diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 1282 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1402 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 61 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8932 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 3104 |
5 files changed, 7395 insertions, 7386 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index a8f3a706..bb9886f6 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2265141 . 3477435921) +(2265897 . 3477490099) (-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."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4434 . T) (-4432 . T) (-4431 . T) ((-4439 "*") . T) (-4430 . T) (-4435 . T) (-4429 . T)) +((-4440 . T) (-4438 . T) (-4437 . T) ((-4445 "*") . T) (-4436 . T) (-4441 . T) (-4435 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -3508) +(-32 R -3514) ((|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 -1044) (QUOTE (-551))))) (-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 -4437))) +((|HasAttribute| |#1| (QUOTE -4443))) (-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}."))) -((-4437 . T) (-4438 . T)) +((-4443 . T) (-4444 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,17 +82,17 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . 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 -3508 UP UPUP -3026) +(-40 -3514 UP UPUP -3032) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4430 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) (-4429 |has| (-412 |#2|) (-367)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-354))) (-3972 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-3972 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (-3972 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-354))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-551)))) (-3972 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) -(-41 R -3508) +((-4436 |has| (-412 |#2|) (-367)) (-4441 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-354))) (-3978 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-3978 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (-3978 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-354))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-551)))) (-3978 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) +(-41 R -3514) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -426) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-310)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4434 |has| |#1| (-562)) (-4432 . T) (-4431 . T)) +((-4440 |has| |#1| (-562)) (-4438 . T) (-4437 . T)) ((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-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."))) -((-4437 . T) (-4438 . T)) -((-3972 (-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-855)))) (-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))))) +((-4443 . T) (-4444 . T)) +((-3978 (-12 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2264) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-855)))) (-12 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2264) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107))))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-3978 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (-3978 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2264) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-367)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-551))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4434 . T)) +((-4440 . T)) NIL (-51) ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and AnyFunctions1.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3508) +(-54 |Base| R -3514) ((|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 @@ -158,77 +158,77 @@ 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"))) -((-4437 . T) (-4438 . T)) +((-4443 . T) (-4444 . T)) NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL NIL (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) -(-61 -3985) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +(-61 -3991) ((|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 -(-62 -3985) +(-62 -3991) ((|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 -(-63 -3985) +(-63 -3991) ((|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 -(-64 -3985) +(-64 -3991) ((|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 -(-65 -3985) +(-65 -3991) ((|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 -3985) +(-66 -3991) ((|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 -3985) +(-67 -3991) ((|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 -3985) +(-68 -3991) ((|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 -3985) +(-69 -3991) ((|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 -3985) +(-70 -3991) ((|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 -3985) +(-71 -3991) ((|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 -3985) +(-72 -3991) ((|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 -3985) +(-73 -3991) ((|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 -3985) +(-74 -3991) ((|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 -(-75 -3985) +(-75 -3991) ((|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 @@ -240,51 +240,51 @@ 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 -(-78 -3985) +(-78 -3991) ((|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 -(-79 -3985) +(-79 -3991) ((|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 -3985) +(-80 -3991) ((|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 -3985) +(-81 -3991) ((|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 -3985) +(-82 -3991) ((|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 -(-83 -3985) +(-83 -3991) ((|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 -(-84 -3985) +(-84 -3991) ((|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 -(-85 -3985) +(-85 -3991) ((|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 -(-86 -3985) +(-86 -3991) ((|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 -(-87 -3985) +(-87 -3991) ((|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 -(-88 -3985) +(-88 -3991) ((|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 -(-89 -3985) +(-89 -3991) ((|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 (-367)))) (-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}."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-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\"."))) -((-4437 . T)) +((-4443 . 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."))) -((-4437 . T) ((-4439 "*") . T) (-4438 . T) (-4434 . T) (-4432 . T) (-4431 . T) (-4430 . T) (-4435 . T) (-4429 . T) (-4428 . T) (-4427 . T) (-4426 . T) (-4425 . T) (-4433 . T) (-4436 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4424 . T)) +((-4443 . T) ((-4445 "*") . T) (-4444 . T) (-4440 . T) (-4438 . T) (-4437 . T) (-4436 . T) (-4441 . T) (-4435 . T) (-4434 . T) (-4433 . T) (-4432 . T) (-4431 . T) (-4439 . T) (-4442 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4430 . 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}."))) -((-4434 . T)) +((-4440 . T)) NIL (-100 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) @@ -342,15 +342,15 @@ NIL NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-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 (-4439 "*")))) +((|HasAttribute| |#1| (QUOTE (-4445 "*")))) (-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"))) -((-4437 . T)) +((-4443 . 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."))) -((-4438 . T)) +((-4444 . 