((-1210 . -1012) NIL) ((-1067 . -130) T) ((-862 . -786) 141203) ((-143 . -102) T) ((-40 . -1087) T) ((-862 . -783) 141182) ((-635 . -1000) 141166) ((-574 . -1046) T) ((-558 . -1046) T) ((-493 . -1046) T) ((-406 . -450) T) ((-358 . -130) T) ((-315 . -399) 141150) ((-312 . -399) 141111) ((-352 . -130) T) ((-344 . -130) T) ((-1168 . -1087) T) ((-1107 . -38) 141098) ((-1081 . -605) 141065) ((-108 . -130) T) ((-944 . -1087) T) ((-911 . -1087) T) ((-762 . -1087) T) ((-662 . -1087) T) ((-691 . -146) T) ((-116 . -146) T) ((-1268 . -21) T) ((-1268 . -25) T) ((-1266 . -21) T) ((-1266 . -25) T) ((-654 . -1045) 141049) ((-529 . -841) T) ((-498 . -841) T) ((-354 . -1045) 141001) ((-351 . -1045) 140953) ((-343 . -1045) 140905) ((-250 . -1200) T) ((-249 . -1200) T) ((-263 . -1045) 140748) ((-246 . -1045) 140591) ((-654 . -111) 140570) ((-354 . -111) 140508) ((-351 . -111) 140446) ((-343 . -111) 140384) ((-263 . -111) 140213) ((-246 . -111) 140042) ((-808 . -1204) 140021) ((-615 . -410) 140005) ((-44 . -21) T) ((-44 . -25) T) ((-806 . -631) 139911) ((-808 . -550) 139890) ((-250 . -1028) 139717) ((-249 . -1028) 139544) ((-126 . -119) 139528) ((-900 . -1045) 139493) ((-703 . -102) T) ((-689 . -1046) T) ((-534 . -610) 139396) ((-342 . -171) T) ((-151 . -21) T) ((-151 . -25) T) ((-88 . -605) 139378) ((-900 . -111) 139334) ((-40 . -708) 139279) ((-860 . -1087) T) ((-654 . -608) 139256) ((-636 . -608) 139237) ((-354 . -608) 139174) ((-351 . -608) 139111) ((-343 . -608) 139048) ((-326 . -606) 139009) ((-326 . -605) 138921) ((-263 . -608) 138674) ((-246 . -608) 138459) ((-1209 . -783) 138412) ((-1209 . -786) 138365) ((-250 . -376) 138334) ((-249 . -376) 138303) ((-644 . -38) 138273) ((-600 . -34) T) ((-480 . -1099) 138183) ((-473 . -34) T) ((-1100 . -130) 138053) ((-954 . -25) 137864) ((-900 . -608) 137814) ((-864 . -605) 137796) ((-954 . -21) 137751) ((-806 . -21) 137661) ((-806 . -25) 137512) ((-615 . -1046) T) ((-1165 . -550) 137491) ((-1159 . -47) 137468) ((-354 . -1039) T) ((-351 . -1039) T) ((-480 . -23) 137338) ((-343 . -1039) T) ((-246 . -1039) T) ((-263 . -1039) T) ((-1112 . -47) 137310) ((-117 . -1046) T) ((-1024 . -638) 137284) ((-948 . -34) T) ((-354 . -232) 137263) ((-354 . -242) T) ((-351 . -232) 137242) ((-351 . -242) T) ((-343 . -232) 137221) ((-343 . -242) T) ((-246 . -325) 137178) ((-263 . -325) 137150) ((-263 . -232) 137129) ((-1143 . -150) 137113) ((-250 . -890) 137045) ((-249 . -890) 136977) ((-1069 . -841) T) ((-413 . -1099) T) ((-1043 . -23) T) ((-900 . -1039) T) ((-321 . -638) 136959) ((-1014 . -839) T) ((-1194 . -992) 136925) ((-1160 . -910) 136904) ((-1154 . -910) 136883) ((-1154 . -811) NIL) ((-900 . -242) T) ((-808 . -362) 136862) ((-384 . -23) T) ((-127 . -1087) 136840) ((-121 . -1087) 136818) ((-900 . -232) T) ((-128 . -34) T) ((-378 . -638) 136783) ((-860 . -708) 136770) ((-1036 . -150) 136735) ((-40 . -171) T) ((-684 . -410) 136717) ((-703 . -308) 136704) ((-827 . -638) 136664) ((-818 . -638) 136638) ((-318 . -25) T) ((-318 . -21) T) ((-648 . -285) 136617) ((-574 . -1087) T) ((-558 . -1087) T) ((-493 . -1087) T) ((-244 . -287) 136594) ((-312 . -230) 136555) ((-1159 . -876) NIL) ((-55 . -1087) T) ((-1112 . -876) 136414) ((-129 . -841) T) ((-1159 . -1028) 136294) ((-1112 . -1028) 136177) ((-182 . -605) 136159) ((-845 . -1028) 136055) ((-773 . -285) 135982) ((-808 . -1099) T) ((-1024 . -717) T) ((-594 . -641) 135966) ((-1036 . -966) 135895) ((-989 . -102) T) ((-808 . -23) T) ((-703 . -1138) 135873) ((-684 . -1046) T) ((-594 . -372) 135857) ((-350 . -450) T) ((-342 . -289) T) ((-1247 . -1087) T) ((-247 . -1087) T) ((-398 . -102) T) ((-288 . -21) T) ((-288 . -25) T) ((-360 . -717) T) ((-701 . -1087) T) ((-689 . -1087) T) ((-360 . -471) T) ((-1194 . -605) 135839) ((-1159 . -376) 135823) ((-1112 . -376) 135807) ((-1014 . -410) 135769) ((-140 . -228) 135751) ((-378 . -785) T) ((-378 . -782) T) ((-860 . -171) T) ((-378 . -717) T) ((-702 . -605) 135733) ((-703 . -38) 135562) ((-1246 . -1244) 135546) ((-350 . -401) T) ((-1246 . -1087) 135496) ((-574 . -708) 135483) ((-558 . -708) 135470) ((-493 . -708) 135435) ((-315 . -621) 135414) ((-827 . -717) T) ((-818 . -717) T) ((-635 . -1200) T) ((-1067 . -631) 135362) ((-1159 . -890) 135305) ((-1112 . -890) 135289) ((-652 . -1045) 135273) ((-108 . -631) 135255) ((-480 . -130) 135125) ((-1165 . -1099) T) ((-942 . -47) 135094) ((-615 . -1087) T) ((-652 . -111) 135073) ((-489 . -605) 135039) ((-326 . -287) 135016) ((-479 . -47) 134973) ((-1165 . -23) T) ((-117 . -1087) T) ((-103 . -102) 134951) ((-1258 . -1099) T) ((-1043 . -130) T) ((-1014 . -1046) T) ((-810 . -1028) 134935) ((-993 . -715) 134907) ((-1258 . -23) T) ((-689 . -708) 134872) ((-579 . -605) 134854) ((-385 . -1028) 134838) ((-353 . -1046) T) ((-384 . -130) T) ((-323 . -1028) 134822) ((-224 . -876) 134804) ((-994 . -910) T) ((-91 . -34) T) ((-994 . -811) T) ((-904 . -910) T) ((-1180 . -605) 134786) ((-1107 . -819) T) ((-485 . -1204) T) ((-1092 . -1087) T) ((-1067 . -21) T) ((-1067 . -25) T) ((-216 . -1204) T) ((-989 . -308) 134751) ((-224 . -1028) 134711) ((-40 . -289) T) ((-705 . -638) 134671) ((-671 . -608) 134652) ((-666 . -608) 134633) ((-485 . -550) T) ((-476 . -608) 134614) ((-358 . -25) T) ((-358 . -21) T) ((-352 . -25) T) ((-216 . -550) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-244 . -608) 134591) ((-137 . -608) 134572) ((-136 . -608) 134553) ((-132 . -608) 134534) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1046) T) ((-574 . -171) T) ((-558 . -171) T) ((-493 . -171) T) ((-648 . -605) 134516) ((-728 . -727) 134500) ((-335 . -605) 134482) ((-68 . -382) T) ((-68 . -394) T) ((-1089 . -107) 134466) ((-1050 . -876) 134448) ((-942 . -876) 134373) ((-643 . -1099) T) ((-615 . -708) 134360) ((-479 . -876) NIL) ((-1133 . -102) T) ((-1081 . -610) 134344) ((-1050 . -1028) 134326) ((-97 . -605) 134308) ((-475 . -146) T) ((-942 . -1028) 134188) ((-117 . -708) 134133) ((-643 . -23) T) ((-479 . -1028) 134009) ((-1074 . -606) NIL) ((-1074 . -605) 133991) ((-773 . -606) NIL) ((-773 . -605) 133952) ((-771 . -606) 133586) ((-771 . -605) 133500) ((-1100 . -631) 133406) ((-459 . -605) 133388) ((-452 . -605) 133370) ((-452 . -606) 133231) ((-1025 . -228) 133177) ((-862 . -899) 133156) ((-126 . -34) T) ((-808 . -130) T) ((-639 . -605) 133138) ((-572 . -102) T) ((-354 . -1265) 133122) ((-351 . -1265) 133106) ((-343 . -1265) 133090) 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. -394) T) ((-216 . -23) T) ((-1270 . -1263) 130940) ((-574 . -289) T) ((-558 . -289) T) ((-667 . -1028) 130924) ((-493 . -289) T) ((-135 . -468) 130879) ((-48 . -1087) T) ((-703 . -230) 130863) ((-861 . -890) NIL) ((-1219 . -876) NIL) ((-879 . -102) T) ((-875 . -102) T) ((-387 . -1087) T) ((-168 . -376) 130847) ((-168 . -337) 130831) ((-1219 . -1028) 130711) ((-846 . -1028) 130607) ((-1129 . -102) T) ((-643 . -130) T) ((-117 . -512) 130515) ((-652 . -783) 130494) ((-652 . -786) 130473) ((-565 . -1028) 130455) ((-293 . -1253) 130425) ((-856 . -102) T) ((-953 . -550) 130404) ((-1194 . -1045) 130287) ((-480 . -631) 130193) ((-894 . -1087) T) ((-1014 . -708) 130130) ((-702 . -1045) 130095) ((-609 . -102) T) ((-594 . -34) T) ((-1134 . -1200) T) ((-1194 . -111) 129964) ((-472 . -638) 129861) ((-353 . -708) 129806) ((-168 . -890) 129765) ((-689 . -289) T) ((-684 . -171) T) ((-702 . -111) 129721) ((-1274 . -1046) T) ((-1219 . -376) 129705) ((-417 . -1204) 129683) ((-1105 . -605) 129665) 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. -778) T) ((-493 . -992) T) ((-273 . -830) T) ((-272 . -830) T) ((-271 . -830) T) ((-270 . -830) T) ((-48 . -289) T) ((-269 . -830) T) ((-268 . -830) T) ((-267 . -830) T) ((-192 . -778) T) ((-604 . -841) T) ((-644 . -410) 123574) ((-222 . -608) 123536) ((-110 . -841) T) ((-643 . -21) T) ((-643 . -25) T) ((-1269 . -38) 123506) ((-117 . -285) 123457) ((-1246 . -19) 123441) ((-1246 . -596) 123418) ((-1259 . -1087) T) ((-1064 . -1087) T) ((-977 . -1087) T) ((-953 . -130) T) ((-728 . -1087) T) ((-726 . -130) T) ((-706 . -130) T) ((-509 . -784) T) ((-406 . -1138) 123396) ((-451 . -130) T) ((-509 . -785) T) ((-222 . -1039) T) ((-293 . -102) 123178) ((-140 . -1087) T) ((-689 . -992) T) ((-91 . -1200) T) ((-127 . -605) 123110) ((-121 . -605) 123042) ((-1274 . -171) T) ((-1160 . -362) 123021) ((-1154 . -362) 123000) ((-315 . -1087) T) ((-417 . -130) T) ((-312 . -1087) T) ((-406 . -38) 122952) ((-1120 . -102) T) ((-1232 . -708) 122844) ((-644 . -1046) T) ((-1122 . -1241) T) ((-318 . -144) 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. -1046) T) ((-684 . -992) NIL) ((-3 . |UnionCategory|) T) ((-1230 . -47) 121198) ((-1209 . -47) 121175) ((-1128 . -1000) 121146) ((-224 . -910) T) ((-40 . -111) 121075) ((-862 . -1028) 120939) ((-1107 . -708) 120926) ((-1092 . -605) 120908) ((-1067 . -146) 120887) ((-1067 . -144) 120838) ((-994 . -362) T) ((-318 . -1188) 120804) ((-378 . -306) T) ((-318 . -1185) 120770) ((-315 . -171) 120749) ((-312 . -171) T) ((-993 . -230) 120726) ((-904 . -362) T) ((-575 . -1265) 120713) ((-516 . -1265) 120690) ((-358 . -146) 120669) ((-358 . -144) 120620) ((-352 . -146) 120599) ((-352 . -144) 120550) ((-600 . -1176) 120526) ((-344 . -146) 120505) ((-344 . -144) 120456) ((-318 . -35) 120422) ((-473 . -1176) 120401) ((0 . |EnumerationCategory|) T) ((-318 . -95) 120367) ((-378 . -1012) T) ((-108 . -146) T) ((-108 . -144) NIL) ((-45 . -234) 120317) ((-644 . -1087) T) ((-600 . -107) 120264) ((-483 . -130) T) ((-473 . -107) 120214) ((-239 . -1099) 120124) ((-862 . -376) 120108) ((-862 . -337) 120092) 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-786) T) ((-558 . -783) T) ((-1051 . -234) 112796) ((-358 . -401) 112747) ((-352 . -401) 112698) ((-344 . -401) 112649) ((-1261 . -1099) T) ((-684 . -608) 112584) ((-1261 . -23) T) ((-1248 . -102) T) ((-174 . -605) 112566) ((-1129 . -1046) T) ((-660 . -735) 112550) ((-1165 . -144) 112529) ((-1165 . -146) 112508) ((-1133 . -1087) T) ((-1133 . -1059) 112477) ((-69 . -1200) T) ((-1014 . -1045) 112414) ((-856 . -1046) T) ((-239 . -631) 112320) ((-684 . -1039) T) ((-353 . -1045) 112265) ((-61 . -1200) T) ((-1014 . -111) 112181) ((-891 . -605) 112092) ((-684 . -242) T) ((-684 . -232) NIL) ((-834 . -839) 112071) ((-689 . -786) T) ((-689 . -783) T) ((-993 . -410) 112048) ((-353 . -111) 111977) ((-378 . -910) T) ((-406 . -839) 111956) ((-703 . -289) 111867) ((-222 . -717) T) ((-1238 . -491) 111833) ((-1231 . -491) 111799) ((-1210 . -491) 111765) ((-572 . -1087) T) ((-315 . -992) 111744) ((-221 . -1087) 111722) ((-318 . -963) 111684) ((-105 . -102) T) ((-48 . -1045) 111649) ((-1270 . -102) T) 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-606) 110392) ((-728 . -605) 110374) ((-790 . -841) 110353) ((-1146 . -150) 110300) ((-989 . -512) 110212) ((-353 . -232) T) ((-353 . -242) T) ((-387 . -608) 110193) ((-994 . -25) T) ((-140 . -605) 110175) ((-140 . -606) 110134) ((-900 . -306) T) ((-994 . -21) T) ((-961 . -25) T) ((-904 . -21) T) ((-904 . -25) T) ((-426 . -21) T) ((-426 . -25) T) ((-834 . -410) 110118) ((-48 . -1039) T) ((-1268 . -1260) 110102) ((-1266 . -1260) 110086) ((-1025 . -596) 110061) ((-315 . -606) 109922) ((-315 . -605) 109904) ((-312 . -606) NIL) ((-312 . -605) 109886) ((-48 . -242) T) ((-48 . -232) T) ((-644 . -285) 109847) ((-544 . -234) 109797) ((-138 . -605) 109764) ((-135 . -605) 109746) ((-114 . -605) 109728) ((-475 . -38) 109693) ((-1270 . -1267) 109672) ((-1261 . -130) T) ((-1269 . -1046) T) ((-1069 . -102) T) ((-88 . -1200) T) ((-498 . -308) NIL) ((-990 . -107) 109656) ((-879 . -1087) T) ((-875 . -1087) T) ((-1246 . -641) 109640) ((-1246 . -372) 109624) ((-326 . -1200) T) ((-586 . -841) T) ((-1129 . -1087) T) ((-1129 . -1042) 109564) ((-103 . -512) 109497) ((-917 . -605) 109479) ((-342 . -717) T) ((-30 . -605) 109461) ((-856 . -1087) T) ((-834 . -1046) 109440) ((-40 . -638) 109385) ((-224 . -1204) T) ((-406 . -1046) T) ((-1145 . -150) 109367) ((-989 . -289) 109318) ((-609 . -1087) T) ((-224 . -550) T) ((-318 . -1227) 109302) ((-318 . -1224) 109272) ((-1173 . -1176) 109251) ((-1062 . -605) 109233) ((-637 . -150) 109217) ((-624 . -150) 109163) ((-1173 . -107) 109113) ((-477 . -1176) 109092) ((-485 . -146) T) ((-485 . -144) NIL) ((-1107 . -606) 109007) ((-437 . -605) 108989) ((-216 . -146) T) ((-216 . -144) NIL) ((-1107 . -605) 108971) ((-129 . -102) T) ((-52 . -102) T) ((-1210 . -631) 108923) ((-477 . -107) 108873) ((-983 . -23) T) ((-1270 . -38) 108843) ((-1159 . -1099) T) ((-1112 . -1099) T) ((-1050 . -1204) T) ((-310 . -102) T) ((-845 . -1099) T) ((-942 . -1204) 108822) ((-479 . -1204) 108801) ((-722 . -841) 108780) ((-1050 . -550) T) ((-942 . -550) 108711) ((-1159 . -23) T) 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108120) ((-861 . -550) T) ((-684 . -367) NIL) ((-1274 . -608) 108102) ((-358 . -1253) 108086) ((-660 . -102) T) ((-352 . -1253) 108070) ((-344 . -1253) 108054) ((-1269 . -1087) T) ((-518 . -841) 108033) ((-808 . -450) 108012) ((-1036 . -1087) T) ((-1036 . -1059) 107941) ((-1017 . -966) 107910) ((-810 . -1099) T) ((-993 . -708) 107855) ((-385 . -1099) T) ((-474 . -966) 107824) ((-461 . -966) 107793) ((-110 . -150) 107775) ((-73 . -605) 107757) ((-883 . -605) 107739) ((-1067 . -715) 107718) ((-1274 . -1039) T) ((-807 . -631) 107666) ((-293 . -1046) 107608) ((-168 . -1204) 107513) ((-224 . -1099) T) ((-323 . -23) T) ((-1154 . -982) 107465) ((-834 . -1087) T) ((-1232 . -1045) 107370) ((-1113 . -731) 107349) ((-1230 . -910) 107328) ((-1209 . -910) 107307) ((-860 . -717) T) ((-168 . -550) 107218) ((-574 . -638) 107205) ((-558 . -638) 107192) ((-406 . -1087) T) ((-262 . -1087) T) ((-212 . -605) 107174) ((-493 . -638) 107139) ((-224 . -23) T) ((-1209 . -811) 107092) ((-1268 . -102) T) ((-353 . -1265) 107069) ((-1266 . -102) T) ((-1232 . -111) 106961) ((-143 . -605) 106943) ((-983 . -130) T) ((-44 . -102) T) ((-239 . -841) 106894) ((-1219 . -1204) 106873) ((-103 . -487) 106857) ((-1269 . -708) 106827) ((-1074 . -47) 106788) ((-1050 . -1099) T) ((-942 . -1099) T) ((-127 . -34) T) ((-121 . -34) T) ((-773 . -47) 106765) ((-771 . -47) 106737) ((-1219 . -550) 106648) ((-353 . -367) T) ((-479 . -1099) T) ((-1159 . -130) T) ((-1112 . -130) T) ((-452 . -47) 106627) ((-861 . -362) T) ((-845 . -130) T) ((-151 . -102) T) ((-1050 . -23) T) ((-942 . -23) T) ((-565 . -550) T) ((-807 . -25) T) ((-807 . -21) T) ((-1129 . -512) 106560) ((-585 . -1070) T) ((-579 . -1028) 106544) ((-1232 . -608) 106418) ((-479 . -23) T) ((-350 . -1046) T) ((-1194 . -890) 106399) ((-660 . -308) 106337) ((-1100 . -1253) 106307) ((-689 . -638) 106272) ((-993 . -171) T) ((-953 . -144) 106251) ((-627 . -1087) T) ((-599 . -1087) T) ((-953 . -146) 106230) ((-994 . -841) T) ((-726 . -146) 106209) ((-726 . -144) 106188) ((-961 . -841) T) ((-472 . -910) 106167) ((-315 . -1045) 106077) ((-312 . -1045) 106006) ((-989 . -285) 105964) ((-406 . -708) 105916) ((-691 . -839) T) ((-1232 . -1039) T) ((-315 . -111) 105812) ((-312 . -111) 105725) ((-954 . -102) T) ((-806 . -102) 105515) ((-703 . -606) NIL) ((-703 . -605) 105497) ((-648 . -1028) 105393) ((-1232 . -325) 105337) ((-1025 . -287) 105312) ((-574 . -717) T) ((-558 . -785) T) ((-168 . -362) 105263) ((-558 . -782) T) ((-558 . -717) T) ((-493 . -717) T) ((-1133 . -487) 105247) ((-1074 . -876) NIL) ((-861 . -1099) T) ((-117 . -899) NIL) ((-1268 . -1267) 105223) ((-1266 . -1267) 105202) ((-773 . -876) NIL) ((-771 . -876) 105061) ((-1261 . -25) T) ((-1261 . -21) T) ((-1197 . -102) 105039) ((-1093 . -394) T) ((-615 . -638) 105026) ((-452 . -876) NIL) ((-665 . -102) 105004) ((-1074 . -1028) 104831) ((-861 . -23) T) ((-773 . -1028) 104690) ((-771 . -1028) 104547) ((-117 . -638) 104492) ((-452 . -1028) 104368) ((-315 . -608) 103932) ((-312 . -608) 103815) ((-639 . -1028) 103799) ((-619 . -102) T) ((-221 . -487) 103783) ((-1246 . -34) T) ((-135 . -608) 103767) ((-627 . -708) 103751) ((-599 . -708) 103735) ((-660 . -38) 103695) ((-318 . -102) T) ((-85 . -605) 103677) ((-50 . -1028) 103661) ((-1107 . -1045) 103648) ((-1074 . -376) 103632) ((-773 . -376) 103616) ((-60 . -57) 103578) ((-689 . -785) T) ((-689 . -782) T) ((-575 . -1028) 103565) ((-516 . -1028) 103542) ((-689 . -717) T) ((-323 . -130) T) ((-315 . -1039) 103432) ((-312 . -1039) T) ((-168 . -1099) T) ((-771 . -376) 103416) ((-45 . -150) 103366) ((-994 . -982) 103348) ((-452 . -376) 103332) ((-406 . -171) T) ((-315 . -242) 103311) ((-312 . -242) T) ((-312 . -232) NIL) ((-293 . -1087) 103093) ((-224 . -130) T) ((-1107 . -111) 103078) ((-168 . -23) T) ((-790 . -146) 103057) ((-790 . -144) 103036) ((-250 . -631) 102942) ((-249 . -631) 102848) ((-318 . -283) 102814) ((-1143 . -512) 102747) ((-1120 . -1087) T) ((-224 . -1048) T) ((-806 . -308) 102685) ((-1074 . -890) 102620) ((-773 . -890) 102563) ((-771 . -890) 102547) ((-1268 . -38) 102517) ((-1266 . -38) 102487) ((-1219 . -1099) T) ((-846 . -1099) T) ((-452 . -890) 102464) ((-849 . -1087) T) ((-1219 . -23) T) ((-1107 . -608) 102436) ((-565 . -1099) T) ((-846 . -23) T) ((-615 . -717) T) ((-354 . -910) T) ((-351 . -910) T) ((-288 . -102) T) ((-343 . -910) T) ((-1050 . -130) T) ((-960 . -1070) T) ((-942 . -130) T) ((-117 . -785) NIL) ((-117 . -782) NIL) ((-117 . -717) T) ((-684 . -899) NIL) ((-1036 . -512) 102337) ((-479 . -130) T) ((-565 . -23) T) ((-665 . -308) 102275) ((-627 . -752) T) ((-599 . -752) T) ((-1210 . -841) NIL) ((-993 . -289) T) ((-250 . -21) T) ((-684 . -638) 102225) ((-350 . -1087) T) ((-250 . -25) T) ((-249 . -21) T) ((-249 . -25) T) ((-151 . -38) 102209) ((-2 . -102) T) ((-900 . -910) T) ((-480 . -1253) 102179) ((-222 . -1028) 102156) ((-1107 . -1039) T) ((-702 . -306) T) ((-293 . -708) 102098) ((-691 . -1046) T) ((-485 . -450) T) ((-406 . -512) 102010) ((-216 . -450) T) ((-1107 . -232) T) ((-294 . -150) 101960) ((-989 . -606) 101921) ((-989 . -605) 101903) ((-979 . -605) 101885) ((-116 . -1046) T) ((-644 . -1045) 101869) ((-224 . -491) T) ((-398 . -605) 101851) ((-398 . -606) 101828) ((-1043 . -1253) 101798) ((-644 . -111) 101777) ((-1129 . -487) 101761) ((-806 . -38) 101731) ((-63 . -439) T) ((-63 . -394) T) ((-1146 . -102) T) ((-861 . -130) T) ((-482 . -102) 101709) ((-1274 . -367) T) ((-1067 . -102) T) ((-1049 . -102) T) ((-350 . -708) 101654) ((-722 . -146) 101633) ((-722 . -144) 101612) ((-644 . -608) 101530) ((-1014 . -638) 101467) ((-521 . -1087) 101445) ((-358 . -102) T) ((-352 . -102) T) ((-344 . -102) T) ((-108 . -102) T) ((-502 . -1087) T) ((-353 . -638) 101390) ((-1159 . -631) 101338) ((-1112 . -631) 101286) ((-384 . -507) 101265) ((-824 . -839) 101244) ((-378 . -1204) T) ((-684 . -717) T) ((-338 . -1046) T) ((-1210 . -982) 101196) ((-173 . -1046) T) ((-103 . -605) 101128) ((-1161 . -144) 101107) ((-1161 . -146) 101086) ((-378 . -550) T) ((-1160 . -146) 101065) ((-1160 . -144) 101044) ((-1154 . -144) 100951) ((-406 . -289) T) ((-1154 . -146) 100858) ((-1113 . -146) 100837) ((-1113 . -144) 100816) ((-318 . -38) 100657) ((-168 . -130) T) ((-312 . -786) NIL) ((-312 . -783) NIL) ((-644 . -1039) T) ((-48 . -638) 100622) ((-883 . -608) 100599) ((-1153 . -102) T) ((-984 . -102) T) ((-983 . -21) T) ((-127 . -1000) 100583) ((-121 . -1000) 100567) ((-983 . -25) T) ((-891 . -119) 100551) ((-1145 . -102) T) ((-807 . -841) 100530) ((-1219 . -130) T) ((-1159 . -25) T) ((-1159 . -21) T) ((-846 . -130) T) ((-1112 . -25) T) ((-1112 . -21) T) ((-845 . -25) T) ((-845 . -21) T) ((-773 . -306) 100509) ((-637 . -102) 100487) ((-624 . -102) T) ((-1146 . -308) 100282) ((-565 . -130) T) ((-613 . -839) 100261) ((-1143 . -487) 100245) ((-1137 . -150) 100195) ((-1133 . -605) 100157) ((-1133 . -606) 100118) ((-1014 . -782) T) ((-1014 . -785) T) ((-1014 . -717) T) ((-703 . -1045) 99941) ((-482 . -308) 99879) ((-451 . -416) 99849) ((-350 . -171) T) ((-288 . -38) 99836) ((-273 . -102) T) ((-272 . -102) T) ((-271 . -102) T) ((-270 . -102) T) ((-269 . -102) T) ((-268 . -102) T) ((-342 . -1028) 99813) ((-267 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-208 . -102) T) ((-207 . -102) T) ((-206 . -102) T) ((-205 . -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) ((-194 . -102) T) ((-193 . -102) T) ((-192 . -102) T) ((-353 . -717) T) ((-703 . -111) 99622) ((-660 . -230) 99606) ((-575 . -306) T) ((-516 . -306) T) ((-293 . -512) 99555) ((-108 . -308) NIL) ((-72 . -394) T) ((-1100 . -102) 99345) ((-824 . -410) 99329) ((-1107 . -786) T) ((-1107 . -783) T) ((-691 . -1087) T) ((-572 . -605) 99311) ((-378 . -362) T) ((-168 . -491) 99289) ((-221 . -605) 99221) ((-133 . -1087) T) ((-116 . -1087) T) ((-48 . -717) T) ((-1036 . -487) 99186) ((-140 . -424) 99168) ((-140 . -367) T) ((-1017 . -102) T) ((-510 . -507) 99147) ((-703 . -608) 98903) ((-474 . -102) T) 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T) ((-691 . -708) 97555) ((-338 . -1087) T) ((-173 . -1087) T) ((-330 . -841) T) ((-417 . -450) 97505) ((-378 . -23) T) ((-358 . -38) 97470) ((-352 . -38) 97435) ((-344 . -38) 97400) ((-80 . -439) T) ((-80 . -394) T) ((-224 . -25) T) ((-224 . -21) T) ((-827 . -1099) T) ((-108 . -38) 97350) ((-818 . -1099) T) ((-765 . -1087) T) ((-116 . -708) 97337) ((-662 . -1028) 97321) ((-604 . -102) T) ((-827 . -23) T) ((-818 . -23) T) ((-1143 . -285) 97298) ((-1100 . -308) 97236) ((-1089 . -234) 97220) ((-64 . -395) T) ((-64 . -394) T) ((-110 . -102) T) ((-40 . -376) 97197) ((-96 . -102) T) ((-643 . -843) 97181) ((-1122 . -1070) T) ((-1050 . -21) T) ((-1050 . -25) T) ((-806 . -230) 97150) ((-942 . -25) T) ((-942 . -21) T) ((-613 . -1046) T) ((-1107 . -367) T) ((-479 . -25) T) ((-479 . -21) T) ((-1017 . -308) 97088) ((-879 . -605) 97070) ((-875 . -605) 97052) ((-250 . -841) 97003) ((-249 . -841) 96954) ((-521 . -512) 96887) ((-861 . -631) 96864) ((-474 . -308) 96802) ((-461 . -308) 96740) ((-350 . -289) T) ((-1143 . -1234) 96724) ((-1129 . -605) 96686) ((-1129 . -606) 96647) ((-1127 . -102) T) ((-989 . -1045) 96543) ((-40 . -890) 96495) ((-1143 . -596) 96472) ((-1274 . -638) 96459) ((-856 . -488) 96436) ((-1051 . -150) 96382) ((-862 . -1204) T) ((-989 . -111) 96264) ((-338 . -708) 96248) ((-856 . -605) 96210) ((-173 . -708) 96142) ((-406 . -285) 96100) ((-862 . -550) T) ((-108 . -399) 96082) ((-84 . -383) T) ((-84 . -394) T) ((-691 . -171) T) ((-609 . -605) 96064) ((-99 . -717) T) ((-480 . -102) 95854) ((-99 . -471) T) ((-116 . -171) T) ((-1100 . -38) 95824) ((-168 . -631) 95772) ((-1043 . -102) T) ((-989 . -608) 95662) ((-861 . -25) T) ((-806 . -237) 95641) ((-861 . -21) T) ((-809 . -102) T) ((-413 . -102) T) ((-384 . -102) T) ((-110 . -308) NIL) ((-226 . -102) 95619) ((-127 . -1200) T) ((-121 . -1200) T) ((-1024 . -130) T) ((-660 . -366) 95603) ((-989 . -1039) T) ((-1219 . -631) 95551) ((-1091 . -605) 95533) ((-993 . -605) 95515) ((-513 . -23) T) ((-508 . -23) T) ((-342 . -306) T) ((-506 . -23) T) ((-321 . -130) T) ((-3 . -1087) T) ((-993 . -606) 95499) ((-989 . -242) 95478) ((-989 . -232) 95457) ((-1274 . -717) T) ((-1238 . -144) 95436) ((-824 . -1087) T) ((-1238 . -146) 95415) ((-1231 . -146) 95394) ((-1231 . -144) 95373) ((-1230 . -1204) 95352) ((-1210 . -144) 95259) ((-1210 . -146) 95166) ((-1209 . -1204) 95145) ((-378 . -130) T) ((-558 . -876) 95127) ((0 . -1087) T) ((-173 . -171) T) ((-168 . -21) T) ((-168 . -25) T) ((-49 . -1087) T) ((-1232 . -638) 95032) ((-1230 . -550) 94983) ((-705 . -1099) T) ((-1209 . -550) 94934) ((-558 . -1028) 94916) ((-588 . -146) 94895) ((-588 . -144) 94874) ((-493 . -1028) 94817) ((-1122 . -1124) T) ((-87 . -383) T) ((-87 . -394) T) ((-862 . -362) T) ((-827 . -130) T) ((-818 . -130) T) ((-705 . -23) T) ((-504 . -605) 94783) ((-500 . -605) 94765) ((-1270 . -1046) T) ((-378 . -1048) T) ((-1016 . -1087) 94743) ((-55 . -1028) 94725) ((-891 . -34) T) ((-480 . -308) 94663) ((-585 . -102) T) ((-1143 . -606) 94624) ((-1143 . -605) 94556) ((-1159 . -841) 94535) ((-45 . -102) T) ((-1112 . -841) 94514) ((-808 . -102) T) ((-1219 . -25) T) ((-1219 . -21) T) ((-846 . -25) T) ((-44 . -366) 94498) ((-846 . -21) T) ((-722 . -450) 94449) ((-1269 . -605) 94431) ((-1043 . -308) 94369) ((-661 . -1070) T) ((-598 . -1070) T) ((-389 . -1087) T) ((-565 . -25) T) ((-565 . -21) T) ((-179 . -1070) T) ((-160 . -1070) T) ((-155 . -1070) T) ((-153 . -1070) T) ((-613 . -1087) T) ((-689 . -876) 94351) ((-1246 . -1200) T) ((-226 . -308) 94289) ((-143 . -367) T) ((-1036 . -606) 94231) ((-1036 . -605) 94174) ((-312 . -899) NIL) ((-689 . -1028) 94119) ((-702 . -910) T) ((-472 . -1204) 94098) ((-1160 . -450) 94077) ((-1154 . -450) 94056) ((-329 . -102) T) ((-862 . -1099) T) ((-315 . -638) 93877) ((-312 . -638) 93806) ((-472 . -550) 93757) ((-338 . -512) 93723) ((-544 . -150) 93673) ((-40 . -306) T) ((-834 . -605) 93655) ((-691 . -289) T) ((-862 . -23) T) ((-378 . -491) T) ((-1067 . -230) 93625) ((-510 . -102) T) ((-406 . -606) 93432) 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-963) 89455) ((-76 . -605) 89437) ((-689 . -306) T) ((-168 . -841) 89416) ((-900 . -362) T) ((-378 . -25) T) ((-378 . -21) T) ((-900 . -328) 89403) ((-86 . -605) 89385) ((-689 . -1012) T) ((-667 . -841) T) ((-1230 . -130) T) ((-1209 . -130) T) ((-891 . -1000) 89369) ((-827 . -21) T) ((-48 . -1028) 89312) ((-827 . -25) T) ((-818 . -25) T) ((-818 . -21) T) ((-1268 . -1046) T) ((-1266 . -1046) T) ((-644 . -717) T) ((-1091 . -610) 89215) ((-993 . -608) 89145) ((-1269 . -1045) 89129) ((-1219 . -841) 89108) ((-806 . -410) 89077) ((-103 . -119) 89061) ((-129 . -1087) T) ((-52 . -1087) T) ((-916 . -605) 89043) ((-861 . -982) 89020) ((-814 . -102) T) ((-1269 . -111) 88999) ((-643 . -38) 88969) ((-565 . -841) T) ((-354 . -1099) T) ((-351 . -1099) T) ((-343 . -1099) T) ((-263 . -1099) T) ((-246 . -1099) T) ((-615 . -306) 88948) ((-1137 . -308) 88752) ((-522 . -1070) T) ((-310 . -1087) T) ((-654 . -23) T) ((-480 . -230) 88721) ((-151 . -1046) T) ((-354 . -23) T) ((-351 . -23) T) ((-343 . -23) T) 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-367) NIL) ((-661 . -102) T) ((-179 . -102) T) ((-160 . -102) T) ((-155 . -102) T) ((-153 . -102) T) ((-103 . -34) T) ((-728 . -1200) T) ((-44 . -752) T) ((-586 . -102) T) ((-77 . -395) T) ((-77 . -394) T) ((-643 . -646) 84794) ((-140 . -1200) T) ((-861 . -146) T) ((-861 . -144) NIL) ((-1199 . -93) T) ((-350 . -1039) T) ((-70 . -382) T) ((-70 . -394) T) ((-1152 . -102) T) ((-660 . -512) 84727) ((-679 . -308) 84665) ((-953 . -38) 84562) ((-726 . -38) 84532) ((-544 . -308) 84336) ((-315 . -1200) T) ((-350 . -232) T) ((-350 . -242) T) ((-312 . -1200) T) ((-288 . -1087) T) ((-1167 . -605) 84318) ((-702 . -1204) T) ((-1143 . -641) 84302) ((-1194 . -550) 84281) ((-702 . -550) T) ((-315 . -874) 84265) ((-315 . -876) 84190) ((-312 . -874) 84151) ((-312 . -876) NIL) ((-790 . -308) 84116) ((-318 . -708) 83957) ((-323 . -322) 83934) ((-483 . -102) T) ((-472 . -25) T) ((-472 . -21) T) ((-417 . -38) 83908) ((-315 . -1028) 83571) ((-224 . -1185) T) ((-224 . -1188) T) ((-3 . -605) 83553) ((-312 . -1028) 83483) ((-2 . -1087) T) ((-2 . |RecordCategory|) T) ((-824 . -605) 83465) ((-1100 . -1046) 83395) ((-574 . -910) T) ((-558 . -811) T) ((-558 . -910) T) ((-493 . -910) T) ((-135 . -1028) 83379) ((-224 . -95) T) ((-75 . -439) T) ((-75 . -394) T) ((0 . -605) 83361) ((-168 . -146) 83340) ((-168 . -144) 83291) ((-224 . -35) T) ((-49 . -605) 83273) ((-475 . -1046) T) ((-485 . -230) 83255) ((-482 . -958) 83239) ((-480 . -839) 83218) ((-216 . -230) 83200) ((-81 . -439) T) ((-81 . -394) T) ((-1133 . -34) T) ((-806 . -171) 83179) ((-722 . -102) T) ((-1016 . -605) 83146) ((-498 . -285) 83121) ((-315 . -376) 83090) ((-312 . -376) 83051) ((-312 . -337) 83012) ((-1072 . -605) 82994) ((-807 . -939) 82941) ((-652 . -130) T) ((-1219 . -144) 82920) ((-1219 . -146) 82899) ((-1161 . -102) T) ((-1160 . -102) T) ((-1154 . -102) T) ((-1146 . -1087) T) ((-1113 . -102) T) ((-221 . -34) T) ((-288 . -708) 82886) ((-1146 . -602) 82862) ((-586 . -308) NIL) ((-482 . -1087) 82840) ((-389 . -605) 82822) ((-508 . -841) T) ((-1137 . -228) 82772) ((-1238 . -1237) 82756) ((-1238 . -1224) 82733) ((-1231 . -1229) 82694) ((-1231 . -1224) 82664) ((-1231 . -1227) 82648) ((-1210 . -1208) 82609) ((-1210 . -1224) 82586) ((-613 . -605) 82568) ((-1210 . -1206) 82552) ((-689 . -910) T) ((-1161 . -283) 82518) ((-1160 . -283) 82484) ((-1154 . -283) 82450) ((-1067 . -1087) T) ((-1049 . -1087) T) ((-48 . -301) T) ((-315 . -890) 82416) ((-312 . -890) NIL) ((-1049 . -1056) 82395) ((-1107 . -876) 82377) ((-790 . -38) 82361) ((-263 . -631) 82309) ((-246 . -631) 82257) ((-691 . -1045) 82244) ((-588 . -1224) 82221) ((-1113 . -283) 82187) ((-318 . -171) 82118) ((-358 . -1087) T) ((-352 . -1087) T) ((-344 . -1087) T) ((-498 . -19) 82100) ((-1107 . -1028) 82082) ((-1089 . -150) 82066) ((-108 . -1087) T) ((-116 . -1045) 82053) ((-702 . -362) T) ((-498 . -596) 82028) ((-691 . -111) 82013) ((-435 . -102) T) ((-45 . -1136) 81963) ((-116 . -111) 81948) ((-627 . -711) T) ((-599 . -711) T) ((-806 . -512) 81881) ((-1025 . -1200) T) ((-933 . -150) 81865) ((-1159 . -450) 81796) ((-1153 . -1087) T) ((-1145 . -1087) T) ((-523 . -102) T) ((-518 . -102) 81746) ((-1129 . -638) 81720) ((-1112 . -450) 81671) ((-1074 . -1204) 81650) ((-773 . -1204) 81629) ((-771 . -1204) 81608) ((-62 . -1200) T) ((-475 . -605) 81560) ((-475 . -606) 81482) ((-1074 . -550) 81413) ((-984 . -1087) T) ((-773 . -550) 81324) ((-771 . -550) 81255) ((-480 . -410) 81224) ((-615 . -910) 81203) ((-452 . -1204) 81182) ((-722 . -308) 81169) ((-691 . -608) 81141) ((-397 . -605) 81123) ((-665 . -512) 81056) ((-654 . -25) T) ((-654 . -21) T) ((-452 . -550) 80987) ((-354 . -25) T) ((-354 . -21) T) ((-117 . -910) T) ((-117 . -811) NIL) ((-351 . -25) T) ((-351 . -21) T) ((-343 . -25) T) ((-343 . -21) T) ((-263 . -25) T) ((-263 . -21) T) ((-246 . -25) T) ((-246 . -21) T) ((-83 . -383) T) ((-83 . -394) T) ((-133 . -608) 80969) ((-116 . -608) 80941) ((-1248 . -605) 80923) ((-1194 . -1099) T) ((-1194 . -23) T) ((-1154 . -308) 80808) ((-1113 . -308) 80795) ((-1067 . -708) 80663) ((-856 . -638) 80623) ((-933 . -970) 80607) ((-900 . -21) T) ((-288 . -171) T) ((-900 . -25) T) ((-310 . -93) T) ((-862 . -841) 80558) ((-702 . -1099) T) ((-702 . -23) T) ((-691 . -1039) T) ((-637 . -1087) 80536) ((-624 . -1087) T) ((-575 . -1204) T) ((-516 . -1204) T) ((-624 . -602) 80511) ((-575 . -550) T) ((-516 . -550) T) ((-358 . -708) 80463) ((-352 . -708) 80415) ((-338 . -1045) 80399) ((-344 . -708) 80351) ((-173 . -111) 80262) ((-173 . -1045) 80194) ((-108 . -708) 80144) ((-338 . -111) 80123) ((-273 . -1087) T) ((-272 . -1087) T) ((-271 . -1087) T) ((-270 . -1087) T) ((-269 . -1087) T) ((-268 . -1087) T) ((-267 . -1087) T) ((-211 . -1087) T) ((-210 . -1087) T) ((-208 . -1087) T) ((-168 . -1188) 80101) ((-168 . -1185) 80079) ((-207 . -1087) T) ((-206 . -1087) T) ((-116 . -1039) T) ((-205 . -1087) T) ((-202 . -1087) T) ((-691 . -232) T) ((-201 . -1087) T) ((-200 . -1087) T) ((-199 . -1087) T) ((-198 . -1087) T) ((-197 . -1087) T) ((-196 . -1087) T) 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T) ((-808 . -1046) T) ((-773 . -23) T) ((-771 . -23) T) ((-479 . -450) 77509) ((-1146 . -512) 77292) ((-380 . -381) 77271) ((-1165 . -410) 77255) ((-459 . -23) T) ((-452 . -23) T) ((-96 . -1087) T) ((-482 . -512) 77188) ((-288 . -289) T) ((-1069 . -605) 77170) ((-1069 . -606) 77151) ((-406 . -899) 77130) ((-50 . -1099) T) ((-1014 . -910) T) ((-993 . -717) T) ((-703 . -876) NIL) ((-575 . -1099) T) ((-516 . -1099) T) ((-834 . -638) 77103) ((-1194 . -130) T) ((-1154 . -399) 77055) ((-994 . -308) NIL) ((-806 . -487) 77039) ((-353 . -910) T) ((-1143 . -34) T) ((-406 . -638) 76991) ((-50 . -23) T) ((-702 . -130) T) ((-703 . -1028) 76871) ((-575 . -23) T) ((-108 . -512) NIL) ((-516 . -23) T) ((-168 . -408) 76842) ((-1127 . -1087) T) ((-1261 . -1260) 76826) ((-691 . -786) T) ((-691 . -783) T) ((-1107 . -306) T) ((-378 . -146) T) ((-279 . -605) 76808) ((-1209 . -982) 76778) ((-48 . -910) T) ((-665 . -487) 76762) ((-250 . -1253) 76732) ((-249 . -1253) 76702) ((-1163 . -841) T) ((-1100 . -171) 76681) ((-1107 . -1012) T) ((-1036 . -34) T) ((-827 . -146) 76660) ((-827 . -144) 76639) ((-728 . -107) 76623) ((-604 . -131) T) ((-480 . -1087) 76413) ((-1165 . -1046) T) ((-861 . -450) T) ((-85 . -1200) T) ((-239 . -38) 76383) ((-140 . -107) 76365) ((-703 . -376) 76349) ((-824 . -608) 76217) ((-1107 . -543) T) ((-573 . -102) T) ((-129 . -488) 76199) ((-389 . -1045) 76183) ((-1269 . -717) T) ((-1159 . -939) 76152) ((-129 . -605) 76119) ((-52 . -605) 76101) ((-1112 . -939) 76068) ((-643 . -410) 76052) ((-1258 . -1046) T) ((-613 . -1045) 76036) ((-652 . -25) T) ((-652 . -21) T) ((-1145 . -512) NIL) ((-1238 . -102) T) ((-1231 . -102) T) ((-389 . -111) 76015) ((-221 . -253) 75999) ((-1210 . -102) T) ((-1043 . -1087) T) ((-994 . -1138) T) ((-1043 . -1042) 75939) ((-809 . -1087) T) ((-342 . -1204) T) ((-627 . -638) 75923) ((-613 . -111) 75902) ((-599 . -638) 75886) ((-589 . -102) T) ((-310 . -488) 75867) ((-579 . -130) T) ((-588 . -102) T) ((-413 . -1087) T) ((-384 . -1087) T) ((-310 . -605) 75833) ((-226 . -1087) 75811) ((-637 . -512) 75744) ((-624 . -512) 75588) ((-824 . -1039) 75567) ((-635 . -150) 75551) ((-342 . -550) T) ((-703 . -890) 75494) ((-544 . -228) 75444) ((-1238 . -283) 75410) ((-1067 . -289) 75361) ((-485 . -839) T) ((-222 . -1099) T) ((-1231 . -283) 75327) ((-1210 . -283) 75293) ((-994 . -38) 75243) ((-216 . -839) T) ((-1194 . -491) 75209) ((-904 . -38) 75161) ((-834 . -785) 75140) ((-834 . -782) 75119) ((-834 . -717) 75098) ((-358 . -289) T) ((-352 . -289) T) ((-344 . -289) T) ((-168 . -450) 75029) ((-426 . -38) 75013) ((-108 . -289) T) ((-222 . -23) T) ((-406 . -785) 74992) ((-406 . -782) 74971) ((-406 . -717) T) ((-498 . -287) 74946) ((-475 . -1045) 74911) ((-648 . -130) T) ((-613 . -608) 74880) ((-1100 . -512) 74813) ((-335 . -130) T) ((-168 . -401) 74792) ((-480 . -708) 74734) ((-806 . -285) 74711) ((-475 . -111) 74667) ((-643 . -1046) T) ((-1219 . -450) 74598) ((-1257 . -1070) T) ((-1256 . -1070) T) ((-1074 . -130) T) ((-1043 . -708) 74540) ((-263 . -841) 74519) ((-246 . -841) 74498) ((-773 . -130) T) ((-771 . -130) T) ((-565 . -450) T) ((-1017 . -512) 74431) ((-613 . -1039) T) ((-585 . -1087) T) ((-531 . -172) T) ((-459 . -130) T) ((-452 . -130) T) ((-45 . -1087) T) ((-384 . -708) 74401) ((-808 . -1087) T) ((-474 . -512) 74334) ((-461 . -512) 74267) ((-451 . -366) 74237) ((-45 . -602) 74216) ((-315 . -301) T) ((-475 . -608) 74166) ((-660 . -605) 74128) ((-59 . -841) 74107) ((-1210 . -308) 73992) ((-994 . -399) 73974) ((-806 . -596) 73951) ((-514 . -841) 73930) ((-494 . -841) 73909) ((-40 . -1204) T) ((-989 . -1028) 73805) ((-50 . -130) T) ((-575 . -130) T) ((-516 . -130) T) ((-293 . -638) 73665) ((-342 . -328) 73642) ((-342 . -362) T) ((-321 . -322) 73619) ((-318 . -285) 73604) ((-40 . -550) T) ((-378 . -1185) T) ((-378 . -1188) T) ((-1025 . -1176) 73579) ((-1173 . -234) 73529) ((-1154 . -230) 73481) ((-329 . -1087) T) ((-378 . -95) T) ((-378 . -35) T) ((-1025 . -107) 73427) ((-475 . -1039) T) ((-477 . -234) 73377) ((-1146 . -487) 73311) ((-1270 . -1045) 73295) ((-380 . -1045) 73279) ((-475 . -242) T) ((-807 . -102) T) ((-705 . -146) 73258) ((-705 . -144) 73237) ((-482 . -487) 73221) ((-483 . -334) 73190) ((-1270 . -111) 73169) ((-510 . -1087) T) ((-480 . -171) 73148) ((-989 . -376) 73132) ((-412 . -102) T) ((-380 . -111) 73111) ((-989 . -337) 73095) ((-278 . -973) 73079) ((-277 . -973) 73063) ((-1268 . -605) 73045) ((-1266 . -605) 73027) ((-110 . -512) NIL) ((-1159 . -1222) 73011) ((-845 . -843) 72995) ((-1165 . -1087) T) ((-103 . -1200) T) ((-942 . -939) 72956) ((-808 . -708) 72898) ((-1210 . -1138) NIL) ((-479 . -939) 72843) ((-1050 . -142) T) ((-60 . -102) 72821) ((-44 . -605) 72803) ((-78 . -605) 72785) ((-350 . -638) 72730) ((-1258 . -1087) T) ((-509 . -841) T) ((-342 . -1099) T) ((-294 . -1087) T) ((-989 . -890) 72689) ((-294 . -602) 72668) ((-1270 . -608) 72617) ((-1238 . -38) 72514) ((-1231 . -38) 72355) ((-1210 . -38) 72151) ((-485 . -1046) T) ((-380 . -608) 72135) ((-216 . -1046) T) 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-512) 70802) ((-613 . -786) 70781) ((-613 . -783) 70760) ((-1197 . -605) 70672) ((-221 . -1200) T) ((-665 . -605) 70604) ((-1143 . -1000) 70588) ((-933 . -102) 70538) ((-350 . -717) T) ((-852 . -605) 70520) ((-1210 . -399) 70472) ((-1100 . -487) 70456) ((-60 . -308) 70394) ((-330 . -102) T) ((-1194 . -21) T) ((-1194 . -25) T) ((-40 . -1099) T) ((-702 . -21) T) ((-619 . -605) 70376) ((-513 . -322) 70355) ((-702 . -25) T) ((-108 . -285) NIL) ((-911 . -1099) T) ((-40 . -23) T) ((-762 . -1099) T) ((-558 . -1204) T) ((-493 . -1204) T) ((-318 . -605) 70337) ((-994 . -230) 70319) ((-168 . -165) 70303) ((-574 . -550) T) ((-558 . -550) T) ((-493 . -550) T) ((-762 . -23) T) ((-1230 . -146) 70282) ((-1146 . -596) 70258) ((-1230 . -144) 70237) ((-1017 . -487) 70221) ((-1209 . -144) 70146) ((-1209 . -146) 70071) ((-1261 . -1267) 70050) ((-474 . -487) 70034) ((-461 . -487) 70018) ((-521 . -34) T) ((-643 . -708) 69988) ((-112 . -957) T) ((-652 . -841) 69967) ((-1165 . -171) 69918) ((-364 . -102) T) 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. -230) 58897) ((-353 . -23) T) ((-71 . -1200) T) ((-224 . -38) 58862) ((-108 . -111) 58796) ((-40 . -25) T) ((-40 . -21) T) ((-660 . -711) T) ((-168 . -283) 58774) ((-48 . -1099) T) ((-911 . -25) T) ((-762 . -25) T) ((-1137 . -487) 58711) ((-483 . -1087) T) ((-1270 . -638) 58685) ((-1219 . -102) T) ((-846 . -102) T) ((-239 . -1046) 58615) ((-1050 . -1138) T) ((-954 . -783) 58568) ((-380 . -638) 58552) ((-48 . -23) T) ((-954 . -786) 58505) ((-806 . -786) 58456) ((-806 . -783) 58407) ((-294 . -596) 58386) ((-475 . -717) T) ((-565 . -102) T) ((-1067 . -608) 58204) ((-248 . -184) T) ((-186 . -184) T) ((-861 . -308) 58161) ((-643 . -285) 58140) ((-112 . -651) T) ((-358 . -608) 58077) ((-352 . -608) 58014) ((-344 . -608) 57951) ((-76 . -1200) T) ((-108 . -608) 57901) ((-1050 . -38) 57888) ((-654 . -373) 57867) ((-942 . -38) 57716) ((-722 . -1087) T) ((-479 . -38) 57565) ((-86 . -1200) T) ((-585 . -488) 57546) ((-565 . -283) T) ((-1210 . -839) NIL) ((-585 . -605) 57512) ((-1161 . -1087) T) 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. -1046) T) ((-588 . -1046) T) ((-1274 . -1099) T) ((-1161 . -171) 53128) ((-1160 . -171) 53059) ((-1154 . -171) 52990) ((-1113 . -171) 52941) ((-994 . -1087) T) ((-961 . -1087) T) ((-904 . -1087) T) ((-1194 . -146) 52920) ((-790 . -788) 52904) ((-689 . -25) T) ((-689 . -21) T) ((-117 . -631) 52881) ((-691 . -876) 52863) ((-426 . -1087) T) ((-315 . -1204) 52842) ((-312 . -1204) T) ((-168 . -399) 52826) ((-1194 . -144) 52805) ((-472 . -963) 52767) ((-128 . -102) T) ((-72 . -605) 52749) ((-108 . -786) T) ((-108 . -783) T) ((-691 . -1028) 52731) ((-315 . -550) 52710) ((-312 . -550) T) ((-1274 . -23) T) ((-133 . -1028) 52692) ((-96 . -608) 52673) ((-480 . -1045) 52570) ((-45 . -287) 52495) ((-239 . -708) 52437) ((-515 . -102) T) ((-480 . -111) 52327) ((-1079 . -102) 52305) ((-1024 . -102) T) ((-635 . -819) 52284) ((-722 . -512) 52227) ((-1043 . -1045) 52211) ((-1122 . -93) T) ((-1051 . -285) 52186) ((-615 . -21) T) ((-615 . -25) T) ((-522 . -1087) T) ((-360 . -102) T) ((-321 . -102) T) 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. -605) 50372) ((-1268 . -638) 50346) ((-1051 . -596) 50321) ((-809 . -608) 50305) ((-59 . -150) 50289) ((-514 . -150) 50273) ((-494 . -150) 50257) ((-358 . -1265) 50241) ((-352 . -1265) 50225) ((-344 . -1265) 50209) ((-315 . -362) 50188) ((-312 . -362) T) ((-480 . -1039) 50118) ((-684 . -631) 50100) ((-1266 . -638) 50074) ((-128 . -308) NIL) ((-1232 . -23) T) ((-679 . -487) 50058) ((-64 . -605) 50040) ((-1100 . -786) 49991) ((-1100 . -783) 49942) ((-544 . -487) 49879) ((-660 . -34) T) ((-480 . -232) 49831) ((-294 . -287) 49810) ((-239 . -171) 49789) ((-807 . -1046) T) ((-44 . -638) 49747) ((-1067 . -367) 49698) ((-722 . -289) 49629) ((-518 . -512) 49562) ((-808 . -1045) 49513) ((-1074 . -144) 49492) ((-358 . -367) 49471) ((-352 . -367) 49450) ((-344 . -367) 49429) ((-1074 . -146) 49408) ((-861 . -230) 49385) ((-808 . -111) 49327) ((-773 . -144) 49306) ((-773 . -146) 49285) ((-263 . -939) 49252) ((-250 . -839) 49231) ((-246 . -939) 49176) ((-249 . -839) 49155) ((-771 . -144) 49134) 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. -102) T) ((-911 . -102) T) ((-1113 . -717) T) ((-762 . -102) T) ((-662 . -102) T) ((-472 . -1087) T) ((-338 . -1099) T) ((-173 . -1099) T) ((-318 . -910) 11313) ((-1230 . -708) 11154) ((-862 . -171) T) ((-1209 . -708) 10968) ((-834 . -21) 10920) ((-834 . -25) 10872) ((-244 . -1136) 10856) ((-126 . -512) 10789) ((-406 . -25) T) ((-406 . -21) T) ((-338 . -23) T) ((-168 . -606) 10555) ((-168 . -605) 10537) ((-173 . -23) T) ((-635 . -287) 10514) ((-518 . -34) T) ((-888 . -605) 10496) ((-89 . -1200) T) ((-832 . -605) 10478) ((-799 . -605) 10460) ((-760 . -605) 10442) ((-667 . -605) 10424) ((-239 . -638) 10272) ((-1163 . -1087) T) ((-1159 . -1045) 10095) ((-1137 . -1200) T) ((-1112 . -1045) 9938) ((-845 . -1045) 9922) ((-1213 . -610) 9906) ((-1159 . -111) 9715) ((-1112 . -111) 9544) ((-845 . -111) 9523) ((-1219 . -606) NIL) ((-1219 . -605) 9505) ((-342 . -1138) T) ((-846 . -605) 9487) ((-1063 . -285) 9466) ((-80 . -1200) T) ((-994 . -899) NIL) ((-600 . -285) 9442) ((-1186 . -512) 9375) 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-308) 142109) ((-674 . -488) 142090) ((-568 . -720) T) ((-669 . -488) 142071) ((-674 . -608) 142021) ((-669 . -608) 141987) ((-655 . -608) 141969) ((-476 . -488) 141950) ((-476 . -608) 141916) ((-244 . -609) 141877) ((-244 . -488) 141854) ((-137 . -488) 141835) ((-136 . -488) 141816) ((-132 . -488) 141797) ((-244 . -608) 141689) ((-212 . -102) T) ((-137 . -608) 141655) ((-136 . -608) 141621) ((-132 . -608) 141587) ((-1137 . -34) T) ((-936 . -1205) T) ((-342 . -711) 141532) ((-663 . -25) T) ((-663 . -21) T) ((-1166 . -611) 141513) ((-472 . -1042) T) ((-630 . -416) 141478) ((-602 . -416) 141443) ((-1110 . -1141) T) ((-578 . -289) T) ((-516 . -289) T) ((-1238 . -306) 141422) ((-472 . -232) 141374) ((-472 . -242) 141353) ((-1217 . -306) 141332) ((-1217 . -1015) NIL) ((-1070 . -130) T) ((-865 . -789) 141311) ((-143 . -102) T) ((-40 . -1090) T) ((-865 . -786) 141290) ((-638 . -1003) 141274) ((-577 . -1049) T) ((-561 . -1049) T) ((-493 . -1049) T) ((-406 . -450) T) ((-358 . -130) T) ((-315 . -399) 141258) ((-312 . -399) 141219) ((-352 . -130) T) ((-344 . -130) T) ((-1171 . -1090) T) ((-1110 . -38) 141206) ((-1084 . -608) 141173) ((-108 . -130) T) ((-947 . -1090) T) ((-914 . -1090) T) ((-765 . -1090) T) ((-665 . -1090) T) ((-694 . -146) T) ((-116 . -146) T) ((-1275 . -21) T) ((-1275 . -25) T) ((-1273 . -21) T) ((-1273 . -25) T) ((-657 . -1048) 141157) ((-529 . -844) T) ((-498 . -844) T) ((-354 . -1048) 141109) ((-351 . -1048) 141061) ((-343 . -1048) 141013) ((-250 . -1205) T) ((-249 . -1205) T) ((-263 . -1048) 140856) ((-246 . -1048) 140699) ((-657 . -111) 140678) ((-545 . -838) T) ((-354 . -111) 140616) ((-351 . -111) 140554) ((-343 . -111) 140492) ((-263 . -111) 140321) ((-246 . -111) 140150) ((-811 . -1209) 140129) ((-618 . -410) 140113) ((-44 . -21) T) ((-44 . -25) T) ((-809 . -634) 140019) ((-811 . -553) 139998) ((-250 . -1031) 139825) ((-249 . -1031) 139652) ((-126 . -119) 139636) ((-903 . -1048) 139601) ((-706 . -102) T) ((-692 . -1049) T) ((-534 . -613) 139504) ((-342 . -171) T) ((-151 . -25) T) ((-88 . -608) 139486) ((-151 . -21) T) ((-903 . -111) 139442) ((-40 . -711) 139387) ((-863 . -1090) T) ((-657 . -611) 139364) ((-639 . -611) 139345) ((-354 . -611) 139282) ((-351 . -611) 139219) ((-545 . -1090) T) ((-343 . -611) 139156) ((-326 . -609) 139117) ((-326 . -608) 139029) ((-263 . -611) 138782) ((-246 . -611) 138567) ((-1216 . -786) 138520) ((-1216 . -789) 138473) ((-250 . -376) 138442) ((-249 . -376) 138411) ((-647 . -38) 138381) ((-603 . -34) T) ((-480 . -1102) 138291) ((-473 . -34) T) ((-1103 . -130) 138161) ((-957 . -25) 137972) ((-903 . -611) 137922) ((-867 . -608) 137904) ((-957 . -21) 137859) ((-809 . -21) 137769) ((-809 . -25) 137620) ((-1211 . -367) T) ((-618 . -1049) T) ((-1168 . -553) 137599) ((-1162 . -47) 137576) ((-354 . -1042) T) ((-351 . -1042) T) ((-480 . -23) 137446) ((-343 . -1042) T) ((-246 . -1042) T) ((-263 . -1042) T) ((-1115 . -47) 137418) ((-117 . -1049) T) ((-1027 . -641) 137392) ((-951 . -34) T) ((-354 . -232) 137371) ((-354 . -242) T) ((-351 . -232) 137350) ((-351 . -242) T) ((-343 . -232) 137329) ((-343 . -242) T) ((-246 . -325) 137286) ((-263 . -325) 137258) ((-263 . -232) 137237) ((-1146 . -150) 137221) ((-250 . -893) 137153) ((-249 . -893) 137085) ((-1072 . -844) T) ((-413 . -1102) T) ((-1046 . -23) T) ((-903 . -1042) T) ((-321 . -641) 137067) ((-1017 . -842) T) ((-1199 . -995) 137033) ((-1163 . -913) 137012) ((-1157 . -913) 136991) ((-1157 . -814) NIL) ((-903 . -242) T) ((-811 . -362) 136970) ((-384 . -23) T) ((-127 . -1090) 136948) ((-121 . -1090) 136926) ((-903 . -232) T) ((-128 . -34) T) ((-378 . -641) 136891) ((-863 . -711) 136878) ((-1039 . -150) 136843) ((-40 . -171) T) ((-687 . -410) 136825) ((-706 . -308) 136812) ((-830 . -641) 136772) ((-821 . -641) 136746) ((-318 . -25) T) ((-318 . -21) T) ((-651 . -285) 136725) ((-577 . -1090) T) ((-561 . -1090) T) ((-493 . -1090) T) ((-244 . -287) 136702) ((-312 . -230) 136663) ((-1162 . -879) NIL) ((-55 . -1090) T) ((-1115 . -879) 136522) 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-25) T) ((-358 . -21) T) ((-352 . -25) T) ((-216 . -553) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-244 . -611) 134699) ((-137 . -611) 134680) ((-136 . -611) 134661) ((-132 . -611) 134642) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1049) T) ((-577 . -171) T) ((-561 . -171) T) ((-493 . -171) T) ((-651 . -608) 134624) ((-731 . -730) 134608) ((-335 . -608) 134590) ((-68 . -382) T) ((-68 . -394) T) ((-1092 . -107) 134574) ((-1053 . -879) 134556) ((-945 . -879) 134481) ((-646 . -1102) T) ((-618 . -711) 134468) ((-479 . -879) NIL) ((-1136 . -102) T) ((-1084 . -613) 134452) ((-1053 . -1031) 134434) ((-97 . -608) 134416) ((-475 . -146) T) ((-945 . -1031) 134296) ((-117 . -711) 134241) ((-646 . -23) T) ((-479 . -1031) 134117) ((-1077 . -609) NIL) ((-1077 . -608) 134099) ((-776 . -609) NIL) ((-776 . -608) 134060) ((-774 . -609) 133694) ((-774 . -608) 133608) ((-1103 . -634) 133514) ((-459 . -608) 133496) ((-452 . -608) 133478) ((-452 . -609) 133339) ((-1028 . -228) 133285) ((-865 . -902) 133264) ((-126 . -34) T) ((-811 . -130) T) ((-642 . -608) 133246) ((-575 . -102) T) ((-354 . -1272) 133230) ((-351 . -1272) 133214) ((-343 . -1272) 133198) ((-127 . -512) 133131) ((-121 . -512) 133064) ((-509 . -786) T) ((-509 . -789) T) ((-508 . -788) T) ((-103 . -308) 133002) ((-221 . -102) 132980) ((-687 . -1090) T) ((-692 . -171) T) ((-865 . -641) 132932) ((-65 . -383) T) ((-274 . -608) 132914) ((-65 . -394) T) ((-945 . -376) 132898) ((-863 . -289) T) ((-50 . -608) 132880) ((-992 . -38) 132828) ((-578 . -608) 132810) ((-479 . -376) 132794) ((-578 . -609) 132776) ((-516 . -608) 132758) ((-903 . -1272) 132745) ((-864 . -1205) T) ((-694 . -450) T) ((-493 . -512) 132711) ((-485 . -362) T) ((-354 . -367) 132690) ((-351 . -367) 132669) ((-343 . -367) 132648) ((-708 . -720) T) ((-216 . -362) T) ((-116 . -450) T) ((-1276 . -1267) 132632) ((-864 . -877) 132609) ((-864 . -879) NIL) ((-957 . -844) 132508) ((-809 . -844) 132459) ((-647 . -649) 132443) ((-1191 . -34) T) ((-170 . -608) 132425) ((-1103 . -21) 132335) ((-1103 . -25) 132186) ((-864 . -1031) 132163) ((-945 . -893) 132144) ((-1226 . -47) 132121) ((-903 . -367) T) ((-59 . -644) 132105) ((-514 . -644) 132089) ((-479 . -893) 132066) ((-71 . -439) T) ((-71 . -394) T) ((-494 . -644) 132050) ((-59 . -372) 132034) ((-618 . -171) T) ((-514 . -372) 132018) ((-494 . -372) 132002) ((-821 . -702) 131986) ((-1162 . -306) 131965) ((-1168 . -130) T) ((-117 . -171) T) ((-1136 . -308) 131903) ((-168 . -1205) T) ((-630 . -738) 131887) ((-602 . -738) 131871) ((-1265 . -130) T) ((-1238 . -913) 131850) ((-1217 . -913) 131829) ((-1217 . -814) NIL) ((-687 . -711) 131779) ((-1216 . -902) 131732) ((-1017 . -1090) T) ((-864 . -376) 131709) ((-864 . -337) 131686) ((-898 . -1102) T) ((-168 . -877) 131670) ((-168 . -879) 131595) ((-485 . -1102) T) ((-353 . -1090) T) ((-216 . -1102) T) ((-76 . -439) T) ((-76 . -394) T) ((-168 . -1031) 131491) ((-318 . -844) T) ((-1253 . -512) 131424) ((-1237 . -641) 131321) ((-1216 . -641) 131191) ((-865 . -788) 131170) ((-865 . -785) 131149) ((-865 . -720) T) ((-485 . -23) T) ((-222 . -608) 131131) ((-173 . -450) T) ((-221 . -308) 131069) ((-86 . -439) T) ((-86 . -394) T) ((-216 . -23) T) ((-1277 . -1270) 131048) ((-577 . -289) T) ((-561 . -289) T) ((-670 . -1031) 131032) ((-493 . -289) T) ((-135 . -468) 130987) ((-48 . -1090) T) ((-706 . -230) 130971) ((-864 . -893) NIL) ((-1226 . -879) NIL) ((-882 . -102) T) ((-878 . -102) T) ((-387 . -1090) T) ((-168 . -376) 130955) ((-168 . -337) 130939) ((-1226 . -1031) 130819) ((-849 . -1031) 130715) ((-1132 . -102) T) ((-646 . -130) T) ((-117 . -512) 130623) ((-655 . -786) 130602) ((-655 . -789) 130581) ((-568 . -1031) 130563) ((-293 . -1260) 130533) ((-859 . -102) T) ((-956 . -553) 130512) ((-1199 . -1048) 130395) ((-480 . -634) 130301) ((-897 . -1090) T) ((-1017 . -711) 130238) ((-705 . -1048) 130203) ((-612 . -102) T) ((-597 . -34) T) ((-1137 . -1205) T) ((-1199 . -111) 130072) ((-472 . -641) 129969) ((-353 . -711) 129914) ((-168 . -893) 129873) ((-692 . -289) T) ((-687 . -171) T) ((-705 . -111) 129829) ((-1281 . -1049) T) ((-1226 . -376) 129813) ((-417 . -1209) 129791) ((-1108 . -608) 129773) ((-312 . -842) NIL) ((-417 . -553) T) ((-224 . -306) T) ((-1216 . -785) 129726) ((-1216 . -788) 129679) ((-1237 . -720) T) ((-1216 . -720) T) ((-48 . -711) 129644) ((-224 . -1015) T) ((-350 . -1260) 129621) ((-1239 . -410) 129587) ((-712 . -720) T) ((-1226 . -893) 129530) ((-1199 . -611) 129412) ((-112 . -608) 129394) ((-112 . -609) 129376) ((-712 . -471) T) ((-705 . -611) 129326) ((-480 . -21) 129236) ((-127 . -487) 129220) ((-121 . -487) 129204) ((-480 . -25) 129055) ((-618 . -289) T) ((-582 . -1048) 129030) ((-436 . -1090) T) ((-1053 . -306) T) ((-117 . -289) T) ((-1094 . -102) T) ((-996 . -102) T) ((-582 . -111) 128998) ((-1132 . -308) 128936) ((-1199 . -1042) T) ((-1053 . -1015) T) ((-66 . -1205) T) ((-1046 . -25) T) ((-1046 . -21) T) ((-705 . -1042) T) ((-384 . -21) T) ((-384 . -25) T) ((-687 . -512) NIL) ((-1017 . -171) T) ((-705 . -242) T) ((-1053 . -543) T) ((-504 . -102) T) ((-500 . -102) T) ((-353 . -171) T) ((-342 . -608) 128918) ((-393 . -608) 128900) ((-472 . -720) T) ((-1110 . -842) T) ((-885 . -1031) 128868) ((-108 . -844) T) ((-651 . -1048) 128852) ((-485 . -130) T) ((-1239 . -1049) T) ((-216 . -130) T) ((-1146 . -102) 128830) ((-99 . -1090) T) ((-244 . -659) 128814) ((-244 . -644) 128798) ((-651 . -111) 128777) ((-582 . -611) 128761) ((-315 . -410) 128745) ((-244 . -372) 128729) ((-1149 . -234) 128676) ((-992 . -230) 128660) ((-74 . -1205) T) ((-48 . -171) T) ((-694 . -386) T) ((-694 . -142) T) ((-1276 . -102) T) ((-1185 . -611) 128642) ((-1077 . -1048) 128485) ((-263 . -902) 128464) ((-246 . -902) 128443) ((-776 . -1048) 128266) ((-774 . -1048) 128109) ((-603 . -1205) T) ((-1154 . -608) 128091) ((-1077 . -111) 127920) ((-1039 . -102) T) ((-473 . -1205) T) ((-459 . -1048) 127891) ((-452 . -1048) 127734) ((-657 . -641) 127718) ((-864 . -306) T) ((-776 . -111) 127527) ((-774 . -111) 127356) ((-354 . -641) 127308) ((-351 . -641) 127260) ((-343 . -641) 127212) ((-263 . -641) 127137) ((-246 . -641) 127062) ((-1148 . -844) T) ((-1078 . -1031) 127046) ((-459 . -111) 127007) ((-452 . -111) 126836) ((-1066 . -1031) 126813) ((-993 . -34) T) ((-959 . -608) 126795) ((-951 . -1205) T) ((-126 . -1003) 126779) ((-956 . -1102) T) ((-864 . -1015) NIL) ((-729 . -1102) T) ((-709 . -1102) T) ((-651 . -611) 126697) ((-1253 . -487) 126681) ((-1132 . -38) 126641) ((-956 . -23) T) ((-837 . -102) T) ((-811 . -21) T) ((-811 . -25) T) ((-729 . -23) T) ((-709 . -23) T) ((-110 . -654) T) ((-903 . -641) 126606) ((-578 . -1048) 126571) ((-516 . -1048) 126516) ((-226 . -57) 126474) ((-451 . -23) T) ((-406 . -102) T) ((-262 . -102) T) ((-687 . -289) T) ((-859 . -38) 126444) ((-578 . -111) 126400) ((-516 . -111) 126329) ((-1077 . -611) 126065) ((-417 . -1102) T) ((-315 . -1049) 125955) ((-312 . -1049) T) ((-128 . -1205) T) ((-776 . -611) 125703) ((-774 . -611) 125469) ((-651 . -1042) T) ((-1281 . -1090) T) ((-452 . -611) 125254) ((-168 . -306) 125185) ((-417 . -23) T) ((-40 . -608) 125167) ((-40 . -609) 125151) ((-108 . -985) 125133) ((-116 . -862) 125117) ((-642 . -611) 125101) ((-48 . -512) 125067) ((-1191 . -1003) 125051) ((-1171 . -608) 125018) ((-1178 . -34) T) ((-947 . -608) 124984) ((-914 . -608) 124966) ((-1103 . -844) 124917) ((-765 . -608) 124899) ((-665 . -608) 124881) ((-1146 . -308) 124819) ((-477 . -34) T) ((-1082 . -1205) T) ((-475 . -450) T) ((-1131 . -34) T) ((-1077 . -1042) T) ((-50 . -611) 124788) ((-776 . -1042) T) ((-774 . -1042) T) ((-640 . -234) 124772) ((-627 . -234) 124718) ((-578 . -611) 124668) ((-516 . -611) 124598) ((-1226 . -306) 124577) ((-1077 . -325) 124538) ((-452 . -1042) T) ((-1168 . -21) T) ((-1077 . -232) 124517) ((-776 . -325) 124494) ((-776 . -232) T) ((-774 . -325) 124466) ((-725 . -1209) 124445) ((-326 . -644) 124429) ((-1168 . -25) T) ((-59 . -34) T) ((-517 . -34) T) ((-514 . -34) T) ((-452 . -325) 124408) ((-326 . -372) 124392) 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-362) 123090) ((-315 . -1090) T) ((-417 . -130) T) ((-312 . -1090) T) ((-406 . -38) 123042) ((-1123 . -102) T) ((-1239 . -711) 122934) ((-647 . -1049) T) ((-1125 . -1248) T) ((-318 . -144) 122913) ((-318 . -146) 122892) ((-138 . -1090) T) ((-135 . -1090) T) ((-114 . -1090) T) ((-852 . -102) T) ((-577 . -608) 122874) ((-561 . -609) 122773) ((-561 . -608) 122755) ((-493 . -608) 122737) ((-493 . -609) 122682) ((-483 . -23) T) ((-480 . -844) 122633) ((-485 . -634) 122615) ((-958 . -608) 122597) ((-216 . -634) 122579) ((-224 . -403) T) ((-655 . -641) 122563) ((-55 . -608) 122545) ((-1162 . -913) 122524) ((-725 . -1102) T) ((-350 . -102) T) ((-1204 . -1073) T) ((-1110 . -838) T) ((-812 . -844) T) ((-725 . -23) T) ((-342 . -1048) 122469) ((-1148 . -1147) T) ((-1137 . -107) 122453) ((-1164 . -1102) T) ((-1163 . -1102) T) ((-513 . -1031) 122437) ((-1157 . -1102) T) ((-1116 . -1102) T) ((-342 . -111) 122366) ((-997 . -1209) T) ((-126 . -1205) T) ((-907 . -1209) T) ((-687 . -285) NIL) ((-1254 . -608) 122348) ((-1164 . -23) T) ((-1163 . -23) T) ((-1157 . -23) T) ((-997 . -553) T) ((-1132 . -230) 122332) ((-907 . -553) T) ((-1116 . -23) T) ((-247 . -608) 122314) ((-1065 . -1090) T) ((-793 . -130) T) ((-704 . -608) 122296) ((-315 . -711) 122206) ((-312 . -711) 122135) ((-692 . -608) 122117) ((-692 . -609) 122062) ((-406 . -399) 122046) ((-437 . -1090) T) ((-485 . -25) T) ((-485 . -21) T) ((-1110 . -1090) T) ((-216 . -25) T) ((-216 . -21) T) ((-706 . -410) 122030) ((-708 . -1031) 121999) ((-1253 . -608) 121911) ((-1253 . -609) 121872) ((-1239 . -171) T) ((-244 . -34) T) ((-342 . -611) 121802) ((-393 . -611) 121784) ((-919 . -967) T) ((-1191 . -1205) T) ((-655 . -785) 121763) ((-655 . -788) 121742) ((-397 . -394) T) ((-521 . -102) 121720) ((-1028 . -1090) T) ((-221 . -988) 121704) ((-502 . -102) T) ((-618 . -608) 121686) ((-45 . -844) NIL) ((-618 . -609) 121663) ((-1028 . -605) 121638) ((-894 . -512) 121571) ((-342 . -1042) T) ((-117 . -609) NIL) ((-117 . -608) 121553) ((-865 . 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. -21) T) ((-709 . -25) T) ((-705 . -641) 118263) ((-451 . -21) T) ((-451 . -25) T) ((-338 . -102) T) ((-173 . -102) T) ((-992 . -1049) T) ((-863 . -1042) T) ((-768 . -102) T) ((-1238 . -362) 118242) ((-1237 . -893) 118148) ((-1217 . -362) 118127) ((-1216 . -893) 117978) ((-1017 . -608) 117960) ((-406 . -822) 117913) ((-1164 . -491) 117879) ((-168 . -913) 117810) ((-1163 . -491) 117776) ((-1157 . -491) 117742) ((-706 . -1090) T) ((-1116 . -491) 117708) ((-577 . -1048) 117695) ((-561 . -1048) 117682) ((-493 . -1048) 117647) ((-315 . -289) 117626) ((-312 . -289) T) ((-353 . -608) 117608) ((-417 . -25) T) ((-417 . -21) T) ((-99 . -285) 117587) ((-577 . -111) 117572) ((-561 . -111) 117557) ((-493 . -111) 117513) ((-1166 . -879) 117480) ((-894 . -487) 117464) ((-48 . -608) 117446) ((-48 . -609) 117391) ((-239 . -130) 117261) ((-1226 . -913) 117240) ((-810 . -1209) 117219) ((-387 . -488) 117200) ((-1028 . -512) 117044) ((-387 . -608) 117010) ((-810 . -553) 116941) ((-582 . -641) 116916) 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-306) 113147) ((-312 . -285) 113082) ((-108 . -450) T) ((-79 . -439) T) ((-79 . -394) T) ((-475 . -102) T) ((-684 . -611) 113066) ((-1281 . -608) 113048) ((-1281 . -609) 113030) ((-1070 . -401) 113009) ((-1028 . -487) 112940) ((-561 . -789) T) ((-561 . -786) T) ((-1054 . -234) 112886) ((-358 . -401) 112837) ((-352 . -401) 112788) ((-344 . -401) 112739) ((-1268 . -1102) T) ((-687 . -611) 112674) ((-1268 . -23) T) ((-1255 . -102) T) ((-174 . -608) 112656) ((-1132 . -1049) T) ((-545 . -367) T) ((-663 . -738) 112640) ((-1168 . -144) 112619) ((-1168 . -146) 112598) ((-1136 . -1090) T) ((-1136 . -1062) 112567) ((-69 . -1205) T) ((-1017 . -1048) 112504) ((-859 . -1049) T) ((-239 . -634) 112410) ((-687 . -1042) T) ((-353 . -1048) 112355) ((-61 . -1205) T) ((-1017 . -111) 112271) ((-894 . -608) 112182) ((-687 . -242) T) ((-687 . -232) NIL) ((-837 . -842) 112161) ((-692 . -789) T) ((-692 . -786) T) ((-996 . -410) 112138) ((-353 . -111) 112067) ((-378 . -913) T) ((-406 . -842) 112046) ((-706 . 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110735) ((-342 . -641) 110680) ((-616 . -38) 110664) ((-1266 . -608) 110626) ((-1266 . -609) 110587) ((-1067 . -608) 110569) ((-1017 . -242) T) ((-353 . -1042) T) ((-809 . -1260) 110539) ((-250 . -23) T) ((-249 . -23) T) ((-980 . -608) 110521) ((-731 . -609) 110482) ((-731 . -608) 110464) ((-793 . -844) 110443) ((-1149 . -150) 110390) ((-992 . -512) 110302) ((-353 . -232) T) ((-353 . -242) T) ((-387 . -611) 110283) ((-997 . -25) T) ((-140 . -608) 110265) ((-140 . -609) 110224) ((-903 . -306) T) ((-997 . -21) T) ((-964 . -25) T) ((-907 . -21) T) ((-907 . -25) T) ((-426 . -21) T) ((-426 . -25) T) ((-837 . -410) 110208) ((-48 . -1042) T) ((-1275 . -1267) 110192) ((-1273 . -1267) 110176) ((-1028 . -599) 110151) ((-315 . -609) 110012) ((-315 . -608) 109994) ((-312 . -609) NIL) ((-312 . -608) 109976) ((-48 . -242) T) ((-48 . -232) T) ((-647 . -285) 109937) ((-547 . -234) 109887) ((-138 . -608) 109854) ((-135 . -608) 109836) ((-114 . -608) 109818) ((-475 . -38) 109783) ((-1277 . -1274) 109762) ((-1268 . -130) T) ((-1276 . -1049) T) ((-1072 . -102) T) ((-88 . -1205) T) ((-498 . -308) NIL) ((-993 . -107) 109746) ((-882 . -1090) T) ((-878 . -1090) T) ((-1253 . -644) 109730) ((-1253 . -372) 109714) ((-326 . -1205) T) ((-589 . -844) T) ((-1132 . -1090) T) ((-1132 . -1045) 109654) ((-103 . -512) 109587) ((-920 . -608) 109569) ((-342 . -720) T) ((-30 . -608) 109551) ((-859 . -1090) T) ((-837 . -1049) 109530) ((-40 . -641) 109475) ((-224 . -1209) T) ((-406 . -1049) T) ((-1148 . -150) 109457) ((-992 . -289) 109408) ((-612 . -1090) T) ((-224 . -553) T) ((-318 . -1234) 109392) ((-318 . -1231) 109362) ((-1178 . -1181) 109341) ((-1065 . -608) 109323) ((-640 . -150) 109307) ((-627 . -150) 109253) ((-1178 . -107) 109203) ((-477 . -1181) 109182) ((-485 . -146) T) ((-485 . -144) NIL) ((-1110 . -609) 109097) ((-437 . -608) 109079) ((-216 . -146) T) ((-216 . -144) NIL) ((-1110 . -608) 109061) ((-129 . -102) T) ((-52 . -102) T) ((-1217 . -634) 109013) ((-477 . -107) 108963) ((-986 . -23) T) ((-1277 . -38) 108933) ((-1162 . -1102) T) ((-1115 . -1102) T) ((-1053 . -1209) T) ((-310 . -102) T) ((-848 . -1102) T) ((-945 . -1209) 108912) ((-479 . -1209) 108891) ((-725 . -844) 108870) ((-1053 . -553) T) ((-945 . -553) 108801) ((-1162 . -23) T) ((-1115 . -23) T) ((-848 . -23) T) ((-479 . -553) 108732) ((-1132 . -711) 108664) ((-1136 . -512) 108597) ((-1028 . -609) NIL) ((-1028 . -608) 108579) ((-96 . -1073) T) ((-859 . -711) 108549) ((-1199 . -47) 108518) ((-250 . -130) T) ((-249 . -130) T) ((-1094 . -1090) T) ((-996 . -1090) T) ((-62 . -608) 108500) ((-1157 . -844) NIL) ((-1017 . -786) T) ((-1017 . -789) T) ((-1281 . -1048) 108487) ((-1281 . -111) 108472) ((-863 . -641) 108459) ((-1245 . -25) T) ((-1245 . -21) T) ((-1238 . -21) T) ((-1238 . -25) T) ((-1217 . -21) T) ((-1217 . -25) T) ((-1020 . -150) 108443) ((-865 . -814) 108422) ((-865 . -913) T) ((-706 . -285) 108349) ((-592 . -21) T) ((-592 . -25) T) ((-591 . -21) T) ((-40 . -720) T) ((-221 . -512) 108282) ((-591 . -25) T) ((-474 . -150) 108266) ((-461 . -150) 108250) ((-914 . -788) T) ((-914 . -720) T) ((-765 . -787) T) ((-765 . -788) T) ((-504 . -1090) T) ((-500 . -1090) T) ((-765 . -720) T) ((-224 . -362) T) ((-1146 . -1090) 108228) ((-864 . -1209) T) ((-647 . -608) 108210) ((-864 . -553) T) ((-687 . -367) NIL) ((-1281 . -611) 108192) ((-358 . -1260) 108176) ((-663 . -102) T) ((-352 . -1260) 108160) ((-344 . -1260) 108144) ((-1276 . -1090) T) ((-518 . -844) 108123) ((-811 . -450) 108102) ((-1039 . -1090) T) ((-1039 . -1062) 108031) ((-1020 . -969) 108000) ((-813 . -1102) T) ((-996 . -711) 107945) ((-385 . -1102) T) ((-474 . -969) 107914) ((-461 . -969) 107883) ((-110 . -150) 107865) ((-73 . -608) 107847) ((-886 . -608) 107829) ((-1070 . -718) 107808) ((-1281 . -1042) T) ((-810 . -634) 107756) ((-293 . -1049) 107698) ((-168 . -1209) 107603) ((-224 . -1102) T) ((-323 . -23) T) ((-1157 . -985) 107555) ((-837 . -1090) T) ((-1239 . -1048) 107460) ((-1116 . -734) 107439) ((-1237 . -913) 107418) 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-394) T) ((-618 . -641) 105116) ((-452 . -879) NIL) ((-668 . -102) 105094) ((-1077 . -1031) 104921) ((-864 . -23) T) ((-776 . -1031) 104780) ((-774 . -1031) 104637) ((-117 . -641) 104582) ((-452 . -1031) 104458) ((-315 . -611) 104022) ((-312 . -611) 103905) ((-642 . -1031) 103889) ((-622 . -102) T) ((-221 . -487) 103873) ((-1253 . -34) T) ((-135 . -611) 103857) ((-630 . -711) 103841) ((-602 . -711) 103825) ((-663 . -38) 103785) ((-318 . -102) T) ((-85 . -608) 103767) ((-50 . -1031) 103751) ((-1110 . -1048) 103738) ((-1077 . -376) 103722) ((-776 . -376) 103706) ((-60 . -57) 103668) ((-692 . -788) T) ((-692 . -785) T) ((-578 . -1031) 103655) ((-516 . -1031) 103632) ((-692 . -720) T) ((-323 . -130) T) ((-315 . -1042) 103522) ((-312 . -1042) T) ((-168 . -1102) T) ((-774 . -376) 103506) ((-45 . -150) 103456) ((-997 . -985) 103438) ((-452 . -376) 103422) ((-406 . -171) T) ((-315 . -242) 103401) ((-312 . -242) T) ((-312 . -232) NIL) ((-293 . -1090) 103183) ((-224 . -130) T) ((-1110 . -111) 103168) ((-168 . -23) T) ((-793 . -146) 103147) ((-793 . -144) 103126) ((-250 . -634) 103032) ((-249 . -634) 102938) ((-318 . -283) 102904) ((-1146 . -512) 102837) ((-1123 . -1090) T) ((-224 . -1051) T) ((-809 . -308) 102775) ((-1077 . -893) 102710) ((-776 . -893) 102653) ((-774 . -893) 102637) ((-1275 . -38) 102607) ((-1273 . -38) 102577) ((-1226 . -1102) T) ((-849 . -1102) T) ((-452 . -893) 102554) ((-852 . -1090) T) ((-1226 . -23) T) ((-1110 . -611) 102526) ((-568 . -1102) T) ((-849 . -23) T) ((-618 . -720) T) ((-354 . -913) T) ((-351 . -913) T) ((-288 . -102) T) ((-343 . -913) T) ((-1053 . -130) T) ((-963 . -1073) T) ((-945 . -130) T) ((-117 . -788) NIL) ((-117 . -785) NIL) ((-117 . -720) T) ((-687 . -902) NIL) ((-1039 . -512) 102427) ((-479 . -130) T) ((-568 . -23) T) ((-668 . -308) 102365) ((-630 . -755) T) ((-602 . -755) T) ((-1217 . -844) NIL) ((-996 . -289) T) ((-250 . -21) T) ((-687 . -641) 102315) ((-350 . -1090) T) ((-250 . -25) T) ((-249 . -21) T) ((-249 . -25) T) ((-151 . -38) 102299) ((-2 . -102) T) ((-903 . -913) T) ((-480 . -1260) 102269) ((-222 . -1031) 102246) ((-1110 . -1042) T) ((-705 . -306) T) ((-293 . -711) 102188) ((-694 . -1049) T) ((-485 . -450) T) ((-406 . -512) 102100) ((-216 . -450) T) ((-1110 . -232) T) ((-294 . -150) 102050) ((-992 . -609) 102011) ((-992 . -608) 101993) ((-982 . -608) 101975) ((-116 . -1049) T) ((-647 . -1048) 101959) ((-224 . -491) T) ((-398 . -608) 101941) ((-398 . -609) 101918) ((-1046 . -1260) 101888) ((-647 . -111) 101867) ((-1132 . -487) 101851) ((-809 . -38) 101821) ((-63 . -439) T) ((-63 . -394) T) ((-1149 . -102) T) ((-864 . -130) T) ((-482 . -102) 101799) ((-1281 . -367) T) ((-1070 . -102) T) ((-1052 . -102) T) ((-350 . -711) 101744) ((-725 . -146) 101723) ((-725 . -144) 101702) ((-647 . -611) 101620) ((-1017 . -641) 101557) ((-521 . -1090) 101535) ((-358 . -102) T) ((-352 . -102) T) ((-344 . -102) T) ((-108 . -102) T) ((-502 . -1090) T) ((-353 . -641) 101480) ((-1162 . -634) 101428) ((-1115 . -634) 101376) 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-102) T) ((-110 . -308) NIL) ((-226 . -102) 95709) ((-127 . -1205) T) ((-121 . -1205) T) ((-1027 . -130) T) ((-663 . -366) 95693) ((-992 . -1042) T) ((-1226 . -634) 95641) ((-1094 . -608) 95623) ((-996 . -608) 95605) ((-513 . -23) T) ((-508 . -23) T) ((-342 . -306) T) ((-506 . -23) T) ((-321 . -130) T) ((-3 . -1090) T) ((-996 . -609) 95589) ((-992 . -242) 95568) ((-992 . -232) 95547) ((-1281 . -720) T) ((-1245 . -144) 95526) ((-827 . -1090) T) ((-1245 . -146) 95505) ((-1238 . -146) 95484) ((-1238 . -144) 95463) ((-1237 . -1209) 95442) ((-1217 . -144) 95349) ((-1217 . -146) 95256) ((-1216 . -1209) 95235) ((-378 . -130) T) ((-561 . -879) 95217) ((0 . -1090) T) ((-173 . -171) T) ((-168 . -21) T) ((-168 . -25) T) ((-49 . -1090) T) ((-1239 . -641) 95122) ((-1237 . -553) 95073) ((-708 . -1102) T) ((-1216 . -553) 95024) ((-561 . -1031) 95006) ((-591 . -146) 94985) ((-591 . -144) 94964) ((-493 . -1031) 94907) ((-1125 . -1127) T) ((-87 . -383) T) ((-87 . -394) T) ((-865 . -362) T) ((-830 . -130) T) ((-821 . -130) T) ((-708 . -23) T) ((-504 . -608) 94873) ((-500 . -608) 94855) ((-1277 . -1049) T) ((-378 . -1051) T) ((-1019 . -1090) 94833) ((-55 . -1031) 94815) ((-894 . -34) T) ((-480 . -308) 94753) ((-588 . -102) T) ((-1146 . -609) 94714) ((-1146 . -608) 94646) ((-1162 . -844) 94625) ((-45 . -102) T) ((-1115 . -844) 94604) ((-811 . -102) T) ((-1226 . -25) T) ((-1226 . -21) T) ((-849 . -25) T) ((-44 . -366) 94588) ((-849 . -21) T) ((-725 . -450) 94539) ((-1276 . -608) 94521) ((-1046 . -308) 94459) ((-664 . -1073) T) ((-601 . -1073) T) ((-389 . -1090) T) ((-568 . -25) T) ((-568 . -21) T) ((-179 . -1073) T) ((-160 . -1073) T) ((-155 . -1073) T) ((-153 . -1073) T) ((-616 . -1090) T) ((-692 . -879) 94441) ((-1253 . -1205) T) ((-226 . -308) 94379) ((-143 . -367) T) ((-1039 . -609) 94321) ((-1039 . -608) 94264) ((-312 . -902) NIL) ((-692 . -1031) 94209) ((-705 . -913) T) ((-472 . -1209) 94188) ((-1163 . -450) 94167) ((-1157 . -450) 94146) ((-329 . -102) T) ((-865 . -1102) T) 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. -130) T) ((-1110 . -785) T) ((-1268 . -1270) 90925) ((-1110 . -720) T) ((-647 . -641) 90899) ((-293 . -608) 90640) ((-1132 . -611) 90558) ((-1028 . -34) T) ((-809 . -842) 90537) ((-577 . -306) T) ((-561 . -306) T) ((-493 . -306) T) ((-1277 . -711) 90507) ((-687 . -376) 90489) ((-687 . -337) 90471) ((-475 . -171) T) ((-380 . -711) 90441) ((-859 . -611) 90376) ((-864 . -844) NIL) ((-561 . -1015) T) ((-493 . -1015) T) ((-1123 . -608) 90358) ((-1103 . -237) 90337) ((-213 . -102) T) ((-1140 . -102) T) ((-71 . -608) 90319) ((-1132 . -1042) T) ((-1168 . -38) 90216) ((-852 . -608) 90198) ((-561 . -543) T) ((-663 . -1049) T) ((-725 . -942) 90151) ((-1132 . -232) 90130) ((-1072 . -1090) T) ((-1027 . -25) T) ((-1027 . -21) T) ((-996 . -1048) 90075) ((-898 . -102) T) ((-859 . -1042) T) ((-687 . -893) NIL) ((-354 . -328) 90059) ((-354 . -362) T) ((-351 . -328) 90043) ((-351 . -362) T) ((-343 . -328) 90027) ((-343 . -362) T) ((-485 . -102) T) ((-1265 . -38) 89997) ((-544 . -844) T) ((-521 . -680) 89947) ((-216 . -102) T) ((-1017 . -1031) 89827) ((-996 . -111) 89756) ((-1164 . -966) 89725) ((-1163 . -966) 89687) ((-518 . -150) 89671) ((-1070 . -369) 89650) ((-350 . -608) 89632) ((-321 . -21) T) ((-353 . -1031) 89609) ((-321 . -25) T) ((-1157 . -966) 89578) ((-1116 . -966) 89545) ((-76 . -608) 89527) ((-692 . -306) T) ((-168 . -844) 89506) ((-129 . -838) T) ((-903 . -362) T) ((-378 . -25) T) ((-378 . -21) T) ((-903 . -328) 89493) ((-86 . -608) 89475) ((-692 . -1015) T) ((-670 . -844) T) ((-1237 . -130) T) ((-1216 . -130) T) ((-894 . -1003) 89459) ((-830 . -21) T) ((-48 . -1031) 89402) ((-830 . -25) T) ((-821 . -25) T) ((-821 . -21) T) ((-1275 . -1049) T) ((-546 . -102) T) ((-1273 . -1049) T) ((-647 . -720) T) ((-1094 . -613) 89305) ((-996 . -611) 89235) ((-1276 . -1048) 89219) ((-1226 . -844) 89198) ((-809 . -410) 89167) ((-103 . -119) 89151) ((-129 . -1090) T) ((-52 . -1090) T) ((-919 . -608) 89133) ((-864 . -985) 89110) ((-817 . -102) T) ((-1276 . -111) 89089) ((-646 . -38) 89059) ((-568 . -844) T) ((-354 . -1102) T) ((-351 . -1102) T) ((-343 . -1102) T) ((-263 . -1102) T) ((-246 . -1102) T) ((-618 . -306) 89038) ((-1140 . -308) 88842) ((-522 . -1073) T) ((-310 . -1090) T) ((-657 . -23) T) ((-480 . -230) 88811) ((-151 . -1049) T) ((-354 . -23) T) ((-351 . -23) T) ((-343 . -23) T) ((-117 . -306) T) ((-263 . -23) T) ((-246 . -23) T) ((-996 . -1042) T) ((-706 . -902) 88790) ((-1146 . -611) 88767) ((-996 . -232) 88739) ((-996 . -242) T) ((-117 . -1015) NIL) ((-903 . -1102) T) ((-1238 . -450) 88718) ((-1217 . -450) 88697) ((-521 . -608) 88629) ((-706 . -641) 88554) ((-406 . -1048) 88506) ((-502 . -608) 88488) ((-903 . -23) T) ((-485 . -308) NIL) ((-1276 . -611) 88444) ((-472 . -130) T) ((-216 . -308) NIL) ((-406 . -111) 88382) ((-809 . -1049) 88312) ((-731 . -1088) 88296) ((-1237 . -491) 88262) ((-1216 . -491) 88228) ((-140 . -1088) 88210) ((-475 . -289) T) ((-1276 . -1042) T) ((-1210 . -102) T) ((-1054 . -102) T) ((-837 . -611) 88078) ((-498 . -512) NIL) ((-696 . -102) T) ((-480 . -237) 88057) ((-406 . -611) 87955) ((-1162 . -144) 87934) ((-1162 . -146) 87913) ((-1115 . -146) 87892) ((-1115 . -144) 87871) ((-630 . -1048) 87855) ((-602 . -1048) 87839) ((-663 . -1090) T) ((-663 . -1045) 87779) ((-1164 . -1244) 87763) ((-1164 . -1231) 87740) ((-485 . -1141) T) ((-1163 . -1236) 87701) ((-1163 . -1231) 87671) ((-1163 . -1234) 87655) ((-216 . -1141) T) ((-342 . -913) T) ((-812 . -265) 87639) ((-630 . -111) 87618) ((-602 . -111) 87597) ((-1157 . -1215) 87558) ((-837 . -1042) 87537) ((-1157 . -1231) 87514) ((-513 . -25) T) ((-493 . -301) T) ((-509 . -23) T) ((-508 . -25) T) ((-506 . -25) T) ((-505 . -23) T) ((-1157 . -1213) 87498) ((-406 . -1042) T) ((-318 . -1049) T) ((-687 . -306) T) ((-108 . -842) T) ((-706 . -720) T) ((-406 . -242) T) ((-406 . -232) 87477) ((-485 . -38) 87427) ((-216 . -38) 87377) ((-472 . -491) 87343) ((-1148 . -1134) T) ((-1091 . -102) T) ((-694 . -608) 87325) ((-694 . -609) 87240) ((-708 . -21) T) ((-708 . -25) T) 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85245) ((-417 . -308) 85184) ((-466 . -102) T) ((-591 . -966) 85153) ((-318 . -1090) T) ((-406 . -789) 85132) ((-406 . -786) 85111) ((-498 . -487) 85093) ((-1239 . -1031) 85059) ((-1237 . -21) T) ((-1237 . -25) T) ((-1216 . -21) T) ((-1216 . -25) T) ((-809 . -711) 85001) ((-350 . -611) 84931) ((-692 . -403) T) ((-1266 . -1205) T) ((-601 . -102) T) ((-1103 . -410) 84900) ((-996 . -367) NIL) ((-664 . -102) T) ((-179 . -102) T) ((-160 . -102) T) ((-155 . -102) T) ((-153 . -102) T) ((-103 . -34) T) ((-731 . -1205) T) ((-44 . -755) T) ((-589 . -102) T) ((-77 . -395) T) ((-77 . -394) T) ((-646 . -649) 84884) ((-140 . -1205) T) ((-864 . -146) T) ((-864 . -144) NIL) ((-1204 . -93) T) ((-350 . -1042) T) ((-70 . -382) T) ((-70 . -394) T) ((-1155 . -102) T) ((-663 . -512) 84817) ((-682 . -308) 84755) ((-956 . -38) 84652) ((-729 . -38) 84622) ((-547 . -308) 84426) ((-315 . -1205) T) ((-350 . -232) T) ((-350 . -242) T) ((-312 . -1205) T) ((-288 . -1090) T) ((-1170 . -608) 84408) ((-705 . -1209) T) 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((-312 . -376) 83141) ((-312 . -337) 83102) ((-1075 . -608) 83084) ((-810 . -942) 83031) ((-655 . -130) T) ((-1226 . -144) 83010) ((-1226 . -146) 82989) ((-1164 . -102) T) ((-1163 . -102) T) ((-1157 . -102) T) ((-1149 . -1090) T) ((-1116 . -102) T) ((-221 . -34) T) ((-288 . -711) 82976) ((-1149 . -605) 82952) ((-589 . -308) NIL) ((-482 . -1090) 82930) ((-389 . -608) 82912) ((-508 . -844) T) ((-1140 . -228) 82862) ((-1245 . -1244) 82846) ((-1245 . -1231) 82823) ((-1238 . -1236) 82784) ((-1238 . -1231) 82754) ((-1238 . -1234) 82738) ((-1217 . -1215) 82699) ((-1217 . -1231) 82676) ((-616 . -608) 82658) ((-1217 . -1213) 82642) ((-692 . -913) T) ((-1164 . -283) 82608) ((-1163 . -283) 82574) ((-1157 . -283) 82540) ((-1070 . -1090) T) ((-1052 . -1090) T) ((-48 . -301) T) ((-315 . -893) 82506) ((-312 . -893) NIL) ((-1052 . -1059) 82485) ((-1110 . -879) 82467) ((-793 . -38) 82451) ((-263 . -634) 82399) ((-246 . -634) 82347) ((-694 . -1048) 82334) ((-591 . -1231) 82311) ((-1116 . -283) 82277) ((-318 . -171) 82208) ((-358 . -1090) T) ((-352 . -1090) T) ((-344 . -1090) T) ((-498 . -19) 82190) ((-1110 . -1031) 82172) ((-1092 . -150) 82156) ((-108 . -1090) T) ((-116 . -1048) 82143) ((-705 . -362) T) ((-498 . -599) 82118) ((-694 . -111) 82103) ((-435 . -102) T) ((-45 . -1139) 82053) ((-116 . -111) 82038) ((-630 . -714) T) ((-602 . -714) T) ((-809 . -512) 81971) ((-1028 . -1205) T) ((-936 . -150) 81955) ((-1162 . -450) 81886) ((-1156 . -1090) T) ((-1148 . -1090) T) ((-523 . -102) T) ((-518 . -102) 81836) ((-1132 . -641) 81810) ((-1115 . -450) 81761) ((-1077 . -1209) 81740) ((-776 . -1209) 81719) ((-774 . -1209) 81698) ((-62 . -1205) T) ((-475 . -608) 81650) ((-475 . -609) 81572) ((-1077 . -553) 81503) ((-987 . -1090) T) ((-776 . -553) 81414) ((-774 . -553) 81345) ((-480 . -410) 81314) ((-618 . -913) 81293) ((-452 . -1209) 81272) ((-725 . -308) 81259) ((-694 . -611) 81231) ((-397 . -608) 81213) ((-668 . -512) 81146) ((-657 . -25) T) ((-657 . -21) T) ((-452 . -553) 81077) ((-354 . -25) T) ((-354 . -21) T) ((-117 . -913) T) ((-117 . -814) NIL) ((-351 . -25) T) ((-351 . -21) T) ((-343 . -25) T) ((-343 . -21) T) ((-263 . -25) T) ((-263 . -21) T) ((-246 . -25) T) ((-246 . -21) T) ((-83 . -383) T) ((-83 . -394) T) ((-133 . -611) 81059) ((-116 . -611) 81031) ((-1255 . -608) 81013) ((-1211 . -844) T) ((-1199 . -1102) T) ((-1199 . -23) T) ((-1157 . -308) 80898) ((-1116 . -308) 80885) ((-1070 . -711) 80753) ((-859 . -641) 80713) ((-936 . -973) 80697) ((-903 . -21) T) ((-288 . -171) T) ((-903 . -25) T) ((-310 . -93) T) ((-865 . -844) 80648) ((-705 . -1102) T) ((-705 . -23) T) ((-694 . -1042) T) ((-640 . -1090) 80626) ((-627 . -1090) T) ((-578 . -1209) T) ((-516 . -1209) T) ((-694 . -232) T) ((-627 . -605) 80601) ((-578 . -553) T) ((-516 . -553) T) ((-358 . -711) 80553) ((-338 . -1048) 80537) ((-352 . -711) 80489) ((-344 . -711) 80441) ((-173 . -1048) 80373) ((-173 . -111) 80284) ((-108 . -711) 80234) ((-338 . -111) 80213) ((-273 . -1090) T) ((-272 . -1090) T) ((-271 . -1090) T) ((-270 . -1090) T) ((-269 . -1090) T) ((-268 . -1090) T) ((-267 . -1090) T) ((-211 . -1090) T) ((-210 . -1090) T) ((-168 . -1193) 80191) ((-168 . -1190) 80169) ((-208 . -1090) T) ((-207 . -1090) T) ((-116 . -1042) T) ((-206 . -1090) T) ((-205 . -1090) T) ((-202 . -1090) T) ((-201 . -1090) T) ((-200 . -1090) T) ((-199 . -1090) T) ((-198 . -1090) T) ((-197 . -1090) T) ((-196 . -1090) T) ((-195 . -1090) T) ((-194 . -1090) T) ((-193 . -1090) T) ((-192 . -1090) T) ((-239 . -102) 79959) ((-168 . -35) 79937) ((-168 . -95) 79915) ((-647 . -1031) 79811) ((-480 . -1049) 79741) ((-1103 . -1090) 79531) ((-1132 . -34) T) ((-663 . -487) 79515) ((-73 . -1205) T) ((-105 . -608) 79497) ((-1277 . -608) 79479) ((-380 . -608) 79461) ((-338 . -611) 79413) ((-173 . -611) 79330) ((-1204 . -488) 79311) ((-725 . -38) 79160) ((-568 . -1193) T) ((-568 . -1190) T) ((-529 . -608) 79142) ((-518 . -308) 79080) ((-498 . -608) 79062) ((-498 . -609) 79044) ((-1204 . -608) 79010) ((-1157 . -1141) NIL) ((-1020 . -1062) 78979) ((-1020 . -1090) T) ((-997 . -102) T) ((-964 . -102) T) ((-907 . -102) T) ((-886 . -1031) 78956) ((-1132 . -720) T) ((-996 . -641) 78901) ((-474 . -1090) T) ((-461 . -1090) T) ((-582 . -23) T) ((-568 . -35) T) ((-568 . -95) T) ((-426 . -102) T) ((-1054 . -228) 78847) ((-1164 . -38) 78744) ((-859 . -720) T) ((-687 . -913) T) ((-509 . -25) T) ((-505 . -21) T) ((-505 . -25) T) ((-1163 . -38) 78585) ((-338 . -1042) T) ((-1157 . -38) 78381) ((-1070 . -171) T) ((-173 . -1042) T) ((-1116 . -38) 78278) ((-706 . -47) 78255) ((-358 . -171) T) ((-352 . -171) T) ((-517 . -57) 78229) ((-495 . -57) 78179) ((-350 . -1272) 78156) ((-224 . -450) T) ((-318 . -289) 78107) ((-344 . -171) T) ((-173 . -242) T) ((-1216 . -844) 78006) ((-108 . -171) T) ((-865 . -985) 77990) ((-651 . -1102) T) ((-578 . -362) T) ((-578 . -328) 77977) ((-516 . -328) 77954) ((-516 . -362) T) ((-315 . -306) 77933) ((-312 . -306) T) ((-597 . -844) 77912) ((-1103 . -711) 77854) ((-518 . -281) 77838) ((-651 . -23) T) 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-130) T) ((-706 . -1031) 76961) ((-578 . -23) T) ((-108 . -512) NIL) ((-516 . -23) T) ((-168 . -408) 76932) ((-1130 . -1090) T) ((-1268 . -1267) 76916) ((-694 . -789) T) ((-694 . -786) T) ((-1110 . -306) T) ((-378 . -146) T) ((-279 . -608) 76898) ((-1216 . -985) 76868) ((-48 . -913) T) ((-668 . -487) 76852) ((-250 . -1260) 76822) ((-249 . -1260) 76792) ((-1166 . -844) T) ((-1103 . -171) 76771) ((-1110 . -1015) T) ((-1039 . -34) T) ((-830 . -146) 76750) ((-830 . -144) 76729) ((-731 . -107) 76713) ((-607 . -131) T) ((-480 . -1090) 76503) ((-1168 . -1049) T) ((-864 . -450) T) ((-85 . -1205) T) ((-239 . -38) 76473) ((-140 . -107) 76455) ((-706 . -376) 76439) ((-827 . -611) 76307) ((-1110 . -543) T) ((-576 . -102) T) ((-129 . -488) 76289) ((-389 . -1048) 76273) ((-1276 . -720) T) ((-1162 . -942) 76242) ((-129 . -608) 76209) ((-52 . -608) 76191) ((-1115 . -942) 76158) ((-646 . -410) 76142) ((-1265 . -1049) T) ((-616 . -1048) 76126) ((-655 . -25) T) ((-655 . -21) T) ((-1148 . -512) NIL) 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-788) 75082) ((-406 . -785) 75061) ((-406 . -720) T) ((-498 . -287) 75036) ((-475 . -1048) 75001) ((-651 . -130) T) ((-616 . -611) 74970) ((-1103 . -512) 74903) ((-335 . -130) T) ((-168 . -401) 74882) ((-480 . -711) 74824) ((-809 . -285) 74801) ((-475 . -111) 74757) ((-646 . -1049) T) ((-1226 . -450) 74688) ((-1264 . -1073) T) ((-1263 . -1073) T) ((-1077 . -130) T) ((-1046 . -711) 74630) ((-263 . -844) 74609) ((-246 . -844) 74588) ((-776 . -130) T) ((-774 . -130) T) ((-568 . -450) T) ((-1020 . -512) 74521) ((-616 . -1042) T) ((-588 . -1090) T) ((-531 . -172) T) ((-459 . -130) T) ((-452 . -130) T) ((-45 . -1090) T) ((-384 . -711) 74491) ((-811 . -1090) T) ((-474 . -512) 74424) ((-461 . -512) 74357) ((-451 . -366) 74327) ((-45 . -605) 74306) ((-315 . -301) T) ((-475 . -611) 74256) ((-663 . -608) 74218) ((-59 . -844) 74197) ((-1217 . -308) 74082) ((-997 . -399) 74064) ((-809 . -599) 74041) ((-514 . -844) 74020) ((-494 . -844) 73999) ((-40 . -1209) T) ((-992 . -1031) 73895) ((-50 . -130) 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71222) ((-646 . -1090) T) ((-855 . -854) T) ((-435 . -363) 71196) ((-1092 . -102) T) ((-963 . -1090) T) ((-858 . -1090) T) ((-810 . -308) 71183) ((-531 . -525) T) ((-531 . -573) T) ((-1273 . -381) 71155) ((-1046 . -512) 71088) ((-1149 . -285) 71064) ((-239 . -230) 71033) ((-1265 . -711) 71003) ((-1156 . -93) T) ((-987 . -93) T) ((-811 . -171) 70982) ((-1202 . -488) 70959) ((-226 . -512) 70892) ((-616 . -789) 70871) ((-616 . -786) 70850) ((-1202 . -608) 70762) ((-221 . -1205) T) ((-668 . -608) 70694) ((-1146 . -1003) 70678) ((-936 . -102) 70628) ((-350 . -720) T) ((-855 . -608) 70610) ((-1217 . -399) 70562) ((-1103 . -487) 70546) ((-60 . -308) 70484) ((-330 . -102) T) ((-1199 . -21) T) ((-1199 . -25) T) ((-40 . -1102) T) ((-705 . -21) T) ((-622 . -608) 70466) ((-513 . -322) 70445) ((-705 . -25) T) ((-108 . -285) NIL) ((-914 . -1102) T) ((-40 . -23) T) ((-765 . -1102) T) ((-561 . -1209) T) ((-493 . -1209) T) ((-318 . -608) 70427) ((-997 . -230) 70409) ((-168 . -165) 70393) ((-577 . -553) 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-289) 68683) ((-1275 . -1048) 68667) ((-817 . -1090) T) ((-1273 . -1048) 68651) ((-959 . -960) T) ((-663 . -111) 68630) ((-294 . -512) 68422) ((-1237 . -1190) 68388) ((-1237 . -1193) 68354) ((-1237 . -95) 68320) ((-250 . -308) 68258) ((-249 . -308) 68196) ((-1220 . -102) 68174) ((-1149 . -609) NIL) ((-1149 . -608) 68156) ((-1217 . -230) 68108) ((-1216 . -1190) 68074) ((-1216 . -1193) 68040) ((-96 . -93) T) ((-1210 . -838) T) ((-1132 . -376) 68024) ((-1110 . -814) T) ((-1110 . -913) T) ((-1103 . -599) 68001) ((-1070 . -609) 67985) ((-482 . -608) 67917) ((-809 . -287) 67894) ((-603 . -150) 67841) ((-417 . -1049) T) ((-485 . -711) 67791) ((-480 . -487) 67775) ((-326 . -844) 67754) ((-338 . -641) 67728) ((-50 . -21) T) ((-50 . -25) T) ((-216 . -711) 67678) ((-168 . -718) 67649) ((-173 . -641) 67581) ((-578 . -21) T) ((-578 . -25) T) ((-516 . -25) T) ((-516 . -21) T) ((-473 . -150) 67531) ((-1070 . -608) 67513) ((-1052 . -608) 67495) ((-986 . -102) T) ((-856 . -102) T) ((-793 . -410) 67459) 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. -171) T) ((-222 . -25) T) ((-472 . -1193) 65713) ((-472 . -1190) 65679) ((-273 . -608) 65661) ((-272 . -608) 65643) ((-271 . -608) 65625) ((-270 . -608) 65607) ((-269 . -608) 65589) ((-498 . -644) 65571) ((-268 . -608) 65553) ((-338 . -720) T) ((-267 . -608) 65535) ((-110 . -19) 65517) ((-173 . -720) T) ((-498 . -372) 65499) ((-211 . -608) 65481) ((-518 . -1139) 65465) ((-498 . -123) T) ((-110 . -599) 65440) ((-210 . -608) 65422) ((-472 . -35) 65388) ((-472 . -95) 65354) ((-208 . -608) 65336) ((-207 . -608) 65318) ((-206 . -608) 65300) ((-205 . -608) 65282) ((-202 . -608) 65264) ((-201 . -608) 65246) ((-200 . -608) 65228) ((-199 . -608) 65210) ((-198 . -608) 65192) ((-197 . -608) 65174) ((-196 . -608) 65156) ((-534 . -1093) 65108) ((-195 . -608) 65090) ((-194 . -608) 65072) ((-45 . -487) 65009) ((-193 . -608) 64991) ((-192 . -608) 64973) ((-151 . -611) 64942) ((-1105 . -102) T) ((-809 . -111) 64832) ((-638 . -102) 64782) ((-480 . -285) 64759) ((-1103 . -608) 64490) ((-1091 . -1090) T) ((-1039 . -1205) T) ((-1276 . -1031) 64474) ((-618 . -1102) T) ((-1162 . -308) 64461) ((-1125 . -1090) T) ((-1115 . -308) 64448) ((-1086 . -1073) T) ((-1080 . -1073) T) ((-1064 . -1073) T) ((-1057 . -1073) T) ((-1029 . -1073) T) ((-1012 . -1073) T) ((-117 . -1102) T) ((-813 . -102) T) ((-621 . -1073) T) ((-618 . -23) T) ((-1140 . -512) 64240) ((-481 . -1073) T) ((-996 . -893) 64192) ((-385 . -102) T) ((-323 . -102) T) ((-217 . -1073) T) ((-956 . -1090) T) ((-151 . -1042) T) ((-725 . -410) 64176) ((-117 . -23) T) ((-729 . -1090) T) ((-709 . -1090) T) ((-696 . -131) T) ((-451 . -1090) T) ((-406 . -1205) T) ((-315 . -429) 64160) ((-588 . -93) T) ((-1020 . -609) 64121) ((-1017 . -1209) T) ((-224 . -102) T) ((-1020 . -608) 64083) ((-810 . -230) 64067) ((-809 . -611) 63797) ((-1017 . -553) T) ((-827 . -641) 63770) ((-353 . -1209) T) ((-474 . -608) 63732) ((-474 . -609) 63693) ((-461 . -609) 63654) ((-461 . -608) 63616) ((-406 . -877) 63600) ((-318 . -1048) 63435) ((-406 . -879) 63360) 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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 e16e998e..a2c44b20 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3440300496) -(4386 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3440472335) +(4393 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -193,13 +193,14 @@ |InfiniteProductCharacteristicZero| |InnerNumericFloatSolvePackage| |InnerModularGcd| |InnerMultFact| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerPolySign| |IntegerNumberSystem&| - |IntegerNumberSystem| |InnerTable| |AlgebraicIntegration| - |AlgebraicIntegrate| |IntegerBits| |IntervalCategory| - |IntegralDomain&| |IntegralDomain| |ElementaryIntegration| - |IntegerFactorizationPackage| |IntegrationFunctionsTable| - |GenusZeroIntegration| |IntegerNumberTheoryFunctions| - |AlgebraicHermiteIntegration| |TranscendentalHermiteIntegration| - |Integer| |AnnaNumericalIntegrationPackage| |PureAlgebraicIntegration| + |IntegerNumberSystem| |Int16| |Int32| |Int8| |InnerTable| + |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| + |IntervalCategory| |IntegralDomain&| |IntegralDomain| + |ElementaryIntegration| |IntegerFactorizationPackage| + |IntegrationFunctionsTable| |GenusZeroIntegration| + |IntegerNumberTheoryFunctions| |AlgebraicHermiteIntegration| + |TranscendentalHermiteIntegration| |Integer| + |AnnaNumericalIntegrationPackage| |PureAlgebraicIntegration| |PatternMatchIntegration| |RationalIntegration| |IntegerRetractions| |RationalFunctionIntegration| |Interval| |IntegerSolveLinearPolynomialEquation| |IntegrationTools| @@ -428,18 +429,19 @@ |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |Syntax| - |SystemSolvePackage| |System| |TableauxBumpers| |Tableau| |Table| - |TangentExpansions| |TableAggregate&| |TableAggregate| - |TabulatedComputationPackage| |TemplateUtilities| |TexFormat1| - |TexFormat| |TextFile| |ToolsForSign| |TopLevelThreeSpace| - |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| - |Tree| |TrigonometricFunctionCategory&| - |TrigonometricFunctionCategory| |TrigonometricManipulations| - |TriangularMatrixOperations| |TranscendentalManipulations| - |TriangularSetCategory&| |TriangularSetCategory| |TaylorSeries| - |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| |TypeAst| |Type| - |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| - |UniqueFactorizationDomain&| |UniqueFactorizationDomain| + |SystemInteger| |SystemNonNegativeInteger| |SystemSolvePackage| + |System| |TableauxBumpers| |Tableau| |Table| |TangentExpansions| + |TableAggregate&| |TableAggregate| |TabulatedComputationPackage| + |TemplateUtilities| |TexFormat1| |TexFormat| |TextFile| |ToolsForSign| + |TopLevelThreeSpace| |TranscendentalFunctionCategory&| + |TranscendentalFunctionCategory| |Tree| + |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| + |TrigonometricManipulations| |TriangularMatrixOperations| + |TranscendentalManipulations| |TriangularSetCategory&| + |TriangularSetCategory| |TaylorSeries| |TubePlot| |TubePlotTools| + |Tuple| |TwoFactorize| |TypeAst| |Type| |UserDefinedPartialOrdering| + |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| + |UniqueFactorizationDomain| |UInt16| |UInt32| |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| @@ -474,661 +476,659 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - 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|basisOfLeftAnnihilator| |iiasec| |id| |setValue!| |debug3D| |nodes| - |alphabetic?| |relerror| |normInvertible?| |c05pbf| |f04mcf| |points| - |brillhartTrials| |leftZero| |heapSort| |product| |insert| - |whitePoint| |stop| |cCosh| |lazy?| |slex| |eval| LODO2FUN |putGraph| - |GospersMethod| |applyRules| |formula| |pushucoef| |repeatUntilLoop| - |characteristicSet| |rightZero| |table| |nil| |infix?| - |stoseInvertible?reg| |minimize| |children| |OMUnknownSymbol?| - |bernoulli| |squareFreeLexTriangular| |close!| |interpret| |eulerE| - |limitPlus| |subResultantsChain| |postfix| |mapSolve| |new| - |rationalApproximation| |mask| |rightRegularRepresentation| |pureLex| - |dmpToHdmp| |initiallyReduce| |obj| |frst| |invmultisect| |arity| - |infLex?| |e04ycf| |nativeModuleExtension| |subCase?| |top!| - |componentUpperBound| |cyclic| |pmComplexintegrate| |cache| |graphs| - |balancedBinaryTree| |safetyMargin| |parabolicCylindrical| |Lazard| - |goodnessOfFit| |cycle| |approximate| |norm| |inrootof| |edf2df| |int| - |cfirst| |randomLC| |setAdaptive3D| |nrows| |axes| |dioSolve| - |edf2efi| |definingEquations| |coHeight| |complex| |e01baf| |iibinom| - |symmetricProduct| |extractBottom!| |unitVector| |singleFactorBound| - |leviCivitaSymbol| |ncols| |gcdPrimitive| |subSet| - |PollardSmallFactor| |multiplyCoefficients| |acotIfCan| - |functionIsOscillatory| |e01bhf| |useSingleFactorBound?| |outputAsTex| - |optional?| |status| |argumentListOf| |constantLeft| |readLineIfCan!| - |biRank| |OMlistCDs| |lfextlimint| |roman| |equiv?| |close| - |wordsForStrongGenerators| |expandTrigProducts| |getRef| - |doublyTransitive?| |just| |dim| |optpair| |knownInfBasis| - |BasicMethod| |var2StepsDefault| |leftAlternative?| |d02gaf| |s15adf| - |minColIndex| |lagrange| |clipPointsDefault| |leftMult| |split!| - |useEisensteinCriterion?| |setMinPoints3D| |cartesian| |lookup| - |charthRoot| |remove| |rank| |display| |RittWuCompare| - |stopTableInvSet!| |besselK| BY |odd?| |exteriorDifferential| - |integralLastSubResultant| |inspect| |distdfact| |lcm| - 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|squareFreePart| |qfactor| |var1Steps| |cAsin| |back| |leftOne| - |lfextendedint| |mainKernel| |toroidal| |maxdeg| |rischDE| - |incrementBy| |minrank| |orOperands| |negative?| |normalize| - |triangSolve| |setLegalFortranSourceExtensions| |qualifier| - |swapRows!| |acsch| |getMeasure| |expand| |infinityNorm| |s17dcf| - |laguerreL| |iiasin| |shiftRoots| |UpTriBddDenomInv| |divideIfCan!| - |s14abf| |diagonalMatrix| |filterWhile| |bandedJacobian| - |padicFraction| |antisymmetricTensors| |factorAndSplit| |tanh2coth| - |subscript| |prinshINFO| |paren| |morphism| |cylindrical| - |filterUntil| |cCot| |fixedPoint| |point| |oddInfiniteProduct| - |kovacic| |erf| |dn| |OMsupportsCD?