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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3972 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3978 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3978 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1107))) (|HasCategory| (-112) (LIST (QUOTE -312) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-112) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-112) (QUOTE (-1107))) (|HasCategory| (-112) (LIST (QUOTE -618) (QUOTE (-868))))) (-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}"))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . 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}."))) @@ -388,22 +388,22 @@ NIL ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [foo1,{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) NIL NIL -(-115 -3508 UP) +(-115 -3514 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}."))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . 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}."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-916))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-116 |#1|) (QUOTE (-1026))) (|HasCategory| (-116 |#1|) (QUOTE (-825))) (-3972 (|HasCategory| (-116 |#1|) (QUOTE (-825))) (|HasCategory| (-116 |#1|) (QUOTE (-855)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (QUOTE (-1157))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (QUOTE (-234))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-310))) (|HasCategory| (-116 |#1|) (QUOTE (-550))) (|HasCategory| (-116 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-916)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-916))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-116 |#1|) (QUOTE (-1026))) (|HasCategory| (-116 |#1|) (QUOTE (-825))) (-3978 (|HasCategory| (-116 |#1|) (QUOTE (-825))) (|HasCategory| (-116 |#1|) (QUOTE (-855)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (QUOTE (-1157))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (QUOTE (-234))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-310))) (|HasCategory| (-116 |#1|) (QUOTE (-550))) (|HasCategory| (-116 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-916)))) (-3978 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-916)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4438))) +((|HasAttribute| |#1| (QUOTE -4444))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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"))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,24 +430,24 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4437 . T) (-4438 . T)) +((-4443 . T) (-4444 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-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."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-128) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL NIL (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128)))))) (-3972 (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-128) (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-128) (QUOTE (-1107)))) (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128)))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128)))))) (-3978 (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-128) (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-128) (QUOTE (-1107)))) (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128)))))) (-130) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -466,13 +466,13 @@ NIL NIL (-134) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4439 "*") . T)) +(((-4445 "*") . T)) NIL -(-135 |minix| -3033 R) +(-135 |minix| -3039 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 -(-136 |minix| -3033 S T$) +(-136 |minix| -3039 S T$) ((|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 @@ -494,8 +494,8 @@ NIL NIL (-141) ((|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}."))) -((-4437 . T) (-4427 . T) (-4438 . T)) -((-3972 (-12 (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +((-4443 . T) (-4433 . T) (-4444 . T)) +((-3978 (-12 (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -510,7 +510,7 @@ NIL NIL (-145) ((|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."))) -((-4434 . T)) +((-4440 . T)) NIL (-146 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}."))) @@ -518,9 +518,9 @@ NIL NIL (-147) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4434 . T)) +((-4440 . T)) NIL -(-148 -3508 UP UPUP) +(-148 -3514 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 @@ -531,14 +531,14 @@ NIL (-150 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 -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasAttribute| |#1| (QUOTE -4437))) +((|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasAttribute| |#1| (QUOTE -4443))) (-151 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 (-152 |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."))) -((-4432 . T) (-4431 . T) (-4434 . T)) +((-4438 . T) (-4437 . T) (-4440 . T)) NIL (-153) ((|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."))) @@ -560,7 +560,7 @@ 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 -(-158 R -3508) +(-158 R -3514) ((|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 @@ -591,10 +591,10 @@ NIL (-165 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1008))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4433)) (|HasAttribute| |#2| (QUOTE -4436)) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-562)))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1008))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4439)) (|HasAttribute| |#2| (QUOTE -4442)) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-562)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4430 -3972 (|has| |#1| (-562)) (-12 (|has| |#1| (-310)) (|has| |#1| (-916)))) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4433 |has| |#1| (-6 -4433)) (-4436 |has| |#1| (-6 -4436)) (-1466 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 -3978 (|has| |#1| (-562)) (-12 (|has| |#1| (-310)) (|has| |#1| (-916)))) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4439 |has| |#1| (-6 -4439)) (-4442 |has| |#1| (-6 -4442)) (-1466 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-167 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."))) @@ -606,8 +606,8 @@ NIL NIL (-169 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}."))) -((-4430 -3972 (|has| |#1| (-562)) (-12 (|has| |#1| (-310)) (|has| |#1| (-916)))) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4433 |has| |#1| (-6 -4433)) (-4436 |has| |#1| (-6 -4436)) (-1466 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . 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(|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-367)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-234))) (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasAttribute| |#1| (QUOTE -4439)) (|HasAttribute| |#1| (QUOTE -4442)) (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-354))))) (-170 R S) ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -622,7 +622,7 @@ NIL NIL (-173) ((|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."))) -(((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-174) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -630,7 +630,7 @@ NIL NIL (-175 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4439 "*") . T) (-4430 . T) (-4435 . T) (-4429 . T) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") . T) (-4436 . T) (-4441 . T) (-4435 . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-176) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -684,7 +684,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-189 R -3508) +(-189 R -3514) ((|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 @@ -792,23 +792,23 @@ 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 -(-216 -3508 UP UPUP R) +(-216 -3514 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 -(-217 -3508 FP) +(-217 -3514 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 (-218) ((|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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3972 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3978 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3978 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) (-219) ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-220 R -3508) +(-220 R -3514) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -822,19 +822,19 @@ NIL NIL (-223 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-224 |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}."))) -((-4434 . T)) +((-4440 . T)) NIL -(-225 R -3508) +(-225 R -3514) ((|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 (-226) ((|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}."))) -((-4213 . T) (-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4219 . T) (-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-227) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -842,15 +842,15 @@ NIL NIL (-228 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}"))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4439 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4445 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-229 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 (-230 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."))) -((-4438 . T)) +((-4444 . T)) NIL (-231 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}."))) @@ -858,7 +858,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234)))) (-232 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}."))) -((-4434 . T)) +((-4440 . T)) NIL (-233 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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -866,33 +866,33 @@ NIL NIL (-234) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4434 . T)) +((-4440 . T)) NIL (-235 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4437))) +((|HasAttribute| |#1| (QUOTE -4443))) (-236 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}."))) -((-4438 . T)) +((-4444 . T)) NIL (-237) ((|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 -(-238 S -3033 R) +(-238 S -3039 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 (-367))) (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (QUOTE (-853))) (|HasAttribute| |#3| (QUOTE -4434)) (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (QUOTE (-1107)))) -(-239 -3033 R) +((|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (QUOTE (-853))) (|HasAttribute| |#3| (QUOTE -4440)) (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (QUOTE (-1107)))) +(-239 -3039 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"))) -((-4431 |has| |#2| (-1055)) (-4432 |has| |#2| (-1055)) (-4434 |has| |#2| (-6 -4434)) ((-4439 "*") |has| |#2| (-173)) (-4437 . T)) +((-4437 |has| |#2| (-1055)) (-4438 |has| |#2| (-1055)) (-4440 |has| |#2| (-6 -4440)) ((-4445 "*") |has| |#2| (-173)) (-4443 . T)) NIL -(-240 -3033 R) +(-240 -3039 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."))) -((-4431 |has| |#2| (-1055)) (-4432 |has| |#2| (-1055)) (-4434 |has| |#2| (-6 -4434)) ((-4439 "*") |has| |#2| (-173)) (-4437 . 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(|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3978 (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-1055)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasAttribute| |#2| (QUOTE -4440)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))))) +(-241 -3039 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 @@ -906,7 +906,7 @@ NIL NIL (-244) ((|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}."))) -((-4430 . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-245 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."))) @@ -914,16 +914,16 @@ NIL NIL (-246 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}"))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-247 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 (-248 |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.")) 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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 (-234)))) (-255 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."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) NIL (-256 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}."))) -((-4437 . T) (-4438 . T)) +((-4443 . T) (-4444 . T)) NIL (-257 |Ex|) ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -994,8 +994,8 @@ NIL NIL (-266 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"))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3978 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-267 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 @@ -1040,11 +1040,11 @@ 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 -(-278 R -3508) +(-278 R -3514) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-279 R -3508) +(-279 R -3514) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1070,7 +1070,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107)))) (-285 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}."))) -((-4438 . T)) +((-4444 . T)) NIL (-286 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}."))) @@ -1091,18 +1091,18 @@ NIL (-290 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 -4438))) +((|HasAttribute| |#1| (QUOTE -4444))) (-291 |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 -(-292 S R |Mod| -2224 -3953 |exactQuo|) +(-292 S R |Mod| -2225 -3959 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-293) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4430 . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-294) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Identifier|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}.")) (|setProperty!| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{setProperty!(n,p,v,e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `nothing.