| |createThreeSpace| - |toseInvertibleSet| |select| |extractSplittingLeaf| |pow| - |nextsousResultant2| |computePowers| |connect| |genericLeftTrace| - |lflimitedint| |minPol| |resultantReduitEuclidean| |algDsolve| - |s14aaf| |inconsistent?| |LyndonBasis| |symmetric?| |delay| - |OMgetAttr| |OMgetEndApp| |startTable!| |byteBuffer| |factorials| - 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|unaryFunction| |mainVariables| |iterators| |listYoungTableaus| - |complexForm| |KrullNumber| |lazyPquo| |integralRepresents| |implies| - |groebner?| |rangeIsFinite| |useSingleFactorBound| |routines| - |viewThetaDefault| |goto| |reverseLex| |coshIfCan| |airyBi| - |evenlambert| |monom| |equivOperands| |complexRoots| |OMsend| |index| - |LazardQuotient| |unparse| |rationalPoints| |fortranCarriageReturn| - |enqueue!| |derivationCoordinates| |sub| |SturmHabichtSequence| - |lowerPolynomial| |s17ajf| |fillPascalTriangle| |height| |argument| - |rootOf| |c06ecf| |constDsolve| |logpart| |initials| |trunc| - |OMgetFloat| |symbolTableOf| |bfEntry| |lhs| |linearPart| - |squareFreePrim| |remove!| |repeating?| |common| |getBadValues| - |bezoutDiscriminant| |operators| |opeval| |union| |sin?| |pair| |rhs| - |addBadValue| |iiasinh| |reduceByQuasiMonic| |traverse| |tree| - |finiteBound| |rightDiscriminant| |iiperm| |halfExtendedResultant1| - |countRealRoots| |s14baf| |divideExponents| |cycleLength| |makeCrit| - 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|redmat| |enterInCache| |reducedDiscriminant| |localIntegralBasis| - |cap| |cAtanh| |output| |compose| |numerator| |mkAnswer| - |clearFortranOutputStack| |thenBranch| |mapExponents| - |monomialIntPoly| |noLinearFactor?| |aLinear| |scale| |printingInfo?| - |splitSquarefree| |OMconnOutDevice| |henselFact| |innerSolve1| - |divideIfCan| |any| |d03eef| |accuracyIF| |inf| |adaptive?| |lp| - |setleft!| |padicallyExpand| |internalIntegrate| |factorPolynomial| - |raisePolynomial| |upperCase?| |tube| |factorOfDegree| |d01apf| - |digamma| |torsion?| |lexTriangular| |realSolve| |OMreadStr| - |symmetricGroup| |open?| |neglist| |inR?| |getCode| - |commutativeEquality| |iiatanh| |center| |leftNorm| |doubleResultant| - |f01bsf| |leftTrace| |isTimes| |find| |extension| |coleman| |dot| - |torsionIfCan| |dAndcExp| |nsqfree| |quasiMonicPolynomials| |point?| - |rootPoly| |fill!| |any?| |setprevious!| |edf2ef| |copyInto!| - |antiAssociative?| |host| |lyndon?| |polynomialZeros| |updateStatus!| - |node| |changeVar| |createNormalPrimitivePoly| |uncouplingMatrices| - |divisorCascade| |stopTableGcd!| |pushFortranOutputStack| - |expintegrate| |symbol?| |measure2Result| |wordInStrongGenerators| - |setlast!| |preprocess| |functionIsFracPolynomial?| |integerIfCan| - |separate| |popFortranOutputStack| |headReduced?| |continue| - |interpolate| |bezoutMatrix| |exquo| |resultant| |exptMod| |coerceS| - |logGamma| |style| |iiacosh| |variationOfParameters| |div| - |selectOptimizationRoutines| |cond| |firstDenom| |exp1| |mathieu24| - |Not| |empty| |ocf2ocdf| |sorted?| |closed?| |escape| |quo| - |insertMatch| |stack| |generalPosition| |blue| |squareFreeFactors| - |dimension| |setleaves!| |leftCharacteristicPolynomial| - |getIdentifier| |option?| |leastAffineMultiple| |f04adf| - |toseLastSubResultant| |setClipValue| |groebnerIdeal| |lowerCase?| - |groebSolve| |rightMult| |optimize| |iiGamma| |OMsupportsSymbol?| - |OMreadFile| |positiveSolve| |coerceP| |solveLinearlyOverQ| - |systemCommand| |hasHi| |totalDegree| |cycleRagits| |setClosed| - |ceiling| |rootBound| |geometric| |reduction| |baseRDE| |parts| - |maximumExponent| |ip4Address| |unexpand| |stirling1| |rationalPoint?| - |front| |mainSquareFreePart| |nextSubsetGray| - |semiResultantEuclidean2| |log10| |s18aff| |normDeriv2| |rdregime| - |resetBadValues| |scalarTypeOf| |createPrimitiveElement| |innerSolve| - |normal| |bitand| |representationType| |rombergo| |htrigs| - |arrayStack| |tensorProduct| |normalElement| |rightPower| - |primlimintfrac| |gradient| |bitior| - |zeroSetSplitIntoTriangularSystems| |fibonacci| |s17dgf| |c06fuf| - |epilogue| |s19acf| |part?| |palgextint| |sinIfCan| |edf2fi| - |signAround| |length| |patternVariable| |integral?| |numberOfDivisors| - |nthExponent| |graphCurves| |zeroDimensional?| |sinh2csch| |comp| - |trueEqual| |minset| |scripts| |implies?| |aQuadratic| - |leftScalarTimes!| |internal?| |zeroDim?| |f01ref| |gderiv| - |abelianGroup| |rquo| |coordinates| |equation| |hitherPlane| - |numerators| |simplifyPower| |showIntensityFunctions| - |setScreenResolution| |viewWriteDefault| |numberOfMonomials| |e01sef| - |An| |purelyAlgebraicLeadingMonomial?| |position!| |prime?| |hermiteH| - |failed?| |makeFR| |lazyPseudoDivide| |curve?| |mathieu23| - |integralBasis| |constant?| |denomRicDE| |sylvesterMatrix| - |fortranTypeOf| |maxPoints3D| |exprHasWeightCosWXorSinWX| - |makeViewport2D| |lazyGintegrate| |modularGcdPrimitive| |findBinding| - |SturmHabichtCoefficients| |myDegree| |content| |showTheRoutinesTable| - |leftLcm| |stoseInvertibleSet| UP2UTS |drawToScale| |e04mbf| |s19aaf| - |laplace| |monicDecomposeIfCan| |irreducible?| |setLabelValue| - |shufflein| |writeBytes!| |extractTop!| |backOldPos| |algebraicSort| - |debug| |showScalarValues| |repeating| |arg1| |factorsOfDegree| - |divisor| |digits| |quasiMonic?| |integralCoordinates| |s19abf| - |evaluateInverse| |nthFractionalTerm| |sort!| D |arg2| |cosSinInfo| - |light| |stFunc2| |palgintegrate| |exponential1| |factorGroebnerBasis| - |modifyPointData| |indices| |stoseInvertible?| |primintegrate| - |hconcat| |zeroSetSplit| |e02bdf| |mainMonomials| |palginfieldint| - |infix| |basisOfMiddleNucleus| |polygon| |conditions| - |genericRightTrace| |nlde| |janko2| |primPartElseUnitCanonical!| - |tableForDiscreteLogarithm| |conjugate| |sPol| |cycleTail| - |cardinality| |commutator| |match| |kroneckerDelta| |e02dcf| - |getStream| |f04qaf| |nand| |logical?| |fractRagits| - |viewWriteAvailable| |integral| |setvalue!| |iidprod| |schwerpunkt| - |cyclicParents| |Beta| |palgLODE0| |quadraticForm| |computeInt| - |d01fcf| |getOrder| |zoom| |sequence| |Lazard2| |OMserve| |wholeRadix| - |readIfCan!| |resetAttributeButtons| |hexDigit| |e01bff| - |makeVariable| |localReal?| |zeroMatrix| |coerceListOfPairs| |push!| - |sec2cos| |generalTwoFactor| |iiacot| |genericRightMinimalPolynomial| - |OMputAtp| |rightQuotient| |lambert| |hasPredicate?| |resultantnaif| - |cross| |nodeOf?| |ScanFloatIgnoreSpaces| |purelyAlgebraic?| - |sparsityIF| |collectUpper| |curryLeft| |pointLists| |zero?| - |rowEchelon| |pleskenSplit| |complexNumericIfCan| |moebius| - |fixedPoints| |print| |logIfCan| |directory| |reset| |lfunc| - |curveColor| |supersub| |userOrdered?| |clipBoolean| |resolve| - |OMputEndApp| |acschIfCan| |modulus| |coefficient| |identityMatrix| - |flexible?| |reorder| |choosemon| |quoByVar| |expenseOfEvaluation| - |prepareSubResAlgo| |generalizedInverse| |d02ejf| |write| - |outputAsFortran| |getlo| |first| |checkRur| |f04arf| |limit| - |sizePascalTriangle| Y |iisech| |increment| |outputGeneral| |plus!| - |save| |testDim| |rest| |clip| |cAcot| |OMputEndBind| - |rectangularMatrix| |splitConstant| |f01qcf| - |conditionsForIdempotents| |c06ekf| |reify| |substitute| |name| - |d01asf| |string?| |linearDependenceOverZ| |solid?| |e02zaf| |besselY| - |maxIndex| |imagi| |removeDuplicates| F |body| |inverse| |pmintegrate| - |patternMatch| |LagrangeInterpolation| |f04faf| |evaluate| |phiCoord| - |d03edf| |primitivePart| |untab| |normalizeIfCan| |badNum| |rotate| - |subset?| |createIrreduciblePoly| |Is| |binomial| |pair?| ~ |f04mbf| - |cCoth| |less?| |Nul| |basicSet| |csubst| |findCycle| |dmp2rfi| - |birth| |powers| |moduleSum| |infinite?| |vark| - |topFortranOutputStack| |OMconnInDevice| |primPartElseUnitCanonical| - |retract| |maxint| |makeResult| |open| |squareTop| |rightNorm| |fmecg| - |rootSimp| |/\\| |normal?| |numberOfComponents| |scripted?| - |principalIdeal| |stopTable!| |flatten| |selectNonFiniteRoutines| - |brillhartIrreducible?| |ListOfTerms| |unitCanonical| |\\/| - |OMgetEndAttr| |numberOfComposites| |recip| |leadingCoefficientRicDE| - |refine| |cAcoth| |port| |goodPoint| |ratDsolve| |ef2edf| |iisin| - |scopes| |dark| |quatern| |generalInfiniteProduct| |f02bjf| - |rightUnit| |hclf| |meshFun2Var| |s17akf| |appendPoint| - |factorFraction| |randomR| |clipSurface| |cAsec| ** |checkPrecision| - |t| |f02adf| |clearDenominator| |absolutelyIrreducible?| |shift| - |perfectNthPower?| |getMatch| |orbit| |direction| |unitsColorDefault| - |legendreP| |replace| |rightFactorIfCan| |e02agf| |cyclicGroup| - |impliesOperands| |subResultantChain| |ipow| |shiftLeft| |secIfCan| - |iisec| |collect| |transpose| |rischNormalize| EQ |fglmIfCan| |term| - |clearTheSymbolTable| |ode| |retractIfCan| |ScanArabic| - |extendedEuclidean| |listBranches| |callForm?| |multiEuclideanTree| - |revert| |transcendentalDecompose| |makingStats?| |subMatrix| - |property| |specialTrigs| |every?| |Ei| |numer| |generateIrredPoly| - |clearCache| |f2df| |changeName| |innerint| |permutation| |bottom!| - |rightMinimalPolynomial| |f07fef| |cyclotomic| |denom| |c06ebf| - |leadingBasisTerm| |exprToUPS| |autoReduced?| |OMencodingBinary| - |exactQuotient| |leastPower| |outerProduct| |key?| - |algebraicCoefficients?| |c05nbf| |sincos| - |rewriteSetByReducingWithParticularGenerators| |cosh2sech| |aCubic| - |pseudoDivide| |units| |setProperty| |cRationalPower| |leftUnits| |pi| - |OMputError| |selectFiniteRoutines| |triangulate| |makeCos| - |decompose| |setProperties| |leaf?| |updatF| |showTheIFTable| - |bumprow| |infinity| |green| |removeRedundantFactorsInContents| - |ReduceOrder| |genericRightTraceForm| |outputForm| |makeSeries| - |intChoose| |category| |zeroOf| |trivialIdeal?| - |standardBasisOfCyclicSubmodule| |super| |lazyVariations| |elementary| - |reflect| |inverseIntegralMatrixAtInfinity| |connectTo| |domain| - |insertBottom!| |identity| |supRittWu?| |factors| |eq?| |compBound| - |elem?| |sqfree| |package| |nextPrimitiveNormalPoly| - |degreeSubResultantEuclidean| |makeGraphImage| |kernel| |merge| - |bindings| |code| |axesColorDefault| |simplify| |graphState| |map| - |modTree| |draw| |pointData| |drawCurves| |viewSizeDefault| - |fprindINFO| |lyndonIfCan| |iisqrt2| |iiexp| |printCode| |magnitude| - |traceMatrix| |d01aqf| |wrregime| |e02ahf| |realEigenvalues| |terms| - |lazyPremWithDefault| |satisfy?| |nextSublist| |mergeDifference| - |genericPosition| |clikeUniv| |e01sbf| |lquo| |mapUnivariate| |lex| - |setRow!| |rationalFunction| |internalZeroSetSplit| |dom| |ramified?| - |solveLinear| |represents| |totalGroebner| |f02agf| |makeObject| - |yCoordinates| |physicalLength!| |inputOutputBinaryFile| |numeric| - |diagonal| |removeCoshSq| |convert| |iidsum| |computeBasis| - |ScanRoman| |expr| |radical| |monicDivide| |isobaric?| |s17dhf| - |nextNormalPrimitivePoly| |startTableInvSet!| |d01gbf| |sayLength| - |cyclicSubmodule| |coef| |setColumn!| |sample| |changeWeightLevel| - |pole?| |tanSum| |llprop| |stripCommentsAndBlanks| |pointSizeDefault| - |imaginary| |quadratic?| |unit| |antiCommutator| |OMgetAtp| UTS2UP - |currentScope| |selectAndPolynomials| |primitivePart!| |title| - |patternMatchTimes| |acosIfCan| |factorsOfCyclicGroupSize| - |nextNormalPoly| |cExp| |options| |f07aef| |differentialVariables| - |expandPower| |getMultiplicationTable| |scan| |iiacsc| |members| - |s18acf| |nil?| |invertIfCan| |intersect| |anfactor| |mindegTerm| - |integralDerivationMatrix| |optAttributes| |currentCategoryFrame| - |mkcomm| |e04ucf| |hermite| |e| |ran| |f02axf| |overlabel| |string| - |strongGenerators| |nthFlag| |simplifyExp| |s21bbf| |maxColIndex| - |bat| |sumSquares| |moduloP| |bitLength| |nthCoef| |parametersOf| - |nonSingularModel| |cot2trig| |mapdiv| |copies| |readByte!| - |showTypeInOutput| |bivariate?| |pquo| |pdf2df| - |genericRightDiscriminant| |viewport2D| |mesh?| |polygon?| |polyRDE| - |lighting| |baseRDEsys| |returnType!| |next| |regularRepresentation| - |seriesSolve| |getOperands| |gcdprim| |continuedFraction| - |constantCoefficientRicDE| |lllip| |setelt!| |mainVariable?| - |removeRoughlyRedundantFactorsInContents| |leadingExponent| - |trapezoidalo| |iiabs| |completeHensel| |predicate| |linGenPos| - |null?| |setTopPredicate| |antisymmetric?| |swap!| - |ScanFloatIgnoreSpacesIfCan| |roughBase?| |rightExtendedGcd| - |semiResultantReduitEuclidean| |is?| |critpOrder| |asechIfCan| - |leadingIndex| |divisors| |makeTerm| |s19adf| |plusInfinity| - |completeEchelonBasis| |split| |primitiveElement| |high| |mainContent| - |normalise| |setCondition!| |nthFactor| |typeLists| - |rootOfIrreduciblePoly| |rk4a| |minusInfinity| |realRoots| - |internalSubPolSet?| |algint| |e01daf| |degreePartition| - |messagePrint| |solid| |multiple?| |tubePoints| - |sumOfKthPowerDivisors| |declare| |curve| |completeSmith| |resetNew| - |Vectorise| |width| |tubeRadiusDefault| |monomial?| |OMread| - |selectODEIVPRoutines| |integerBound| |resize| |ODESolve| - |rubiksGroup| |unknown| |errorKind| |f02ajf| |distribute| |addPoint2| - |decrease| |Frobenius| |factorial| |palgLODE| |fixedPointExquo| |kmax| - |linear?| |spherical| |roughUnitIdeal?| |complexIntegrate| - |OMgetEndBind| |primitive?| |intcompBasis| |sts2stst| |qelt| - |universe| |in?| |getButtonValue| |signatureAst| - |integralBasisAtInfinity| |lfintegrate| |graeffe| |qsetelt| - |primaryDecomp| |leader| |contract| |palgint| |isPower| |parameters| - |linearAssociatedExp| |createRandomElement| |isExpt| |plotPolar| - |derivative| |type| |toseSquareFreePart| |d01gaf| |xRange| |multMonom| - |deepCopy| |nextPrimitivePoly| |f04axf| |sort| |ramifiedAtInfinity?| - |e02akf| |size?| |insertTop!| |binaryFunction| |yRange| - |blankSeparate| |selectPolynomials| |paraboloidal| |subPolSet?| - |rootKerSimp| |identification| |fortran| |module| |over| |mulmod| - |zRange| |realEigenvectors| |contours| |optional| |mdeg| - |extensionDegree| |numericalOptimization| |minimumDegree| - |getConstant| |map!| |Ci| |OMputEndAttr| |iicsc| |thetaCoord| - |fortranDoubleComplex| |meshPar1Var| |makeUnit| |exactQuotient!| - |qsetelt!| |safeCeiling| |d03faf| |iteratedInitials| |ref| - |algebraicDecompose| |currentEnv| |rangePascalTriangle| |delta| - |random| |nullSpace| |and?| |real?| |root?| |setchildren!| - |mainDefiningPolynomial| |tRange| |lazyPrem| |quadratic| |mat| - |createNormalElement| |shallowExpand| |expandLog| |operation| - |tanhIfCan| |complexEigenvectors| |evenInfiniteProduct| |cAcsc| - |empty?| |coefficients| |repSq| |graphStates| |constantIfCan| |f02akf| - |cothIfCan| |setnext!| |printInfo!| |nullary?| |binaryTournament| - |unravel| |companionBlocks| |mapExpon| |outputBinaryFile| |datalist| - |totalfract| |e04fdf| |symmetricTensors| |realElementary| |c06gbf| - |dequeue| |complement| |head| |elements| |exprHasLogarithmicWeights| - |getSyntaxFormsFromFile| |delete!| |subQuasiComponent?| |singular?| - |tanAn| |ptFunc| |inGroundField?| |complementaryBasis| |augment| - SEGMENT |numberOfHues| |polygamma| |minGbasis| |besselI| |e02dff| - |depth| |eigenvectors| |elliptic| |computeCycleEntry| |trim| - |startPolynomial| |prindINFO| |partitions| |createNormalPoly| |e04jaf| - |lambda| |message| |member?| |Gamma| |singularitiesOf| |startStats!| - |vector| |categoryFrame| |moreAlgebraic?| |stoseInvertible?sqfreg| - |printHeader| |comment| |beauzamyBound| |integralAtInfinity?| |taylor| - |overbar| |parabolic| |solveLinearPolynomialEquationByRecursion| - |differentiate| |innerEigenvectors| |ksec| |leaves| |setEpilogue!| - |getGoodPrime| |replaceKthElement| |explogs2trigs| |laurent| - |discriminant| |atanIfCan| |getGraph| |script| |df2st| |iicot| - |acothIfCan| |exprToXXP| |solveid| |tower| |euclideanGroebner| - |dimensionsOf| |puiseux| |makeop| |radix| |extendedIntegrate| - |ratDenom| |halfExtendedResultant2| |seed| |radicalEigenvectors| - |dihedral| |s18dcf| |linearAssociatedLog| |padecf| |setStatus| - |condition| |mantissa| |pToHdmp| |associatorDependence| - |taylorQuoByVar| |basisOfCentroid| |numberOfNormalPoly| |setImagSteps| - |critBonD| |inv| |fintegrate| |presuper| |SturmHabichtMultiple| - |elRow1!| |tex| |cons| |adjoint| |expressIdealMember| |level| - |ParCond| |discriminantEuclidean| |hessian| |extendedSubResultantGcd| - |ground?| |mapGen| |nonQsign| |integer?| |tab1| |d02bhf| |determinant| - |e02bef| |relativeApprox| |eq| |upperCase| |domainOf| |rowEch| |lift| - |error| |outputFixed| |ground| |returnTypeOf| - |cyclotomicFactorization| |selectSumOfSquaresRoutines| - |sortConstraints| |modularFactor| |iter| |d01bbf| |euler| - |pseudoQuotient| |showTheFTable| |numberOfImproperPartitions| - |shanksDiscLogAlgorithm| |reduce| |leadingMonomial| |leftDivide| - |assert| |oddintegers| |someBasis| |complexNumeric| |enterPointData| - |OMputAttr| |bright| |wreath| |viewPosDefault| - |stoseInternalLastSubResultant| |infRittWu?| |weights| - |leadingCoefficient| |resetVariableOrder| |mirror| |e02baf| |rules| - |mr| |iicos| |insertRoot!| |rightRankPolynomial| |rightTrace| |quote| - |kernels| |makeSin| |primitiveMonomials| |regime| |quasiAlgebraicSet| - |randnum| |Si| |balancedFactorisation| |leftRankPolynomial| |legendre| - |divide| |leadingIdeal| |rationalIfCan| |reductum| - |indiceSubResultantEuclidean| |univariate| |upDateBranches| - |alphanumeric| |source| |rightLcm| |leastMonomial| |s21bcf| |term?| - |dec| |harmonic| |e02aef| |romberg| |extractClosed| - |mainCharacterization| |superHeight| |listOfLists| |lexico| |tableau| - |fortranCharacter| |primextintfrac| |f04asf| |polyRicDE| ~= - |quasiRegular| |basisOfCenter| |c02agf| |genericLeftNorm| - |radicalEigenvector| |associatedEquations| |pol| |s17acf| - |selectfirst| |factor| |coerce| |ParCondList| |minRowIndex| - |pointColorDefault| |exp| |pascalTriangle| |pushdown| - |curveColorPalette| |sqrt| |aromberg| |notOperand| |create| - |construct| |groebgen| |f02wef| |inverseLaplace| - |firstUncouplingMatrix| |normalForm| |subNode?| |physicalLength| - |fractionFreeGauss!| |OMgetString| |column| |real| |lazyEvaluate| - |d01alf| |move| |target| |showRegion| |tablePow| |mainPrimitivePart| - |palglimint0| |perfectSquare?| |slash| |bounds| |imag| |delete| - |laguerre| |stiffnessAndStabilityFactor| |quasiRegular?| |f02fjf| - |monomRDE| |directProduct| NOT |fixPredicate| |probablyZeroDim?| - |cyclePartition| |internalAugment| |compile| |diophantineSystem| - |multinomial| |jacobi| |gcdcofact| |univariatePolynomialsGcds| OR - |npcoef| |semiLastSubResultantEuclidean| |complexSolve| |drawStyle| - |one?| |iiasech| |e01saf| |doubleRank| |mainExpression| |polar| AND - |permanent| |more?| |brace| |cycleEntry| |atrapezoidal| |viewport3D| - |has?| |complexLimit| |hypergeometric0F1| - |rewriteIdealWithQuasiMonicGenerators| |OMputEndAtp| |destruct| - |tan2trig| |d02raf| |functionIsContinuousAtEndPoints| |gcdPolynomial| - |stopMusserTrials| |linearlyDependent?| |numericIfCan| - |indicialEquations| |shade| |sechIfCan| |Aleph| |ravel| - |partialFraction| |parent| |monicRightDivide| |monomials| |generic?| - |sinhIfCan| |validExponential| |frobenius| |dualSignature| |reshape| - |OMgetEndObject| |coordinate| |nextLatticePermutation| |clearTable!| - |writable?| |hspace| |rowEchLocal| |complexZeros| |cTanh| |chiSquare| - |meshPar2Var| |lo| |numberOfCycles| |positive?| |iicoth| - |linkToFortran| |monomial| |truncate| |digit?| |branchPoint?| - |predicates| |restorePrecision| |algebraic?| |char| |setPoly| - |factorSFBRlcUnit| |addMatch| |numFunEvals3D| |multivariate| - |lastSubResultant| |anticoord| |f02aef| |unitNormalize| - |insertionSort!| |digit| |roughBasicSet| |leftRank| |setelt| - |variables| |shallowCopy| |listRepresentation| |rotatey| |f02aff| - |expenseOfEvaluationIF| |stoseLastSubResultant| |nary?| |varselect| - |makeSUP| |setProperty!| |positiveRemainder| |conjug| - |transcendenceDegree| |update| |combineFeatureCompatibility| |e02bbf| - * |rootSplit| |times!| |copy| |initTable!| |directSum| |subTriSet?| - |simpleBounds?| |fortranCompilerName| |rotatex| |problemPoints| - |fortranComplex| |uniform01| |d02kef| |possiblyNewVariety?| - |squareFree| |testModulus| |headAst| |ellipticCylindrical| |float| - |qqq| |initial| |halfExtendedSubResultantGcd2| |alternating| |e02gaf| - |critB| |f02awf| |prevPrime| |OMgetVariable| |expIfCan| - |removeConstantTerm| |swapColumns!| |autoCoerce| |splitNodeOf!| - |rCoord| |asinhIfCan| |measure| |cycleSplit!| |prologue| - |principalAncestors| |csc2sin| |zeroDimPrimary?| |dequeue!| - |leftRegularRepresentation| |diagonalProduct| |makeRecord| - |stoseIntegralLastSubResultant| |dflist| |match?| |prime| |position| - |iipow| |s17def| |generalLambert| |yellow| |merge!| - |possiblyInfinite?| |cSin| |maxRowIndex| |nonLinearPart| - |radicalRoots| |lprop| |rightTraceMatrix| |nextPrime| |e04dgf| - |FormatArabic| |factorByRecursion| |newSubProgram| |cotIfCan| |acosh| - |jordanAlgebra?| |exponents| |getMultiplicationMatrix| |finiteBasis| - |mergeFactors| |mapDown!| |child?| |convergents| |weight| |flagFactor| - |atanh| |numericalIntegration| |iflist2Result| - |stoseInvertibleSetsqfreg| |symmetricSquare| |pile| |d01akf| |e02adf| - |f07fdf| |multiplyExponents| |acoth| |makeViewport3D| |push| - |numberOfVariables| |univariatePolynomial| |calcRanges| - |decomposeFunc| |weakBiRank| |ord| |iomode| |isPlus| |assign| |asech| - |failed| |iiacsch| |numberOfPrimitivePoly| |f01rdf| GE |rootNormalize| - |primlimitedint| |linSolve| |df2ef| |setFieldInfo| |radicalSimplify| - |eisensteinIrreducible?| |removeCosSq| |commutative?| |sumOfDivisors| - |radicalEigenvalues| |yCoord| |iFTable| GT - |tryFunctionalDecomposition| |denominator| |laurentIfCan| - |numberOfIrreduciblePoly| |normalizedAssociate| |f04maf| |tan2cot| - |multiple| |controlPanel| |monomialIntegrate| |e02bcf| |normalized?| - |changeThreshhold| |removeSuperfluousQuasiComponents| LE - |basisOfLeftNucleus| |binaryTree| |primintfldpoly| |printStatement| - |quasiComponent| |zero| |applyQuote| |lifting1| |normalizedDivide| - |abs| |diag| |OMgetSymbol| |solveInField| LT |increasePrecision| - |splitDenominator| |exponential| |iifact| |s15aef| |intensity| - |rotatez| |numberOfOperations| |even?| |youngGroup| - |rewriteIdealWithHeadRemainder| |denominators| |schema| |floor| - |gcdcofactprim| |And| |droot| |degree| |rst| |f04jgf| |capacity| - |iicosh| |cAtan| |e02ajf| |updatD| |screenResolution| |symFunc| - |stirling2| |distFact| |Or| |coord| |conditionP| |indiceSubResultant| - |ruleset| |clipWithRanges| |c06gsf| |s20acf| |enumerate| |palgRDE0| - |viewDeltaXDefault| |closeComponent| |numberOfChildren| |element?| - |ode2| |OMconnectTCP| |diagonals| |e01sff| |maxrank| |invertible?| - |currentSubProgram| |branchPointAtInfinity?| |polyPart| - |reciprocalPolynomial| |completeEval| |leftRecip| |ricDsolve| - |groebnerFactorize| |certainlySubVariety?| |cSinh| |rischDEsys| - |trigs2explogs| |stoseSquareFreePart| |OMopenFile| |primes| - |deepestInitial| |rightRank| |getDatabase| |monicModulo| - |outputAsScript| |totolex| |suchThat| |selectPDERoutines| |entries| - |complexNormalize| |rowEchelonLocal| |hdmpToDmp| |mapUnivariateIfCan| - |LiePolyIfCan| |makeSketch| |powern| |unit?| |expt| - |solveLinearPolynomialEquationByFractions| |imagK| - |semiDegreeSubResultantEuclidean| |lowerCase| |result| |vectorise| - |fractRadix| |algintegrate| |primeFactor| |plenaryPower| - |radicalOfLeftTraceForm| |subresultantVector| |consnewpol| - |substring?| |log| |OMgetType| |ode1| |mightHaveRoots| |mvar| - |properties| |singularAtInfinity?| |mathieu11| |root| |hdmpToP| |cup| - |returns| |alternatingGroup| |fi2df| |getCurve| |reduceLODE| - |var1StepsDefault| |OMputEndObject| |translate| |adaptive3D?| - |primeFrobenius| |addmod| |nil| |infinite| |arbitraryExponent| - |approximate| |complex| |shallowMutable| |canonical| |noetherian| - |central| |partiallyOrderedSet| |arbitraryPrecision| - |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| - |additiveValuation| |unitsKnown| |canonicalUnitNormal| - |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| - |commutative|)
\ No newline at end of file + |Record| |Union| |moebiusMu| |factorset| |powmod| |sort| |deref| + |extendedResultant| |gcdPrimitive| |tubePlot| |rotate| + |brillhartIrreducible?| |zeroSetSplitIntoTriangularSystems| |freeOf?| + |rowEchelon| |complementaryBasis| |evenInfiniteProduct| |separate| + |lagrange| |setMinPoints| |fortran| |members| |mapUnivariate| + |quotient| |generalizedContinuumHypothesisAssumed| |poisson| |cAcoth| + |cyclePartition| |rightUnits| |sub| |palginfieldint| |asinhIfCan| + |setPredicates| |startStats!| |makeGraphImage| |sequence| + |safeCeiling| |bat| |LazardQuotient2| |initTable!| + |topFortranOutputStack| |showArrayValues| |cos2sec| |dot| |null?| + |stoseInvertible?| |find| |signAround| |random| |radPoly| + |OMputEndAtp| |e04fdf| |e02dff| |getMeasure| |OMgetApp| + |viewWriteAvailable| |complexEigenvectors| |rectangularMatrix| |critT| + |setIntersection| |cyclicSubmodule| |iiabs| |lazyPquo| |finite?| + |perfectNthRoot| |removeSuperfluousQuasiComponents| |rootNormalize| + |presub| |presuper| |setrest!| |leftRegularRepresentation| |setUnion| + |rightMult| |const| |mainVariable| |ideal| |setnext!| |roughBase?| + |extractProperty| |reciprocalPolynomial| |power| |copyInto!| + |bivariateSLPEBR| |apply| |digits| |mapdiv| |datalist| + |patternMatchTimes| |currentEnv| |s17aef| |OMgetVariable| |green| + |createNormalPoly| |pushdown| |nil| |virtualDegree| |wholeRadix| + |rightDiscriminant| |diagonalProduct| |bit?| |leadingIdeal| + |symmetricProduct| |OMsetEncoding| |monomial| |floor| |df2ef| |index?| + |integralBasisAtInfinity| |coth2trigh| |size| |derivative| + |quotientByP| |call| |palgint| |capacity| |c05nbf| |satisfy?| + |multivariate| |removeCoshSq| |preprocess| |depth| |quasiComponent| + |limitedIntegrate| |merge| |e02zaf| |interReduce| |imagj| + |monicDecomposeIfCan| |variables| |leftQuotient| |RittWuCompare| + |setProperties| |extend| |approximate| |function| |reduceLODE| + |characteristicSerie| |curryLeft| |float?| |scopes| |repeatUntilLoop| + |makingStats?| |makeUnit| |roughBasicSet| |linSolve| |id| |complex| + |factorByRecursion| |qroot| |first| |rk4a| |rationalFunction| + |besselI| |byte| |monicRightDivide| |argscript| |coerceImages| + |stoseInvertibleSetreg| |predicates| |squareFreeFactors| |eval| |rest| + |jordanAdmissible?| |OMunhandledSymbol| |list?| |computeCycleEntry| + |script| |formula| |numericIfCan| |hasoln| |screenResolution| |delay| + |table| |problemPoints| |iflist2Result| |substitute| |f04atf| |close| + |numberOfCycles| |rk4f| |exponentialOrder| |groebnerIdeal| |f07fdf| + |qinterval| |e01bff| |closedCurve?| |new| |obj| |removeDuplicates| + |romberg| |selectFiniteRoutines| |clearFortranOutputStack| + |chebyshevT| |charpol| |dihedralGroup| |zeroVector| |c06gcf| + |cosIfCan| |taylor| |getOperator| |generalPosition| |search| + |arrayStack| |genericLeftNorm| |ParCondList| |remove| + |sturmVariationsOf| |display| |wordsForStrongGenerators| |printTypes| + |cache| |sinh2csch| |tex| BY |tab1| |laurent| |monicLeftDivide| + |cycleRagits| |leftFactor| |fintegrate| |setErrorBound| |checkForZero| + |operation| |OMgetAtp| |orbit| |monic?| |tower| |heap| |and?| |nrows| + |constant| |puiseux| |fractRagits| |setref| |froot| |stopTableGcd!| + |last| |cyclicCopy| |fixedPointExquo| |mesh| |stripCommentsAndBlanks| + |addPointLast| |ncols| |roman| |totalDifferential| |internal?| + |frobenius| |indicialEquationAtInfinity| |assoc| |someBasis| |Si| + |intcompBasis| |oddlambert| |mkcomm| |bezoutMatrix| + |leftCharacteristicPolynomial| |inv| |stFuncN| |e02ahf| |evenlambert| + |genericRightTrace| |squareMatrix| |s17dcf| |listRepresentation| + |vertConcat| |tubePoints| |leftRemainder| |ground?| |rdregime| + |noLinearFactor?| |OMgetEndObject| |input| |showScalarValues| + |vectorise| |diff| |yCoord| |lazyPrem| |ground| |cRationalPower| + |subResultantsChain| |graphs| |OMputEndBVar| |nextPartition| + |computeInt| |clip| |rank| |coth2tanh| |library| |outputForm| |curry| + |oneDimensionalArray| |primeFrobenius| |s17aff| |complexNumeric| + |leadingMonomial| |getCurve| |listLoops| |cartesian| |lcm| |e01saf| + |distribute| |epilogue| |d01ajf| |option?| |factorsOfDegree| + |OMputString| |leadingCoefficient| |squareFreePart| + |setScreenResolution3D| |rules| |idealiser| |univariate?| |mapDown!| + |euler| |algebraicDecompose| |bezoutDiscriminant| |kernels| |plus!| + |primitiveMonomials| |parametersOf| |region| |left| |exactQuotient| + |pack!| |append| |modifyPoint| |selectPolynomials| |powern| + |bipolarCylindrical| |coerceP| |sayLength| |dAndcExp| |frst| + |viewZoomDefault| |semicolonSeparate| |reductum| |univariate| |right| + |exprToXXP| |gcd| |cycleLength| |integralBasis| |headAst| |set| + |zeroDimensional?| |removeRoughlyRedundantFactorsInContents| |size?| + |lastSubResultant| |partition| |possiblyNewVariety?| |prefixRagits| + |factorFraction| |palgRDE0| |cAtan| |false| |iiacos| |primextintfrac| + |polyRDE| |returnType!| |insertRoot!| |iiasinh| |appendPoint| + |primextendedint| |sum| |f02agf| |pureLex| |pushdterm| + |currentSubProgram| |nextNormalPoly| |ratPoly| |complexIntegrate| + |evaluate| |integral?| |factor| |binaryTree| + |rightCharacteristicPolynomial| |putColorInfo| |var1Steps| |randomLC| + |nextItem| |isPlus| |sqrt| |OMputError| |startPolynomial| |gderiv| + |string?| |shanksDiscLogAlgorithm| |sizeLess?| |norm| |real| |htrigs| + |aQuartic| |prinb| |geometric| |lp| |swapRows!| |internalIntegrate0| + |backOldPos| |lexGroebner| |semiDegreeSubResultantEuclidean| |imag| + |s18def| |ptree| |equality| |changeMeasure| |c05adf| |directProduct| + |topPredicate| |idealSimplify| |remainder| |OMopenFile| |superscript| + |showSummary| |insertBottom!| |numberOfFractionalTerms| |coleman| + |probablyZeroDim?| |radicalEigenvectors| |interpretString| |midpoints| + |integralLastSubResultant| |iiacsc| |leftLcm| + |internalLastSubResultant| |binary| |maxColIndex| |brace| + |binomThmExpt| |inconsistent?| |point?| |hash| |showAttributes| + |f02aef| |ScanFloatIgnoreSpacesIfCan| |rubiksGroup| |operators| + |OMencodingBinary| |destruct| |edf2fi| |show| |count| |smith| + |setlast!| |clikeUniv| |reducedContinuedFraction| |e02aef| |symbol| + |solid?| |midpoint| = |slex| |makeViewport3D| |constDsolve| + |viewport3D| |palgLODE| |expression| |setPrologue!| |pquo| + |singleFactorBound| |listOfMonoms| |trace| |lo| |laplace| |asinIfCan| + |realSolve| |fortranLinkerArgs| |integer| |algebraic?| |edf2ef| + |gbasis| < |collectUpper| |exquo| |incr| |associatorDependence| + |cycle| |charthRoot| |antiCommutator| > |div| |latex| |cot2trig| + |build| |iterationVar| |diophantineSystem| |unitNormal| + |pushNewContour| |makeSketch| |drawComplex| <= |quo| + |quasiMonicPolynomials| |changeThreshhold| |OMlistSymbols| + |incrementKthElement| |bat1| |viewDefaults| |mkAnswer| >= + |scanOneDimSubspaces| |label| |llprop| |purelyAlgebraic?| |adaptive| + |limitPlus| |sdf2lst| |linearlyDependentOverZ?| |drawToScale| + |inGroundField?| |rem| |partialFraction| |newTypeLists| + |createPrimitiveElement| |updatD| |realEigenvectors| |fill!| + |fixedDivisor| |ip4Address| |expandPower| |primitive?| |measure| + |listConjugateBases| |LyndonCoordinates| |eisensteinIrreducible?| + |prevPrime| |skewSFunction| |symmetric?| |branchPoint?| |compBound| + + |equiv?| |d01akf| |sPol| |f01rdf| |upperCase!| |credPol| |transpose| + |SFunction| |zeroSquareMatrix| |groebSolve| - + |rewriteIdealWithRemainder| |outputArgs| |mapUnivariateIfCan| |isList| + |initiallyReduce| |critBonD| |setAdaptive3D| |numericalIntegration| / + |ode2| |plotPolar| |points| |e02daf| |f04jgf| |setProperty!| |imagE| + |partitions| |integrate| |leftExtendedGcd| |basisOfLeftNucleus| + |infLex?| |expIfCan| |nor| |rCoord| |constructor| |s17ahf| + |monomRDEsys| |rquo| |divideExponents| |symmetricRemainder| |trim| + |element?| |findCycle| |f04faf| |pdct| + |createLowComplexityNormalBasis| |nextPrimitiveNormalPoly| |option| + |signatureAst| |mergeFactors| |critMonD1| |low| |elliptic| |e02bdf| + |errorInfo| |rootSimp| |color| |argument| |f02ajf| |blankSeparate| + |symmetricGroup| |nothing| |createRandomElement| |addBadValue| + |listYoungTableaus| |FormatRoman| |polyRicDE| |setStatus| |refine| + |exprHasWeightCosWXorSinWX| |d01bbf| |diagonal| |airyAi| |f04mbf| + |mainValue| |paren| |zoom| |graphImage| |univcase| |leftZero| + |divisor| |charClass| |complete| |hexDigit| |OMputBind| + |representationType| |s20adf| |binaryTournament| |testDim| + |goodnessOfFit| |addMatch| |cothIfCan| |kovacic| |acscIfCan| + |pascalTriangle| |wordInGenerators| |objectOf| |basisOfCentroid| + |discreteLog| |permanent| |cardinality| |lfextlimint| |UnVectorise| + |schema| |nullary| |outputList| |rightTrim| |powerAssociative?| + |coerceListOfPairs| |invertible?| |debug3D| |quadratic| + |leftExactQuotient| |empty?| |factorOfDegree| |OMencodingUnknown| + |leftTrim| |myDegree| |hexDigit?| |resultantReduit| |gcdcofactprim| + |nextColeman| |qPot| |po| |simpleBounds?| |nodes| |rightFactorIfCan| + |mainMonomial| |karatsubaOnce| UP2UTS |Hausdorff| + |factorSquareFreeByRecursion| |setScreenResolution| |bipolar| |s17akf| + |enumerate| |roughSubIdeal?| |allRootsOf| |yellow| |elem?| |multiple?| + |nlde| |rarrow| |axesColorDefault| |randnum| |exteriorDifferential| + |squareTop| |hMonic| |resultantEuclidean| |s18adf| |sample| |s21bbf| + |collect| |BumInSepFFE| |setvalue!| |orthonormalBasis| |divide| |li| + |ran| |setright!| |drawCurves| |monomialIntPoly| |degreeSubResultant| + |trivialIdeal?| |fTable| |stoseSquareFreePart| |initials| |e01sff| + |setleft!| |choosemon| |zeroDimPrime?| |addiag| |quadraticForm| + |applyRules| |s14aaf| |reflect| |minimumExponent| |optional?| + |composite| |tubeRadius| |acschIfCan| |module| |testModulus| + |selectsecond| |lazyPremWithDefault| |generalInfiniteProduct| |light| + |roughUnitIdeal?| |seed| |distance| |rroot| |coord| |getPickedPoints| + |lieAlgebra?| |selectMultiDimensionalRoutines| |OMputEndObject| + |hasPredicate?| |mainKernel| |bsolve| |c02agf| |comparison| |back| + |keys| |positiveSolve| |hi| |sortConstraints| |relationsIdeal| + |primitiveElement| |iExquo| |autoReduced?| |e02gaf| |eulerE| + |composites| |expenseOfEvaluation| |outputGeneral| |e02akf| |root?| + |s21baf| |irreducibleFactors| |OMbindTCP| |scalarTypeOf| |acoshIfCan| + |constantLeft| |maxint| |denomRicDE| |iteratedInitials| |intChoose| + |removeRedundantFactorsInPols| |binarySearchTree| |totalGroebner| + |unprotectedRemoveRedundantFactors| |yRange| |alphabetic| |repeating| + |fibonacci| |OMgetSymbol| |uncouplingMatrices| |normalElement| + |constantIfCan| |digamma| |extractPoint| |zRange| |BasicMethod| + |areEquivalent?| |jacobi| |tRange| |cAsech| |e04dgf| + |fullPartialFraction| |gcdPolynomial| |map!| |intPatternMatch| + |numberOfMonomials| |rationalPower| |stopTableInvSet!| |ode| + |fixPredicate| |numberOfImproperPartitions| |qsetelt!| + |collectQuasiMonic| |explicitlyEmpty?| |atanhIfCan| |B1solve| + |irreducibleRepresentation| |complement| |checkRur| |OMputApp| + |overbar| |test| |e02bef| |showFortranOutputStack| + |internalSubQuasiComponent?| |indicialEquations| |tubePointsDefault| + |factorList| |sup| |decompose| |monomial?| |minordet| |tanh2coth| + |reduced?| |airyBi| |generate| |iiexp| |getConstant| |symFunc| + |factorial| |insertMatch| |pomopo!| |rightUnit| |bytes| |arbitrary| + |prefix| |df2st| |lazyPseudoQuotient| |negative?| + |createNormalElement| |simplifyExp| |rk4| |delete!| |equiv| + |OMreceive| |particularSolution| |expressIdealMember| |tan2cot| + |c06fpf| |f01bsf| |raisePolynomial| |every?| |integralMatrix| |acsch| + |double?| |compose| |semiSubResultantGcdEuclidean1| |karatsuba| + |getBadValues| |generalTwoFactor| |nary?| |associatedSystem| + |rightOne| |limit| |resultantReduitEuclidean| |rootsOf| |algintegrate| + |d02raf| |pointColorDefault| |subscriptedVariables| |OMconnOutDevice| + |generic?| |byteBuffer| |bfEntry| |cTanh| |null| |uniform01| |or?| + |clearTable!| |f04mcf| |extendedIntegrate| |initiallyReduced?| + |innerint| |getCode| |singularAtInfinity?| |useEisensteinCriterion?| + |extendedint| |not| |stoseInternalLastSubResultant| |f04adf| + |overset?| |acothIfCan| |dim| |simplifyLog| |extractTop!| |implies| + |d02gbf| |wordInStrongGenerators| |and| |se2rfi| |Is| |mathieu11| + |untab| |eigenvalues| |rotatez| |commaSeparate| |getGoodPrime| + |anfactor| |or| |exprHasAlgebraicWeight| |diagonal?| |c06ebf| + |halfExtendedSubResultantGcd1| |conjug| |diagonals| |outputFloating| + |nextsousResultant2| |stopTable!| |xor| |nextPrime| |integerBound| + |Nul| |overlabel| |userOrdered?| |front| |parametric?| |setLength!| + |elseBranch| |indicialEquation| |case| |monomRDE| |multiEuclideanTree| + |cCot| |isobaric?| |prepareSubResAlgo| |graphCurves| |quatern| + |mainVariables| |round| |Zero| |symbolTable| |OMParseError?| |term?| + |iiatanh| |associative?| |readLineIfCan!| |wholeRagits| + |basisOfMiddleNucleus| |certainlySubVariety?| |viewDeltaYDefault| + |One| |baseRDE| |startTableInvSet!| |/\\| |SturmHabichtCoefficients| + |permutation| |rightTrace| |OMputAttr| |less?| + |semiResultantEuclideannaif| |asecIfCan| |ode1| |localUnquote| + |useNagFunctions| |\\/| |buildSyntax| |edf2df| |shiftLeft| + |var2StepsDefault| |OMsupportsCD?| |primPartElseUnitCanonical| + |arguments| |elementary| |bandedJacobian| |ratpart| + |definingEquations| |s20acf| |subtractIfCan| |thetaCoord| + |getOperands| |key| |connect| |csubst| |prod| |divideIfCan| + |represents| |lazy?| |e01sef| |conjugate| |c06ekf| |center| + |increment| |resetAttributeButtons| |upperCase| |quadratic?| |cCsc| + |whitePoint| |inverseIntegralMatrixAtInfinity| |filename| |palglimint| + |mapGen| |root| |splitNodeOf!| |rk4qc| |outputAsTex| |elt| |csc2sin| + |multiplyCoefficients| |log2| |primintegrate| |npcoef| |crest| |not?| + |second| |selectOptimizationRoutines| |vspace| |cycles| + |oddInfiniteProduct| |range| |mainCoefficients| |palgLODE0| + |irreducibleFactor| |parse| |third| |mainContent| |cyclicEqual?| + |style| |tensorProduct| |linearAssociatedOrder| + |pushFortranOutputStack| |coefChoose| |createIrreduciblePoly| + |factorAndSplit| |f02bjf| |setelt!| |cross| |computeBasis| |modTree| + |orOperands| |popFortranOutputStack| |leftDivide| |lazyPseudoDivide| + |univariatePolynomials| |clearTheFTable| |limitedint| + |sizePascalTriangle| |balancedBinaryTree| |inR?| |diag| |split| |cup| + |removeSinSq| |cylindrical| |errorKind| |queue| |createThreeSpace| + |lyndon| |maxrow| |normalDenom| |lazyVariations| |setprevious!| + |setProperties!| |splitSquarefree| |factorials| |outputFixed| + |expintfldpoly| |getlo| |shuffle| |innerSolve1| |numberOfComposites| + |bits| |hcrf| |minPoints3D| |expr| |totalLex| |complexNormalize| + |cAtanh| |goto| |fixedPoints| |lepol| |sec2cos| |fillPascalTriangle| + |genericRightTraceForm| |cAcsch| |cAcosh| |explogs2trigs| + |atrapezoidal| |sqfrFactor| |clearTheSymbolTable| |shrinkable| + |tan2trig| |systemCommand| |kind| |OMputFloat| |f02axf| + |primPartElseUnitCanonical!| |transcendenceDegree| + |basisOfRightAnnihilator| |safeFloor| |principalIdeal| |escape| + |setClipValue| |c05pbf| |op| |highCommonTerms| |leftMinimalPolynomial| + |interval| |cCoth| |rightAlternative?| |minPol| |integer?| + |permutationRepresentation| |subNodeOf?| |stack| |oblateSpheroidal| + |cCosh| |createGenericMatrix| |variable| |dn| |symmetricTensors| + |rightMinimalPolynomial| |minimumDegree| |move| |doubleResultant| + |integralAtInfinity?| |normal| |cAsinh| |clearTheIFTable| |iterators| + |primitivePart| |computePowers| |extractIndex| |hermite| |f04maf| + |nextLatticePermutation| |complex?| |repeating?| |linearAssociatedLog| + |semiResultantEuclidean1| |leftGcd| |makeResult| |index| + |returnTypeOf| |indiceSubResultantEuclidean| |groebnerFactorize| + |lambert| |physicalLength| |degreeSubResultantEuclidean| |mainForm| + |pr2dmp| |completeSmith| |genericLeftTrace| |ddFact| |symbolTableOf| + |unaryFunction| |stronglyReduce| |singular?| |toseInvertible?| + |solveLinearPolynomialEquationByRecursion| |callForm?| |ceiling| + |partialQuotients| |s01eaf| |lifting| |loadNativeModule| |moduleSum| + |adjoint| |makeSin| |showTheFTable| |reify| |sinhIfCan| |union| + |number?| |leftUnit| |pair| |viewWriteDefault| |c06gbf| |pow| + |diagonalMatrix| |indices| |viewPosDefault| |specialTrigs| + |chineseRemainder| |trigs| |palglimint0| |terms| + |selectSumOfSquaresRoutines| |infiniteProduct| |triangularSystems| + |principalAncestors| |reopen!| |makeTerm| |alphanumeric| |generalSqFr| + |decimal| |rowEch| |hasHi| |measure2Result| |setEpilogue!| + |complexSolve| |lastSubResultantEuclidean| |stoseLastSubResultant| + |linearPart| |chebyshevU| |normalise| |OMcloseConn| |numberOfHues| + |dimensionsOf| |dequeue| |double| |outputSpacing| |rightTraceMatrix| + |value| |characteristicPolynomial| |ipow| |square?| |horizConcat| + |shade| |getGraph| |c06eaf| |adaptive?| |f02fjf| |factorSquareFree| + |nullary?| |setRealSteps| |seriesSolve| |newReduc| |f04arf| + |antiCommutative?| |alphanumeric?| |leftRankPolynomial| |makeFR| + |tubeRadiusDefault| |complexExpand| |enterPointData| |cosh2sech| + |conditionsForIdempotents| |iCompose| |cSin| |edf2efi| |hex| |s21bcf| + |interpolate| |getDatabase| |OMputSymbol| |supersub| |tablePow| + |simpson| |elColumn2!| |stirling1| |gradient| |tab| + |algebraicVariables| |setAdaptive| |cyclotomic| |exponential| + |normalize| |localIntegralBasis| |e02bbf| |setleaves!| |solveRetract| + |decrease| |tube| |droot| |contains?| |selectODEIVPRoutines| + |commutativeEquality| |changeVar| |rule| |high| |nullSpace| + |associatedEquations| |removeIrreducibleRedundantFactors| + |primlimitedint| |nativeModuleExtension| |say| |removeConstantTerm| + |int| |setRow!| |monicDivide| |polynomialZeros| |discriminant| + |systemSizeIF| |singularitiesOf| |nthRoot| |declare!| |c06fqf| + |e02dcf| |duplicates?| |is?| |readLine!| |multiEuclidean| + |factorSFBRlcUnit| |bitCoef| |cAsec| |viewport2D| |readByte!| + |writeBytes!| |screenResolution3D| |rootRadius| |rootBound| + |firstDenom| |enterInCache| |cTan| |iisqrt3| |notOperand| |f02xef| + |intersect| |hitherPlane| |HermiteIntegrate| |OMputEndError| + |setLegalFortranSourceExtensions| |contours| |bothWays| |graeffe| + |att2Result| |imaginary| |useEisensteinCriterion| |e04naf| + |meshPar2Var| |radix| |e02bcf| |quoByVar| |nthr| |cCsch| |mirror| + |middle| |intensity| |OMgetEndBVar| |univariatePolynomialsGcds| + |structuralConstants| |variationOfParameters| |setFormula!| + |linearDependence| |bracket| |orbits| |subTriSet?| |void| |directory| + |reset| |subst| |symmetricDifference| |ocf2ocdf| + |extendedSubResultantGcd| |startTable!| |d02gaf| |rowEchLocal| + |supRittWu?| |lowerPolynomial| |outlineRender| |determinant| + |writeByte!| |getMatch| |resultantnaif| |linearlyDependent?| |slash| + |constantRight| |segment| |f02bbf| |rombergo| |write| + |outputAsFortran| |coefficient| |times!| |stoseInvertible?sqfreg| + |controlPanel| |reverse| 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|chainSubResultants| + |triangular?| |iitan| |d01gaf| |recolor| |nonLinearPart| |localAbs| + |d01amf| |pointColorPalette| |normDeriv2| |totalDegree| |iiasin| + |s17adf| |iiasech| |flatten| |e01bef| |laguerre| |hasTopPredicate?| + |iibinom| |mathieu24| |factor1| |ratDsolve| |open?| |isOpen?| + |rightZero| |concat| |node?| |rootDirectory| |iisin| + |createPrimitiveNormalPoly| |squareFreeLexTriangular| |GospersMethod| + |perfectSqrt| |trunc| |tanhIfCan| |top| |even?| |prime?| + |lineColorDefault| |minGbasis| |nthFactor| |prem| |coefficients| + |convergents| |trailingCoefficient| |column| |trapezoidalo| + |firstUncouplingMatrix| |ref| |definingInequation| |domainOf| + |getZechTable| |constantCoefficientRicDE| |child| |true| + |laurentIfCan| |f01ref| |insertionSort!| |ffactor| |constantOpIfCan| + |eulerPhi| |mainCharacterization| |identitySquareMatrix| |getRef| + |maxdeg| |OMencodingXML| |radicalEigenvalues| |bringDown| |multisect| + |linear?| |mainExpression| |modularGcdPrimitive| |denomLODE| + |lowerCase| |fortranLogical| |factorGroebnerBasis| |s13adf| |exQuo| + |currentScope| |divisorCascade| |maxIndex| |functionIsOscillatory| + |f07aef| |mvar| |euclideanNormalForm| |central?| |physicalLength!| + |LazardQuotient| |ramified?| |s18aef| |previous| + |useSingleFactorBound| |bezoutResultant| |c06fuf| |collectUnder| + |exp1| |internalDecompose| |printInfo| |bumprow| |leadingIndex| + |zero?| |outputMeasure| |outerProduct| |nthExpon| |minColIndex| + |contract| |bernoulli| |signature| |logical?| |parent| |meshPar1Var| + |internalSubPolSet?| |rootOfIrreduciblePoly| |varList| |pToDmp| + |tanh2trigh| |setCondition!