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1114,16 +1114,16 @@ NIL NIL (-296 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4434 -3972 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4431 |has| |#1| (-1055)) (-4432 |has| |#1| (-1055))) -((|HasCategory| |#1| (QUOTE (-367))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055)))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-3972 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-1055)))) (-3972 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731)))) (|HasCategory| |#1| (QUOTE (-478))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1118)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-301))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478)))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731)))) (-3972 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-731)))) +((-4440 -3978 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4437 |has| |#1| (-1055)) (-4438 |has| |#1| (-1055))) +((|HasCategory| |#1| (QUOTE (-367))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055)))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-3978 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3978 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3978 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-1055)))) (-3978 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731)))) (|HasCategory| |#1| (QUOTE (-478))) (-3978 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3978 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1118)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-301))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478)))) (-3978 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731)))) (-3978 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-731)))) (-297 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL NIL (-298 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2264) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-299) ((|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 @@ -1136,11 +1136,11 @@ NIL ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-302 -3508 S) +(-302 -3514 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 -(-303 E -3508) +(-303 E -3514) ((|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 @@ -1170,7 +1170,7 @@ NIL NIL (-310) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-311 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1180,7 +1180,7 @@ 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 -(-313 -3508) +(-313 -3514) ((|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 @@ -1194,12 +1194,12 @@ NIL NIL (-316 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))}."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . 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T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . 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(|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4434 -3972 (-3268 (|has| |#1| (-1055)) (|has| |#1| (-644 (-551)))) (-12 (|has| |#1| (-562)) (-3972 (-3268 (|has| |#1| (-1055)) (|has| |#1| (-644 (-551)))) (|has| |#1| (-1055)) (|has| |#1| (-478)))) (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) ((-4439 "*") |has| |#1| (-562)) (-4430 |has| |#1| (-562)) (-4435 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(QUOTE (-551))))) (-3978 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562)))) (-3978 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-1118)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-21)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-25)))) (-3978 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1055)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-551))))) (-318 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 @@ -1208,7 +1208,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-320 R -3508) +(-320 R -3514) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1218,8 +1218,8 @@ NIL NIL (-322 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."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . 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T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4396) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4262) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3503) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-323 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 @@ -1230,7 +1230,7 @@ NIL NIL (-325 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . T)) ((|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-797)))) (-326 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1246,19 +1246,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173)))) (-329 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-330 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."))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) -(-331 S -3508) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +(-331 S -3514) ((|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 (-372)))) -(-332 -3508) +(-332 -3514) ((|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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-333) ((|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."))) @@ -1276,7 +1276,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-337 -3508 UP UPUP R) +(-337 -3514 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 @@ -1284,11 +1284,11 @@ 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 -(-339 S -3508 UP UPUP R) +(-339 S -3514 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 -(-340 -3508 UP UPUP R) +(-340 -3514 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 @@ -1302,19 +1302,19 @@ NIL NIL (-343 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-382)))) (|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-551))))) (-344 |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}."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((-3972 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) -(-345 S -3508 UP UPUP) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3978 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) +(-345 S -3514 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-367)))) -(-346 -3508 UP UPUP) +(-346 -3514 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4430 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) (-4429 |has| (-412 |#2|) (-367)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 |has| (-412 |#2|) (-367)) (-4441 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-347 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}."))) @@ -1322,16 +1322,16 @@ NIL NIL (-348 |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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((-3972 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3978 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) (-349 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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3978 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-350 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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3978 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-351 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 @@ -1346,51 +1346,51 @@ NIL NIL (-354) ((|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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL -(-355 R UP -3508) +(-355 R UP -3514) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-356 |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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((-3972 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3978 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) (-357 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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3978 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-358 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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3978 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-359 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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3978 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-360 GF) ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\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 -(-361 -3508 GF) +(-361 -3514 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 -(-362 -3508 FP FPP) +(-362 -3514 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-363 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}."