| |pmComplexintegrate| |cotIfCan| |chvar| + |fi2df| |OMread| |finiteBound| |infinityNorm| |dfRange| |connectTo| + |adaptive3D?| |algebraicCoefficients?| |weakBiRank| |distdfact| + |external?| |fortranCharacter| |semiSubResultantGcdEuclidean2| + |rightGcd| |packageCall| |space| |close!| |linGenPos| |subPolSet?| + |subMatrix| |acosIfCan| |redPo| |consnewpol| 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|fortranLiteralLine| |zag| |makeYoungTableau| |extendIfCan| + |goodPoint| |ScanFloatIgnoreSpaces| |leftTraceMatrix| |Or| + |removeRedundantFactors| |forLoop| |unitVector| |digit?| |OMgetFloat| + |cond| |bombieriNorm| |OMopenString| |alternatingGroup| |augment| + |Not| |block| |normInvertible?| |constantOperator| + |sumOfKthPowerDivisors| |cubic| |rationalIfCan| |twist| |mkIntegral| + |doubleDisc| |zCoord| |asechIfCan| |stoseIntegralLastSubResultant| + |OMgetString| |setAttributeButtonStep| |sech2cosh| + |rangePascalTriangle| |plus| |wholePart| F2FG |OMputBVar| + |patternVariable| |viewpoint| |mindeg| |toroidal| + |cyclotomicDecomposition| |imagJ| |realElementary| |roughEqualIdeals?| + |iiGamma| |internalAugment| |integralRepresents| |cschIfCan| |zeroOf| + |perfectNthPower?| |OMgetEndApp| |setStatus!| |cosh| |noKaratsuba| + |polyred| |setColumn!| |stoseInvertibleSetsqfreg| + |rightFactorCandidate| |besselY| |log10| |inverseLaplace| |cscIfCan| + |tanh| |setClosed| |showRegion| |solveLinearlyOverQ| |extension| + |internalInfRittWu?| |makeCrit| |pointLists| |max| + |lastSubResultantElseSplit| |atom?| |leftRank| |biRank| |leftUnits| + |bitand| |f07fef| |OMgetBind| |coth| |times| |csch2sinh| |kmax| + |radicalEigenvector| |quartic| |extractIfCan| |overlap| |isQuotient| + |generalizedInverse| |besselJ| |bitior| |OMputObject| |bumptab| |sech| + |stronglyReduced?| |cycleElt| |genericPosition| |cyclicEntries| + |subSet| |addPoint2| |eq?| |numberOfOperations| |bottom!| |laplacian| + |setPoly| |csch| |pToHdmp| |basisOfRightNucleus| |swap!| |bag| + |pointSizeDefault| |unit| |linears| |exponential1| |characteristicSet| + |asinh| |possiblyInfinite?| |normalized?| |e02ddf| |mpsode| + |bivariatePolynomials| |showAll?| |combineFeatureCompatibility| + |iiacot| |uniform| |integral| |subResultantChain| |acosh| |monom| + |qualifier| |showTheIFTable| |zeroSetSplit| |quasiMonic?| + |SturmHabichtSequence| |dihedral| |resultant| |nonSingularModel| + |commutative?| |palgint0| |atanh| |createZechTable| |firstSubsetGray| + |saturate| |expandTrigProducts| |dominantTerm| |height| + |radicalOfLeftTraceForm| |polygon| |binaryFunction| + |subResultantGcdEuclidean| |acoth| |leaf?| |nextSubsetGray| |quoted?| + |newSubProgram| |solveLinearPolynomialEquationByFractions| |hdmpToP| + |cn| |cap| |common| |exprex| |d01apf| |s13acf| |invmultisect| + |semiIndiceSubResultantEuclidean| |asech| |factorsOfCyclicGroupSize| + |rename!| |dimension| |ellipticCylindrical| |toseSquareFreePart| + |pointColor| |readBytes!| |maxRowIndex| |traverse| |tree| |merge!| + |contractSolve| |trueEqual| |sin?| |processTemplate| |s19acf| + |mapmult| |setPosition| |rangeIsFinite| |iisech| |declare| |bounds| + |noncommutativeJordanAlgebra?| |multiple| |s21bdf| |hdmpToDmp| + |extractClosed| UTS2UP |laguerreL| |debug| |quickSort| |one?| + |increasePrecision| |zeroDim?| |fracPart| |applyQuote| + |balancedFactorisation| |baseRDEsys| |bernoulliB| |rspace| D |child?| + |tValues| |postfix| |ListOfTerms| |mesh?| 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|rename| |makeFloatFunction| |polygamma| |unrankImproperPartitions0| + |lookup| |f02awf| |branchPointAtInfinity?| |positive?| + |functionIsContinuousAtEndPoints| |plenaryPower| |implies?| |tanSum| + |reducedForm| |cyclotomicFactorization| |sechIfCan| |ignore?| + |ODESolve| |inspect| |prindINFO| |vector| F |numFunEvals3D| + |magnitude| |minPoly| |exprToGenUPS| |separateFactors| |infinite?| + |fortranComplex| |cycleTail| |primintfldpoly| |closedCurve| |print| + |startTableGcd!| |generators| |cAsin| |OMReadError?| |lflimitedint| + |setValue!| |iisec| |imagI| |lexTriangular| |e02ajf| |resolve| + |lazyGintegrate| |differentiate| |bivariate?| |palgintegrate| + |components| |notelem| |polCase| |multiplyExponents| |c06ecf| |OMsend| + |countRealRootsMultiple| |direction| |basisOfCenter| |d01anf| + |resetBadValues| |dequeue!| |palgextint0| |d03faf| |radicalSimplify| + |indiceSubResultant| |decomposeFunc| |OMconnectTCP| |s14baf| + |normal01| |printStats!| |optAttributes| |rst| |bindings| + |companionBlocks| |rotatey| |solveid| |LiePoly| |name| + |absolutelyIrreducible?| |graphStates| |SturmHabicht| + |parabolicCylindrical| |changeNameToObjf| |constantToUnaryFunction| + |LyndonBasis| |iFTable| |ptFunc| |body| |finiteBasis| |pole?| + |parents| |inputOutputBinaryFile| |lfinfieldint| |pair?| + |var1StepsDefault| |xn| |palgRDE| |sin2csc| |trigs2explogs| |c06gqf| + |chiSquare1| |pseudoRemainder| |prinpolINFO| |retractable?| + |schwerpunkt| |pop!| ** |maximumExponent| |box| |dmp2rfi| + |maxPoints3D| |outputBinaryFile| |stop| |imports| |rightExactQuotient| + |showTheRoutinesTable| |f01qef| |withPredicates| ~ |alternating| + |insert| |tableau| |LiePolyIfCan| |polar| |invertibleSet| |solid| + |generateIrredPoly| |primes| |removeZero| |cfirst| |precision| + |sinIfCan| |OMputEndAttr| |OMgetEndBind| |pile| |mat| EQ + |showIntensityFunctions| |constant?| |rootPoly| |leadingSupport| + |open| |condition| |rowEchelonLocal| |flagFactor| + |rightRankPolynomial| |inRadical?| |integralDerivationMatrix| |cSech| + |basisOfLeftNucloid| |twoFactor| |prinshINFO| |OMencodingSGML| + |mkPrim| |level| |port| |zeroMatrix| |linearDependenceOverZ| |linear| + |algebraicSort| |listexp| |fractRadix| |rational| |eigenMatrix| + |transcendent?| |mapMatrixIfCan| |replace| |unit?| |eq| + |matrixDimensions| |pushup| |denominators| |numberOfPrimitivePoly| + |rootPower| |generalizedEigenvector| |iter| |shift| |t| |nullity| + |monomials| |reduceByQuasiMonic| |polynomial| |numberOfChildren| + |s19aaf| |point| |getExplanations| |univariateSolve| |f01qdf| + |abelianGroup| |quasiAlgebraicSet| |nilFactor| |addmod| |compdegd| + |OMlistCDs| |mulmod| |cosSinInfo| |select!| |makeSeries| + |getVariableOrder| |vedf2vef| |associator| |OMreadStr| |leftPower| + |iprint| |factorSquareFreePolynomial| |powerSum| |hasSolution?| + |category| |top!| |modularFactor| |odd?| |lSpaceBasis| |f2st| + |reorder| |series| |linearPolynomials| |infieldint| |property| + |domain| |truncate| |createMultiplicationMatrix| |numFunEvals| + |separant| |redPol| |dimensions| |permutations| |badNum| |package| + |submod| |taylorQuoByVar| |squareFree| |OMreadFile| |clearCache| + |s13aaf| |LagrangeInterpolation| |createNormalPrimitivePoly| |f04asf| + |identification| |distFact| |isExpt| |mathieu12| |iiasec| |makeSUP| + |OMputEndApp| |getOrder| |units| |cAcos| |getSyntaxFormsFromFile| + |exp| |generalLambert| |expPot| |min| |atoms| |iiacoth| |fmecg| + |fractionFreeGauss!| |initializeGroupForWordProblem| + |factorPolynomial| |logpart| |prolateSpheroidal| |identity| |makeCos| + |ranges| |mix| |any| |inrootof| |numerator| |super| |legendre| + |totolex| |unrankImproperPartitions1| |lfextendedint| + |halfExtendedResultant2| |shellSort| |recip| |hypergeometric0F1| + |expextendedint| |nthExponent| |nthFlag| |reduction| |output| + |compile| |e04ucf| |printCode| |fprindINFO| |maxrank| + |partialNumerators| |operator| |cot2tan| |code| |exprToUPS| + |matrixGcd| |showTypeInOutput| |leastAffineMultiple| |externalList| + |principal?| |OMgetInteger| |printingInfo?| |setProperty| + |nextNormalPrimitivePoly| |e04gcf| |parseString| |rightRecip| + |stoseInvertibleSet| |corrPoly| |sequences| |#| |meshFun2Var| + |rightDivide| |iicot| |argumentListOf| |doubleComplex?| |coordinate| + |bfKeys| |minimize| |algDsolve| |tanintegrate| |removeCosSq| + |knownInfBasis| |inHallBasis?| |OMgetObject| |dom| |minRowIndex| + |setOrder| |getMultiplicationMatrix| |in?| |incrementBy| |isOp| + |changeName| |numeric| |extract!| |sumOfSquares| |mapExponents| + |transcendentalDecompose| |psolve| |regime| |rischDEsys| |expand| + |radical| |positiveRemainder| |critB| |f04axf| |node| |lexico| |tanAn| + |prepareDecompose| |filterWhile| |scalarMatrix| + |genericLeftMinimalPolynomial| |torsion?| |unvectorise| + |makeViewport2D| |groebner?| |s17agf| |filterUntil| |fortranTypeOf| + |coshIfCan| |moebius| |deleteRoutine!| |ldf2vmf| |conditionP| + |pushuconst| |solveInField| |setTex!| |select| |sncndn| |dioSolve| + |rootOf| |brillhartTrials| |numberOfNormalPoly| |title| |localReal?| + |drawStyle| |groebgen| |options| |standardBasisOfCyclicSubmodule| + |nextsubResultant2| |euclideanSize| |pointPlot| |parts| + |generalizedContinuumHypothesisAssumed?| |internalIntegrate| |head| + |zeroDimPrimary?| |OMserve| |unravel| |coerceL| |dictionary| + |andOperands| |boundOfCauchy| |getProperties| |subspace| |normal?| + |axes| |increase| |scripted?| |leviCivitaSymbol| |rightNorm| |e| + |initial| |expenseOfEvaluationIF| |mainMonomials| |stFunc2| |string| + |dimensionOfIrreducibleRepresentation| |karatsubaDivide| + |integralMatrixAtInfinity| |binomial| |fortranLiteral| + |normalizeIfCan| |reducedSystem| |plusInfinity| |iisinh| |s17dgf| + |FormatArabic| |meatAxe| |s14abf| |content| |gcdprim| |perspective| + |gcdcofact| |makeRecord| |minusInfinity| |product| |ParCond| |length| + |leftTrace| |blue| |graphState| |resize| |clipBoolean| |s18aff| + |newLine| |linkToFortran| |mappingAst| |scripts| |rotatex| |d01gbf| + |simplifyPower| |patternMatch| |ratDenom| |heapSort| |rootKerSimp| + |curveColor| |changeWeightLevel| |mapExpon| |isTimes| |Ei| + |crushedSet| FG2F |OMputInteger| |weight| |power!| |ScanArabic| + |colorFunction| |iomode| |predicate| |cPower| |messagePrint| + |leadingBasisTerm| |leftOne| |var2Steps| |stirling2| |minPoints| + |rationalApproximation| |tanNa| |removeRoughlyRedundantFactorsInPol| + |kroneckerDelta| |definingPolynomial| |OMgetEndAttr| + |sylvesterSequence| |exprHasLogarithmicWeights| |recur| + |selectNonFiniteRoutines| |nodeOf?| |elRow2!| |numberOfComponents| + |hyperelliptic| |permutationGroup| |insert!| |cLog| |e04ycf| |type| + |equation| |safetyMargin| |OMwrite| |cCos| |multiset| + |resultantEuclideannaif| |create3Space| |complexRoots| |divergence| + |iidprod| |hclf| |palgextint| |sylvesterMatrix| |janko2| + |rightRegularRepresentation| |closeComponent| |width| |inf| + |setMaxPoints| |secIfCan| |deepestTail| |jacobiIdentity?| |pdf2ef| + |complexForm| |simplify| |laurentRep| |flexible?| |sort!| |entry?| + |showAllElements| |LyndonWordsList1| |compiledFunction| |variable?| + |list| |genericLeftDiscriminant| |harmonic| |basis| + |rewriteIdealWithHeadRemainder| |beauzamyBound| |LowTriBddDenomInv| + |any?| |fortranCompilerName| |besselK| |taylorRep| |car| + |setMinPoints3D| |init| |primlimintfrac| |endSubProgram| |transform| + |pushucoef| |leader| |rationalPoints| |e02adf| |findBinding| + |conjugates| |cdr| |character?| |medialSet| |parameters| |arg1| + |varselect| |ricDsolve| |basisOfRightNucloid| |recoverAfterFail| + |Aleph| |setDifference| |antisymmetricTensors| + |removeSuperfluousCases| |more?| |curryRight| |mathieu23| |arg2| + |completeEchelonBasis| |abs| |fortranDouble| |rightRemainder| + |divisors| |Ci| |aspFilename| |accuracyIF| |d03eef| |stopMusserTrials| + |Gamma| |nthRootIfCan| |push!| |solveLinear| |nthCoef| + |genericLeftTraceForm| |iicosh| |f02abf| |conditions| |optional| + |directSum| |term| |largest| LODO2FUN |isPower| |c06gsf| + |flexibleArray| |cSinh| |removeDuplicates!| |mindegTerm| |match| + |tanQ| |sizeMultiplication| |mergeDifference| |over| |result| + |shiftRight| |tanIfCan| |mapBivariate| |d02kef| |s17def| |oddintegers| + |delta| |substring?| |relativeApprox| |resetVariableOrder| + |decreasePrecision| |compound?| |properties| |wronskianMatrix| + |rational?| |clearDenominator| |commutator| |OMputVariable| + |OMconnInDevice| |zerosOf| |useSingleFactorBound?| |wreath| + |pseudoDivide| |translate| |OMgetError| |d03edf| |minset| |conical| + |stiffnessAndStabilityOfODEIF| |getMultiplicationTable| |suffix?| + |generic| |ksec| |symmetricPower| |calcRanges| |morphism| |iicos| + |viewSizeDefault| |writable?| |curve?| |logGamma| |pattern| |hspace| + |tryFunctionalDecomposition?| |subscript| |quasiRegular| |rotate!| + |lquo| |nextPrimitivePoly| |f01maf| |prefix?| |iilog| |rightQuotient| + |triangulate| |revert| |s17ajf| |sn| |fractionPart| |iipow| + |pmintegrate| |elRow1!| |row| |upperCase?| |leftNorm| SEGMENT + |cyclic?| |getIdentifier| |curve| |homogeneous?| |Lazard2| + |numberOfFactors| |unexpand| |strongGenerators| |subQuasiComponent?| + |completeHermite| |semiResultantEuclidean2| |HenselLift| |setfirst!| + |OMgetType| |infRittWu?| |lambda| |message| |wrregime| |solve| + |gramschmidt| |closed?| |iidsum| |purelyTranscendental?| |lfunc| + |maxPoints| |weights| |evaluateInverse| |createMultiplicationTable| + |aromberg| |f02akf| |s17dhf| |neglist| |torsionIfCan| |Beta| + |semiResultantReduitEuclidean| |leaves| |f2df| |shallowExpand| + |iicsch| |outputAsScript| |semiLastSubResultantEuclidean| + |hostPlatform| |nextIrreduciblePoly| |rightRank| |f01mcf| + |setchildren!| |f01qcf| |OMUnknownCD?| |infix?| |iiacsch| |fixedPoint| + |approxSqrt| |nonQsign| |interpret| |subset?| |makeVariable| + |ReduceOrder| |pleskenSplit| |nthFractionalTerm| |mask| |binding| + |d02ejf| |rootProduct| |thenBranch| |parabolic| |padicallyExpand| + |chiSquare| |e01daf| |scale| |d01alf| |numericalOptimization| + |henselFact| |viewPhiDefault| |UP2ifCan| |mantissa| |complexLimit| + |swapColumns!| |hessian| |cons| |rightPower| |realEigenvalues| + |e01baf| |normalizedAssociate| |invertIfCan| |subNode?| + |subresultantSequence| |exponents| |socf2socdf| + |rewriteSetByReducingWithParticularGenerators| |retract| |surface| + |bumptab1| |error| |lintgcd| |minrank| |quote| |shufflein| |dark| + |algSplitSimple| |idealiserMatrix| |moreAlgebraic?| |just| + |lazyResidueClass| |cyclic| |octon| |assert| |innerSolve| + |branchIfCan| |status| |bright| |Lazard| |padicFraction| + |splitDenominator| |degreePartition| |redpps| |basisOfLeftAnnihilator| + |viewThetaDefault| |leastMonomial| |modifyPointData| |mr| + |coordinates| |sumOfDivisors| |listOfLists| |divideIfCan!| |optpair| + |write!| |minIndex| |badValues| |lprop| |printInfo!| |d02cjf| + |listBranches| |sturmSequence| |changeBase| |getProperty| |sh| + |movedPoints| |quasiRegular?| |computeCycleLength| |linearMatrix| + |source| |removeSquaresIfCan| |enqueue!| |erf| |complexEigenvalues| + |dec| NOT |OMclose| |symbol?| |toseLastSubResultant| |remove!| + |d02bhf| |qfactor| |mightHaveRoots| |fglmIfCan| |UpTriBddDenomInv| + |iiperm| |categories| OR |e01bgf| |extractSplittingLeaf| + |complexElementary| ~= |bandedHessian| |arity| |typeList| + |tracePowMod| |df2fi| |retractIfCan| |constantKernel| AND |Vectorise| + |invertibleElseSplit?| |coerce| |check| |mapCoef| |dilog| |jacobian| + |isConnected?| |reverseLex| |basisOfNucleus| |numer| |construct| + |expandLog| |headReduced?| |pseudoQuotient| |whileLoop| + |showClipRegion| |basisOfCommutingElements| |countable?| |redmat| + |lowerCase!| |sin| |nand| |fortranReal| |RemainderList| |denom| + |squareFreePolynomial| |solve1| |infix| |iiatan| |categoryFrame| + |f07adf| |target| |radicalSolve| |cos| |sumSquares| |putGraph| + |duplicates| |prologue| |whatInfinity| |splitConstant| |sqfree| + |mapSolve| |leftRecip| |tan| |intermediateResultsIF| + |fortranDoubleComplex| |pi| |makeop| |xCoord| |asimpson| |integers| + |mdeg| |cot| |continue| |reverse!| |SturmHabichtMultiple| |iisqrt2| + |clipPointsDefault| |infinity| |universe| |iiacosh| + |functionIsFracPolynomial?| |rightExtendedGcd| |normalizedDivide| + |sec| |numerators| |member?| |paraboloidal| |realRoots| |ScanRoman| + |s18dcf| |elements| |lex| |complexNumericIfCan| |csc| + |seriesToOutputForm| |colorDef| |copies| |failed?| |upDateBranches| + |mainSquareFreePart| |returns| |inc| |lifting1| |asin| + |curveColorPalette| |componentUpperBound| |deepExpand| |kernel| + |unmakeSUP| |extractBottom!| |iicoth| |e02agf| |f02adf| |ravel| + |e04jaf| |acos| |headReduce| |critMTonD1| |map| |updatF| * |draw| + |completeHensel| |s15aef| |ldf2lst| |phiCoord| |create| + |numberOfDivisors| |reshape| |f01brf| |atan| |setFieldInfo| + |monicModulo| |exportedOperators| |explimitedint| |gethi| + |stosePrepareSubResAlgo| |sincos| |nextSublist| |dmpToP| |acot| + |equivOperands| |setOfMinN| |regularRepresentation| |clipParametric| + |deriv| |selectPDERoutines| |asec| |extensionDegree| |char| + |identityMatrix| |setsubMatrix!| |validExponential| + |doubleFloatFormat| |mathieu22| |has?| |pol| |OMgetAttr| |acsc| + |coHeight| |f04qaf| |order| |stiffnessAndStabilityFactor| |resetNew| + |makeObject| |setelt| |isAbsolutelyIrreducible?| |eof?| |pointData| + |iroot| |sinh| |concat!| |convert| |readable?| |lazyEvaluate| |hue| + |red| |rootSplit| |multinomial| |setVariableOrder| |update| + |leastPower| |s19adf| |relerror| |squareFreePrim| |copy| |coef| + |removeRoughlyRedundantFactorsInPols| |scaleRoots| |f02aaf| |ridHack1| + |subCase?| |reduceBasisAtInfinity| |OMputAtp| |exponent| |rightLcm| + |part?| |genus| |superHeight| |getStream| |rur| |hconcat| |rdHack1| + |float| |digit| |tableForDiscreteLogarithm| |push| |insertTop!| + |logIfCan| |lllip| |deepCopy| |expintegrate| |d01aqf| |expt| + |monicRightFactorIfCan| |autoCoerce| |df2mf| |unparse| |s19abf| + |discriminantEuclidean| |inverse| |failed| |pdf2df| |OMmakeConn| + |lazyPseudoRemainder| |univariatePolynomial| |selectfirst| + |leadingExponent| |groebner| |lyndon?| |f01rcf| |prime| |match?| + |position| |assign| |commonDenominator| |LyndonWordsList| RF2UTS + |padecf| |cExp| |e02baf| |addMatchRestricted| |multMonom| + |countRealRoots| |innerEigenvectors| |antisymmetric?| |setLabelValue| + |aCubic| |mainPrimitivePart| |clipWithRanges| |extendedEuclidean| + |plot| |rischNormalize| |split!| |youngGroup| |children| |iifact| + |characteristic| |monomialIntegrate| |position!| |complexZeros| + |fortranCarriageReturn| |shiftRoots| |setTopPredicate| |coerceS| + |lazyIrreducibleFactors| |sorted?| |printHeader| |triangSolve| + |typeLists| |bitLength| |matrixConcat3D| |algint| |aLinear| + |numberOfIrreduciblePoly| |imagk| |normalForm| |radicalRoots| + |approximants| |approxNthRoot| |factors| |monicCompleteDecompose| + |makeEq| |Frobenius| |comp| |rischDE| |setEmpty!| GE |quadraticNorm| + |rightScalarTimes!| |normalDeriv| |lhs| |difference| |rationalPoint?| + |simpsono| |ord| |OMgetBVar| |explicitEntries?| |opeval| |makeprod| GT + |critpOrder| |hermiteH| |invmod| |rhs| |addPoint| |repSq| + |eyeDistance| |completeEval| |weighted| |next| |lighting| |randomR| + |routines| LE |leftScalarTimes!| |headRemainder| |reducedDiscriminant| + |lllp| |setButtonValue| |defineProperty| |doublyTransitive?| + |endOfFile?| |mapUp!| |alternative?| LT |summation| + |normalizeAtInfinity| |swap| |sparsityIF| |spherical| |removeSinhSq| + |modularGcd| |pade| |isMult| |bubbleSort!| |lyndonIfCan| |powers| + |updateStatus!| |elliptic?| |stFunc1| |leadingTerm| |qelt| + |trapezoidal| |legendreP| |symbolIfCan| |log| |e01bhf| |normFactors| + |generalizedEigenvectors| |nil?| |eigenvector| |qsetelt| + |cyclicParents| |e01sbf| |selectAndPolynomials| |imagi| + |halfExtendedSubResultantGcd2| |singRicDE| |vconcat| + |stoseInvertible?reg| |loopPoints| |cycleSplit!| |unknown| |pastel| + |jordanAlgebra?| |deepestInitial| |f02wef| |xRange| |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=(-406 (-558))) -3994 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-38 |#1|) . T) ((-38 $) -3994 (|has| |#1| (-550)) (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-35) |has| |#1| (-1185)) ((-95) |has| |#1| (-1185)) ((-102) . T) ((-111 #0# #0#) -3994 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-130) . T) ((-144) -3994 (|has| |#1| (-348)) (|has| |#1| (-144))) ((-146) |has| |#1| (-146)) ((-608 #0#) -3994 (|has| |#1| (-1028 (-406 (-558)))) (|has| |#1| (-348)) (|has| |#1| (-362))) ((-608 (-558)) . T) ((-608 |#1|) . T) ((-608 $) -3994 (|has| |#1| (-550)) (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-605 (-853)) . T) ((-171) . T) ((-606 (-168 (-224))) |has| |#1| (-1012)) ((-606 (-168 (-378))) |has| |#1| (-1012)) ((-606 (-534)) |has| |#1| (-606 (-534))) ((-606 (-882 (-378))) |has| |#1| (-606 (-882 (-378)))) ((-606 (-882 (-558))) |has| |#1| (-606 (-882 (-558)))) ((-606 #1=(-1159 |#1|)) . 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T) ((-38 |#2|) |has| |#2| (-171)) ((-102) -3994 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3994 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-111 $ $) |has| |#2| (-171)) ((-130) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130))) ((-608 #0=(-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-608 (-558)) -3994 (|has| |#2| (-1039)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-608 |#2|) -3994 (|has| |#2| (-1087)) (|has| |#2| (-171))) ((-605 (-853)) -3994 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-605 (-853))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-605 (-1246 |#2|)) . T) ((-171) |has| |#2| (-171)) ((-230 |#2|) |has| |#2| (-1039)) ((-232) -12 (|has| |#2| (-232)) (|has| |#2| (-1039))) ((-285 #1=(-558) |#2|) . T) ((-287 #1# |#2|) . T) ((-308 |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-367) |has| |#2| (-367)) ((-376 |#2|) |has| |#2| (-1039)) ((-410 |#2|) |has| |#2| (-1087)) ((-487 |#2|) . T) ((-596 #1# |#2|) . T) ((-512 |#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-638 |#2|) -3994 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-638 $) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-631 (-558)) -12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039))) ((-631 |#2|) |has| |#2| (-1039)) ((-708 |#2|) -3994 (|has| |#2| (-362)) (|has| |#2| (-171))) ((-717) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-782) |has| |#2| (-839)) ((-783) -3994 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-784) |has| |#2| (-784)) ((-785) -3994 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-786) -3994 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-839) |has| |#2| (-839)) ((-841) -3994 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-890 (-1163)) -12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039))) ((-1028 #0#) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-1028 (-558)) -12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) ((-1028 |#2|) |has| |#2| (-1087)) ((-1045 |#2|) -3994 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-1045 $) |has| |#2| (-171)) ((-1039) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1046) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1099) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-1087) -3994 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1200) . 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T) ((-171) |has| |#2| (-171)) ((-230 |#2|) |has| |#2| (-1042)) ((-232) -12 (|has| |#2| (-232)) (|has| |#2| (-1042))) ((-285 #1=(-561) |#2|) . T) ((-287 #1# |#2|) . T) ((-308 |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) ((-367) |has| |#2| (-367)) ((-376 |#2|) |has| |#2| (-1042)) ((-410 |#2|) |has| |#2| (-1090)) ((-487 |#2|) . T) ((-599 #1# |#2|) . T) ((-512 |#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) ((-641 |#2|) -4007 (|has| |#2| (-1042)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-641 $) -4007 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-171))) ((-634 (-561)) -12 (|has| |#2| (-634 (-561))) (|has| |#2| (-1042))) ((-634 |#2|) |has| |#2| (-1042)) ((-711 |#2|) -4007 (|has| |#2| (-362)) (|has| |#2| (-171))) ((-720) -4007 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-720)) (|has| |#2| (-171))) ((-785) |has| |#2| (-842)) ((-786) -4007 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-787) |has| |#2| (-787)) ((-788) -4007 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-789) -4007 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-842) |has| |#2| (-842)) ((-844) -4007 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-893 (-1166)) -12 (|has| |#2| (-893 (-1166))) (|has| |#2| (-1042))) ((-1031 #0#) -12 (|has| |#2| (-1031 (-406 (-561)))) (|has| |#2| (-1090))) ((-1031 (-561)) -12 (|has| |#2| (-1031 (-561))) (|has| |#2| (-1090))) ((-1031 |#2|) |has| |#2| (-1090)) ((-1048 |#2|) -4007 (|has| |#2| (-1042)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-1048 $) |has| |#2| (-171)) ((-1042) -4007 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-171))) ((-1049) -4007 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-171))) ((-1102) -4007 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-720)) (|has| |#2| (-171))) ((-1090) -4007 (|has| |#2| (-1090)) (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-787)) (|has| |#2| (-720)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1205) . 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(-1149 2752172 2753468 2754779 "STTF" 2757539 NIL STTF (NIL T) -7 NIL NIL NIL) (-1148 2746345 2747465 2748612 "STTFNC" 2751072 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1147 2737660 2739527 2741321 "STTAYLOR" 2744586 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1146 2730904 2737524 2737607 "STRTBL" 2737612 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1145 2726295 2730859 2730890 "STRING" 2730895 T STRING (NIL) -8 NIL NIL NIL) (-1144 2721183 2725668 2725698 "STRICAT" 2725757 T STRICAT (NIL) -9 NIL 2725819 NIL) (-1143 2713993 2718802 2719413 "STREAM" 2720607 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1142 2713503 2713580 2713724 "STREAM3" 2713910 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1141 2712485 2712668 2712903 "STREAM2" 2713316 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1140 2712173 2712225 2712318 "STREAM1" 2712427 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1139 2711189 2711370 2711601 "STINPROD" 2711989 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1138 2710767 2710951 2710981 "STEP" 2711061 T STEP (NIL) -9 NIL 2711139 NIL) (-1137 2704310 2710666 2710743 "STBL" 2710748 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1136 2699484 2703531 2703574 "STAGG" 2703727 NIL STAGG (NIL T) -9 NIL 2703816 NIL) (-1135 2697186 2697788 2698660 "STAGG-" 2698665 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1134 2695381 2696956 2697048 "STACK" 2697129 NIL STACK (NIL T) -8 NIL NIL NIL) (-1133 2688106 2693522 2693978 "SREGSET" 2695011 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1132 2680532 2681900 2683413 "SRDCMPK" 2686712 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1131 2673499 2677972 2678002 "SRAGG" 2679305 T SRAGG (NIL) -9 NIL 2679913 NIL) (-1130 2672516 2672771 2673150 "SRAGG-" 2673155 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1129 2667011 2671463 2671884 "SQMATRIX" 2672142 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1128 2660760 2663729 2664456 "SPLTREE" 2666356 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1127 2656750 2657416 2658062 "SPLNODE" 2660186 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1126 2655797 2656030 2656060 "SPFCAT" 2656504 T SPFCAT (NIL) -9 NIL NIL NIL) (-1125 2654534 2654744 2655008 "SPECOUT" 2655555 T SPECOUT (NIL) -7 NIL NIL NIL) (-1124 2646186 2647930 2647960 "SPADXPT" 2652352 T SPADXPT (NIL) -9 NIL 2654386 NIL) (-1123 2645947 2645987 2646056 "SPADPRSR" 2646139 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1122 2644130 2645902 2645933 "SPADAST" 2645938 T SPADAST (NIL) -8 NIL NIL NIL) (-1121 2636101 2637848 2637891 "SPACEC" 2642264 NIL SPACEC (NIL T) -9 NIL 2644080 NIL) (-1120 2634272 2636033 2636082 "SPACE3" 2636087 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1119 2633024 2633195 2633486 "SORTPAK" 2634077 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1118 2631074 2631377 2631796 "SOLVETRA" 2632688 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1117 2630085 2630307 2630581 "SOLVESER" 2630847 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1116 2625305 2626186 2627188 "SOLVERAD" 2629137 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1115 2621120 2621729 2622458 "SOLVEFOR" 2624672 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1114 2615417 2620469 2620566 "SNTSCAT" 2620571 NIL SNTSCAT (NIL T T T T) -9 NIL 2620641 NIL) (-1113 2609560 2613740 2614131 "SMTS" 2615107 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1112 2604011 2609448 2609525 "SMP" 2609530 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1111 2602170 2602471 2602869 "SMITH" 2603708 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1110 2595065 2599221 2599324 "SMATCAT" 2600675 NIL SMATCAT (NIL NIL T T T) -9 NIL 2601225 NIL) (-1109 2592005 2592828 2594006 "SMATCAT-" 2594011 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1108 2589718 2591241 2591284 "SKAGG" 2591545 NIL SKAGG (NIL T) -9 NIL 2591680 NIL) (-1107 2586060 2589134 2589329 "SINT" 2589516 T SINT (NIL) -8 NIL NIL 2589689) (-1106 2585832 2585870 2585936 "SIMPAN" 2586016 T SIMPAN (NIL) -7 NIL NIL NIL) (-1105 2585139 2585367 2585507 "SIG" 2585714 T SIG (NIL) -8 NIL NIL NIL) (-1104 2583977 2584198 2584473 "SIGNRF" 2584898 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1103 2582782 2582933 2583224 "SIGNEF" 2583806 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1102 2582115 2582365 2582489 "SIGAST" 2582680 T SIGAST (NIL) -8 NIL NIL NIL) (-1101 2579805 2580259 2580765 "SHP" 2581656 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1100 2573711 2579706 2579782 "SHDP" 2579787 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1099 2573310 2573476 2573506 "SGROUP" 2573599 T SGROUP (NIL) -9 NIL 2573661 NIL) (-1098 2573168 2573194 2573267 "SGROUP-" 2573272 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1097 2570004 2570701 2571424 "SGCF" 2572467 T SGCF (NIL) -7 NIL NIL NIL) (-1096 2564399 2569451 2569548 "SFRTCAT" 2569553 NIL SFRTCAT (NIL T T T T) -9 NIL 2569592 NIL) (-1095 2557823 2558838 2559974 "SFRGCD" 2563382 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1094 2550951 2552022 2553208 "SFQCMPK" 2556756 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1093 2550573 2550662 2550772 "SFORT" 2550892 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1092 2549718 2550413 2550534 "SEXOF" 2550539 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1091 2548852 2549599 2549667 "SEX" 2549672 T SEX (NIL) -8 NIL NIL NIL) (-1090 2544391 2545080 2545175 "SEXCAT" 2548112 NIL SEXCAT (NIL T T T T T) -9 NIL 2548690 NIL) (-1089 2541571 2544325 2544373 "SET" 2544378 NIL SET (NIL T) -8 NIL NIL NIL) (-1088 2539822 2540284 2540589 "SETMN" 2541312 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1087 2539428 2539554 2539584 "SETCAT" 2539701 T SETCAT (NIL) -9 NIL 2539786 NIL) (-1086 2539208 2539260 2539359 "SETCAT-" 2539364 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1085 2535595 2537669 2537712 "SETAGG" 2538582 NIL SETAGG (NIL T) -9 NIL 2538922 NIL) (-1084 2535053 2535169 2535406 "SETAGG-" 2535411 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1083 2534523 2534749 2534850 "SEQAST" 2534974 T SEQAST (NIL) -8 NIL NIL NIL) (-1082 2533722 2534016 2534077 "SEGXCAT" 2534363 NIL SEGXCAT (NIL T T) -9 NIL 2534483 NIL) (-1081 2532778 2533388 2533570 "SEG" 2533575 NIL SEG (NIL T) -8 NIL NIL NIL) (-1080 2531757 2531971 2532014 "SEGCAT" 2532536 NIL SEGCAT (NIL T) -9 NIL 2532757 NIL) (-1079 2530806 2531136 2531336 "SEGBIND" 2531592 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1078 2530427 2530486 2530599 "SEGBIND2" 2530741 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1077 2530028 2530228 2530305 "SEGAST" 2530372 T SEGAST (NIL) -8 NIL NIL NIL) (-1076 2529247 2529373 2529577 "SEG2" 2529872 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1075 2528684 2529182 2529229 "SDVAR" 2529234 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1074 2520974 2528454 2528584 "SDPOL" 2528589 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1073 2519567 2519833 2520152 "SCPKG" 2520689 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1072 2518703 2518883 2519083 "SCOPE" 2519389 T SCOPE (NIL) -8 NIL NIL NIL) (-1071 2517924 2518057 2518236 "SCACHE" 2518558 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1070 2517596 2517756 2517786 "SASTCAT" 2517791 T SASTCAT (NIL) -9 NIL 2517804 NIL) (-1069 2517110 2517431 2517507 "SAOS" 2517542 T SAOS (NIL) -8 NIL NIL NIL) (-1068 2516675 2516710 2516883 "SAERFFC" 2517069 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1067 2510649 2516572 2516652 "SAE" 2516657 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1066 2510242 2510277 2510436 "SAEFACT" 2510608 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1065 2508563 2508877 2509278 "RURPK" 2509908 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1064 2507199 2507478 2507790 "RULESET" 2508397 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1063 2504386 2504889 2505354 "RULE" 2506880 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1062 2504025 2504180 2504263 "RULECOLD" 2504338 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1061 2503523 2503742 2503836 "RSTRCAST" 2503953 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1060 2498372 2499166 2500086 "RSETGCD" 2502722 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1059 2487629 2492681 2492778 "RSETCAT" 2496897 NIL RSETCAT (NIL T T T T) -9 NIL 2497994 NIL) (-1058 2485556 2486095 2486919 "RSETCAT-" 2486924 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1057 2477943 2479318 2480838 "RSDCMPK" 2484155 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1056 2475948 2476389 2476463 "RRCC" 2477549 NIL RRCC (NIL T T) -9 NIL 2477893 NIL) (-1055 2475299 2475473 2475752 "RRCC-" 2475757 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1054 2474769 2474995 2475096 "RPTAST" 2475220 T RPTAST (NIL) -8 NIL NIL NIL) (-1053 2448775 2458362 2458429 "RPOLCAT" 2469093 NIL RPOLCAT (NIL T T T) -9 NIL 2472252 NIL) (-1052 2440275 2442613 2445735 "RPOLCAT-" 2445740 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1051 2431322 2438486 2438968 "ROUTINE" 2439815 T ROUTINE (NIL) -8 NIL NIL NIL) (-1050 2428155 2430948 2431088 "ROMAN" 2431204 T ROMAN (NIL) -8 NIL NIL NIL) (-1049 2426430 2427015 2427275 "ROIRC" 2427960 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1048 2422823 2425066 2425096 "RNS" 2425400 T RNS (NIL) -9 NIL 2425673 NIL) (-1047 2421332 2421715 2422249 "RNS-" 2422324 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1046 2420781 2421163 2421193 "RNG" 2421198 T RNG (NIL) -9 NIL 2421219 NIL) (-1045 2420173 2420535 2420578 "RMODULE" 2420640 NIL RMODULE (NIL T) -9 NIL 2420682 NIL) (-1044 2419009 2419103 2419439 "RMCAT2" 2420074 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1043 2415886 2418355 2418652 "RMATRIX" 2418771 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1042 2408828 2411062 2411177 "RMATCAT" 2414536 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2415518 NIL) (-1041 2408203 2408350 2408657 "RMATCAT-" 2408662 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1040 2407770 2407845 2407973 "RINTERP" 2408122 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1039 2406903 2407423 2407453 "RING" 2407509 T RING (NIL) -9 NIL 2407595 NIL) (-1038 2406695 2406739 2406836 "RING-" 2406841 NIL RING- (NIL T) -8 NIL NIL NIL) (-1037 2405536 2405773 2406031 "RIDIST" 2406459 T RIDIST (NIL) -7 NIL NIL NIL) (-1036 2396852 2405004 2405210 "RGCHAIN" 2405384 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1035 2396228 2396608 2396649 "RGBCSPC" 2396707 NIL RGBCSPC (NIL T) -9 NIL 2396759 NIL) (-1034 2395412 2395767 2395808 "RGBCMDL" 2396040 NIL RGBCMDL (NIL T) -9 NIL 2396154 NIL) (-1033 2392406 2393020 2393690 "RF" 2394776 NIL RF (NIL T) -7 NIL NIL NIL) (-1032 2392052 2392115 2392218 "RFFACTOR" 2392337 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1031 2391777 2391812 2391909 "RFFACT" 2392011 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1030 2389894 2390258 2390640 "RFDIST" 2391417 T RFDIST (NIL) -7 NIL NIL NIL) (-1029 2389347 2389439 2389602 "RETSOL" 2389796 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1028 2388983 2389063 2389106 "RETRACT" 2389239 NIL RETRACT (NIL T) -9 NIL 2389326 NIL) (-1027 2388832 2388857 2388944 "RETRACT-" 2388949 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1026 2388461 2388654 2388724 "RETAST" 2388784 T RETAST (NIL) -8 NIL NIL NIL) (-1025 2381315 2388114 2388241 "RESULT" 2388356 T RESULT (NIL) -8 NIL NIL NIL) (-1024 2379941 2380584 2380783 "RESRING" 2381218 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1023 2379577 2379626 2379724 "RESLATC" 2379878 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1022 2379283 2379317 2379424 "REPSQ" 2379536 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1021 2376705 2377285 2377887 "REP" 2378703 T REP (NIL) -7 NIL NIL NIL) (-1020 2376403 2376437 2376548 "REPDB" 2376664 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1019 2370313 2371692 2372915 "REP2" 2375215 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1018 2366690 2367371 2368179 "REP1" 2369540 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1017 2359416 2364831 2365287 "REGSET" 2366320 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2358229 2358564 2358814 "REF" 2359201 NIL REF (NIL T) -8 NIL NIL NIL) (-1015 2357606 2357709 2357876 "REDORDER" 2358113 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1014 2353611 2356819 2357046 "RECLOS" 2357434 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1013 2352663 2352844 2353059 "REALSOLV" 2353418 T REALSOLV (NIL) -7 NIL NIL NIL) (-1012 2352509 2352550 2352580 "REAL" 2352585 T REAL (NIL) -9 NIL 2352620 NIL) (-1011 2348992 2349794 2350678 "REAL0Q" 2351674 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1010 2344593 2345581 2346642 "REAL0" 2347973 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1009 2344091 2344310 2344404 "RDUCEAST" 2344521 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1008 2343496 2343568 2343775 "RDIV" 2344013 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1007 2342564 2342738 2342951 "RDIST" 2343318 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1006 2341161 2341448 2341820 "RDETRS" 2342272 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1005 2338973 2339427 2339965 "RDETR" 2340703 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1004 2337584 2337862 2338266 "RDEEFS" 2338689 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1003 2336079 2336385 2336817 "RDEEF" 2337272 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1002 2330340 2333215 2333245 "RCFIELD" 2334540 T RCFIELD (NIL) -9 NIL 2335270 NIL) (-1001 2328404 2328908 2329604 "RCFIELD-" 2329679 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1000 2324720 2326505 2326548 "RCAGG" 2327632 NIL RCAGG (NIL T) -9 NIL 2328097 NIL) (-999 2324350 2324444 2324605 "RCAGG-" 2324610 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-998 2323690 2323802 2323965 "RATRET" 2324234 NIL RATRET (NIL T) -7 NIL NIL NIL) (-997 2323247 2323314 2323433 "RATFACT" 2323618 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-996 2322562 2322682 2322832 "RANDSRC" 2323117 T RANDSRC (NIL) -7 NIL NIL NIL) (-995 2322299 2322343 2322414 "RADUTIL" 2322511 T RADUTIL (NIL) -7 NIL NIL NIL) (-994 2315461 2321141 2321449 "RADIX" 2322023 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-993 2307118 2315305 2315433 "RADFF" 2315438 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-992 2306770 2306845 2306873 "RADCAT" 2307030 T RADCAT (NIL) -9 NIL NIL NIL) (-991 2306555 2306603 2306700 "RADCAT-" 2306705 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-990 2304706 2306330 2306419 "QUEUE" 2306499 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-989 2301282 2304643 2304688 "QUAT" 2304693 NIL QUAT (NIL T) -8 NIL NIL NIL) (-988 2300920 2300963 2301090 "QUATCT2" 2301233 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-987 2294667 2297969 2298009 "QUATCAT" 2298789 NIL QUATCAT (NIL T) -9 NIL 2299555 NIL) (-986 2290811 2291848 2293235 "QUATCAT-" 2293329 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-985 2288331 2289895 2289936 "QUAGG" 2290311 NIL QUAGG (NIL T) -9 NIL 2290486 NIL) (-984 2287963 2288156 2288224 "QQUTAST" 2288283 T QQUTAST (NIL) -8 NIL NIL NIL) (-983 2286888 2287361 2287533 "QFORM" 2287835 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-982 2278100 2283305 2283345 "QFCAT" 2284003 NIL QFCAT (NIL T) -9 NIL 2285004 NIL) (-981 2273672 2274873 2276464 "QFCAT-" 2276558 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-980 2273310 2273353 2273480 "QFCAT2" 2273623 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-979 2272770 2272880 2273010 "QEQUAT" 2273200 T QEQUAT (NIL) -8 NIL NIL NIL) (-978 2265918 2266989 2268173 "QCMPACK" 2271703 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-977 2263494 2263915 2264343 "QALGSET" 2265573 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-976 2262739 2262913 2263145 "QALGSET2" 2263314 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-975 2261430 2261653 2261970 "PWFFINTB" 2262512 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-974 2259612 2259780 2260134 "PUSHVAR" 2261244 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-973 2255530 2256584 2256625 "PTRANFN" 2258509 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-972 2253932 2254223 2254545 "PTPACK" 2255241 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-971 2253564 2253621 2253730 "PTFUNC2" 2253869 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-970 2248091 2252436 2252477 "PTCAT" 2252773 NIL PTCAT (NIL T) -9 NIL 2252926 NIL) (-969 2247749 2247784 2247908 "PSQFR" 2248050 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-968 2246344 2246642 2246976 "PSEUDLIN" 2247447 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-967 2233114 2235478 2237802 "PSETPK" 2244104 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-966 2226158 2228872 2228968 "PSETCAT" 2231989 NIL PSETCAT (NIL T T T T) -9 NIL 2232803 NIL) (-965 2223994 2224628 2225449 "PSETCAT-" 2225454 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-964 2223343 2223508 2223536 "PSCURVE" 2223804 T PSCURVE (NIL) -9 NIL 2223971 NIL) (-963 2219699 2221181 2221246 "PSCAT" 2222090 NIL PSCAT (NIL T T T) -9 NIL 2222330 NIL) (-962 2218762 2218978 2219378 "PSCAT-" 2219383 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-961 2217494 2218127 2218332 "PRTITION" 2218577 T PRTITION (NIL) -8 NIL NIL NIL) (-960 2216996 2217215 2217307 "PRTDAST" 2217422 T PRTDAST (NIL) -8 NIL NIL NIL) (-959 2206094 2208300 2210488 "PRS" 2214858 NIL PRS (NIL T T) -7 NIL NIL NIL) (-958 2203952 2205444 2205484 "PRQAGG" 2205667 NIL PRQAGG (NIL T) -9 NIL 2205769 NIL) (-957 2203338 2203567 2203595 "PROPLOG" 2203780 T PROPLOG (NIL) -9 NIL 2203902 NIL) (-956 2200508 2201152 2201616 "PROPFRML" 2202906 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-955 2199968 2200078 2200208 "PROPERTY" 2200398 T PROPERTY (NIL) -8 NIL NIL NIL) (-954 2194053 2198134 2198954 "PRODUCT" 2199194 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-953 2191366 2193511 2193745 "PR" 2193864 NIL PR (NIL T T) -8 NIL NIL NIL) (-952 2191162 2191194 2191253 "PRINT" 2191327 T PRINT (NIL) -7 NIL NIL NIL) (-951 2190502 2190619 2190771 "PRIMES" 2191042 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-950 2188567 2188968 2189434 "PRIMELT" 2190081 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-949 2188296 2188345 2188373 "PRIMCAT" 2188497 T PRIMCAT (NIL) -9 NIL NIL NIL) (-948 2184457 2188234 2188279 "PRIMARR" 2188284 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-947 2183464 2183642 2183870 "PRIMARR2" 2184275 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-946 2183107 2183163 2183274 "PREASSOC" 2183402 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-945 2182582 2182715 2182743 "PPCURVE" 2182948 T PPCURVE (NIL) -9 NIL 2183084 NIL) (-944 2182204 2182377 2182460 "PORTNUM" 2182519 T PORTNUM (NIL) -8 NIL NIL NIL) (-943 2179563 2179962 2180554 "POLYROOT" 2181785 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-942 2173508 2179167 2179327 "POLY" 2179436 NIL POLY (NIL T) -8 NIL NIL NIL) (-941 2172891 2172949 2173183 "POLYLIFT" 2173444 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-940 2169166 2169615 2170244 "POLYCATQ" 2172436 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-939 2155983 2161341 2161406 "POLYCAT" 2164920 NIL POLYCAT (NIL T T T) -9 NIL 2166848 NIL) (-938 2149433 2151294 2153678 "POLYCAT-" 2153683 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-937 2149020 2149088 2149208 "POLY2UP" 2149359 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-936 2148652 2148709 2148818 "POLY2" 2148957 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-935 2147337 2147576 2147852 "POLUTIL" 2148426 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-934 2145692 2145969 2146300 "POLTOPOL" 2147059 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-933 2141210 2145628 2145674 "POINT" 2145679 NIL POINT (NIL T) -8 NIL NIL NIL) (-932 2139397 2139754 2140129 "PNTHEORY" 2140855 T PNTHEORY (NIL) -7 NIL NIL NIL) (-931 2137816 2138113 2138525 "PMTOOLS" 2139095 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-930 2137409 2137487 2137604 "PMSYM" 2137732 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-929 2136919 2136988 2137162 "PMQFCAT" 2137334 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-928 2136274 2136384 2136540 "PMPRED" 2136796 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-927 2135670 2135756 2135917 "PMPREDFS" 2136175 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-926 2134313 2134521 2134906 "PMPLCAT" 2135432 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-925 2133845 2133924 2134076 "PMLSAGG" 2134228 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-924 2133320 2133396 2133577 "PMKERNEL" 2133763 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-923 2132937 2133012 2133125 "PMINS" 2133239 NIL PMINS (NIL T) -7 NIL NIL NIL) (-922 2132365 2132434 2132650 "PMFS" 2132862 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-921 2131593 2131711 2131916 "PMDOWN" 2132242 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-920 2130756 2130915 2131097 "PMASS" 2131431 T PMASS (NIL) -7 NIL NIL NIL) (-919 2130030 2130141 2130304 "PMASSFS" 2130642 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-918 2129685 2129753 2129847 "PLOTTOOL" 2129956 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-917 2124307 2125496 2126644 "PLOT" 2128557 T PLOT (NIL) -8 NIL NIL NIL) (-916 2120121 2121155 2122076 "PLOT3D" 2123406 T PLOT3D (NIL) -8 NIL NIL NIL) (-915 2119033 2119210 2119445 "PLOT1" 2119925 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-914 2094427 2099099 2103950 "PLEQN" 2114299 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-913 2093745 2093867 2094047 "PINTERP" 2094292 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-912 2093438 2093485 2093588 "PINTERPA" 2093692 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-911 2092686 2093207 2093294 "PI" 2093334 T PI (NIL) -8 NIL NIL 2093401) (-910 2091083 2092024 2092052 "PID" 2092234 T PID (NIL) -9 NIL 2092368 NIL) (-909 2090808 2090845 2090933 "PICOERCE" 2091040 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-908 2090128 2090267 2090443 "PGROEB" 2090664 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-907 2085715 2086529 2087434 "PGE" 2089243 T PGE (NIL) -7 NIL NIL NIL) (-906 2083839 2084085 2084451 "PGCD" 2085432 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-905 2083177 2083280 2083441 "PFRPAC" 2083723 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-904 2079857 2081725 2082078 "PFR" 2082856 NIL PFR (NIL T) -8 NIL NIL NIL) (-903 2078246 2078490 2078815 "PFOTOOLS" 2079604 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-902 2076779 2077018 2077369 "PFOQ" 2078003 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-901 2075252 2075464 2075827 "PFO" 2076563 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-900 2071840 2075141 2075210 "PF" 2075215 NIL PF (NIL NIL) -8 NIL NIL NIL) (-899 2069274 2070511 2070539 "PFECAT" 2071124 T PFECAT (NIL) -9 NIL 2071508 NIL) (-898 2068719 2068873 2069087 "PFECAT-" 2069092 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-897 2067323 2067574 2067875 "PFBRU" 2068468 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-896 2065190 2065541 2065973 "PFBR" 2066974 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-895 2061106 2062566 2063242 "PERM" 2064547 NIL PERM (NIL T) -8 NIL NIL NIL) (-894 2056372 2057313 2058183 "PERMGRP" 2060269 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-893 2054504 2055435 2055476 "PERMCAT" 2055922 NIL PERMCAT (NIL T) -9 NIL 2056227 NIL) (-892 2054157 2054198 2054322 "PERMAN" 2054457 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-891 2051693 2053822 2053944 "PENDTREE" 2054068 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-890 2049786 2050520 2050561 "PDRING" 2051218 NIL PDRING (NIL T) -9 NIL 2051504 NIL) (-889 2048889 2049107 2049469 "PDRING-" 2049474 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-888 2046131 2046882 2047550 "PDEPROB" 2048241 T PDEPROB (NIL) -8 NIL NIL NIL) (-887 2043678 2044180 2044735 "PDEPACK" 2045596 T PDEPACK (NIL) -7 NIL NIL NIL) (-886 2042590 2042780 2043031 "PDECOMP" 2043477 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-885 2040195 2041012 2041040 "PDECAT" 2041827 T PDECAT (NIL) -9 NIL 2042540 NIL) (-884 2039946 2039979 2040069 "PCOMP" 2040156 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-883 2038151 2038747 2039044 "PBWLB" 2039675 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-882 2030656 2032224 2033562 "PATTERN" 2036834 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-881 2030288 2030345 2030454 "PATTERN2" 2030593 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-880 2028045 2028433 2028890 "PATTERN1" 2029877 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-879 2025440 2025994 2026475 "PATRES" 2027610 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-878 2025004 2025071 2025203 "PATRES2" 2025367 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-877 2022887 2023292 2023699 "PATMATCH" 2024671 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-876 2022423 2022606 2022647 "PATMAB" 2022754 NIL PATMAB (NIL T) -9 NIL 2022837 NIL) (-875 2020968 2021277 2021535 "PATLRES" 2022228 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-874 2020514 2020637 2020678 "PATAB" 2020683 NIL PATAB (NIL T) -9 NIL 2020855 NIL) (-873 2017995 2018527 2019100 "PARTPERM" 2019961 T PARTPERM (NIL) -7 NIL NIL NIL) (-872 2017616 2017679 2017781 "PARSURF" 2017926 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-871 2017248 2017305 2017414 "PARSU2" 2017553 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-870 2017012 2017052 2017119 "PARSER" 2017201 T PARSER (NIL) -7 NIL NIL NIL) (-869 2016633 2016696 2016798 "PARSCURV" 2016943 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-868 2016265 2016322 2016431 "PARSC2" 2016570 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-867 2015904 2015962 2016059 "PARPCURV" 2016201 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-866 2015536 2015593 2015702 "PARPC2" 2015841 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-865 2015056 2015142 2015261 "PAN2EXPR" 2015437 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-864 2013862 2014177 2014405 "PALETTE" 2014848 T PALETTE (NIL) -8 NIL NIL NIL) (-863 2012330 2012867 2013227 "PAIR" 2013548 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-862 2006236 2011589 2011783 "PADICRC" 2012185 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-861 1999500 2005582 2005766 "PADICRAT" 2006084 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-860 1997850 1999437 1999482 "PADIC" 1999487 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-859 1995060 1996590 1996630 "PADICCT" 1997211 NIL PADICCT (NIL NIL) -9 NIL 1997493 NIL) (-858 1994017 1994217 1994485 "PADEPAC" 1994847 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-857 1993229 1993362 1993568 "PADE" 1993879 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-856 1991651 1992437 1992717 "OWP" 1993033 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-855 1990724 1991256 1991428 "OVAR" 1991519 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-854 1989988 1990109 1990270 "OUT" 1990583 T OUT (NIL) -7 NIL NIL NIL) (-853 1978895 1981097 1983297 "OUTFORM" 1987808 T OUTFORM (NIL) -8 NIL NIL NIL) (-852 1978311 1978492 1978619 "OUTBFILE" 1978788 T OUTBFILE (NIL) -8 NIL NIL NIL) (-851 1977933 1978021 1978049 "OUTBCON" 1978205 T OUTBCON (NIL) -9 NIL 1978295 NIL) (-850 1977776 1977810 1977885 "OUTBCON-" 1977890 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-849 1977184 1977505 1977594 "OSI" 1977707 T OSI (NIL) -8 NIL NIL NIL) (-848 1976740 1977052 1977080 "OSGROUP" 1977085 T OSGROUP (NIL) -9 NIL 1977107 NIL) (-847 1975485 1975712 1975997 "ORTHPOL" 1976487 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-846 1973071 1975320 1975441 "OREUP" 1975446 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-845 1970509 1972762 1972889 "ORESUP" 1973013 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-844 1968037 1968537 1969098 "OREPCTO" 1969998 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-843 1961861 1964028 1964069 "OREPCAT" 1966417 NIL OREPCAT (NIL T) -9 NIL 1967521 NIL) (-842 1959008 1959790 1960848 "OREPCAT-" 1960853 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-841 1958185 1958457 1958485 "ORDSET" 1958794 T ORDSET (NIL) -9 NIL 1958958 NIL) (-840 1957704 1957826 1958019 "ORDSET-" 1958024 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-839 1956338 1957095 1957123 "ORDRING" 1957325 T ORDRING (NIL) -9 NIL 1957450 NIL) (-838 1955983 1956077 1956221 "ORDRING-" 1956226 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-837 1955389 1955826 1955854 "ORDMON" 1955859 T ORDMON (NIL) -9 NIL 1955880 NIL) (-836 1954551 1954698 1954893 "ORDFUNS" 1955238 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-835 1953915 1954308 1954336 "ORDFIN" 1954401 T ORDFIN (NIL) -9 NIL 1954475 NIL) (-834 1950507 1952501 1952910 "ORDCOMP" 1953539 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-833 1949773 1949900 1950086 "ORDCOMP2" 1950367 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-832 1946381 1947264 1948078 "OPTPROB" 1948979 T OPTPROB (NIL) -8 NIL NIL NIL) (-831 1943183 1943822 1944526 "OPTPACK" 1945697 T OPTPACK (NIL) -7 NIL NIL NIL) (-830 1940896 1941636 1941664 "OPTCAT" 1942483 T OPTCAT (NIL) -9 NIL 1943133 NIL) (-829 1940339 1940573 1940678 "OPSIG" 1940811 T OPSIG (NIL) -8 NIL NIL NIL) (-828 1940107 1940146 1940212 "OPQUERY" 1940293 T OPQUERY (NIL) -7 NIL NIL NIL) (-827 1937273 1938418 1938922 "OP" 1939636 NIL OP (NIL T) -8 NIL NIL NIL) (-826 1936808 1936979 1937020 "OPERCAT" 1937155 NIL OPERCAT (NIL T) -9 NIL 1937223 NIL) (-825 1936654 1936681 1936767 "OPERCAT-" 1936772 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-824 1933499 1935451 1935820 "ONECOMP" 1936318 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-823 1932804 1932919 1933093 "ONECOMP2" 1933371 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-822 1932223 1932329 1932459 "OMSERVER" 1932694 T OMSERVER (NIL) -7 NIL NIL NIL) (-821 1929111 1931663 1931703 "OMSAGG" 1931764 NIL OMSAGG (NIL T) -9 NIL 1931828 NIL) (-820 1927734 1927997 1928279 "OMPKG" 1928849 T OMPKG (NIL) -7 NIL NIL NIL) (-819 1927164 1927267 1927295 "OM" 1927594 T OM (NIL) -9 NIL NIL NIL) (-818 1925746 1926713 1926882 "OMLO" 1927045 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-817 1924671 1924818 1925045 "OMEXPR" 1925572 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-816 1923989 1924217 1924353 "OMERR" 1924555 T OMERR (NIL) -8 NIL NIL NIL) (-815 1923167 1923410 1923570 "OMERRK" 1923849 T OMERRK (NIL) -8 NIL NIL NIL) (-814 1922645 1922844 1922952 "OMENC" 1923079 T OMENC (NIL) -8 NIL NIL NIL) (-813 1916540 1917725 1918896 "OMDEV" 1921494 T OMDEV (NIL) -8 NIL NIL NIL) (-812 1915609 1915780 1915974 "OMCONN" 1916366 T OMCONN (NIL) -8 NIL NIL NIL) (-811 1914230 1915172 1915200 "OINTDOM" 1915205 T OINTDOM (NIL) -9 NIL 1915226 NIL) (-810 1910036 1911220 1911936 "OFMONOID" 1913546 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-809 1909474 1909973 1910018 "ODVAR" 1910023 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-808 1906932 1909219 1909374 "ODR" 1909379 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-807 1899276 1906708 1906834 "ODPOL" 1906839 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-806 1893152 1899148 1899253 "ODP" 1899258 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-805 1891918 1892133 1892408 "ODETOOLS" 1892926 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-804 1888887 1889543 1890259 "ODESYS" 1891251 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-803 1883769 1884677 1885702 "ODERTRIC" 1887962 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-802 1883195 1883277 1883471 "ODERED" 1883681 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-801 1880083 1880631 1881308 "ODERAT" 1882618 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-800 1877043 1877507 1878104 "ODEPRRIC" 1879612 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-799 1875013 1875582 1876068 "ODEPROB" 1876577 T ODEPROB (NIL) -8 NIL NIL NIL) (-798 1871535 1872018 1872665 "ODEPRIM" 1874492 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-797 1870784 1870886 1871146 "ODEPAL" 1871427 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-796 1866946 1867737 1868601 "ODEPACK" 1869940 T ODEPACK (NIL) -7 NIL NIL NIL) (-795 1865979 1866086 1866315 "ODEINT" 1866835 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-794 1860080 1861505 1862952 "ODEIFTBL" 1864552 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-793 1855415 1856201 1857160 "ODEEF" 1859239 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-792 1854750 1854839 1855069 "ODECONST" 1855320 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-791 1852901 1853536 1853564 "ODECAT" 1854169 T ODECAT (NIL) -9 NIL 1854700 NIL) (-790 1849808 1852613 1852732 "OCT" 1852814 NIL OCT (NIL T) -8 NIL NIL NIL) (-789 1849446 1849489 1849616 "OCTCT2" 1849759 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-788 1844220 1846620 1846660 "OC" 1847757 NIL OC (NIL T) -9 NIL 1848615 NIL) (-787 1841447 1842195 1843185 "OC-" 1843279 NIL OC- (NIL T T) -8 NIL NIL NIL) (-786 1840825 1841267 1841295 "OCAMON" 1841300 T OCAMON (NIL) -9 NIL 1841321 NIL) (-785 1840382 1840697 1840725 "OASGP" 1840730 T OASGP (NIL) -9 NIL 1840750 NIL) (-784 1839669 1840132 1840160 "OAMONS" 1840200 T OAMONS (NIL) -9 NIL 1840243 NIL) (-783 1839109 1839516 1839544 "OAMON" 1839549 T OAMON (NIL) -9 NIL 1839569 NIL) (-782 1838413 1838905 1838933 "OAGROUP" 1838938 T OAGROUP (NIL) -9 NIL 1838958 NIL) (-781 1838103 1838153 1838241 "NUMTUBE" 1838357 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-780 1831676 1833194 1834730 "NUMQUAD" 1836587 T NUMQUAD (NIL) -7 NIL NIL NIL) (-779 1827432 1828420 1829445 "NUMODE" 1830671 T NUMODE (NIL) -7 NIL NIL NIL) (-778 1824813 1825667 1825695 "NUMINT" 1826618 T NUMINT (NIL) -9 NIL 1827382 NIL) (-777 1823761 1823958 1824176 "NUMFMT" 1824615 T NUMFMT (NIL) -7 NIL NIL NIL) (-776 1810120 1813065 1815597 "NUMERIC" 1821268 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-775 1804517 1809569 1809664 "NTSCAT" 1809669 NIL NTSCAT (NIL T T T T) -9 NIL 1809708 NIL) (-774 1803711 1803876 1804069 "NTPOLFN" 1804356 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-773 1791551 1800536 1801348 "NSUP" 1802932 NIL NSUP (NIL T) -8 NIL NIL NIL) (-772 1791183 1791240 1791349 "NSUP2" 1791488 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-771 1781180 1790957 1791090 "NSMP" 1791095 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-770 1779612 1779913 1780270 "NREP" 1780868 NIL NREP (NIL T) -7 NIL NIL NIL) (-769 1778203 1778455 1778813 "NPCOEF" 1779355 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-768 1777269 1777384 1777600 "NORMRETR" 1778084 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-767 1775310 1775600 1776009 "NORMPK" 1776977 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-766 1774995 1775023 1775147 "NORMMA" 1775276 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-765 1774822 1774952 1774981 "NONE" 1774986 T NONE (NIL) -8 NIL NIL NIL) (-764 1774611 1774640 1774709 "NONE1" 1774786 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-763 1774094 1774156 1774342 "NODE1" 1774543 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-762 1772365 1773188 1773443 "NNI" 1773790 T NNI (NIL) -8 NIL NIL 1774025) (-761 1770785 1771098 1771462 "NLINSOL" 1772033 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-760 1767053 1768021 1768920 "NIPROB" 1769906 T NIPROB (NIL) -8 NIL NIL NIL) (-759 1765810 1766044 1766346 "NFINTBAS" 1766815 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-758 1765250 1765460 1765501 "NETCLT" 1765673 NIL NETCLT (NIL T) -9 NIL 1765755 NIL) (-757 1763958 1764189 1764470 "NCODIV" 1765018 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-756 1763720 1763757 1763832 "NCNTFRAC" 1763915 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-755 1761900 1762264 1762684 "NCEP" 1763345 NIL NCEP (NIL T) -7 NIL NIL NIL) (-754 1760811 1761550 1761578 "NASRING" 1761688 T NASRING (NIL) -9 NIL 1761762 NIL) (-753 1760606 1760650 1760744 "NASRING-" 1760749 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-752 1759759 1760258 1760286 "NARNG" 1760403 T NARNG (NIL) -9 NIL 1760494 NIL) (-751 1759451 1759518 1759652 "NARNG-" 1759657 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-750 1758330 1758537 1758772 "NAGSP" 1759236 T NAGSP (NIL) -7 NIL NIL NIL) (-749 1749602 1751286 1752959 "NAGS" 1756677 T NAGS (NIL) -7 NIL NIL NIL) (-748 1748150 1748458 1748789 "NAGF07" 1749291 T NAGF07 (NIL) -7 NIL NIL NIL) (-747 1742688 1743979 1745286 "NAGF04" 1746863 T NAGF04 (NIL) -7 NIL NIL NIL) (-746 1735656 1737270 1738903 "NAGF02" 1741075 T NAGF02 (NIL) -7 NIL NIL NIL) (-745 1730880 1731980 1733097 "NAGF01" 1734559 T NAGF01 (NIL) -7 NIL NIL NIL) (-744 1724508 1726074 1727659 "NAGE04" 1729315 T NAGE04 (NIL) -7 NIL NIL NIL) (-743 1715677 1717798 1719928 "NAGE02" 1722398 T NAGE02 (NIL) -7 NIL NIL NIL) (-742 1711630 1712577 1713541 "NAGE01" 1714733 T NAGE01 (NIL) -7 NIL NIL NIL) (-741 1709425 1709959 1710517 "NAGD03" 1711092 T NAGD03 (NIL) -7 NIL NIL NIL) (-740 1701175 1703103 1705057 "NAGD02" 1707491 T NAGD02 (NIL) -7 NIL NIL NIL) (-739 1694986 1696411 1697851 "NAGD01" 1699755 T NAGD01 (NIL) -7 NIL NIL NIL) (-738 1691195 1692017 1692854 "NAGC06" 1694169 T NAGC06 (NIL) -7 NIL NIL NIL) (-737 1689660 1689992 1690348 "NAGC05" 1690859 T NAGC05 (NIL) -7 NIL NIL NIL) (-736 1689036 1689155 1689299 "NAGC02" 1689536 T NAGC02 (NIL) -7 NIL NIL NIL) (-735 1688096 1688653 1688693 "NAALG" 1688772 NIL NAALG (NIL T) -9 NIL 1688833 NIL) (-734 1687931 1687960 1688050 "NAALG-" 1688055 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-733 1681881 1682989 1684176 "MULTSQFR" 1686827 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-732 1681200 1681275 1681459 "MULTFACT" 1681793 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-731 1674293 1678163 1678216 "MTSCAT" 1679286 NIL MTSCAT (NIL T T) -9 NIL 1679800 NIL) (-730 1674005 1674059 1674151 "MTHING" 1674233 NIL MTHING (NIL T) -7 NIL NIL NIL) (-729 1673797 1673830 1673890 "MSYSCMD" 1673965 T MSYSCMD (NIL) -7 NIL NIL NIL) (-728 1669909 1672552 1672872 "MSET" 1673510 NIL MSET (NIL T) -8 NIL NIL NIL) (-727 1667004 1669470 1669511 "MSETAGG" 1669516 NIL MSETAGG (NIL T) -9 NIL 1669550 NIL) (-726 1662887 1664383 1665128 "MRING" 1666304 NIL MRING (NIL T T) -8 NIL NIL NIL) (-725 1662453 1662520 1662651 "MRF2" 1662814 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-724 1662071 1662106 1662250 "MRATFAC" 1662412 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-723 1659683 1659978 1660409 "MPRFF" 1661776 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-722 1653743 1659537 1659634 "MPOLY" 1659639 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-721 1653233 1653268 1653476 "MPCPF" 1653702 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-720 1652747 1652790 1652974 "MPC3" 1653184 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-719 1651942 1652023 1652244 "MPC2" 1652662 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-718 1650243 1650580 1650970 "MONOTOOL" 1651602 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-717 1649494 1649785 1649813 "MONOID" 1650032 T MONOID (NIL) -9 NIL 1650179 NIL) (-716 1649040 1649159 1649340 "MONOID-" 1649345 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-715 1639899 1645807 1645866 "MONOGEN" 1646540 NIL MONOGEN (NIL T T) -9 NIL 1646996 NIL) (-714 1637117 1637852 1638852 "MONOGEN-" 1638971 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-713 1635976 1636396 1636424 "MONADWU" 1636816 T MONADWU (NIL) -9 NIL 1637054 NIL) (-712 1635348 1635507 1635755 "MONADWU-" 1635760 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-711 1634733 1634951 1634979 "MONAD" 1635186 T MONAD (NIL) -9 NIL 1635298 NIL) (-710 1634418 1634496 1634628 "MONAD-" 1634633 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-709 1632734 1633331 1633610 "MOEBIUS" 1634171 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-708 1632126 1632504 1632544 "MODULE" 1632549 NIL MODULE (NIL T) -9 NIL 1632575 NIL) (-707 1631694 1631790 1631980 "MODULE-" 1631985 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-706 1629409 1630058 1630385 "MODRING" 1631518 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-705 1626395 1627514 1628035 "MODOP" 1628938 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-704 1625010 1625462 1625739 "MODMONOM" 1626258 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-703 1614817 1623301 1623715 "MODMON" 1624647 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-702 1612008 1613661 1613937 "MODFIELD" 1614692 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-701 1611012 1611289 1611479 "MMLFORM" 1611838 T MMLFORM (NIL) -8 NIL NIL NIL) (-700 1610538 1610581 1610760 "MMAP" 1610963 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-699 1608755 1609488 1609529 "MLO" 1609952 NIL MLO (NIL T) -9 NIL 1610194 NIL) (-698 1606122 1606637 1607239 "MLIFT" 1608236 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-697 1605513 1605597 1605751 "MKUCFUNC" 1606033 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-696 1605112 1605182 1605305 "MKRECORD" 1605436 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-695 1604160 1604321 1604549 "MKFUNC" 1604923 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-694 1603548 1603652 1603808 "MKFLCFN" 1604043 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-693 1603091 1603458 1603517 "MKCHSET" 1603522 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-692 1602368 1602470 1602655 "MKBCFUNC" 1602984 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-691 1599110 1601922 1602058 "MINT" 1602252 T MINT (NIL) -8 NIL NIL NIL) (-690 1597922 1598165 1598442 "MHROWRED" 1598865 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-689 1593348 1596457 1596862 "MFLOAT" 1597537 T MFLOAT (NIL) -8 NIL NIL NIL) (-688 1592705 1592781 1592952 "MFINFACT" 1593260 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-687 1589020 1589868 1590752 "MESH" 1591841 T MESH (NIL) -7 NIL NIL NIL) (-686 1587410 1587722 1588075 "MDDFACT" 1588707 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-685 1584252 1586569 1586610 "MDAGG" 1586865 NIL MDAGG (NIL T) -9 NIL 1587008 NIL) (-684 1574030 1583545 1583752 "MCMPLX" 1584065 T MCMPLX (NIL) -8 NIL NIL NIL) (-683 1573171 1573317 1573517 "MCDEN" 1573879 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-682 1571061 1571331 1571711 "MCALCFN" 1572901 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-681 1569986 1570226 1570459 "MAYBE" 1570867 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-680 1567598 1568121 1568683 "MATSTOR" 1569457 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-679 1563604 1566970 1567218 "MATRIX" 1567383 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-678 1559373 1560077 1560813 "MATLIN" 1562961 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-677 1549527 1552665 1552742 "MATCAT" 1557622 NIL MATCAT (NIL T T T) -9 NIL 1559039 NIL) (-676 1545891 1546904 1548260 "MATCAT-" 1548265 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-675 1544485 1544638 1544971 "MATCAT2" 1545726 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-674 1542597 1542921 1543305 "MAPPKG3" 1544160 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-673 1541578 1541751 1541973 "MAPPKG2" 1542421 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-672 1540077 1540361 1540688 "MAPPKG1" 1541284 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-671 1539183 1539483 1539660 "MAPPAST" 1539920 T MAPPAST (NIL) -8 NIL NIL NIL) (-670 1538794 1538852 1538975 "MAPHACK3" 1539119 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-669 1538386 1538447 1538561 "MAPHACK2" 1538726 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-668 1537824 1537927 1538069 "MAPHACK1" 1538277 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-667 1535930 1536524 1536828 "MAGMA" 1537552 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-666 1535436 1535654 1535745 "MACROAST" 1535859 T MACROAST (NIL) -8 NIL NIL NIL) (-665 1531903 1533675 1534136 "M3D" 1535008 NIL M3D (NIL T) -8 NIL NIL NIL) (-664 1526057 1530272 1530313 "LZSTAGG" 1531095 NIL LZSTAGG (NIL T) -9 NIL 1531390 NIL) (-663 1522031 1523188 1524645 "LZSTAGG-" 1524650 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-662 1519145 1519922 1520409 "LWORD" 1521576 NIL LWORD (NIL T) -8 NIL NIL NIL) (-661 1518748 1518949 1519024 "LSTAST" 1519090 T LSTAST (NIL) -8 NIL NIL NIL) (-660 1511949 1518519 1518653 "LSQM" 1518658 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-659 1511173 1511312 1511540 "LSPP" 1511804 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-658 1508985 1509286 1509742 "LSMP" 1510862 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-657 1505764 1506438 1507168 "LSMP1" 1508287 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-656 1499689 1504931 1504972 "LSAGG" 1505034 NIL LSAGG (NIL T) -9 NIL 1505112 NIL) (-655 1496384 1497308 1498521 "LSAGG-" 1498526 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-654 1494010 1495528 1495777 "LPOLY" 1496179 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-653 1493592 1493677 1493800 "LPEFRAC" 1493919 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-652 1491939 1492686 1492939 "LO" 1493424 NIL LO (NIL T T T) -8 NIL NIL NIL) (-651 1491591 1491703 1491731 "LOGIC" 1491842 T LOGIC (NIL) -9 NIL 1491923 NIL) (-650 1491453 1491476 1491547 "LOGIC-" 1491552 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-649 1490646 1490786 1490979 "LODOOPS" 1491309 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-648 1488104 1490562 1490628 "LODO" 1490633 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-647 1486642 1486877 1487230 "LODOF" 1487851 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-646 1482998 1485395 1485436 "LODOCAT" 1485874 NIL LODOCAT (NIL T) -9 NIL 1486085 NIL) (-645 1482731 1482789 1482916 "LODOCAT-" 1482921 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-644 1480086 1482572 1482690 "LODO2" 1482695 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-643 1477556 1480023 1480068 "LODO1" 1480073 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-642 1476416 1476581 1476893 "LODEEF" 1477379 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-641 1471702 1474546 1474587 "LNAGG" 1475534 NIL LNAGG (NIL T) -9 NIL 1475978 NIL) (-640 1470849 1471063 1471405 "LNAGG-" 1471410 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-639 1467012 1467774 1468413 "LMOPS" 1470264 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-638 1466407 1466769 1466810 "LMODULE" 1466871 NIL LMODULE (NIL T) -9 NIL 1466913 NIL) (-637 1463653 1466052 1466175 "LMDICT" 1466317 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-636 1463379 1463561 1463621 "LITERAL" 1463626 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-635 1456606 1462325 1462623 "LIST" 1463114 NIL LIST (NIL T) -8 NIL NIL NIL) (-634 1456131 1456205 1456344 "LIST3" 1456526 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-633 1455138 1455316 1455544 "LIST2" 1455949 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-632 1453272 1453584 1453983 "LIST2MAP" 1454785 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-631 1452002 1452638 1452679 "LINEXP" 1452934 NIL LINEXP (NIL T) -9 NIL 1453083 NIL) (-630 1450649 1450909 1451206 "LINDEP" 1451754 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-629 1447416 1448135 1448912 "LIMITRF" 1449904 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-628 1445692 1445987 1446403 "LIMITPS" 1447111 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-627 1440147 1445203 1445431 "LIE" 1445513 NIL LIE (NIL T T) -8 NIL NIL NIL) (-626 1439196 1439639 1439679 "LIECAT" 1439819 NIL LIECAT (NIL T) -9 NIL 1439970 NIL) (-625 1439037 1439064 1439152 "LIECAT-" 1439157 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-624 1431649 1438486 1438651 "LIB" 1438892 T LIB (NIL) -8 NIL NIL NIL) (-623 1427286 1428167 1429102 "LGROBP" 1430766 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-622 1425152 1425426 1425788 "LF" 1427007 NIL LF (NIL T T) -7 NIL NIL NIL) (-621 1423992 1424684 1424712 "LFCAT" 1424919 T LFCAT (NIL) -9 NIL 1425058 NIL) (-620 1420896 1421524 1422212 "LEXTRIPK" 1423356 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-619 1417667 1418466 1418969 "LEXP" 1420476 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-618 1417170 1417388 1417480 "LETAST" 1417595 T LETAST (NIL) -8 NIL NIL NIL) (-617 1415568 1415881 1416282 "LEADCDET" 1416852 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-616 1414758 1414832 1415061 "LAZM3PK" 1415489 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-615 1409713 1412835 1413373 "LAUPOL" 1414270 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-614 1409278 1409322 1409490 "LAPLACE" 1409663 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-613 1407252 1408379 1408630 "LA" 1409111 NIL LA (NIL T T T) -8 NIL NIL NIL) (-612 1406333 1406883 1406924 "LALG" 1406986 NIL LALG (NIL T) -9 NIL 1407045 NIL) (-611 1406047 1406106 1406242 "LALG-" 1406247 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-610 1405882 1405906 1405947 "KVTFROM" 1406009 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-609 1404685 1405099 1405328 "KTVLOGIC" 1405673 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-608 1404520 1404544 1404585 "KRCFROM" 1404647 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-607 1403424 1403611 1403910 "KOVACIC" 1404320 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-606 1403259 1403283 1403324 "KONVERT" 1403386 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-605 1403094 1403118 1403159 "KOERCE" 1403221 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-604 1400828 1401588 1401981 "KERNEL" 1402733 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-603 1400330 1400411 1400541 "KERNEL2" 1400742 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-602 1394181 1398869 1398923 "KDAGG" 1399300 NIL KDAGG (NIL T T) -9 NIL 1399506 NIL) (-601 1393710 1393834 1394039 "KDAGG-" 1394044 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1386885 1393371 1393526 "KAFILE" 1393588 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-599 1381340 1386396 1386624 "JORDAN" 1386706 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-598 1380746 1380989 1381110 "JOINAST" 1381239 T JOINAST (NIL) -8 NIL NIL NIL) (-597 1380592 1380651 1380706 "JAVACODE" 1380711 T JAVACODE (NIL) -8 NIL NIL NIL) (-596 1376891 1378797 1378851 "IXAGG" 1379780 NIL IXAGG (NIL T T) -9 NIL 1380239 NIL) (-595 1375810 1376116 1376535 "IXAGG-" 1376540 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-594 1371390 1375732 1375791 "IVECTOR" 1375796 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-593 1370156 1370393 1370659 "ITUPLE" 1371157 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-592 1368592 1368769 1369075 "ITRIGMNP" 1369978 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-591 1367337 1367541 1367824 "ITFUN3" 1368368 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-590 1366969 1367026 1367135 "ITFUN2" 1367274 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-589 1364806 1365831 1366130 "ITAYLOR" 1366703 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-588 1353789 1358943 1360106 "ISUPS" 1363676 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-587 1352893 1353033 1353269 "ISUMP" 1353636 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-586 1348157 1352694 1352773 "ISTRING" 1352846 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-585 1347660 1347878 1347970 "ISAST" 1348085 T ISAST (NIL) -8 NIL NIL NIL) (-584 1346870 1346951 1347167 "IRURPK" 1347574 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-583 1345806 1346007 1346247 "IRSN" 1346650 T IRSN (NIL) -7 NIL NIL NIL) (-582 1343835 1344190 1344626 "IRRF2F" 1345444 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-581 1343582 1343620 1343696 "IRREDFFX" 1343791 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-580 1342197 1342456 1342755 "IROOT" 1343315 NIL IROOT (NIL T) -7 NIL NIL NIL) (-579 1338829 1339881 1340573 "IR" 1341537 NIL IR (NIL T) -8 NIL NIL NIL) (-578 1336442 1336937 1337503 "IR2" 1338307 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-577 1335514 1335627 1335848 "IR2F" 1336325 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-576 1335305 1335339 1335399 "IPRNTPK" 1335474 T IPRNTPK (NIL) -7 NIL NIL NIL) (-575 1331924 1335194 1335263 "IPF" 1335268 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-574 1330287 1331849 1331906 "IPADIC" 1331911 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-573 1329627 1329847 1329977 "IP4ADDR" 1330177 T IP4ADDR (NIL) -8 NIL NIL NIL) (-572 1329127 1329331 1329441 "IOMODE" 1329537 T IOMODE (NIL) -8 NIL NIL NIL) (-571 1328475 1328724 1328851 "IOBFILE" 1329020 T IOBFILE (NIL) -8 NIL NIL NIL) (-570 1328216 1328379 1328407 "IOBCON" 1328412 T IOBCON (NIL) -9 NIL 1328433 NIL) (-569 1327713 1327771 1327961 "INVLAPLA" 1328152 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-568 1317362 1319715 1322101 "INTTR" 1325377 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-567 1313706 1314448 1315312 "INTTOOLS" 1316547 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-566 1313292 1313383 1313500 "INTSLPE" 1313609 T INTSLPE (NIL) -7 NIL NIL NIL) (-565 1311287 1313215 1313274 "INTRVL" 1313279 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-564 1308889 1309401 1309976 "INTRF" 1310772 NIL INTRF (NIL T) -7 NIL NIL NIL) (-563 1308300 1308397 1308539 "INTRET" 1308787 NIL INTRET (NIL T) -7 NIL NIL NIL) (-562 1306297 1306686 1307156 "INTRAT" 1307908 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-561 1303525 1304108 1304734 "INTPM" 1305782 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-560 1300228 1300827 1301572 "INTPAF" 1302911 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-559 1295407 1296369 1297420 "INTPACK" 1299197 T INTPACK (NIL) -7 NIL NIL NIL) (-558 1292319 1295136 1295263 "INT" 1295300 T INT (NIL) -8 NIL NIL NIL) (-557 1291571 1291723 1291931 "INTHERTR" 1292161 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-556 1291010 1291090 1291278 "INTHERAL" 1291485 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-555 1288856 1289299 1289756 "INTHEORY" 1290573 T INTHEORY (NIL) -7 NIL NIL NIL) (-554 1280164 1281785 1283564 "INTG0" 1287208 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-553 1260737 1265527 1270337 "INTFTBL" 1275374 T INTFTBL (NIL) -8 NIL NIL NIL) (-552 1259986 1260124 1260297 "INTFACT" 1260596 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-551 1257371 1257817 1258381 "INTEF" 1259540 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-550 1255838 1256543 1256571 "INTDOM" 1256872 T INTDOM (NIL) -9 NIL 1257079 NIL) (-549 1255207 1255381 1255623 "INTDOM-" 1255628 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-548 1251702 1253591 1253645 "INTCAT" 1254444 NIL INTCAT (NIL T) -9 NIL 1254764 NIL) (-547 1251175 1251277 1251405 "INTBIT" 1251594 T INTBIT (NIL) -7 NIL NIL NIL) (-546 1249846 1250000 1250314 "INTALG" 1251020 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-545 1249303 1249393 1249563 "INTAF" 1249750 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-544 1242757 1249113 1249253 "INTABL" 1249258 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-543 1237772 1240446 1240474 "INS" 1241408 T INS (NIL) -9 NIL 1242073 NIL) (-542 1235012 1235783 1236757 "INS-" 1236830 NIL INS- (NIL T) -8 NIL NIL NIL) (-541 1233787 1234014 1234312 "INPSIGN" 1234765 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-540 1232905 1233022 1233219 "INPRODPF" 1233667 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-539 1231799 1231916 1232153 "INPRODFF" 1232785 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-538 1230799 1230951 1231211 "INNMFACT" 1231635 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-537 1229996 1230093 1230281 "INMODGCD" 1230698 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-536 1228505 1228749 1229073 "INFSP" 1229741 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-535 1227689 1227806 1227989 "INFPROD0" 1228385 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-534 1224571 1225754 1226269 "INFORM" 1227182 T INFORM (NIL) -8 NIL NIL NIL) (-533 1224181 1224241 1224339 "INFORM1" 1224506 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-532 1223704 1223793 1223907 "INFINITY" 1224087 T INFINITY (NIL) -7 NIL NIL NIL) (-531 1223155 1223424 1223525 "INETCLTS" 1223623 T INETCLTS (NIL) -8 NIL NIL NIL) (-530 1221772 1222021 1222342 "INEP" 1222903 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-529 1221048 1221669 1221734 "INDE" 1221739 NIL INDE (NIL T) -8 NIL NIL NIL) (-528 1220612 1220680 1220797 "INCRMAPS" 1220975 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-527 1219625 1219881 1220087 "INBFILE" 1220426 T INBFILE (NIL) -8 NIL NIL NIL) (-526 1214936 1215861 1216805 "INBFF" 1218713 NIL INBFF (NIL T) -7 NIL NIL NIL) (-525 1214590 1214671 1214699 "INBCON" 1214837 T INBCON (NIL) -9 NIL 1214920 NIL) (-524 1214433 1214467 1214542 "INBCON-" 1214547 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-523 1213935 1214154 1214246 "INAST" 1214361 T INAST (NIL) -8 NIL NIL NIL) (-522 1213389 1213614 1213720 "IMPTAST" 1213849 T IMPTAST (NIL) -8 NIL NIL NIL) (-521 1209883 1213233 1213337 "IMATRIX" 1213342 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-520 1208595 1208718 1209033 "IMATQF" 1209739 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-519 1206815 1207042 1207379 "IMATLIN" 1208351 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-518 1201441 1206739 1206797 "ILIST" 1206802 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-517 1199394 1201301 1201414 "IIARRAY2" 1201419 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-516 1194827 1199305 1199369 "IFF" 1199374 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-515 1194201 1194444 1194560 "IFAST" 1194731 T IFAST (NIL) -8 NIL NIL NIL) (-514 1189244 1193493 1193681 "IFARRAY" 1194058 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-513 1188451 1189148 1189221 "IFAMON" 1189226 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-512 1188035 1188100 1188154 "IEVALAB" 1188361 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-511 1187710 1187778 1187938 "IEVALAB-" 1187943 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-510 1187368 1187624 1187687 "IDPO" 1187692 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-509 1186645 1187257 1187332 "IDPOAMS" 1187337 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-508 1185979 1186534 1186609 "IDPOAM" 1186614 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-507 1185064 1185314 1185367 "IDPC" 1185780 NIL IDPC (NIL T T) -9 NIL 1185929 NIL) (-506 1184560 1184956 1185029 "IDPAM" 1185034 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-505 1183963 1184452 1184525 "IDPAG" 1184530 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-504 1183731 1183878 1183928 "IDENT" 1183933 T IDENT (NIL) -8 NIL NIL NIL) (-503 1179986 1180834 1181729 "IDECOMP" 1182888 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-502 1172860 1173909 1174956 "IDEAL" 1179022 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-501 1172024 1172136 1172335 "ICDEN" 1172744 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-500 1171123 1171504 1171651 "ICARD" 1171897 T ICARD (NIL) -8 NIL NIL NIL) (-499 1169183 1169496 1169901 "IBPTOOLS" 1170800 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-498 1164817 1168803 1168916 "IBITS" 1169102 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-497 1161540 1162116 1162811 "IBATOOL" 1164234 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-496 1159320 1159781 1160314 "IBACHIN" 1161075 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-495 1157197 1159166 1159269 "IARRAY2" 1159274 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-494 1153350 1157123 1157180 "IARRAY1" 1157185 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-493 1147344 1151762 1152243 "IAN" 1152889 T IAN (NIL) -8 NIL NIL NIL) (-492 1146855 1146912 1147085 "IALGFACT" 1147281 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-491 1146383 1146496 1146524 "HYPCAT" 1146731 T HYPCAT (NIL) -9 NIL NIL NIL) (-490 1145921 1146038 1146224 "HYPCAT-" 1146229 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-489 1145543 1145716 1145799 "HOSTNAME" 1145858 T HOSTNAME (NIL) -8 NIL NIL NIL) (-488 1145388 1145425 1145466 "HOMOTOP" 1145471 NIL HOMOTOP (NIL T) -9 NIL 1145504 NIL) (-487 1142067 1143398 1143439 "HOAGG" 1144420 NIL HOAGG (NIL T) -9 NIL 1145099 NIL) (-486 1140661 1141060 1141586 "HOAGG-" 1141591 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-485 1134703 1140258 1140406 "HEXADEC" 1140533 T HEXADEC (NIL) -8 NIL NIL NIL) (-484 1133451 1133673 1133936 "HEUGCD" 1134480 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-483 1132554 1133288 1133418 "HELLFDIV" 1133423 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-482 1130782 1132331 1132419 "HEAP" 1132498 NIL HEAP (NIL T) -8 NIL NIL NIL) (-481 1130073 1130334 1130468 "HEADAST" 1130668 T HEADAST (NIL) -8 NIL NIL NIL) (-480 1123993 1129988 1130050 "HDP" 1130055 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-479 1117744 1123628 1123780 "HDMP" 1123894 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-478 1117069 1117208 1117372 "HB" 1117600 T HB (NIL) -7 NIL NIL NIL) (-477 1110566 1116915 1117019 "HASHTBL" 1117024 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-476 1110069 1110287 1110379 "HASAST" 1110494 T HASAST (NIL) -8 NIL NIL NIL) (-475 1107881 1109691 1109873 "HACKPI" 1109907 T HACKPI (NIL) -8 NIL NIL NIL) (-474 1103576 1107734 1107847 "GTSET" 1107852 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-473 1097102 1103454 1103552 "GSTBL" 1103557 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-472 1089415 1096133 1096398 "GSERIES" 1096893 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-471 1088582 1088973 1089001 "GROUP" 1089204 T GROUP (NIL) -9 NIL 1089338 NIL) (-470 1087948 1088107 1088358 "GROUP-" 1088363 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-469 1086317 1086636 1087023 "GROEBSOL" 1087625 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-468 1085257 1085519 1085570 "GRMOD" 1086099 NIL GRMOD (NIL T T) -9 NIL 1086267 NIL) (-467 1085025 1085061 1085189 "GRMOD-" 1085194 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-466 1080351 1081379 1082379 "GRIMAGE" 1084045 T GRIMAGE (NIL) -8 NIL NIL NIL) (-465 1078818 1079078 1079402 "GRDEF" 1080047 T GRDEF (NIL) -7 NIL NIL NIL) (-464 1078262 1078378 1078519 "GRAY" 1078697 T GRAY (NIL) -7 NIL NIL NIL) (-463 1077475 1077855 1077906 "GRALG" 1078059 NIL GRALG (NIL T T) -9 NIL 1078152 NIL) (-462 1077136 1077209 1077372 "GRALG-" 1077377 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-461 1073940 1076721 1076899 "GPOLSET" 1077043 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-460 1073294 1073351 1073609 "GOSPER" 1073877 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-459 1069053 1069732 1070258 "GMODPOL" 1072993 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-458 1068058 1068242 1068480 "GHENSEL" 1068865 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-457 1062109 1062952 1063979 "GENUPS" 1067142 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-456 1061806 1061857 1061946 "GENUFACT" 1062052 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-455 1061218 1061295 1061460 "GENPGCD" 1061724 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-454 1060692 1060727 1060940 "GENMFACT" 1061177 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-453 1059260 1059515 1059822 "GENEEZ" 1060435 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-452 1053173 1058871 1059033 "GDMP" 1059183 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-451 1042550 1046944 1048050 "GCNAALG" 1052156 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-450 1040977 1041805 1041833 "GCDDOM" 1042088 T GCDDOM (NIL) -9 NIL 1042245 NIL) (-449 1040447 1040574 1040789 "GCDDOM-" 1040794 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-448 1039119 1039304 1039608 "GB" 1040226 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-447 1027739 1030065 1032457 "GBINTERN" 1036810 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-446 1025576 1025868 1026289 "GBF" 1027414 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-445 1024357 1024522 1024789 "GBEUCLID" 1025392 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-444 1023706 1023831 1023980 "GAUSSFAC" 1024228 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-443 1022073 1022375 1022689 "GALUTIL" 1023425 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-442 1020381 1020655 1020979 "GALPOLYU" 1021800 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-441 1017746 1018036 1018443 "GALFACTU" 1020078 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-440 1009552 1011051 1012659 "GALFACT" 1016178 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-439 1006940 1007598 1007626 "FVFUN" 1008782 T FVFUN (NIL) -9 NIL 1009502 NIL) (-438 1006206 1006388 1006416 "FVC" 1006707 T FVC (NIL) -9 NIL 1006890 NIL) (-437 1005848 1006003 1006084 "FUNCTION" 1006158 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1003619 1004170 1004636 "FT" 1005402 T FT (NIL) -8 NIL NIL NIL) (-435 1002437 1002920 1003123 "FTEM" 1003436 T FTEM (NIL) -8 NIL NIL NIL) (-434 1000693 1000982 1001386 "FSUPFACT" 1002128 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999090 999379 999711 "FST" 1000381 T FST (NIL) -8 NIL NIL NIL) (-432 998261 998367 998562 "FSRED" 998972 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 996940 997195 997549 "FSPRMELT" 997976 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994025 994463 994962 "FSPECF" 996503 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976085 984528 984568 "FS" 988416 NIL FS (NIL T) -9 NIL 990705 NIL) (-428 964735 967725 971781 "FS-" 972078 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964249 964303 964480 "FSINT" 964676 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 962576 963242 963545 "FSERIES" 964028 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 961590 961706 961937 "FSCINT" 962456 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 957824 960534 960575 "FSAGG" 960945 NIL FSAGG (NIL T) -9 NIL 961204 NIL) (-423 955586 956187 956983 "FSAGG-" 957078 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 954628 954771 954998 "FSAGG2" 955439 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952283 952562 953116 "FS2UPS" 954346 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 951865 951908 952063 "FS2" 952234 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 950722 950893 951202 "FS2EXPXP" 951690 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950148 950263 950415 "FRUTIL" 950602 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 941603 945643 947001 "FR" 948822 NIL FR (NIL T) -8 NIL NIL NIL) (-416 936678 939321 939361 "FRNAALG" 940757 NIL FRNAALG (NIL T) -9 NIL 941364 NIL) (-415 932356 933427 934702 "FRNAALG-" 935452 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 931994 932037 932164 "FRNAAF2" 932307 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 930401 930848 931143 "FRMOD" 931806 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928180 928784 929101 "FRIDEAL" 930192 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 927375 927462 927751 "FRIDEAL2" 928087 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 926508 926922 926963 "FRETRCT" 926968 NIL FRETRCT (NIL T) -9 NIL 927144 NIL) (-409 925620 925851 926202 "FRETRCT-" 926207 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 922832 924008 924067 "FRAMALG" 924949 NIL FRAMALG (NIL T T) -9 NIL 925241 NIL) (-407 920966 921421 922051 "FRAMALG-" 922274 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 914924 920441 920717 "FRAC" 920722 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 914560 914617 914724 "FRAC2" 914861 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914196 914253 914360 "FR2" 914497 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 908869 911721 911749 "FPS" 912868 T FPS (NIL) -9 NIL 913425 NIL) (-402 908318 908427 908591 "FPS-" 908737 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 905772 907407 907435 "FPC" 907660 T FPC (NIL) -9 NIL 907802 NIL) (-400 905565 905605 905702 "FPC-" 905707 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 904443 905053 905094 "FPATMAB" 905099 NIL FPATMAB (NIL T) -9 NIL 905251 NIL) (-398 902143 902619 903045 "FPARFRAC" 904080 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 897537 898035 898717 "FORTRAN" 901575 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895253 895753 896292 "FORT" 897018 T FORT (NIL) -7 NIL NIL NIL) (-395 892929 893491 893519 "FORTFN" 894579 T FORTFN (NIL) -9 NIL 895203 NIL) (-394 892693 892743 892771 "FORTCAT" 892830 T FORTCAT (NIL) -9 NIL 892892 NIL) (-393 890826 891309 891699 "FORMULA" 892323 T FORMULA (NIL) -8 NIL NIL NIL) (-392 890614 890644 890713 "FORMULA1" 890790 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890137 890189 890362 "FORDER" 890556 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889233 889397 889590 "FOP" 889964 T FOP (NIL) -7 NIL NIL NIL) (-389 887841 888513 888687 "FNLA" 889115 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 886596 886985 887013 "FNCAT" 887473 T FNCAT (NIL) -9 NIL 887733 NIL) (-387 886162 886555 886583 "FNAME" 886588 T FNAME (NIL) -8 NIL NIL NIL) (-386 884825 885754 885782 "FMTC" 885787 T FMTC (NIL) -9 NIL 885823 NIL) (-385 881187 882348 882977 "FMONOID" 884229 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 880406 880929 881078 "FM" 881083 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 877830 878476 878504 "FMFUN" 879648 T FMFUN (NIL) -9 NIL 880356 NIL) (-382 877099 877280 877308 "FMC" 877598 T FMC (NIL) -9 NIL 877780 NIL) (-381 874293 875127 875181 "FMCAT" 876376 NIL FMCAT (NIL T T) -9 NIL 876871 NIL) (-380 873186 874059 874159 "FM1" 874238 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 870960 871376 871870 "FLOATRP" 872737 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 864584 868689 869310 "FLOAT" 870359 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862022 862522 863100 "FLOATCP" 864051 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 860831 861635 861676 "FLINEXP" 861681 NIL FLINEXP (NIL T) -9 NIL 861774 NIL) (-375 859985 860220 860548 "FLINEXP-" 860553 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859061 859205 859429 "FLASORT" 859837 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856278 857120 857172 "FLALG" 858399 NIL FLALG (NIL T T) -9 NIL 858866 NIL) (-372 850062 853764 853805 "FLAGG" 855067 NIL FLAGG (NIL T) -9 NIL 855719 NIL) (-371 848788 849127 849617 "FLAGG-" 849622 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 847830 847973 848200 "FLAGG2" 848641 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 844805 845779 845838 "FINRALG" 846966 NIL FINRALG (NIL T T) -9 NIL 847474 NIL) (-368 843965 844194 844533 "FINRALG-" 844538 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 843371 843584 843612 "FINITE" 843808 T FINITE (NIL) -9 NIL 843915 NIL) (-366 835829 837990 838030 "FINAALG" 841697 NIL FINAALG (NIL T) -9 NIL 843150 NIL) (-365 831170 832211 833355 "FINAALG-" 834734 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 830565 830925 831028 "FILE" 831100 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829249 829561 829615 "FILECAT" 830299 NIL FILECAT (NIL T T) -9 NIL 830515 NIL) (-362 827117 828611 828639 "FIELD" 828679 T FIELD (NIL) -9 NIL 828759 NIL) (-361 825737 826122 826633 "FIELD-" 826638 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 823615 824372 824719 "FGROUP" 825423 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 822705 822869 823089 "FGLMICPK" 823447 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 818572 822630 822687 "FFX" 822692 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818173 818234 818369 "FFSLPE" 818505 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814166 814945 815741 "FFPOLY" 817409 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 813670 813706 813915 "FFPOLY2" 814124 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 809556 813589 813652 "FFP" 813657 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 804989 809467 809531 "FF" 809536 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800150 804332 804522 "FFNBX" 804843 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795124 799285 799543 "FFNBP" 800004 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 789792 794408 794619 "FFNB" 794957 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 788624 788822 789137 "FFINTBAS" 789589 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 784852 787031 787059 "FFIELDC" 787679 T FFIELDC (NIL) -9 NIL 788055 NIL) (-347 783515 783885 784382 "FFIELDC-" 784387 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783085 783130 783254 "FFHOM" 783457 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 780783 781267 781784 "FFF" 782600 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 776436 780525 780626 "FFCGX" 780726 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772103 776168 776275 "FFCGP" 776379 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767321 771830 771938 "FFCG" 772039 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749154 758192 758278 "FFCAT" 763443 NIL FFCAT (NIL T T T) -9 NIL 764894 NIL) (-340 744352 745399 746713 "FFCAT-" 747943 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 743763 743806 744041 "FFCAT2" 744303 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 732975 736735 737955 "FEXPR" 742615 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 731975 732410 732451 "FEVALAB" 732535 NIL FEVALAB (NIL T) -9 NIL 732796 NIL) (-336 731134 731344 731682 "FEVALAB-" 731687 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 729727 730517 730720 "FDIV" 731033 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 726793 727508 727623 "FDIVCAT" 729191 NIL FDIVCAT (NIL T T T T) -9 NIL 729628 NIL) (-333 726555 726582 726752 "FDIVCAT-" 726757 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 725775 725862 726139 "FDIV2" 726462 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 724461 724720 725009 "FCPAK1" 725506 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 723589 723961 724102 "FCOMP" 724352 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707326 710739 714277 "FC" 720071 T FC (NIL) -8 NIL NIL NIL) (-328 699905 703890 703930 "FAXF" 705732 NIL FAXF (NIL T) -9 NIL 706424 NIL) (-327 697184 697839 698664 "FAXF-" 699129 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692284 696560 696736 "FARRAY" 697041 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 687537 689569 689622 "FAMR" 690645 NIL FAMR (NIL T T) -9 NIL 691105 NIL) (-324 686427 686729 687164 "FAMR-" 687169 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 685623 686349 686402 "FAMONOID" 686407 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 683435 684119 684172 "FAMONC" 685113 NIL FAMONC (NIL T T) -9 NIL 685499 NIL) (-321 682127 683189 683326 "FAGROUP" 683331 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 679922 680241 680644 "FACUTIL" 681808 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679021 679206 679428 "FACTFUNC" 679732 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 671426 678272 678484 "EXPUPXS" 678877 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 668909 669449 670035 "EXPRTUBE" 670860 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665103 665695 666432 "EXPRODE" 668248 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 650477 663758 664186 "EXPR" 664707 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 644884 645471 646284 "EXPR2UPS" 649775 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 644520 644577 644684 "EXPR2" 644821 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 635925 643652 643949 "EXPEXPAN" 644357 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 635752 635882 635911 "EXIT" 635916 T EXIT (NIL) -8 NIL NIL NIL) (-310 635259 635476 635567 "EXITAST" 635681 T EXITAST (NIL) -8 NIL NIL NIL) (-309 634886 634948 635061 "EVALCYC" 635191 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 634427 634545 634586 "EVALAB" 634756 NIL EVALAB (NIL T) -9 NIL 634860 NIL) (-307 633908 634030 634251 "EVALAB-" 634256 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 631376 632644 632672 "EUCDOM" 633227 T EUCDOM (NIL) -9 NIL 633577 NIL) (-305 629781 630223 630813 "EUCDOM-" 630818 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617321 620079 622829 "ESTOOLS" 627051 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 616953 617010 617119 "ESTOOLS2" 617258 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 616704 616746 616826 "ESTOOLS1" 616905 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 610609 612337 612365 "ES" 615133 T ES (NIL) -9 NIL 616542 NIL) (-300 605557 606843 608660 "ES-" 608824 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 601932 602692 603472 "ESCONT" 604797 T ESCONT (NIL) -7 NIL NIL NIL) (-298 601677 601709 601791 "ESCONT1" 601894 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601352 601402 601502 "ES2" 601621 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 600982 601040 601149 "ES1" 601288 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600198 600327 600503 "ERROR" 600826 T ERROR (NIL) -7 NIL NIL NIL) (-294 593701 600057 600148 "EQTBL" 600153 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586258 589015 590464 "EQ" 592285 NIL -3297 (NIL T) -8 NIL NIL NIL) (-292 585890 585947 586056 "EQ2" 586195 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581182 582228 583321 "EP" 584829 NIL EP (NIL T) -7 NIL NIL NIL) (-290 579764 580065 580382 "ENV" 580885 T ENV (NIL) -8 NIL NIL NIL) (-289 578943 579463 579491 "ENTIRER" 579496 T ENTIRER (NIL) -9 NIL 579542 NIL) (-288 575445 576898 577268 "EMR" 578742 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 574589 574774 574828 "ELTAGG" 575208 NIL ELTAGG (NIL T T) -9 NIL 575419 NIL) (-286 574308 574370 574511 "ELTAGG-" 574516 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574097 574126 574180 "ELTAB" 574264 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573223 573369 573568 "ELFUTS" 573948 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 572965 573021 573049 "ELEMFUN" 573154 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 572835 572856 572924 "ELEMFUN-" 572929 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 567726 570935 570976 "ELAGG" 571916 NIL ELAGG (NIL T) -9 NIL 572379 NIL) (-280 566011 566445 567108 "ELAGG-" 567113 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 564668 564948 565243 "ELABEXPR" 565736 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 557534 559335 560162 "EFUPXS" 563944 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 550984 552785 553595 "EFULS" 556810 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 548406 548764 549243 "EFSTRUC" 550616 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 537478 539043 540603 "EF" 546921 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 536579 536963 537112 "EAB" 537349 T EAB (NIL) -8 NIL NIL NIL) (-273 535788 536538 536566 "E04UCFA" 536571 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 534997 535747 535775 "E04NAFA" 535780 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534206 534956 534984 "E04MBFA" 534989 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 533415 534165 534193 "E04JAFA" 534198 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 532626 533374 533402 "E04GCFA" 533407 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 531837 532585 532613 "E04FDFA" 532618 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531046 531796 531824 "E04DGFA" 531829 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525224 526571 527935 "E04AGNT" 529702 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 523930 524410 524450 "DVARCAT" 524925 NIL DVARCAT (NIL T) -9 NIL 525124 NIL) (-264 523134 523346 523660 "DVARCAT-" 523665 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516034 522933 523062 "DSMP" 523067 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 510844 511979 513047 "DROPT" 514986 T DROPT (NIL) -8 NIL NIL NIL) (-261 510509 510568 510666 "DROPT1" 510779 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 505624 506750 507887 "DROPT0" 509392 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 503969 504294 504680 "DRAWPT" 505258 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 498556 499479 500558 "DRAW" 502943 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498189 498242 498360 "DRAWHACK" 498497 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 496920 497189 497480 "DRAWCX" 497918 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 496436 496504 496655 "DRAWCURV" 496846 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 486907 488866 490981 "DRAWCFUN" 494341 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 483720 485602 485643 "DQAGG" 486272 NIL DQAGG (NIL T) -9 NIL 486545 NIL) (-252 471999 478698 478781 "DPOLCAT" 480633 NIL DPOLCAT (NIL T T T T) -9 NIL 481178 NIL) (-251 466838 468184 470142 "DPOLCAT-" 470147 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 459993 466699 466797 "DPMO" 466802 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453051 459773 459940 "DPMM" 459945 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 452715 452970 453018 "DOMCTOR" 453023 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452010 452237 452374 "DOMAIN" 452598 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 445761 451645 451797 "DMP" 451911 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445361 445417 445561 "DLP" 445699 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439231 444688 444878 "DLIST" 445203 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436075 438084 438125 "DLAGG" 438675 NIL DLAGG (NIL T) -9 NIL 438905 NIL) (-242 434888 435518 435546 "DIVRING" 435638 T DIVRING (NIL) -9 NIL 435721 NIL) (-241 434125 434315 434615 "DIVRING-" 434620 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432227 432584 432990 "DISPLAY" 433739 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426169 432141 432204 "DIRPROD" 432209 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425017 425220 425485 "DIRPROD2" 425962 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414280 420232 420285 "DIRPCAT" 420695 NIL DIRPCAT (NIL NIL T) -9 NIL 421535 NIL) (-236 411606 412248 413129 "DIRPCAT-" 413466 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 410893 411053 411239 "DIOSP" 411440 T DIOSP (NIL) -7 NIL NIL NIL) (-234 407595 409805 409846 "DIOPS" 410280 NIL DIOPS (NIL T) -9 NIL 410509 NIL) (-233 407144 407258 407449 "DIOPS-" 407454 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406036 406630 406658 "DIFRING" 406845 T DIFRING (NIL) -9 NIL 406955 NIL) (-231 405682 405759 405911 "DIFRING-" 405916 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 403487 404725 404766 "DIFEXT" 405129 NIL DIFEXT (NIL T) -9 NIL 405423 NIL) (-229 401772 402200 402866 "DIFEXT-" 402871 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399094 401304 401345 "DIAGG" 401350 NIL DIAGG (NIL T) -9 NIL 401370 NIL) (-227 398478 398635 398887 "DIAGG-" 398892 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 393943 397437 397714 "DHMATRIX" 398247 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 389555 390464 391474 "DFSFUN" 392953 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 384671 388486 388798 "DFLOAT" 389263 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 382899 383180 383576 "DFINTTLS" 384379 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 379964 380920 381320 "DERHAM" 382565 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 377813 379739 379828 "DEQUEUE" 379908 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377028 377161 377357 "DEGRED" 377675 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 373423 374168 375021 "DEFINTRF" 376256 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 370950 371419 372018 "DEFINTEF" 372942 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370327 370570 370685 "DEFAST" 370855 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364369 369924 370072 "DECIMAL" 370199 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 361881 362339 362845 "DDFACT" 363913 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 361477 361520 361671 "DBLRESP" 361832 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359376 359710 360070 "DBASE" 361244 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 358645 358856 359002 "DATAARY" 359275 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 357778 358604 358632 "D03FAFA" 358637 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 356912 357737 357765 "D03EEFA" 357770 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 354862 355328 355817 "D03AGNT" 356443 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354178 354821 354849 "D02EJFA" 354854 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 353494 354137 354165 "D02CJFA" 354170 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 352810 353453 353481 "D02BHFA" 353486 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352126 352769 352797 "D02BBFA" 352802 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345324 346912 348518 "D02AGNT" 350540 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343093 343615 344161 "D01WGTS" 344798 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342188 343052 343080 "D01TRNS" 343085 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341283 342147 342175 "D01GBFA" 342180 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340378 341242 341270 "D01FCFA" 341275 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 339473 340337 340365 "D01ASFA" 340370 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 338568 339432 339460 "D01AQFA" 339465 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 337663 338527 338555 "D01APFA" 338560 T D01APFA (NIL) -8 NIL NIL NIL) (-196 336758 337622 337650 "D01ANFA" 337655 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 335853 336717 336745 "D01AMFA" 336750 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 334948 335812 335840 "D01ALFA" 335845 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334043 334907 334935 "D01AKFA" 334940 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333138 334002 334030 "D01AJFA" 334035 T D01AJFA (NIL) -8 NIL NIL NIL) (-191 326435 327986 329547 "D01AGNT" 331597 T D01AGNT (NIL) -7 NIL NIL NIL) (-190 325772 325900 326052 "CYCLOTOM" 326303 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-189 322507 323220 323947 "CYCLES" 325065 T CYCLES (NIL) -7 NIL NIL NIL) (-188 321819 321953 322124 "CVMP" 322368 NIL CVMP (NIL T) -7 NIL NIL NIL) (-187 319590 319848 320224 "CTRIGMNP" 321547 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-186 319313 319549 319577 "CTOR" 319582 T CTOR (NIL) -8 NIL NIL NIL) (-185 318849 319044 319145 "CTORKIND" 319232 T CTORKIND (NIL) -8 NIL NIL NIL) (-184 318320 318548 318576 "CTORCAT" 318696 T CTORCAT (NIL) -9 NIL 318779 NIL) (-183 318015 318095 318221 "CTORCAT-" 318226 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-182 317531 317718 317816 "CTORCALL" 317937 T CTORCALL (NIL) -8 NIL NIL NIL) (-181 316905 317004 317157 "CSTTOOLS" 317428 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-180 312704 313361 314119 "CRFP" 316217 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-179 312206 312425 312517 "CRCEAST" 312632 T CRCEAST (NIL) -8 NIL NIL NIL) (-178 311253 311438 311666 "CRAPACK" 312010 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-177 310637 310738 310942 "CPMATCH" 311129 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-176 310362 310390 310496 "CPIMA" 310603 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-175 306726 307398 308116 "COORDSYS" 309697 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-174 306110 306239 306389 "CONTOUR" 306596 T CONTOUR (NIL) -8 NIL NIL NIL) (-173 302036 304113 304605 "CONTFRAC" 305650 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-172 301916 301937 301965 "CONDUIT" 302002 T CONDUIT (NIL) -9 NIL NIL NIL) (-171 301089 301609 301637 "COMRING" 301642 T COMRING (NIL) -9 NIL 301694 NIL) (-170 300170 300447 300631 "COMPPROP" 300925 T COMPPROP (NIL) -8 NIL NIL NIL) (-169 299831 299866 299994 "COMPLPAT" 300129 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-168 289888 299640 299749 "COMPLEX" 299754 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289524 289581 289688 "COMPLEX2" 289825 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-166 289242 289277 289375 "COMPFACT" 289483 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-165 273415 283635 283675 "COMPCAT" 284679 NIL COMPCAT (NIL T) -9 NIL 286064 NIL) (-164 262931 265854 269481 "COMPCAT-" 269837 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-163 262660 262688 262791 "COMMUPC" 262897 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-162 262455 262488 262547 "COMMONOP" 262621 T COMMONOP (NIL) -7 NIL NIL NIL) (-161 262038 262206 262293 "COMM" 262388 T COMM (NIL) -8 NIL NIL NIL) (-160 261642 261842 261917 "COMMAAST" 261983 T COMMAAST (NIL) -8 NIL NIL NIL) (-159 260891 261085 261113 "COMBOPC" 261451 T COMBOPC (NIL) -9 NIL 261626 NIL) (-158 259787 259997 260239 "COMBINAT" 260681 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-157 255985 256558 257198 "COMBF" 259209 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-156 254771 255101 255336 "COLOR" 255770 T COLOR (NIL) -8 NIL NIL NIL) (-155 254274 254492 254584 "COLONAST" 254699 T COLONAST (NIL) -8 NIL NIL NIL) (-154 253914 253961 254086 "CMPLXRT" 254221 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-153 253389 253614 253713 "CLLCTAST" 253835 T CLLCTAST (NIL) -8 NIL NIL NIL) (-152 248891 249919 250999 "CLIP" 252329 T CLIP (NIL) -7 NIL NIL NIL) (-151 247273 247997 248236 "CLIF" 248718 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-150 243495 245419 245460 "CLAGG" 246389 NIL CLAGG (NIL T) -9 NIL 246925 NIL) (-149 241917 242374 242957 "CLAGG-" 242962 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-148 241461 241546 241686 "CINTSLPE" 241826 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-147 238962 239433 239981 "CHVAR" 240989 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-146 238205 238725 238753 "CHARZ" 238758 T CHARZ (NIL) -9 NIL 238773 NIL) (-145 237959 237999 238077 "CHARPOL" 238159 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-144 237086 237639 237667 "CHARNZ" 237714 T CHARNZ (NIL) -9 NIL 237770 NIL) (-143 235075 235776 236111 "CHAR" 236771 T CHAR (NIL) -8 NIL NIL NIL) (-142 234801 234862 234890 "CFCAT" 235001 T CFCAT (NIL) -9 NIL NIL NIL) (-141 234046 234157 234339 "CDEN" 234685 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-140 230038 233199 233479 "CCLASS" 233786 T CCLASS (NIL) -8 NIL NIL NIL) (-139 229345 229488 229651 "CATEGORY" 229895 T -10 (NIL) -8 NIL NIL NIL) (-138 229009 229264 229312 "CATCTOR" 229317 T CATCTOR (NIL) -8 NIL NIL NIL) (-137 228483 228709 228808 "CATAST" 228930 T CATAST (NIL) -8 NIL NIL NIL) (-136 227986 228204 228296 "CASEAST" 228411 T CASEAST (NIL) -8 NIL NIL NIL) (-135 223038 224015 224768 "CARTEN" 227289 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 222146 222294 222515 "CARTEN2" 222885 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-133 220488 221296 221553 "CARD" 221909 T CARD (NIL) -8 NIL NIL NIL) (-132 220091 220292 220367 "CAPSLAST" 220433 T CAPSLAST (NIL) -8 NIL NIL NIL) (-131 219463 219791 219819 "CACHSET" 219951 T CACHSET (NIL) -9 NIL 220028 NIL) (-130 218959 219255 219283 "CABMON" 219333 T CABMON (NIL) -9 NIL 219389 NIL) (-129 218107 218505 218641 "BYTE" 218804 T BYTE (NIL) -8 NIL NIL 218920) (-128 213516 217575 217738 "BYTEBUF" 217964 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211073 213208 213315 "BTREE" 213442 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208571 210721 210843 "BTOURN" 210983 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 205988 208041 208082 "BTCAT" 208150 NIL BTCAT (NIL T) -9 NIL 208227 NIL) (-124 205655 205735 205884 "BTCAT-" 205889 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 200947 204798 204826 "BTAGG" 205048 T BTAGG (NIL) -9 NIL 205209 NIL) (-122 200437 200562 200768 "BTAGG-" 200773 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197481 199715 199930 "BSTREE" 200254 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196619 196745 196929 "BRILL" 197337 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193318 195345 195386 "BRAGG" 196035 NIL BRAGG (NIL T) -9 NIL 196293 NIL) (-118 191847 192253 192808 "BRAGG-" 192813 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185111 191193 191377 "BPADICRT" 191695 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183461 185048 185093 "BPADIC" 185098 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183159 183189 183303 "BOUNDZRO" 183425 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL NIL) (-113 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 174997 175719 175912 "BOOLEAN" 176122 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174359 174737 174791 "BMODULE" 174796 NIL BMODULE (NIL T T) -9 NIL 174861 NIL) (-110 170189 174157 174230 "BITS" 174306 T BITS (NIL) -8 NIL NIL NIL) (-109 169601 169723 169865 "BINDING" 170067 T BINDING (NIL) -8 NIL NIL NIL) (-108 163646 169200 169347 "BINARY" 169474 T BINARY (NIL) -8 NIL NIL NIL) (-107 161473 162901 162942 "BGAGG" 163202 NIL BGAGG (NIL T) -9 NIL 163339 NIL) (-106 161304 161336 161427 "BGAGG-" 161432 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150169 150329 150355 "ASTCAT" 150360 T ASTCAT (NIL) -9 NIL 150390 NIL) (-92 149896 149955 150074 "ASTCAT-" 150079 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148093 149672 149760 "ASTACK" 149839 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146598 146895 147260 "ASSOCEQ" 147775 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145630 146257 146381 "ASP9" 146505 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145394 145578 145617 "ASP8" 145622 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144263 144999 145141 "ASP80" 145283 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143162 143898 144030 "ASP7" 144162 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142116 142839 142957 "ASP78" 143075 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141085 141796 141913 "ASP77" 142030 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 139997 140723 140854 "ASP74" 140985 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138897 139632 139764 "ASP73" 139896 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138001 138723 138823 "ASP6" 138828 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 136949 137678 137796 "ASP55" 137914 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135899 136623 136742 "ASP50" 136861 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 134987 135600 135710 "ASP4" 135820 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134075 134688 134798 "ASP49" 134908 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132860 133614 133782 "ASP42" 133964 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131637 132393 132563 "ASP41" 132747 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130587 131314 131432 "ASP35" 131550 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130352 130535 130574 "ASP34" 130579 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130089 130156 130232 "ASP33" 130307 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 128984 129724 129856 "ASP31" 129988 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128749 128932 128971 "ASP30" 128976 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128484 128553 128629 "ASP29" 128704 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128249 128432 128471 "ASP28" 128476 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128014 128197 128236 "ASP27" 128241 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127098 127712 127823 "ASP24" 127934 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126175 126900 127012 "ASP20" 127017 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125263 125876 125986 "ASP1" 126096 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124207 124937 125056 "ASP19" 125175 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 123944 124011 124087 "ASP12" 124162 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122796 123543 123687 "ASP10" 123831 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120695 122640 122731 "ARRAY2" 122736 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116511 120343 120457 "ARRAY1" 120612 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115543 115716 115937 "ARRAY12" 116334 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109902 111773 111848 "ARR2CAT" 114478 NIL ARR2CAT (NIL T T T) -9 NIL 115236 NIL) (-56 107336 108080 109034 "ARR2CAT-" 109039 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106930 107163 107242 "ARITY" 107275 T ARITY (NIL) -8 NIL NIL NIL) (-54 105678 105830 106136 "APPRULE" 106766 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105329 105377 105496 "APPLYORE" 105624 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104303 104594 104789 "ANY" 105152 T ANY (NIL) -8 NIL NIL NIL) (-51 103581 103704 103861 "ANY1" 104177 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101146 102018 102345 "ANTISYM" 103305 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100661 100850 100947 "ANON" 101067 T ANON (NIL) -8 NIL NIL NIL) (-48 94793 99200 99654 "AN" 100225 T AN (NIL) -8 NIL NIL NIL) (-47 91049 92403 92454 "AMR" 93202 NIL AMR (NIL T T) -9 NIL 93802 NIL) (-46 90161 90382 90745 "AMR-" 90750 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74711 90078 90139 "ALIST" 90144 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71548 74305 74474 "ALGSC" 74629 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68104 68658 69265 "ALGPKG" 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T) ((-641 |#2|) |has| |#1| (-362)) ((-641 $) . T) ((-634 (-561)) -12 (|has| |#1| (-362)) (|has| |#2| (-634 (-561)))) ((-634 |#2|) |has| |#1| (-362)) ((-711 #1#) -4007 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-561))))) ((-711 |#1|) |has| |#1| (-171)) ((-711 |#2|) |has| |#1| (-362)) ((-711 $) -4007 (|has| |#1| (-553)) (|has| |#1| (-362))) ((-720) . 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2767902 2768095 2768165 "SUCHTAST" 2768225 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1155 2767224 2767427 2767567 "SUCH" 2767810 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1154 2761118 2762130 2763089 "SUBSPACE" 2766312 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1153 2760548 2760638 2760802 "SUBRESP" 2761006 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1152 2753917 2755213 2756524 "STTF" 2759284 NIL STTF (NIL T) -7 NIL NIL NIL) (-1151 2748090 2749210 2750357 "STTFNC" 2752817 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1150 2739405 2741272 2743066 "STTAYLOR" 2746331 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1149 2732649 2739269 2739352 "STRTBL" 2739357 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1148 2728040 2732604 2732635 "STRING" 2732640 T STRING (NIL) -8 NIL NIL NIL) (-1147 2722928 2727413 2727443 "STRICAT" 2727502 T STRICAT (NIL) -9 NIL 2727564 NIL) (-1146 2715738 2720547 2721158 "STREAM" 2722352 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1145 2715248 2715325 2715469 "STREAM3" 2715655 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1144 2714230 2714413 2714648 "STREAM2" 2715061 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1143 2713918 2713970 2714063 "STREAM1" 2714172 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1142 2712934 2713115 2713346 "STINPROD" 2713734 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1141 2712512 2712696 2712726 "STEP" 2712806 T STEP (NIL) -9 NIL 2712884 NIL) (-1140 2706055 2712411 2712488 "STBL" 2712493 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1139 2701229 2705276 2705319 "STAGG" 2705472 NIL STAGG (NIL T) -9 NIL 2705561 NIL) (-1138 2698931 2699533 2700405 "STAGG-" 2700410 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1137 2697126 2698701 2698793 "STACK" 2698874 NIL STACK (NIL T) -8 NIL NIL NIL) (-1136 2689851 2695267 2695723 "SREGSET" 2696756 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1135 2682277 2683645 2685158 "SRDCMPK" 2688457 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1134 2675244 2679717 2679747 "SRAGG" 2681050 T SRAGG (NIL) -9 NIL 2681658 NIL) (-1133 2674261 2674516 2674895 "SRAGG-" 2674900 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1132 2668756 2673208 2673629 "SQMATRIX" 2673887 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1131 2662505 2665474 2666201 "SPLTREE" 2668101 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1130 2658495 2659161 2659807 "SPLNODE" 2661931 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1129 2657542 2657775 2657805 "SPFCAT" 2658249 T SPFCAT (NIL) -9 NIL NIL NIL) (-1128 2656279 2656489 2656753 "SPECOUT" 2657300 T SPECOUT (NIL) -7 NIL NIL NIL) (-1127 2647931 2649675 2649705 "SPADXPT" 2654097 T SPADXPT (NIL) -9 NIL 2656131 NIL) (-1126 2647692 2647732 2647801 "SPADPRSR" 2647884 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1125 2645875 2647647 2647678 "SPADAST" 2647683 T SPADAST (NIL) -8 NIL NIL NIL) (-1124 2637846 2639593 2639636 "SPACEC" 2644009 NIL SPACEC (NIL T) -9 NIL 2645825 NIL) (-1123 2636017 2637778 2637827 "SPACE3" 2637832 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1122 2634769 2634940 2635231 "SORTPAK" 2635822 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1121 2632819 2633122 2633541 "SOLVETRA" 2634433 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1120 2631830 2632052 2632326 "SOLVESER" 2632592 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1119 2627050 2627931 2628933 "SOLVERAD" 2630882 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1118 2622865 2623474 2624203 "SOLVEFOR" 2626417 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1117 2617162 2622214 2622311 "SNTSCAT" 2622316 NIL SNTSCAT (NIL T T T T) -9 NIL 2622386 NIL) (-1116 2611305 2615485 2615876 "SMTS" 2616852 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1115 2605756 2611193 2611270 "SMP" 2611275 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1114 2603915 2604216 2604614 "SMITH" 2605453 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1113 2596810 2600966 2601069 "SMATCAT" 2602420 NIL SMATCAT (NIL NIL T T T) -9 NIL 2602970 NIL) (-1112 2593750 2594573 2595751 "SMATCAT-" 2595756 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1111 2591463 2592986 2593029 "SKAGG" 2593290 NIL SKAGG (NIL T) -9 NIL 2593425 NIL) (-1110 2587805 2590879 2591074 "SINT" 2591261 T SINT (NIL) -8 NIL NIL 2591434) (-1109 2587577 2587615 2587681 "SIMPAN" 2587761 T SIMPAN (NIL) -7 NIL NIL NIL) (-1108 2586884 2587112 2587252 "SIG" 2587459 T SIG (NIL) -8 NIL NIL NIL) (-1107 2585722 2585943 2586218 "SIGNRF" 2586643 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1106 2584527 2584678 2584969 "SIGNEF" 2585551 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1105 2583860 2584110 2584234 "SIGAST" 2584425 T SIGAST (NIL) -8 NIL NIL NIL) (-1104 2581550 2582004 2582510 "SHP" 2583401 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1103 2575456 2581451 2581527 "SHDP" 2581532 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1102 2575055 2575221 2575251 "SGROUP" 2575344 T SGROUP (NIL) -9 NIL 2575406 NIL) (-1101 2574913 2574939 2575012 "SGROUP-" 2575017 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1100 2571749 2572446 2573169 "SGCF" 2574212 T SGCF (NIL) -7 NIL NIL NIL) (-1099 2566144 2571196 2571293 "SFRTCAT" 2571298 NIL SFRTCAT (NIL T T T T) -9 NIL 2571337 NIL) (-1098 2559568 2560583 2561719 "SFRGCD" 2565127 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1097 2552696 2553767 2554953 "SFQCMPK" 2558501 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1096 2552318 2552407 2552517 "SFORT" 2552637 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1095 2551463 2552158 2552279 "SEXOF" 2552284 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1094 2550597 2551344 2551412 "SEX" 2551417 T SEX (NIL) -8 NIL NIL NIL) (-1093 2546136 2546825 2546920 "SEXCAT" 2549857 NIL SEXCAT (NIL T T T T T) -9 NIL 2550435 NIL) (-1092 2543316 2546070 2546118 "SET" 2546123 NIL SET (NIL T) -8 NIL NIL NIL) (-1091 2541567 2542029 2542334 "SETMN" 2543057 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1090 2541173 2541299 2541329 "SETCAT" 2541446 T SETCAT (NIL) -9 NIL 2541531 NIL) (-1089 2540953 2541005 2541104 "SETCAT-" 2541109 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1088 2537340 2539414 2539457 "SETAGG" 2540327 NIL SETAGG (NIL T) -9 NIL 2540667 NIL) (-1087 2536798 2536914 2537151 "SETAGG-" 2537156 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1086 2536268 2536494 2536595 "SEQAST" 2536719 T SEQAST (NIL) -8 NIL NIL NIL) (-1085 2535467 2535761 2535822 "SEGXCAT" 2536108 NIL SEGXCAT (NIL T T) -9 NIL 2536228 NIL) (-1084 2534523 2535133 2535315 "SEG" 2535320 NIL SEG (NIL T) -8 NIL NIL NIL) (-1083 2533502 2533716 2533759 "SEGCAT" 2534281 NIL SEGCAT (NIL T) -9 NIL 2534502 NIL) (-1082 2532551 2532881 2533081 "SEGBIND" 2533337 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1081 2532172 2532231 2532344 "SEGBIND2" 2532486 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1080 2531773 2531973 2532050 "SEGAST" 2532117 T SEGAST (NIL) -8 NIL NIL NIL) (-1079 2530992 2531118 2531322 "SEG2" 2531617 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1078 2530429 2530927 2530974 "SDVAR" 2530979 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1077 2522719 2530199 2530329 "SDPOL" 2530334 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1076 2521312 2521578 2521897 "SCPKG" 2522434 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1075 2520448 2520628 2520828 "SCOPE" 2521134 T SCOPE (NIL) -8 NIL NIL NIL) (-1074 2519669 2519802 2519981 "SCACHE" 2520303 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1073 2519341 2519501 2519531 "SASTCAT" 2519536 T SASTCAT (NIL) -9 NIL 2519549 NIL) (-1072 2518855 2519176 2519252 "SAOS" 2519287 T SAOS (NIL) -8 NIL NIL NIL) (-1071 2518420 2518455 2518628 "SAERFFC" 2518814 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1070 2512394 2518317 2518397 "SAE" 2518402 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1069 2511987 2512022 2512181 "SAEFACT" 2512353 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1068 2510308 2510622 2511023 "RURPK" 2511653 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1067 2508944 2509223 2509535 "RULESET" 2510142 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1066 2506131 2506634 2507099 "RULE" 2508625 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1065 2505770 2505925 2506008 "RULECOLD" 2506083 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1064 2505268 2505487 2505581 "RSTRCAST" 2505698 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1063 2500117 2500911 2501831 "RSETGCD" 2504467 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1062 2489374 2494426 2494523 "RSETCAT" 2498642 NIL RSETCAT (NIL T T T T) -9 NIL 2499739 NIL) (-1061 2487301 2487840 2488664 "RSETCAT-" 2488669 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1060 2479688 2481063 2482583 "RSDCMPK" 2485900 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2477693 2478134 2478208 "RRCC" 2479294 NIL RRCC (NIL T T) -9 NIL 2479638 NIL) (-1058 2477044 2477218 2477497 "RRCC-" 2477502 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1057 2476514 2476740 2476841 "RPTAST" 2476965 T RPTAST (NIL) -8 NIL NIL NIL) (-1056 2450520 2460107 2460174 "RPOLCAT" 2470838 NIL RPOLCAT (NIL T T T) -9 NIL 2473997 NIL) (-1055 2442020 2444358 2447480 "RPOLCAT-" 2447485 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1054 2433067 2440231 2440713 "ROUTINE" 2441560 T ROUTINE (NIL) -8 NIL NIL NIL) (-1053 2429900 2432693 2432833 "ROMAN" 2432949 T ROMAN (NIL) -8 NIL NIL NIL) (-1052 2428175 2428760 2429020 "ROIRC" 2429705 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1051 2424568 2426811 2426841 "RNS" 2427145 T RNS (NIL) -9 NIL 2427418 NIL) (-1050 2423077 2423460 2423994 "RNS-" 2424069 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1049 2422526 2422908 2422938 "RNG" 2422943 T RNG (NIL) -9 NIL 2422964 NIL) (-1048 2421918 2422280 2422323 "RMODULE" 2422385 NIL RMODULE (NIL T) -9 NIL 2422427 NIL) (-1047 2420754 2420848 2421184 "RMCAT2" 2421819 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1046 2417631 2420100 2420397 "RMATRIX" 2420516 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1045 2410573 2412807 2412922 "RMATCAT" 2416281 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2417263 NIL) (-1044 2409948 2410095 2410402 "RMATCAT-" 2410407 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1043 2409515 2409590 2409718 "RINTERP" 2409867 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1042 2408648 2409168 2409198 "RING" 2409254 T RING (NIL) -9 NIL 2409340 NIL) (-1041 2408440 2408484 2408581 "RING-" 2408586 NIL RING- (NIL T) -8 NIL NIL NIL) (-1040 2407281 2407518 2407776 "RIDIST" 2408204 T RIDIST (NIL) -7 NIL NIL NIL) (-1039 2398597 2406749 2406955 "RGCHAIN" 2407129 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1038 2397973 2398353 2398394 "RGBCSPC" 2398452 NIL RGBCSPC (NIL T) -9 NIL 2398504 NIL) (-1037 2397157 2397512 2397553 "RGBCMDL" 2397785 NIL RGBCMDL (NIL T) -9 NIL 2397899 NIL) (-1036 2394151 2394765 2395435 "RF" 2396521 NIL RF (NIL T) -7 NIL NIL NIL) (-1035 2393797 2393860 2393963 "RFFACTOR" 2394082 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1034 2393522 2393557 2393654 "RFFACT" 2393756 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1033 2391639 2392003 2392385 "RFDIST" 2393162 T RFDIST (NIL) -7 NIL NIL NIL) (-1032 2391092 2391184 2391347 "RETSOL" 2391541 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1031 2390728 2390808 2390851 "RETRACT" 2390984 NIL RETRACT (NIL T) -9 NIL 2391071 NIL) (-1030 2390577 2390602 2390689 "RETRACT-" 2390694 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1029 2390206 2390399 2390469 "RETAST" 2390529 T RETAST (NIL) -8 NIL NIL NIL) (-1028 2383060 2389859 2389986 "RESULT" 2390101 T RESULT (NIL) -8 NIL NIL NIL) (-1027 2381686 2382329 2382528 "RESRING" 2382963 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1026 2381322 2381371 2381469 "RESLATC" 2381623 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1025 2381028 2381062 2381169 "REPSQ" 2381281 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1024 2378450 2379030 2379632 "REP" 2380448 T REP (NIL) -7 NIL NIL NIL) (-1023 2378148 2378182 2378293 "REPDB" 2378409 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1022 2372058 2373437 2374660 "REP2" 2376960 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1021 2368435 2369116 2369924 "REP1" 2371285 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1020 2361161 2366576 2367032 "REGSET" 2368065 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1019 2359974 2360309 2360559 "REF" 2360946 NIL REF (NIL T) -8 NIL NIL NIL) (-1018 2359351 2359454 2359621 "REDORDER" 2359858 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1017 2355356 2358564 2358791 "RECLOS" 2359179 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1016 2354408 2354589 2354804 "REALSOLV" 2355163 T REALSOLV (NIL) -7 NIL NIL NIL) (-1015 2354254 2354295 2354325 "REAL" 2354330 T REAL (NIL) -9 NIL 2354365 NIL) (-1014 2350737 2351539 2352423 "REAL0Q" 2353419 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1013 2346338 2347326 2348387 "REAL0" 2349718 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1012 2345836 2346055 2346149 "RDUCEAST" 2346266 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1011 2345241 2345313 2345520 "RDIV" 2345758 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1010 2344309 2344483 2344696 "RDIST" 2345063 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1009 2342906 2343193 2343565 "RDETRS" 2344017 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1008 2340718 2341172 2341710 "RDETR" 2342448 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1007 2339329 2339607 2340011 "RDEEFS" 2340434 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1006 2337824 2338130 2338562 "RDEEF" 2339017 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1005 2332085 2334960 2334990 "RCFIELD" 2336285 T RCFIELD (NIL) -9 NIL 2337015 NIL) (-1004 2330149 2330653 2331349 "RCFIELD-" 2331424 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1003 2326465 2328250 2328293 "RCAGG" 2329377 NIL RCAGG (NIL T) -9 NIL 2329842 NIL) (-1002 2326093 2326187 2326350 "RCAGG-" 2326355 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1001 2325428 2325540 2325705 "RATRET" 2325977 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1000 2324981 2325048 2325169 "RATFACT" 2325356 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-999 2324296 2324416 2324566 "RANDSRC" 2324851 T RANDSRC (NIL) -7 NIL NIL NIL) (-998 2324033 2324077 2324148 "RADUTIL" 2324245 T RADUTIL (NIL) -7 NIL NIL NIL) (-997 2317195 2322875 2323183 "RADIX" 2323757 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-996 2308852 2317039 2317167 "RADFF" 2317172 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-995 2308504 2308579 2308607 "RADCAT" 2308764 T RADCAT (NIL) -9 NIL NIL NIL) (-994 2308289 2308337 2308434 "RADCAT-" 2308439 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-993 2306440 2308064 2308153 "QUEUE" 2308233 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-992 2303016 2306377 2306422 "QUAT" 2306427 NIL QUAT (NIL T) -8 NIL NIL NIL) (-991 2302654 2302697 2302824 "QUATCT2" 2302967 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-990 2296401 2299703 2299743 "QUATCAT" 2300523 NIL QUATCAT (NIL T) -9 NIL 2301289 NIL) (-989 2292545 2293582 2294969 "QUATCAT-" 2295063 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-988 2290065 2291629 2291670 "QUAGG" 2292045 NIL QUAGG (NIL T) -9 NIL 2292220 NIL) (-987 2289697 2289890 2289958 "QQUTAST" 2290017 T QQUTAST (NIL) -8 NIL NIL NIL) (-986 2288622 2289095 2289267 "QFORM" 2289569 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-985 2279834 2285039 2285079 "QFCAT" 2285737 NIL QFCAT (NIL T) -9 NIL 2286738 NIL) (-984 2275406 2276607 2278198 "QFCAT-" 2278292 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-983 2275044 2275087 2275214 "QFCAT2" 2275357 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-982 2274504 2274614 2274744 "QEQUAT" 2274934 T QEQUAT (NIL) -8 NIL NIL NIL) (-981 2267652 2268723 2269907 "QCMPACK" 2273437 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-980 2265228 2265649 2266077 "QALGSET" 2267307 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-979 2264473 2264647 2264879 "QALGSET2" 2265048 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-978 2263164 2263387 2263704 "PWFFINTB" 2264246 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-977 2261346 2261514 2261868 "PUSHVAR" 2262978 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-976 2257264 2258318 2258359 "PTRANFN" 2260243 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-975 2255666 2255957 2256279 "PTPACK" 2256975 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-974 2255298 2255355 2255464 "PTFUNC2" 2255603 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-973 2249825 2254170 2254211 "PTCAT" 2254507 NIL PTCAT (NIL T) -9 NIL 2254660 NIL) (-972 2249483 2249518 2249642 "PSQFR" 2249784 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-971 2248078 2248376 2248710 "PSEUDLIN" 2249181 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-970 2234848 2237212 2239536 "PSETPK" 2245838 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-969 2227892 2230606 2230702 "PSETCAT" 2233723 NIL PSETCAT (NIL T T T T) -9 NIL 2234537 NIL) (-968 2225728 2226362 2227183 "PSETCAT-" 2227188 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-967 2225077 2225242 2225270 "PSCURVE" 2225538 T PSCURVE (NIL) -9 NIL 2225705 NIL) (-966 2221433 2222915 2222980 "PSCAT" 2223824 NIL PSCAT (NIL T T T) -9 NIL 2224064 NIL) (-965 2220496 2220712 2221112 "PSCAT-" 2221117 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-964 2219228 2219861 2220066 "PRTITION" 2220311 T PRTITION (NIL) -8 NIL NIL NIL) (-963 2218730 2218949 2219041 "PRTDAST" 2219156 T PRTDAST (NIL) -8 NIL NIL NIL) (-962 2207828 2210034 2212222 "PRS" 2216592 NIL PRS (NIL T T) -7 NIL NIL NIL) (-961 2205686 2207178 2207218 "PRQAGG" 2207401 NIL PRQAGG (NIL T) -9 NIL 2207503 NIL) (-960 2205072 2205301 2205329 "PROPLOG" 2205514 T PROPLOG (NIL) -9 NIL 2205636 NIL) (-959 2202242 2202886 2203350 "PROPFRML" 2204640 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-958 2201702 2201812 2201942 "PROPERTY" 2202132 T PROPERTY (NIL) -8 NIL NIL NIL) (-957 2195787 2199868 2200688 "PRODUCT" 2200928 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-956 2193100 2195245 2195479 "PR" 2195598 NIL PR (NIL T T) -8 NIL NIL NIL) (-955 2192896 2192928 2192987 "PRINT" 2193061 T PRINT (NIL) -7 NIL NIL NIL) (-954 2192236 2192353 2192505 "PRIMES" 2192776 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-953 2190301 2190702 2191168 "PRIMELT" 2191815 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-952 2190030 2190079 2190107 "PRIMCAT" 2190231 T PRIMCAT (NIL) -9 NIL NIL NIL) (-951 2186191 2189968 2190013 "PRIMARR" 2190018 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-950 2185198 2185376 2185604 "PRIMARR2" 2186009 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-949 2184841 2184897 2185008 "PREASSOC" 2185136 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-948 2184316 2184449 2184477 "PPCURVE" 2184682 T PPCURVE (NIL) -9 NIL 2184818 NIL) (-947 2183938 2184111 2184194 "PORTNUM" 2184253 T PORTNUM (NIL) -8 NIL NIL NIL) (-946 2181297 2181696 2182288 "POLYROOT" 2183519 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-945 2175242 2180901 2181061 "POLY" 2181170 NIL POLY (NIL T) -8 NIL NIL NIL) (-944 2174625 2174683 2174917 "POLYLIFT" 2175178 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-943 2170900 2171349 2171978 "POLYCATQ" 2174170 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-942 2157717 2163075 2163140 "POLYCAT" 2166654 NIL POLYCAT (NIL T T T) -9 NIL 2168582 NIL) (-941 2151167 2153028 2155412 "POLYCAT-" 2155417 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-940 2150754 2150822 2150942 "POLY2UP" 2151093 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-939 2150386 2150443 2150552 "POLY2" 2150691 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-938 2149071 2149310 2149586 "POLUTIL" 2150160 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-937 2147426 2147703 2148034 "POLTOPOL" 2148793 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-936 2142944 2147362 2147408 "POINT" 2147413 NIL POINT (NIL T) -8 NIL NIL NIL) (-935 2141131 2141488 2141863 "PNTHEORY" 2142589 T PNTHEORY (NIL) -7 NIL NIL NIL) (-934 2139550 2139847 2140259 "PMTOOLS" 2140829 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-933 2139143 2139221 2139338 "PMSYM" 2139466 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-932 2138653 2138722 2138896 "PMQFCAT" 2139068 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-931 2138008 2138118 2138274 "PMPRED" 2138530 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-930 2137404 2137490 2137651 "PMPREDFS" 2137909 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-929 2136047 2136255 2136640 "PMPLCAT" 2137166 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-928 2135579 2135658 2135810 "PMLSAGG" 2135962 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-927 2135054 2135130 2135311 "PMKERNEL" 2135497 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-926 2134671 2134746 2134859 "PMINS" 2134973 NIL PMINS (NIL T) -7 NIL NIL NIL) (-925 2134099 2134168 2134384 "PMFS" 2134596 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-924 2133327 2133445 2133650 "PMDOWN" 2133976 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-923 2132490 2132649 2132831 "PMASS" 2133165 T PMASS (NIL) -7 NIL NIL NIL) (-922 2131764 2131875 2132038 "PMASSFS" 2132376 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-921 2131419 2131487 2131581 "PLOTTOOL" 2131690 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-920 2126041 2127230 2128378 "PLOT" 2130291 T PLOT (NIL) -8 NIL NIL NIL) (-919 2121855 2122889 2123810 "PLOT3D" 2125140 T PLOT3D (NIL) -8 NIL NIL NIL) (-918 2120767 2120944 2121179 "PLOT1" 2121659 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-917 2096161 2100833 2105684 "PLEQN" 2116033 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-916 2095479 2095601 2095781 "PINTERP" 2096026 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-915 2095172 2095219 2095322 "PINTERPA" 2095426 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-914 2094420 2094941 2095028 "PI" 2095068 T PI (NIL) -8 NIL NIL 2095135) (-913 2092817 2093758 2093786 "PID" 2093968 T PID (NIL) -9 NIL 2094102 NIL) (-912 2092542 2092579 2092667 "PICOERCE" 2092774 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-911 2091862 2092001 2092177 "PGROEB" 2092398 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-910 2087449 2088263 2089168 "PGE" 2090977 T PGE (NIL) -7 NIL NIL NIL) (-909 2085573 2085819 2086185 "PGCD" 2087166 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-908 2084911 2085014 2085175 "PFRPAC" 2085457 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-907 2081591 2083459 2083812 "PFR" 2084590 NIL PFR (NIL T) -8 NIL NIL NIL) (-906 2079980 2080224 2080549 "PFOTOOLS" 2081338 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-905 2078513 2078752 2079103 "PFOQ" 2079737 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-904 2076986 2077198 2077561 "PFO" 2078297 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-903 2073574 2076875 2076944 "PF" 2076949 NIL PF (NIL NIL) -8 NIL NIL NIL) (-902 2071008 2072245 2072273 "PFECAT" 2072858 T PFECAT (NIL) -9 NIL 2073242 NIL) (-901 2070453 2070607 2070821 "PFECAT-" 2070826 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-900 2069057 2069308 2069609 "PFBRU" 2070202 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-899 2066924 2067275 2067707 "PFBR" 2068708 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-898 2062840 2064300 2064976 "PERM" 2066281 NIL PERM (NIL T) -8 NIL NIL NIL) (-897 2058106 2059047 2059917 "PERMGRP" 2062003 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-896 2056238 2057169 2057210 "PERMCAT" 2057656 NIL PERMCAT (NIL T) -9 NIL 2057961 NIL) (-895 2055891 2055932 2056056 "PERMAN" 2056191 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-894 2053427 2055556 2055678 "PENDTREE" 2055802 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-893 2051520 2052254 2052295 "PDRING" 2052952 NIL PDRING (NIL T) -9 NIL 2053238 NIL) (-892 2050623 2050841 2051203 "PDRING-" 2051208 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-891 2047865 2048616 2049284 "PDEPROB" 2049975 T PDEPROB (NIL) -8 NIL NIL NIL) (-890 2045412 2045914 2046469 "PDEPACK" 2047330 T PDEPACK (NIL) -7 NIL NIL NIL) (-889 2044324 2044514 2044765 "PDECOMP" 2045211 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-888 2041929 2042746 2042774 "PDECAT" 2043561 T PDECAT (NIL) -9 NIL 2044274 NIL) (-887 2041680 2041713 2041803 "PCOMP" 2041890 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-886 2039885 2040481 2040778 "PBWLB" 2041409 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-885 2032390 2033958 2035296 "PATTERN" 2038568 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-884 2032022 2032079 2032188 "PATTERN2" 2032327 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-883 2029779 2030167 2030624 "PATTERN1" 2031611 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-882 2027174 2027728 2028209 "PATRES" 2029344 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-881 2026738 2026805 2026937 "PATRES2" 2027101 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-880 2024621 2025026 2025433 "PATMATCH" 2026405 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-879 2024157 2024340 2024381 "PATMAB" 2024488 NIL PATMAB (NIL T) -9 NIL 2024571 NIL) (-878 2022702 2023011 2023269 "PATLRES" 2023962 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-877 2022248 2022371 2022412 "PATAB" 2022417 NIL PATAB (NIL T) -9 NIL 2022589 NIL) (-876 2019729 2020261 2020834 "PARTPERM" 2021695 T PARTPERM (NIL) -7 NIL NIL NIL) (-875 2019350 2019413 2019515 "PARSURF" 2019660 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-874 2018982 2019039 2019148 "PARSU2" 2019287 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-873 2018746 2018786 2018853 "PARSER" 2018935 T PARSER (NIL) -7 NIL NIL NIL) (-872 2018367 2018430 2018532 "PARSCURV" 2018677 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-871 2017999 2018056 2018165 "PARSC2" 2018304 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-870 2017638 2017696 2017793 "PARPCURV" 2017935 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-869 2017270 2017327 2017436 "PARPC2" 2017575 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-868 2016790 2016876 2016995 "PAN2EXPR" 2017171 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-867 2015596 2015911 2016139 "PALETTE" 2016582 T PALETTE (NIL) -8 NIL NIL NIL) (-866 2014064 2014601 2014961 "PAIR" 2015282 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-865 2007970 2013323 2013517 "PADICRC" 2013919 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-864 2001234 2007316 2007500 "PADICRAT" 2007818 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-863 1999584 2001171 2001216 "PADIC" 2001221 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-862 1996794 1998324 1998364 "PADICCT" 1998945 NIL PADICCT (NIL NIL) -9 NIL 1999227 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(NIL) -9 NIL 1956209 NIL) (-837 1952241 1954235 1954644 "ORDCOMP" 1955273 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-836 1951507 1951634 1951820 "ORDCOMP2" 1952101 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-835 1948115 1948998 1949812 "OPTPROB" 1950713 T OPTPROB (NIL) -8 NIL NIL NIL) (-834 1944917 1945556 1946260 "OPTPACK" 1947431 T OPTPACK (NIL) -7 NIL NIL NIL) (-833 1942630 1943370 1943398 "OPTCAT" 1944217 T OPTCAT (NIL) -9 NIL 1944867 NIL) (-832 1942073 1942307 1942412 "OPSIG" 1942545 T OPSIG (NIL) -8 NIL NIL NIL) (-831 1941841 1941880 1941946 "OPQUERY" 1942027 T OPQUERY (NIL) -7 NIL NIL NIL) (-830 1939007 1940152 1940656 "OP" 1941370 NIL OP (NIL T) -8 NIL NIL NIL) (-829 1938542 1938713 1938754 "OPERCAT" 1938889 NIL OPERCAT (NIL T) -9 NIL 1938957 NIL) (-828 1938388 1938415 1938501 "OPERCAT-" 1938506 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-827 1935233 1937185 1937554 "ONECOMP" 1938052 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-826 1934538 1934653 1934827 "ONECOMP2" 1935105 NIL ONECOMP2 (NIL T 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"OFMONOID" 1915280 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-812 1911208 1911707 1911752 "ODVAR" 1911757 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-811 1908666 1910953 1911108 "ODR" 1911113 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-810 1901010 1908442 1908568 "ODPOL" 1908573 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-809 1894886 1900882 1900987 "ODP" 1900992 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-808 1893652 1893867 1894142 "ODETOOLS" 1894660 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-807 1890621 1891277 1891993 "ODESYS" 1892985 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-806 1885503 1886411 1887436 "ODERTRIC" 1889696 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-805 1884929 1885011 1885205 "ODERED" 1885415 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-804 1881817 1882365 1883042 "ODERAT" 1884352 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-803 1878777 1879241 1879838 "ODEPRRIC" 1881346 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-802 1876747 1877316 1877802 "ODEPROB" 1878311 T ODEPROB (NIL) -8 NIL NIL NIL) (-801 1873269 1873752 1874399 "ODEPRIM" 1876226 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-800 1872518 1872620 1872880 "ODEPAL" 1873161 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-799 1868680 1869471 1870335 "ODEPACK" 1871674 T ODEPACK (NIL) -7 NIL NIL NIL) (-798 1867713 1867820 1868049 "ODEINT" 1868569 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-797 1861814 1863239 1864686 "ODEIFTBL" 1866286 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-796 1857149 1857935 1858894 "ODEEF" 1860973 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-795 1856484 1856573 1856803 "ODECONST" 1857054 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-794 1854635 1855270 1855298 "ODECAT" 1855903 T ODECAT (NIL) -9 NIL 1856434 NIL) (-793 1851542 1854347 1854466 "OCT" 1854548 NIL OCT (NIL T) -8 NIL NIL NIL) (-792 1851180 1851223 1851350 "OCTCT2" 1851493 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-791 1845954 1848354 1848394 "OC" 1849491 NIL OC (NIL T) -9 NIL 1850349 NIL) (-790 1843181 1843929 1844919 "OC-" 1845013 NIL OC- (NIL T T) -8 NIL NIL NIL) (-789 1842559 1843001 1843029 "OCAMON" 1843034 T OCAMON (NIL) -9 NIL 1843055 NIL) (-788 1842116 1842431 1842459 "OASGP" 1842464 T OASGP (NIL) -9 NIL 1842484 NIL) (-787 1841403 1841866 1841894 "OAMONS" 1841934 T OAMONS (NIL) -9 NIL 1841977 NIL) (-786 1840843 1841250 1841278 "OAMON" 1841283 T OAMON (NIL) -9 NIL 1841303 NIL) (-785 1840147 1840639 1840667 "OAGROUP" 1840672 T OAGROUP (NIL) -9 NIL 1840692 NIL) (-784 1839837 1839887 1839975 "NUMTUBE" 1840091 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-783 1833410 1834928 1836464 "NUMQUAD" 1838321 T NUMQUAD (NIL) -7 NIL NIL NIL) (-782 1829166 1830154 1831179 "NUMODE" 1832405 T NUMODE (NIL) -7 NIL NIL NIL) (-781 1826547 1827401 1827429 "NUMINT" 1828352 T NUMINT (NIL) -9 NIL 1829116 NIL) (-780 1825495 1825692 1825910 "NUMFMT" 1826349 T NUMFMT (NIL) -7 NIL NIL NIL) (-779 1811854 1814799 1817331 "NUMERIC" 1823002 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-778 1806251 1811303 1811398 "NTSCAT" 1811403 NIL NTSCAT (NIL T T T T) -9 NIL 1811442 NIL) (-777 1805445 1805610 1805803 "NTPOLFN" 1806090 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-776 1793285 1802270 1803082 "NSUP" 1804666 NIL NSUP (NIL T) -8 NIL NIL NIL) (-775 1792917 1792974 1793083 "NSUP2" 1793222 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-774 1782914 1792691 1792824 "NSMP" 1792829 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-773 1781346 1781647 1782004 "NREP" 1782602 NIL NREP (NIL T) -7 NIL NIL NIL) (-772 1779937 1780189 1780547 "NPCOEF" 1781089 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-771 1779003 1779118 1779334 "NORMRETR" 1779818 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-770 1777044 1777334 1777743 "NORMPK" 1778711 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-769 1776729 1776757 1776881 "NORMMA" 1777010 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-768 1776556 1776686 1776715 "NONE" 1776720 T NONE (NIL) -8 NIL NIL NIL) (-767 1776345 1776374 1776443 "NONE1" 1776520 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-766 1775828 1775890 1776076 "NODE1" 1776277 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-765 1774099 1774922 1775177 "NNI" 1775524 T NNI (NIL) -8 NIL NIL 1775759) (-764 1772519 1772832 1773196 "NLINSOL" 1773767 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-763 1768787 1769755 1770654 "NIPROB" 1771640 T NIPROB (NIL) -8 NIL NIL NIL) (-762 1767544 1767778 1768080 "NFINTBAS" 1768549 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-761 1766984 1767194 1767235 "NETCLT" 1767407 NIL NETCLT (NIL T) -9 NIL 1767489 NIL) (-760 1765692 1765923 1766204 "NCODIV" 1766752 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-759 1765454 1765491 1765566 "NCNTFRAC" 1765649 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-758 1763634 1763998 1764418 "NCEP" 1765079 NIL NCEP (NIL T) -7 NIL NIL NIL) (-757 1762545 1763284 1763312 "NASRING" 1763422 T NASRING (NIL) -9 NIL 1763496 NIL) (-756 1762340 1762384 1762478 "NASRING-" 1762483 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-755 1761493 1761992 1762020 "NARNG" 1762137 T NARNG (NIL) -9 NIL 1762228 NIL) (-754 1761185 1761252 1761386 "NARNG-" 1761391 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-753 1760064 1760271 1760506 "NAGSP" 1760970 T NAGSP (NIL) -7 NIL NIL NIL) (-752 1751336 1753020 1754693 "NAGS" 1758411 T NAGS (NIL) -7 NIL NIL NIL) (-751 1749884 1750192 1750523 "NAGF07" 1751025 T NAGF07 (NIL) -7 NIL NIL NIL) (-750 1744422 1745713 1747020 "NAGF04" 1748597 T NAGF04 (NIL) -7 NIL NIL NIL) (-749 1737390 1739004 1740637 "NAGF02" 1742809 T NAGF02 (NIL) -7 NIL NIL NIL) (-748 1732614 1733714 1734831 "NAGF01" 1736293 T NAGF01 (NIL) -7 NIL NIL NIL) (-747 1726242 1727808 1729393 "NAGE04" 1731049 T NAGE04 (NIL) -7 NIL NIL NIL) (-746 1717411 1719532 1721662 "NAGE02" 1724132 T NAGE02 (NIL) -7 NIL NIL NIL) (-745 1713364 1714311 1715275 "NAGE01" 1716467 T NAGE01 (NIL) -7 NIL NIL NIL) (-744 1711159 1711693 1712251 "NAGD03" 1712826 T NAGD03 (NIL) -7 NIL NIL NIL) (-743 1702909 1704837 1706791 "NAGD02" 1709225 T NAGD02 (NIL) -7 NIL NIL NIL) (-742 1696720 1698145 1699585 "NAGD01" 1701489 T NAGD01 (NIL) -7 NIL NIL NIL) (-741 1692929 1693751 1694588 "NAGC06" 1695903 T NAGC06 (NIL) -7 NIL NIL NIL) (-740 1691394 1691726 1692082 "NAGC05" 1692593 T NAGC05 (NIL) -7 NIL NIL NIL) (-739 1690770 1690889 1691033 "NAGC02" 1691270 T NAGC02 (NIL) -7 NIL NIL NIL) (-738 1689830 1690387 1690427 "NAALG" 1690506 NIL NAALG (NIL T) -9 NIL 1690567 NIL) (-737 1689665 1689694 1689784 "NAALG-" 1689789 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-736 1683615 1684723 1685910 "MULTSQFR" 1688561 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-735 1682934 1683009 1683193 "MULTFACT" 1683527 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-734 1676027 1679897 1679950 "MTSCAT" 1681020 NIL MTSCAT (NIL T T) -9 NIL 1681534 NIL) (-733 1675739 1675793 1675885 "MTHING" 1675967 NIL MTHING (NIL T) -7 NIL NIL NIL) (-732 1675531 1675564 1675624 "MSYSCMD" 1675699 T MSYSCMD (NIL) -7 NIL NIL NIL) (-731 1671643 1674286 1674606 "MSET" 1675244 NIL MSET (NIL T) -8 NIL NIL NIL) (-730 1668738 1671204 1671245 "MSETAGG" 1671250 NIL MSETAGG (NIL T) -9 NIL 1671284 NIL) (-729 1664621 1666117 1666862 "MRING" 1668038 NIL MRING (NIL T T) -8 NIL NIL NIL) (-728 1664187 1664254 1664385 "MRF2" 1664548 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-727 1663805 1663840 1663984 "MRATFAC" 1664146 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-726 1661417 1661712 1662143 "MPRFF" 1663510 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-725 1655477 1661271 1661368 "MPOLY" 1661373 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-724 1654967 1655002 1655210 "MPCPF" 1655436 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-723 1654481 1654524 1654708 "MPC3" 1654918 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-722 1653676 1653757 1653978 "MPC2" 1654396 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-721 1651977 1652314 1652704 "MONOTOOL" 1653336 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-720 1651228 1651519 1651547 "MONOID" 1651766 T MONOID (NIL) -9 NIL 1651913 NIL) (-719 1650774 1650893 1651074 "MONOID-" 1651079 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-718 1641633 1647541 1647600 "MONOGEN" 1648274 NIL MONOGEN (NIL T T) -9 NIL 1648730 NIL) (-717 1638851 1639586 1640586 "MONOGEN-" 1640705 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-716 1637710 1638130 1638158 "MONADWU" 1638550 T MONADWU (NIL) -9 NIL 1638788 NIL) (-715 1637082 1637241 1637489 "MONADWU-" 1637494 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-714 1636467 1636685 1636713 "MONAD" 1636920 T MONAD (NIL) -9 NIL 1637032 NIL) (-713 1636152 1636230 1636362 "MONAD-" 1636367 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-712 1634468 1635065 1635344 "MOEBIUS" 1635905 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-711 1633860 1634238 1634278 "MODULE" 1634283 NIL MODULE (NIL T) -9 NIL 1634309 NIL) (-710 1633428 1633524 1633714 "MODULE-" 1633719 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-709 1631143 1631792 1632119 "MODRING" 1633252 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-708 1628129 1629248 1629769 "MODOP" 1630672 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-707 1626744 1627196 1627473 "MODMONOM" 1627992 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-706 1616551 1625035 1625449 "MODMON" 1626381 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-705 1613742 1615395 1615671 "MODFIELD" 1616426 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-704 1612746 1613023 1613213 "MMLFORM" 1613572 T MMLFORM (NIL) -8 NIL NIL NIL) (-703 1612272 1612315 1612494 "MMAP" 1612697 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-702 1610489 1611222 1611263 "MLO" 1611686 NIL MLO (NIL T) -9 NIL 1611928 NIL) (-701 1607856 1608371 1608973 "MLIFT" 1609970 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-700 1607247 1607331 1607485 "MKUCFUNC" 1607767 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-699 1606846 1606916 1607039 "MKRECORD" 1607170 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-698 1605894 1606055 1606283 "MKFUNC" 1606657 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-697 1605282 1605386 1605542 "MKFLCFN" 1605777 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-696 1604825 1605192 1605251 "MKCHSET" 1605256 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-695 1604102 1604204 1604389 "MKBCFUNC" 1604718 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-694 1600844 1603656 1603792 "MINT" 1603986 T MINT (NIL) -8 NIL NIL NIL) (-693 1599656 1599899 1600176 "MHROWRED" 1600599 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-692 1595082 1598191 1598596 "MFLOAT" 1599271 T MFLOAT (NIL) -8 NIL NIL NIL) (-691 1594439 1594515 1594686 "MFINFACT" 1594994 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-690 1590754 1591602 1592486 "MESH" 1593575 T MESH (NIL) -7 NIL NIL NIL) (-689 1589144 1589456 1589809 "MDDFACT" 1590441 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-688 1585986 1588303 1588344 "MDAGG" 1588599 NIL MDAGG (NIL T) -9 NIL 1588742 NIL) (-687 1575764 1585279 1585486 "MCMPLX" 1585799 T MCMPLX (NIL) -8 NIL NIL NIL) (-686 1574905 1575051 1575251 "MCDEN" 1575613 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-685 1572795 1573065 1573445 "MCALCFN" 1574635 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-684 1571720 1571960 1572193 "MAYBE" 1572601 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-683 1569332 1569855 1570417 "MATSTOR" 1571191 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-682 1565338 1568704 1568952 "MATRIX" 1569117 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-681 1561107 1561811 1562547 "MATLIN" 1564695 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-680 1551261 1554399 1554476 "MATCAT" 1559356 NIL MATCAT (NIL T T T) -9 NIL 1560773 NIL) (-679 1547625 1548638 1549994 "MATCAT-" 1549999 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-678 1546219 1546372 1546705 "MATCAT2" 1547460 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-677 1544331 1544655 1545039 "MAPPKG3" 1545894 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-676 1543312 1543485 1543707 "MAPPKG2" 1544155 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-675 1541811 1542095 1542422 "MAPPKG1" 1543018 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-674 1540917 1541217 1541394 "MAPPAST" 1541654 T MAPPAST (NIL) -8 NIL NIL NIL) (-673 1540528 1540586 1540709 "MAPHACK3" 1540853 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-672 1540120 1540181 1540295 "MAPHACK2" 1540460 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-671 1539558 1539661 1539803 "MAPHACK1" 1540011 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-670 1537664 1538258 1538562 "MAGMA" 1539286 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-669 1537170 1537388 1537479 "MACROAST" 1537593 T MACROAST (NIL) -8 NIL NIL NIL) (-668 1533637 1535409 1535870 "M3D" 1536742 NIL M3D (NIL T) -8 NIL NIL NIL) (-667 1527791 1532006 1532047 "LZSTAGG" 1532829 NIL LZSTAGG (NIL T) -9 NIL 1533124 NIL) (-666 1523765 1524922 1526379 "LZSTAGG-" 1526384 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-665 1520879 1521656 1522143 "LWORD" 1523310 NIL LWORD (NIL T) -8 NIL NIL NIL) (-664 1520482 1520683 1520758 "LSTAST" 1520824 T LSTAST (NIL) -8 NIL NIL NIL) (-663 1513683 1520253 1520387 "LSQM" 1520392 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-662 1512907 1513046 1513274 "LSPP" 1513538 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-661 1510719 1511020 1511476 "LSMP" 1512596 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-660 1507498 1508172 1508902 "LSMP1" 1510021 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-659 1501423 1506665 1506706 "LSAGG" 1506768 NIL LSAGG (NIL T) -9 NIL 1506846 NIL) (-658 1498118 1499042 1500255 "LSAGG-" 1500260 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-657 1495744 1497262 1497511 "LPOLY" 1497913 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-656 1495326 1495411 1495534 "LPEFRAC" 1495653 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-655 1493673 1494420 1494673 "LO" 1495158 NIL LO (NIL T T T) -8 NIL NIL NIL) (-654 1493325 1493437 1493465 "LOGIC" 1493576 T LOGIC (NIL) -9 NIL 1493657 NIL) (-653 1493187 1493210 1493281 "LOGIC-" 1493286 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-652 1492380 1492520 1492713 "LODOOPS" 1493043 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-651 1489838 1492296 1492362 "LODO" 1492367 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-650 1488376 1488611 1488964 "LODOF" 1489585 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-649 1484732 1487129 1487170 "LODOCAT" 1487608 NIL LODOCAT (NIL T) -9 NIL 1487819 NIL) (-648 1484465 1484523 1484650 "LODOCAT-" 1484655 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-647 1481820 1484306 1484424 "LODO2" 1484429 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-646 1479290 1481757 1481802 "LODO1" 1481807 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-645 1478150 1478315 1478627 "LODEEF" 1479113 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-644 1473436 1476280 1476321 "LNAGG" 1477268 NIL LNAGG (NIL T) -9 NIL 1477712 NIL) (-643 1472583 1472797 1473139 "LNAGG-" 1473144 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-642 1468746 1469508 1470147 "LMOPS" 1471998 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-641 1468141 1468503 1468544 "LMODULE" 1468605 NIL LMODULE (NIL T) -9 NIL 1468647 NIL) (-640 1465387 1467786 1467909 "LMDICT" 1468051 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-639 1465113 1465295 1465355 "LITERAL" 1465360 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-638 1458340 1464059 1464357 "LIST" 1464848 NIL LIST (NIL T) -8 NIL NIL NIL) (-637 1457865 1457939 1458078 "LIST3" 1458260 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-636 1456872 1457050 1457278 "LIST2" 1457683 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-635 1455006 1455318 1455717 "LIST2MAP" 1456519 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-634 1453736 1454372 1454413 "LINEXP" 1454668 NIL LINEXP (NIL T) -9 NIL 1454817 NIL) (-633 1452383 1452643 1452940 "LINDEP" 1453488 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-632 1449150 1449869 1450646 "LIMITRF" 1451638 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-631 1447426 1447721 1448137 "LIMITPS" 1448845 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-630 1441881 1446937 1447165 "LIE" 1447247 NIL LIE (NIL T T) -8 NIL NIL NIL) (-629 1440930 1441373 1441413 "LIECAT" 1441553 NIL LIECAT (NIL T) -9 NIL 1441704 NIL) (-628 1440771 1440798 1440886 "LIECAT-" 1440891 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-627 1433383 1440220 1440385 "LIB" 1440626 T LIB (NIL) -8 NIL NIL NIL) (-626 1429020 1429901 1430836 "LGROBP" 1432500 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-625 1426886 1427160 1427522 "LF" 1428741 NIL LF (NIL T T) -7 NIL NIL NIL) (-624 1425726 1426418 1426446 "LFCAT" 1426653 T LFCAT (NIL) -9 NIL 1426792 NIL) (-623 1422630 1423258 1423946 "LEXTRIPK" 1425090 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-622 1419401 1420200 1420703 "LEXP" 1422210 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-621 1418904 1419122 1419214 "LETAST" 1419329 T LETAST (NIL) -8 NIL NIL NIL) (-620 1417302 1417615 1418016 "LEADCDET" 1418586 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-619 1416492 1416566 1416795 "LAZM3PK" 1417223 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-618 1411447 1414569 1415107 "LAUPOL" 1416004 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-617 1411012 1411056 1411224 "LAPLACE" 1411397 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-616 1408986 1410113 1410364 "LA" 1410845 NIL LA (NIL T T T) -8 NIL NIL NIL) (-615 1408067 1408617 1408658 "LALG" 1408720 NIL LALG (NIL T) -9 NIL 1408779 NIL) (-614 1407781 1407840 1407976 "LALG-" 1407981 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-613 1407616 1407640 1407681 "KVTFROM" 1407743 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-612 1406419 1406833 1407062 "KTVLOGIC" 1407407 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-611 1406254 1406278 1406319 "KRCFROM" 1406381 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-610 1405158 1405345 1405644 "KOVACIC" 1406054 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-609 1404993 1405017 1405058 "KONVERT" 1405120 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-608 1404828 1404852 1404893 "KOERCE" 1404955 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-607 1402562 1403322 1403715 "KERNEL" 1404467 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-606 1402064 1402145 1402275 "KERNEL2" 1402476 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-605 1395915 1400603 1400657 "KDAGG" 1401034 NIL KDAGG (NIL T T) -9 NIL 1401240 NIL) (-604 1395444 1395568 1395773 "KDAGG-" 1395778 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-603 1388619 1395105 1395260 "KAFILE" 1395322 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-602 1383074 1388130 1388358 "JORDAN" 1388440 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-601 1382480 1382723 1382844 "JOINAST" 1382973 T JOINAST (NIL) -8 NIL NIL NIL) (-600 1382326 1382385 1382440 "JAVACODE" 1382445 T JAVACODE (NIL) -8 NIL NIL NIL) (-599 1378625 1380531 1380585 "IXAGG" 1381514 NIL IXAGG (NIL T T) -9 NIL 1381973 NIL) (-598 1377544 1377850 1378269 "IXAGG-" 1378274 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-597 1373124 1377466 1377525 "IVECTOR" 1377530 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-596 1371890 1372127 1372393 "ITUPLE" 1372891 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-595 1370326 1370503 1370809 "ITRIGMNP" 1371712 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-594 1369071 1369275 1369558 "ITFUN3" 1370102 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-593 1368703 1368760 1368869 "ITFUN2" 1369008 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-592 1366540 1367565 1367864 "ITAYLOR" 1368437 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-591 1355523 1360677 1361840 "ISUPS" 1365410 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-590 1354627 1354767 1355003 "ISUMP" 1355370 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-589 1349891 1354428 1354507 "ISTRING" 1354580 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-588 1349394 1349612 1349704 "ISAST" 1349819 T ISAST (NIL) -8 NIL NIL NIL) (-587 1348604 1348685 1348901 "IRURPK" 1349308 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-586 1347540 1347741 1347981 "IRSN" 1348384 T IRSN (NIL) -7 NIL NIL NIL) (-585 1345569 1345924 1346360 "IRRF2F" 1347178 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-584 1345316 1345354 1345430 "IRREDFFX" 1345525 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-583 1343931 1344190 1344489 "IROOT" 1345049 NIL IROOT (NIL T) -7 NIL NIL NIL) (-582 1340563 1341615 1342307 "IR" 1343271 NIL IR (NIL T) -8 NIL NIL NIL) (-581 1338176 1338671 1339237 "IR2" 1340041 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-580 1337248 1337361 1337582 "IR2F" 1338059 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-579 1337039 1337073 1337133 "IPRNTPK" 1337208 T IPRNTPK (NIL) -7 NIL NIL NIL) (-578 1333658 1336928 1336997 "IPF" 1337002 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-577 1332021 1333583 1333640 "IPADIC" 1333645 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-576 1331361 1331581 1331711 "IP4ADDR" 1331911 T IP4ADDR (NIL) -8 NIL NIL NIL) (-575 1330861 1331065 1331175 "IOMODE" 1331271 T IOMODE (NIL) -8 NIL NIL NIL) (-574 1330209 1330458 1330585 "IOBFILE" 1330754 T IOBFILE (NIL) -8 NIL NIL NIL) (-573 1329963 1330113 1330141 "IOBCON" 1330146 T IOBCON (NIL) -9 NIL 1330167 NIL) (-572 1329460 1329518 1329708 "INVLAPLA" 1329899 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-571 1319109 1321462 1323848 "INTTR" 1327124 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-570 1315453 1316195 1317059 "INTTOOLS" 1318294 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-569 1315039 1315130 1315247 "INTSLPE" 1315356 T INTSLPE (NIL) -7 NIL NIL NIL) (-568 1313034 1314962 1315021 "INTRVL" 1315026 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-567 1310636 1311148 1311723 "INTRF" 1312519 NIL INTRF (NIL T) -7 NIL NIL NIL) (-566 1310047 1310144 1310286 "INTRET" 1310534 NIL INTRET (NIL T) -7 NIL NIL NIL) (-565 1308044 1308433 1308903 "INTRAT" 1309655 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-564 1305272 1305855 1306481 "INTPM" 1307529 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-563 1301975 1302574 1303319 "INTPAF" 1304658 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-562 1297154 1298116 1299167 "INTPACK" 1300944 T INTPACK (NIL) -7 NIL NIL NIL) (-561 1294066 1296883 1297010 "INT" 1297047 T INT (NIL) -8 NIL NIL NIL) (-560 1293318 1293470 1293678 "INTHERTR" 1293908 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-559 1292757 1292837 1293025 "INTHERAL" 1293232 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-558 1290603 1291046 1291503 "INTHEORY" 1292320 T INTHEORY (NIL) -7 NIL NIL NIL) (-557 1281911 1283532 1285311 "INTG0" 1288955 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-556 1262484 1267274 1272084 "INTFTBL" 1277121 T INTFTBL (NIL) -8 NIL NIL NIL) (-555 1261733 1261871 1262044 "INTFACT" 1262343 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-554 1259118 1259564 1260128 "INTEF" 1261287 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-553 1257585 1258290 1258318 "INTDOM" 1258619 T INTDOM (NIL) -9 NIL 1258826 NIL) (-552 1256954 1257128 1257370 "INTDOM-" 1257375 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-551 1253449 1255338 1255392 "INTCAT" 1256191 NIL INTCAT (NIL T) -9 NIL 1256511 NIL) (-550 1252922 1253024 1253152 "INTBIT" 1253341 T INTBIT (NIL) -7 NIL NIL NIL) (-549 1251593 1251747 1252061 "INTALG" 1252767 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-548 1251050 1251140 1251310 "INTAF" 1251497 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-547 1244504 1250860 1251000 "INTABL" 1251005 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-546 1243964 1244377 1244405 "INT8" 1244410 T INT8 (NIL) -8 NIL NIL 1244418) (-545 1243423 1243836 1243864 "INT32" 1243869 T INT32 (NIL) -8 NIL NIL 1243877) (-544 1242882 1243295 1243323 "INT16" 1243328 T INT16 (NIL) -8 NIL NIL 1243336) (-543 1237897 1240571 1240599 "INS" 1241533 T INS (NIL) -9 NIL 1242198 NIL) (-542 1235137 1235908 1236882 "INS-" 1236955 NIL INS- (NIL T) -8 NIL NIL NIL) (-541 1233912 1234139 1234437 "INPSIGN" 1234890 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-540 1233030 1233147 1233344 "INPRODPF" 1233792 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-539 1231924 1232041 1232278 "INPRODFF" 1232910 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-538 1230924 1231076 1231336 "INNMFACT" 1231760 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-537 1230121 1230218 1230406 "INMODGCD" 1230823 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-536 1228630 1228874 1229198 "INFSP" 1229866 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-535 1227814 1227931 1228114 "INFPROD0" 1228510 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-534 1224696 1225879 1226394 "INFORM" 1227307 T INFORM (NIL) -8 NIL NIL NIL) (-533 1224306 1224366 1224464 "INFORM1" 1224631 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-532 1223829 1223918 1224032 "INFINITY" 1224212 T INFINITY (NIL) -7 NIL NIL NIL) (-531 1223280 1223549 1223650 "INETCLTS" 1223748 T INETCLTS (NIL) -8 NIL NIL NIL) (-530 1221897 1222146 1222467 "INEP" 1223028 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-529 1221173 1221794 1221859 "INDE" 1221864 NIL INDE (NIL T) -8 NIL NIL NIL) (-528 1220737 1220805 1220922 "INCRMAPS" 1221100 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-527 1219750 1220006 1220212 "INBFILE" 1220551 T INBFILE (NIL) -8 NIL NIL NIL) (-526 1215061 1215986 1216930 "INBFF" 1218838 NIL INBFF (NIL T) -7 NIL NIL NIL) (-525 1214715 1214796 1214824 "INBCON" 1214962 T INBCON (NIL) -9 NIL 1215045 NIL) (-524 1214558 1214592 1214667 "INBCON-" 1214672 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-523 1214060 1214279 1214371 "INAST" 1214486 T INAST (NIL) -8 NIL NIL NIL) (-522 1213514 1213739 1213845 "IMPTAST" 1213974 T IMPTAST (NIL) -8 NIL NIL NIL) (-521 1210008 1213358 1213462 "IMATRIX" 1213467 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-520 1208720 1208843 1209158 "IMATQF" 1209864 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-519 1206940 1207167 1207504 "IMATLIN" 1208476 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-518 1201566 1206864 1206922 "ILIST" 1206927 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-517 1199519 1201426 1201539 "IIARRAY2" 1201544 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-516 1194952 1199430 1199494 "IFF" 1199499 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-515 1194326 1194569 1194685 "IFAST" 1194856 T IFAST (NIL) -8 NIL NIL NIL) (-514 1189369 1193618 1193806 "IFARRAY" 1194183 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-513 1188576 1189273 1189346 "IFAMON" 1189351 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-512 1188160 1188225 1188279 "IEVALAB" 1188486 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-511 1187835 1187903 1188063 "IEVALAB-" 1188068 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-510 1187493 1187749 1187812 "IDPO" 1187817 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-509 1186770 1187382 1187457 "IDPOAMS" 1187462 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-508 1186104 1186659 1186734 "IDPOAM" 1186739 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-507 1185189 1185439 1185492 "IDPC" 1185905 NIL IDPC (NIL T T) -9 NIL 1186054 NIL) (-506 1184685 1185081 1185154 "IDPAM" 1185159 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-505 1184088 1184577 1184650 "IDPAG" 1184655 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-504 1183856 1184003 1184053 "IDENT" 1184058 T IDENT (NIL) -8 NIL NIL NIL) (-503 1180111 1180959 1181854 "IDECOMP" 1183013 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-502 1172985 1174034 1175081 "IDEAL" 1179147 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-501 1172149 1172261 1172460 "ICDEN" 1172869 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-500 1171248 1171629 1171776 "ICARD" 1172022 T ICARD (NIL) -8 NIL NIL NIL) (-499 1169308 1169621 1170026 "IBPTOOLS" 1170925 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-498 1164942 1168928 1169041 "IBITS" 1169227 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-497 1161665 1162241 1162936 "IBATOOL" 1164359 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-496 1159445 1159906 1160439 "IBACHIN" 1161200 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-495 1157322 1159291 1159394 "IARRAY2" 1159399 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-494 1153475 1157248 1157305 "IARRAY1" 1157310 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-493 1147469 1151887 1152368 "IAN" 1153014 T IAN (NIL) -8 NIL NIL NIL) (-492 1146980 1147037 1147210 "IALGFACT" 1147406 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-491 1146508 1146621 1146649 "HYPCAT" 1146856 T HYPCAT (NIL) -9 NIL NIL NIL) (-490 1146046 1146163 1146349 "HYPCAT-" 1146354 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-489 1145668 1145841 1145924 "HOSTNAME" 1145983 T HOSTNAME (NIL) -8 NIL NIL NIL) (-488 1145513 1145550 1145591 "HOMOTOP" 1145596 NIL HOMOTOP (NIL T) -9 NIL 1145629 NIL) (-487 1142192 1143523 1143564 "HOAGG" 1144545 NIL HOAGG (NIL T) -9 NIL 1145224 NIL) (-486 1140786 1141185 1141711 "HOAGG-" 1141716 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-485 1134828 1140383 1140531 "HEXADEC" 1140658 T HEXADEC (NIL) -8 NIL NIL NIL) (-484 1133576 1133798 1134061 "HEUGCD" 1134605 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-483 1132679 1133413 1133543 "HELLFDIV" 1133548 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-482 1130907 1132456 1132544 "HEAP" 1132623 NIL HEAP (NIL T) -8 NIL NIL NIL) (-481 1130198 1130459 1130593 "HEADAST" 1130793 T HEADAST (NIL) -8 NIL NIL NIL) (-480 1124118 1130113 1130175 "HDP" 1130180 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-479 1117869 1123753 1123905 "HDMP" 1124019 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-478 1117194 1117333 1117497 "HB" 1117725 T HB (NIL) -7 NIL NIL NIL) (-477 1110691 1117040 1117144 "HASHTBL" 1117149 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-476 1110194 1110412 1110504 "HASAST" 1110619 T HASAST (NIL) -8 NIL NIL NIL) (-475 1108006 1109816 1109998 "HACKPI" 1110032 T HACKPI (NIL) -8 NIL NIL NIL) (-474 1103701 1107859 1107972 "GTSET" 1107977 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-473 1097227 1103579 1103677 "GSTBL" 1103682 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-472 1089540 1096258 1096523 "GSERIES" 1097018 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-471 1088707 1089098 1089126 "GROUP" 1089329 T GROUP (NIL) -9 NIL 1089463 NIL) (-470 1088073 1088232 1088483 "GROUP-" 1088488 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-469 1086442 1086761 1087148 "GROEBSOL" 1087750 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-468 1085382 1085644 1085695 "GRMOD" 1086224 NIL GRMOD (NIL T T) -9 NIL 1086392 NIL) (-467 1085150 1085186 1085314 "GRMOD-" 1085319 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-466 1080476 1081504 1082504 "GRIMAGE" 1084170 T GRIMAGE (NIL) -8 NIL NIL NIL) (-465 1078943 1079203 1079527 "GRDEF" 1080172 T GRDEF (NIL) -7 NIL NIL NIL) (-464 1078387 1078503 1078644 "GRAY" 1078822 T GRAY (NIL) -7 NIL NIL NIL) (-463 1077600 1077980 1078031 "GRALG" 1078184 NIL GRALG (NIL T T) -9 NIL 1078277 NIL) (-462 1077261 1077334 1077497 "GRALG-" 1077502 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-461 1074065 1076846 1077024 "GPOLSET" 1077168 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-460 1073419 1073476 1073734 "GOSPER" 1074002 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-459 1069178 1069857 1070383 "GMODPOL" 1073118 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-458 1068183 1068367 1068605 "GHENSEL" 1068990 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-457 1062234 1063077 1064104 "GENUPS" 1067267 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-456 1061931 1061982 1062071 "GENUFACT" 1062177 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-455 1061343 1061420 1061585 "GENPGCD" 1061849 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-454 1060817 1060852 1061065 "GENMFACT" 1061302 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-453 1059385 1059640 1059947 "GENEEZ" 1060560 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-452 1053298 1058996 1059158 "GDMP" 1059308 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-451 1042675 1047069 1048175 "GCNAALG" 1052281 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-450 1041102 1041930 1041958 "GCDDOM" 1042213 T GCDDOM (NIL) -9 NIL 1042370 NIL) (-449 1040572 1040699 1040914 "GCDDOM-" 1040919 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-448 1039244 1039429 1039733 "GB" 1040351 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-447 1027864 1030190 1032582 "GBINTERN" 1036935 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-446 1025701 1025993 1026414 "GBF" 1027539 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-445 1024482 1024647 1024914 "GBEUCLID" 1025517 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-444 1023831 1023956 1024105 "GAUSSFAC" 1024353 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-443 1022198 1022500 1022814 "GALUTIL" 1023550 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-442 1020506 1020780 1021104 "GALPOLYU" 1021925 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-441 1017871 1018161 1018568 "GALFACTU" 1020203 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-440 1009677 1011176 1012784 "GALFACT" 1016303 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-439 1007065 1007723 1007751 "FVFUN" 1008907 T FVFUN (NIL) -9 NIL 1009627 NIL) (-438 1006331 1006513 1006541 "FVC" 1006832 T FVC (NIL) -9 NIL 1007015 NIL) (-437 1005973 1006128 1006209 "FUNCTION" 1006283 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1003744 1004295 1004761 "FT" 1005527 T FT (NIL) -8 NIL NIL NIL) (-435 1002562 1003045 1003248 "FTEM" 1003561 T FTEM (NIL) -8 NIL NIL NIL) (-434 1000818 1001107 1001511 "FSUPFACT" 1002253 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999215 999504 999836 "FST" 1000506 T FST (NIL) -8 NIL NIL NIL) (-432 998386 998492 998687 "FSRED" 999097 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 997065 997320 997674 "FSPRMELT" 998101 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994150 994588 995087 "FSPECF" 996628 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976210 984653 984693 "FS" 988541 NIL FS (NIL T) -9 NIL 990830 NIL) (-428 964860 967850 971906 "FS-" 972203 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964374 964428 964605 "FSINT" 964801 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 962701 963367 963670 "FSERIES" 964153 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 961715 961831 962062 "FSCINT" 962581 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 957949 960659 960700 "FSAGG" 961070 NIL FSAGG (NIL T) -9 NIL 961329 NIL) (-423 955711 956312 957108 "FSAGG-" 957203 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 954753 954896 955123 "FSAGG2" 955564 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952408 952687 953241 "FS2UPS" 954471 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 951990 952033 952188 "FS2" 952359 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 950847 951018 951327 "FS2EXPXP" 951815 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950273 950388 950540 "FRUTIL" 950727 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 941728 945768 947126 "FR" 948947 NIL FR (NIL T) -8 NIL NIL NIL) (-416 936803 939446 939486 "FRNAALG" 940882 NIL FRNAALG (NIL T) -9 NIL 941489 NIL) (-415 932481 933552 934827 "FRNAALG-" 935577 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 932119 932162 932289 "FRNAAF2" 932432 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 930526 930973 931268 "FRMOD" 931931 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928305 928909 929226 "FRIDEAL" 930317 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 927500 927587 927876 "FRIDEAL2" 928212 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 926633 927047 927088 "FRETRCT" 927093 NIL FRETRCT (NIL T) -9 NIL 927269 NIL) (-409 925745 925976 926327 "FRETRCT-" 926332 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 922957 924133 924192 "FRAMALG" 925074 NIL FRAMALG (NIL T T) -9 NIL 925366 NIL) (-407 921091 921546 922176 "FRAMALG-" 922399 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 915049 920566 920842 "FRAC" 920847 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 914685 914742 914849 "FRAC2" 914986 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914321 914378 914485 "FR2" 914622 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 908994 911846 911874 "FPS" 912993 T FPS (NIL) -9 NIL 913550 NIL) (-402 908443 908552 908716 "FPS-" 908862 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 905897 907532 907560 "FPC" 907785 T FPC (NIL) -9 NIL 907927 NIL) (-400 905690 905730 905827 "FPC-" 905832 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 904568 905178 905219 "FPATMAB" 905224 NIL FPATMAB (NIL T) -9 NIL 905376 NIL) (-398 902268 902744 903170 "FPARFRAC" 904205 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 897662 898160 898842 "FORTRAN" 901700 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895378 895878 896417 "FORT" 897143 T FORT (NIL) -7 NIL NIL NIL) (-395 893054 893616 893644 "FORTFN" 894704 T FORTFN (NIL) -9 NIL 895328 NIL) (-394 892818 892868 892896 "FORTCAT" 892955 T FORTCAT (NIL) -9 NIL 893017 NIL) (-393 890951 891434 891824 "FORMULA" 892448 T FORMULA (NIL) -8 NIL NIL NIL) (-392 890739 890769 890838 "FORMULA1" 890915 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890262 890314 890487 "FORDER" 890681 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889358 889522 889715 "FOP" 890089 T FOP (NIL) -7 NIL NIL NIL) (-389 887966 888638 888812 "FNLA" 889240 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 886721 887110 887138 "FNCAT" 887598 T FNCAT (NIL) -9 NIL 887858 NIL) (-387 886287 886680 886708 "FNAME" 886713 T FNAME (NIL) -8 NIL NIL NIL) (-386 884950 885879 885907 "FMTC" 885912 T FMTC (NIL) -9 NIL 885948 NIL) (-385 881312 882473 883102 "FMONOID" 884354 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 880531 881054 881203 "FM" 881208 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 877955 878601 878629 "FMFUN" 879773 T FMFUN (NIL) -9 NIL 880481 NIL) (-382 877224 877405 877433 "FMC" 877723 T FMC (NIL) -9 NIL 877905 NIL) (-381 874418 875252 875306 "FMCAT" 876501 NIL FMCAT (NIL T T) -9 NIL 876996 NIL) (-380 873311 874184 874284 "FM1" 874363 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 871085 871501 871995 "FLOATRP" 872862 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 864709 868814 869435 "FLOAT" 870484 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862147 862647 863225 "FLOATCP" 864176 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 860956 861760 861801 "FLINEXP" 861806 NIL FLINEXP (NIL T) -9 NIL 861899 NIL) (-375 860110 860345 860673 "FLINEXP-" 860678 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859186 859330 859554 "FLASORT" 859962 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856403 857245 857297 "FLALG" 858524 NIL FLALG (NIL T T) -9 NIL 858991 NIL) (-372 850187 853889 853930 "FLAGG" 855192 NIL FLAGG (NIL T) -9 NIL 855844 NIL) (-371 848913 849252 849742 "FLAGG-" 849747 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 847955 848098 848325 "FLAGG2" 848766 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 844930 845904 845963 "FINRALG" 847091 NIL FINRALG (NIL T T) -9 NIL 847599 NIL) (-368 844090 844319 844658 "FINRALG-" 844663 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 843496 843709 843737 "FINITE" 843933 T FINITE (NIL) -9 NIL 844040 NIL) (-366 835954 838115 838155 "FINAALG" 841822 NIL FINAALG (NIL T) -9 NIL 843275 NIL) (-365 831295 832336 833480 "FINAALG-" 834859 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 830690 831050 831153 "FILE" 831225 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829374 829686 829740 "FILECAT" 830424 NIL FILECAT (NIL T T) -9 NIL 830640 NIL) (-362 827242 828736 828764 "FIELD" 828804 T FIELD (NIL) -9 NIL 828884 NIL) (-361 825862 826247 826758 "FIELD-" 826763 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 823740 824497 824844 "FGROUP" 825548 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 822830 822994 823214 "FGLMICPK" 823572 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 818697 822755 822812 "FFX" 822817 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818298 818359 818494 "FFSLPE" 818630 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814291 815070 815866 "FFPOLY" 817534 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 813795 813831 814040 "FFPOLY2" 814249 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 809681 813714 813777 "FFP" 813782 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 805114 809592 809656 "FF" 809661 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800275 804457 804647 "FFNBX" 804968 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795249 799410 799668 "FFNBP" 800129 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 789917 794533 794744 "FFNB" 795082 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 788749 788947 789262 "FFINTBAS" 789714 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 784977 787156 787184 "FFIELDC" 787804 T FFIELDC (NIL) -9 NIL 788180 NIL) (-347 783640 784010 784507 "FFIELDC-" 784512 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783210 783255 783379 "FFHOM" 783582 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 780908 781392 781909 "FFF" 782725 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 776561 780650 780751 "FFCGX" 780851 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772228 776293 776400 "FFCGP" 776504 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767446 771955 772063 "FFCG" 772164 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749279 758317 758403 "FFCAT" 763568 NIL FFCAT (NIL T T T) -9 NIL 765019 NIL) (-340 744477 745524 746838 "FFCAT-" 748068 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 743888 743931 744166 "FFCAT2" 744428 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 733100 736860 738080 "FEXPR" 742740 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 732100 732535 732576 "FEVALAB" 732660 NIL FEVALAB (NIL T) -9 NIL 732921 NIL) (-336 731259 731469 731807 "FEVALAB-" 731812 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 729852 730642 730845 "FDIV" 731158 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 726918 727633 727748 "FDIVCAT" 729316 NIL FDIVCAT (NIL T T T T) -9 NIL 729753 NIL) (-333 726680 726707 726877 "FDIVCAT-" 726882 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 725900 725987 726264 "FDIV2" 726587 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 724586 724845 725134 "FCPAK1" 725631 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 723714 724086 724227 "FCOMP" 724477 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707451 710864 714402 "FC" 720196 T FC (NIL) -8 NIL NIL NIL) (-328 700030 704015 704055 "FAXF" 705857 NIL FAXF (NIL T) -9 NIL 706549 NIL) (-327 697309 697964 698789 "FAXF-" 699254 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692409 696685 696861 "FARRAY" 697166 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 687662 689694 689747 "FAMR" 690770 NIL FAMR (NIL T T) -9 NIL 691230 NIL) (-324 686552 686854 687289 "FAMR-" 687294 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 685748 686474 686527 "FAMONOID" 686532 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 683560 684244 684297 "FAMONC" 685238 NIL FAMONC (NIL T T) -9 NIL 685624 NIL) (-321 682252 683314 683451 "FAGROUP" 683456 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 680047 680366 680769 "FACUTIL" 681933 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679146 679331 679553 "FACTFUNC" 679857 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 671551 678397 678609 "EXPUPXS" 679002 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 669034 669574 670160 "EXPRTUBE" 670985 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665228 665820 666557 "EXPRODE" 668373 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 650602 663883 664311 "EXPR" 664832 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 645009 645596 646409 "EXPR2UPS" 649900 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 644645 644702 644809 "EXPR2" 644946 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 636050 643777 644074 "EXPEXPAN" 644482 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 635877 636007 636036 "EXIT" 636041 T EXIT (NIL) -8 NIL NIL NIL) (-310 635384 635601 635692 "EXITAST" 635806 T EXITAST (NIL) -8 NIL NIL NIL) (-309 635011 635073 635186 "EVALCYC" 635316 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 634552 634670 634711 "EVALAB" 634881 NIL EVALAB (NIL T) -9 NIL 634985 NIL) (-307 634033 634155 634376 "EVALAB-" 634381 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 631501 632769 632797 "EUCDOM" 633352 T EUCDOM (NIL) -9 NIL 633702 NIL) (-305 629906 630348 630938 "EUCDOM-" 630943 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617446 620204 622954 "ESTOOLS" 627176 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 617078 617135 617244 "ESTOOLS2" 617383 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 616829 616871 616951 "ESTOOLS1" 617030 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 610734 612462 612490 "ES" 615258 T ES (NIL) -9 NIL 616667 NIL) (-300 605682 606968 608785 "ES-" 608949 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 602057 602817 603597 "ESCONT" 604922 T ESCONT (NIL) -7 NIL NIL NIL) (-298 601802 601834 601916 "ESCONT1" 602019 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601477 601527 601627 "ES2" 601746 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 601107 601165 601274 "ES1" 601413 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600323 600452 600628 "ERROR" 600951 T ERROR (NIL) -7 NIL NIL NIL) (-294 593826 600182 600273 "EQTBL" 600278 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586383 589140 590589 "EQ" 592410 NIL -3328 (NIL T) -8 NIL NIL NIL) (-292 586015 586072 586181 "EQ2" 586320 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581307 582353 583446 "EP" 584954 NIL EP (NIL T) -7 NIL NIL NIL) (-290 579889 580190 580507 "ENV" 581010 T ENV (NIL) -8 NIL NIL NIL) (-289 579068 579588 579616 "ENTIRER" 579621 T ENTIRER (NIL) -9 NIL 579667 NIL) (-288 575570 577023 577393 "EMR" 578867 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 574714 574899 574953 "ELTAGG" 575333 NIL ELTAGG (NIL T T) -9 NIL 575544 NIL) (-286 574433 574495 574636 "ELTAGG-" 574641 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574222 574251 574305 "ELTAB" 574389 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573348 573494 573693 "ELFUTS" 574073 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 573090 573146 573174 "ELEMFUN" 573279 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 572960 572981 573049 "ELEMFUN-" 573054 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 567851 571060 571101 "ELAGG" 572041 NIL ELAGG (NIL T) -9 NIL 572504 NIL) (-280 566136 566570 567233 "ELAGG-" 567238 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 564793 565073 565368 "ELABEXPR" 565861 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 557659 559460 560287 "EFUPXS" 564069 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 551109 552910 553720 "EFULS" 556935 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 548531 548889 549368 "EFSTRUC" 550741 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 537603 539168 540728 "EF" 547046 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 536704 537088 537237 "EAB" 537474 T EAB (NIL) -8 NIL NIL NIL) (-273 535913 536663 536691 "E04UCFA" 536696 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 535122 535872 535900 "E04NAFA" 535905 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534331 535081 535109 "E04MBFA" 535114 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 533540 534290 534318 "E04JAFA" 534323 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 532751 533499 533527 "E04GCFA" 533532 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 531962 532710 532738 "E04FDFA" 532743 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531171 531921 531949 "E04DGFA" 531954 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525349 526696 528060 "E04AGNT" 529827 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 524055 524535 524575 "DVARCAT" 525050 NIL DVARCAT (NIL T) -9 NIL 525249 NIL) (-264 523259 523471 523785 "DVARCAT-" 523790 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516159 523058 523187 "DSMP" 523192 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 510969 512104 513172 "DROPT" 515111 T DROPT (NIL) -8 NIL NIL NIL) (-261 510634 510693 510791 "DROPT1" 510904 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 505749 506875 508012 "DROPT0" 509517 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 504094 504419 504805 "DRAWPT" 505383 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 498681 499604 500683 "DRAW" 503068 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498314 498367 498485 "DRAWHACK" 498622 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 497045 497314 497605 "DRAWCX" 498043 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 496561 496629 496780 "DRAWCURV" 496971 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 487032 488991 491106 "DRAWCFUN" 494466 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 483845 485727 485768 "DQAGG" 486397 NIL DQAGG (NIL T) -9 NIL 486670 NIL) (-252 472124 478823 478906 "DPOLCAT" 480758 NIL DPOLCAT (NIL T T T T) -9 NIL 481303 NIL) (-251 466963 468309 470267 "DPOLCAT-" 470272 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 460118 466824 466922 "DPMO" 466927 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453176 459898 460065 "DPMM" 460070 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 452840 453095 453143 "DOMCTOR" 453148 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452135 452362 452499 "DOMAIN" 452723 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 445886 451770 451922 "DMP" 452036 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445486 445542 445686 "DLP" 445824 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439356 444813 445003 "DLIST" 445328 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436200 438209 438250 "DLAGG" 438800 NIL DLAGG (NIL T) -9 NIL 439030 NIL) (-242 435013 435643 435671 "DIVRING" 435763 T DIVRING (NIL) -9 NIL 435846 NIL) (-241 434250 434440 434740 "DIVRING-" 434745 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432352 432709 433115 "DISPLAY" 433864 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426294 432266 432329 "DIRPROD" 432334 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425142 425345 425610 "DIRPROD2" 426087 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414405 420357 420410 "DIRPCAT" 420820 NIL DIRPCAT (NIL NIL T) -9 NIL 421660 NIL) (-236 411731 412373 413254 "DIRPCAT-" 413591 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 411018 411178 411364 "DIOSP" 411565 T DIOSP (NIL) -7 NIL NIL NIL) (-234 407720 409930 409971 "DIOPS" 410405 NIL DIOPS (NIL T) -9 NIL 410634 NIL) (-233 407269 407383 407574 "DIOPS-" 407579 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406161 406755 406783 "DIFRING" 406970 T DIFRING (NIL) -9 NIL 407080 NIL) (-231 405807 405884 406036 "DIFRING-" 406041 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 403612 404850 404891 "DIFEXT" 405254 NIL DIFEXT (NIL T) -9 NIL 405548 NIL) (-229 401897 402325 402991 "DIFEXT-" 402996 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399219 401429 401470 "DIAGG" 401475 NIL DIAGG (NIL T) -9 NIL 401495 NIL) (-227 398603 398760 399012 "DIAGG-" 399017 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 394068 397562 397839 "DHMATRIX" 398372 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 389680 390589 391599 "DFSFUN" 393078 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 384796 388611 388923 "DFLOAT" 389388 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 383024 383305 383701 "DFINTTLS" 384504 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 380089 381045 381445 "DERHAM" 382690 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 377938 379864 379953 "DEQUEUE" 380033 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377153 377286 377482 "DEGRED" 377800 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 373548 374293 375146 "DEFINTRF" 376381 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 371075 371544 372143 "DEFINTEF" 373067 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370452 370695 370810 "DEFAST" 370980 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364494 370049 370197 "DECIMAL" 370324 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 362006 362464 362970 "DDFACT" 364038 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 361602 361645 361796 "DBLRESP" 361957 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359501 359835 360195 "DBASE" 361369 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 358770 358981 359127 "DATAARY" 359400 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 357903 358729 358757 "D03FAFA" 358762 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 357037 357862 357890 "D03EEFA" 357895 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 354987 355453 355942 "D03AGNT" 356568 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354303 354946 354974 "D02EJFA" 354979 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 353619 354262 354290 "D02CJFA" 354295 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 352935 353578 353606 "D02BHFA" 353611 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352251 352894 352922 "D02BBFA" 352927 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345449 347037 348643 "D02AGNT" 350665 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343218 343740 344286 "D01WGTS" 344923 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342313 343177 343205 "D01TRNS" 343210 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341408 342272 342300 "D01GBFA" 342305 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340503 341367 341395 "D01FCFA" 341400 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 339598 340462 340490 "D01ASFA" 340495 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 338693 339557 339585 "D01AQFA" 339590 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 337788 338652 338680 "D01APFA" 338685 T D01APFA (NIL) -8 NIL NIL NIL) (-196 336883 337747 337775 "D01ANFA" 337780 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 335978 336842 336870 "D01AMFA" 336875 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 335073 335937 335965 "D01ALFA" 335970 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334168 335032 335060 "D01AKFA" 335065 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333263 334127 334155 "D01AJFA" 334160 T D01AJFA (NIL) -8 NIL NIL NIL) (-191 326560 328111 329672 "D01AGNT" 331722 T D01AGNT (NIL) -7 NIL NIL NIL) (-190 325897 326025 326177 "CYCLOTOM" 326428 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-189 322632 323345 324072 "CYCLES" 325190 T CYCLES (NIL) -7 NIL NIL NIL) (-188 321944 322078 322249 "CVMP" 322493 NIL CVMP (NIL T) -7 NIL NIL NIL) (-187 319715 319973 320349 "CTRIGMNP" 321672 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-186 319438 319674 319702 "CTOR" 319707 T CTOR (NIL) -8 NIL NIL NIL) (-185 318974 319169 319270 "CTORKIND" 319357 T CTORKIND (NIL) -8 NIL NIL NIL) (-184 318445 318673 318701 "CTORCAT" 318821 T CTORCAT (NIL) -9 NIL 318904 NIL) (-183 318140 318220 318346 "CTORCAT-" 318351 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-182 317656 317843 317941 "CTORCALL" 318062 T CTORCALL (NIL) -8 NIL NIL NIL) (-181 317030 317129 317282 "CSTTOOLS" 317553 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-180 312829 313486 314244 "CRFP" 316342 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-179 312331 312550 312642 "CRCEAST" 312757 T CRCEAST (NIL) -8 NIL NIL NIL) (-178 311378 311563 311791 "CRAPACK" 312135 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-177 310762 310863 311067 "CPMATCH" 311254 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-176 310487 310515 310621 "CPIMA" 310728 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-175 306851 307523 308241 "COORDSYS" 309822 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-174 306235 306364 306514 "CONTOUR" 306721 T CONTOUR (NIL) -8 NIL NIL NIL) (-173 302161 304238 304730 "CONTFRAC" 305775 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-172 302041 302062 302090 "CONDUIT" 302127 T CONDUIT (NIL) -9 NIL NIL NIL) (-171 301214 301734 301762 "COMRING" 301767 T COMRING (NIL) -9 NIL 301819 NIL) (-170 300295 300572 300756 "COMPPROP" 301050 T COMPPROP (NIL) -8 NIL NIL NIL) (-169 299956 299991 300119 "COMPLPAT" 300254 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-168 290013 299765 299874 "COMPLEX" 299879 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289649 289706 289813 "COMPLEX2" 289950 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-166 289367 289402 289500 "COMPFACT" 289608 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-165 273540 283760 283800 "COMPCAT" 284804 NIL COMPCAT (NIL T) -9 NIL 286189 NIL) (-164 263056 265979 269606 "COMPCAT-" 269962 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-163 262785 262813 262916 "COMMUPC" 263022 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-162 262580 262613 262672 "COMMONOP" 262746 T COMMONOP (NIL) -7 NIL NIL NIL) (-161 262163 262331 262418 "COMM" 262513 T COMM (NIL) -8 NIL NIL NIL) (-160 261767 261967 262042 "COMMAAST" 262108 T COMMAAST (NIL) -8 NIL NIL NIL) (-159 261016 261210 261238 "COMBOPC" 261576 T COMBOPC (NIL) -9 NIL 261751 NIL) (-158 259912 260122 260364 "COMBINAT" 260806 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-157 256110 256683 257323 "COMBF" 259334 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-156 254896 255226 255461 "COLOR" 255895 T COLOR (NIL) -8 NIL NIL NIL) (-155 254399 254617 254709 "COLONAST" 254824 T COLONAST (NIL) -8 NIL NIL NIL) (-154 254039 254086 254211 "CMPLXRT" 254346 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-153 253514 253739 253838 "CLLCTAST" 253960 T CLLCTAST (NIL) -8 NIL NIL NIL) (-152 249016 250044 251124 "CLIP" 252454 T CLIP (NIL) -7 NIL NIL NIL) (-151 247398 248122 248361 "CLIF" 248843 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-150 243620 245544 245585 "CLAGG" 246514 NIL CLAGG (NIL T) -9 NIL 247050 NIL) (-149 242042 242499 243082 "CLAGG-" 243087 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-148 241586 241671 241811 "CINTSLPE" 241951 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-147 239087 239558 240106 "CHVAR" 241114 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-146 238330 238850 238878 "CHARZ" 238883 T CHARZ (NIL) -9 NIL 238898 NIL) (-145 238084 238124 238202 "CHARPOL" 238284 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-144 237211 237764 237792 "CHARNZ" 237839 T CHARNZ (NIL) -9 NIL 237895 NIL) (-143 235200 235901 236236 "CHAR" 236896 T CHAR (NIL) -8 NIL NIL NIL) (-142 234926 234987 235015 "CFCAT" 235126 T CFCAT (NIL) -9 NIL NIL NIL) (-141 234171 234282 234464 "CDEN" 234810 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-140 230163 233324 233604 "CCLASS" 233911 T CCLASS (NIL) -8 NIL NIL NIL) (-139 229470 229613 229776 "CATEGORY" 230020 T -10 (NIL) -8 NIL NIL NIL) (-138 229134 229389 229437 "CATCTOR" 229442 T CATCTOR (NIL) -8 NIL NIL NIL) (-137 228608 228834 228933 "CATAST" 229055 T CATAST (NIL) -8 NIL NIL NIL) (-136 228111 228329 228421 "CASEAST" 228536 T CASEAST (NIL) -8 NIL NIL NIL) (-135 223163 224140 224893 "CARTEN" 227414 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 222271 222419 222640 "CARTEN2" 223010 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-133 220613 221421 221678 "CARD" 222034 T CARD (NIL) -8 NIL NIL NIL) (-132 220216 220417 220492 "CAPSLAST" 220558 T CAPSLAST (NIL) -8 NIL NIL NIL) (-131 219588 219916 219944 "CACHSET" 220076 T CACHSET (NIL) -9 NIL 220153 NIL) (-130 219084 219380 219408 "CABMON" 219458 T CABMON (NIL) -9 NIL 219514 NIL) (-129 218107 218630 218766 "BYTE" 218929 T BYTE (NIL) -8 NIL NIL 219045) (-128 213516 217575 217738 "BYTEBUF" 217964 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211073 213208 213315 "BTREE" 213442 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208571 210721 210843 "BTOURN" 210983 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 205988 208041 208082 "BTCAT" 208150 NIL BTCAT (NIL T) -9 NIL 208227 NIL) (-124 205655 205735 205884 "BTCAT-" 205889 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 200947 204798 204826 "BTAGG" 205048 T BTAGG (NIL) -9 NIL 205209 NIL) (-122 200437 200562 200768 "BTAGG-" 200773 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197481 199715 199930 "BSTREE" 200254 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196619 196745 196929 "BRILL" 197337 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193318 195345 195386 "BRAGG" 196035 NIL BRAGG (NIL T) -9 NIL 196293 NIL) (-118 191847 192253 192808 "BRAGG-" 192813 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185111 191193 191377 "BPADICRT" 191695 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183461 185048 185093 "BPADIC" 185098 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183159 183189 183303 "BOUNDZRO" 183425 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL NIL) (-113 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 174997 175719 175912 "BOOLEAN" 176122 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174359 174737 174791 "BMODULE" 174796 NIL BMODULE (NIL T T) -9 NIL 174861 NIL) (-110 170189 174157 174230 "BITS" 174306 T BITS (NIL) -8 NIL NIL NIL) (-109 169601 169723 169865 "BINDING" 170067 T BINDING (NIL) -8 NIL NIL NIL) (-108 163646 169200 169347 "BINARY" 169474 T BINARY (NIL) -8 NIL NIL NIL) (-107 161473 162901 162942 "BGAGG" 163202 NIL BGAGG (NIL T) -9 NIL 163339 NIL) (-106 161304 161336 161427 "BGAGG-" 161432 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150169 150329 150355 "ASTCAT" 150360 T ASTCAT (NIL) -9 NIL 150390 NIL) (-92 149896 149955 150074 "ASTCAT-" 150079 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148093 149672 149760 "ASTACK" 149839 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146598 146895 147260 "ASSOCEQ" 147775 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145630 146257 146381 "ASP9" 146505 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145394 145578 145617 "ASP8" 145622 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144263 144999 145141 "ASP80" 145283 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143162 143898 144030 "ASP7" 144162 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142116 142839 142957 "ASP78" 143075 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141085 141796 141913 "ASP77" 142030 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 139997 140723 140854 "ASP74" 140985 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138897 139632 139764 "ASP73" 139896 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138001 138723 138823 "ASP6" 138828 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 136949 137678 137796 "ASP55" 137914 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135899 136623 136742 "ASP50" 136861 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 134987 135600 135710 "ASP4" 135820 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134075 134688 134798 "ASP49" 134908 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132860 133614 133782 "ASP42" 133964 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131637 132393 132563 "ASP41" 132747 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130587 131314 131432 "ASP35" 131550 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130352 130535 130574 "ASP34" 130579 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130089 130156 130232 "ASP33" 130307 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 128984 129724 129856 "ASP31" 129988 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128749 128932 128971 "ASP30" 128976 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128484 128553 128629 "ASP29" 128704 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128249 128432 128471 "ASP28" 128476 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128014 128197 128236 "ASP27" 128241 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127098 127712 127823 "ASP24" 127934 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126175 126900 127012 "ASP20" 127017 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125263 125876 125986 "ASP1" 126096 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124207 124937 125056 "ASP19" 125175 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 123944 124011 124087 "ASP12" 124162 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122796 123543 123687 "ASP10" 123831 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120695 122640 122731 "ARRAY2" 122736 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116511 120343 120457 "ARRAY1" 120612 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115543 115716 115937 "ARRAY12" 116334 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109902 111773 111848 "ARR2CAT" 114478 NIL ARR2CAT (NIL T T T) -9 NIL 115236 NIL) (-56 107336 108080 109034 "ARR2CAT-" 109039 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106930 107163 107242 "ARITY" 107275 T ARITY (NIL) -8 NIL NIL NIL) (-54 105678 105830 106136 "APPRULE" 106766 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105329 105377 105496 "APPLYORE" 105624 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104303 104594 104789 "ANY" 105152 T ANY (NIL) -8 NIL NIL NIL) (-51 103581 103704 103861 "ANY1" 104177 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101146 102018 102345 "ANTISYM" 103305 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100661 100850 100947 "ANON" 101067 T ANON (NIL) -8 NIL NIL NIL) (-48 94793 99200 99654 "AN" 100225 T AN (NIL) -8 NIL NIL NIL) (-47 91049 92403 92454 "AMR" 93202 NIL AMR (NIL T T) -9 NIL 93802 NIL) (-46 90161 90382 90745 "AMR-" 90750 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74711 90078 90139 "ALIST" 90144 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71548 74305 74474 "ALGSC" 74629 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68104 68658 69265 "ALGPKG" 70988 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67381 67482 67666 "ALGMFACT" 67990 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63120 63805 64460 "ALGMANIP" 66904 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54526 62746 62896 "ALGFF" 63053 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53722 53853 54032 "ALGFACT" 54384 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52787 53353 53391 "ALGEBRA" 53396 NIL ALGEBRA (NIL T) -9 NIL 53437 NIL) (-37 52505 52564 52696 "ALGEBRA-" 52701 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34764 50507 50559 "ALAGG" 50695 NIL ALAGG (NIL T T) -9 NIL 50856 NIL) (-35 34300 34413 34439 "AHYP" 34640 T AHYP (NIL) -9 NIL NIL NIL) (-34 33231 33479 33505 "AGG" 34004 T AGG (NIL) -9 NIL 34283 NIL) (-33 32665 32827 33041 "AGG-" 33046 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30342 30764 31182 "AF" 32307 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29849 30067 30157 "ADDAST" 30270 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29118 29376 29532 "ACPLOT" 29711 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18410 26331 26382 "ACFS" 27093 NIL ACFS (NIL T) -9 NIL 27332 NIL) (-28 16424 16914 17689 "ACFS-" 17694 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
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(|:| |var| (-1166)) (|:| |fn| (-315 (-224))) + (|:| -2290 (-1084 (-837 (-224)))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) - (|:| -1925 + (|:| -2654 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") @@ -14380,10 +13568,10 @@ (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| - (-3 (|:| |str| (-1143 (-224))) + (-3 (|:| |str| (-1146 (-224))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -2103 + (|:| -2290 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") @@ -14391,1447 +13579,1375 @@ (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) - (-5 *1 (-553))))) -(((*1 *2 *2) - (-12 (-4 *2 (-13 (-362) (-839))) (-5 *1 (-180 *2 *3)) - (-4 *3 (-1222 (-168 *2)))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-550)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2862 *4))) - (-5 *1 (-959 *4 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