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3978 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-364 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 (-365 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4434 . T)) +((-4440 . T)) NIL (-366 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1398,7 +1398,7 @@ NIL NIL (-367) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-368 S) ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) @@ -1414,7 +1414,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-562)))) (-371 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4434 |has| |#1| (-562)) (-4432 . T) (-4431 . T)) +((-4440 |has| |#1| (-562)) (-4438 . T) (-4437 . T)) NIL (-372) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1426,15 +1426,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-367)))) (-374 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) NIL (-375 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4438)) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107)))) +((|HasAttribute| |#1| (QUOTE -4444)) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107)))) (-376 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4437 . T)) +((-4443 . T)) NIL (-377 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1442,7 +1442,7 @@ NIL NIL (-378 |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) (-4432 . T) (-4431 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4438 . T) (-4437 . T)) NIL (-379 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."))) @@ -1454,11 +1454,11 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-381 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}"))) -((-4434 . T)) +((-4440 . T)) NIL (-382) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4420 . T) (-4428 . T) (-4213 . T) (-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4426 . T) (-4434 . T) (-4219 . T) (-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-383 |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}."))) @@ -1470,11 +1470,11 @@ NIL NIL (-385 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."))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . T)) ((|HasCategory| |#1| (QUOTE (-173)))) (-386 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}"))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . T)) ((|HasCategory| |#1| (QUOTE (-173)))) (-387) ((|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}."))) @@ -1482,7 +1482,7 @@ NIL NIL (-388 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}."))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . T)) NIL (-389) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|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.}"))) @@ -1498,7 +1498,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-855)))) (-392) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-393) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1510,13 +1510,13 @@ NIL NIL (-395 |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"))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . T)) NIL (-396) ((|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 -(-397 -3508 UP UPUP R) +(-397 -3514 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 @@ -1540,11 +1540,11 @@ NIL ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|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.}"))) NIL NIL -(-403 -3985 |returnType| -1512 |symbols|) +(-403 -3991 |returnType| -1513 |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 -(-404 -3508 UP) +(-404 -3514 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1558,28 +1558,28 @@ NIL NIL (-407) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-408 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4420)) (|HasAttribute| |#1| (QUOTE -4428))) +((|HasAttribute| |#1| (QUOTE -4426)) (|HasAttribute| |#1| (QUOTE -4434))) (-409) ((|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\"."))) -((-4213 . T) (-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4219 . T) (-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-410 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| #1="nil" #2="sqfr" #3="irred" #4="prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| #1# #2# #3# #4#) $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -312) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -289) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-1227))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-1227)))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-457)))) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -312) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -289) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-1227))) (-3978 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-1227)))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-457)))) (-411 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL NIL (-412 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."))) -((-4424 -12 (|has| |#1| (-6 -4435)) (|has| |#1| (-457)) (|has| |#1| (-6 -4424))) (-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-825))) (-3972 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-855)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-550))) (-12 (|HasAttribute| |#1| (QUOTE -4424)) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +((-4430 -12 (|has| |#1| (-6 -4441)) (|has| |#1| (-457)) (|has| |#1| (-6 -4430))) (-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-825))) (-3978 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-855)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-550))) (-12 (|HasAttribute| |#1| (QUOTE -4430)) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-413 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1590,7 +1590,7 @@ NIL NIL (-415 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) NIL (-416 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1600,15 +1600,15 @@ NIL ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-418 R -3508 UP A) +(-418 R -3514 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4434 . T)) +((-4440 . T)) NIL (-419 R1 F1 U1 A1 R2 F2 U2 A2) ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-420 R -3508 UP A |ibasis|) +(-420 R -3514 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1044) (|devaluate| |#2|)))) @@ -1622,7 +1622,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-423 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|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{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."))) -((-4434 |has| |#1| (-562)) (-4432 . T) (-4431 . T)) +((-4440 |has| |#1| (-562)) (-4438 . T) (-4437 . T)) NIL (-424 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)}."))) @@ -1634,7 +1634,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-1118))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540))))) (-426 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4434 -3972 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) ((-4439 "*") |has| |#1| (-562)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-562)) (-4429 |has| |#1| (-562))) +((-4440 -3978 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) ((-4445 "*") |has| |#1| (-562)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-562)) (-4435 |has| |#1| (-562))) NIL (-427 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} \\spad{->} \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1654,33 +1654,33 @@ NIL ((|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-372)))) (-431 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4437 . T) (-4427 . T) (-4438 . T)) +((-4443 . T) (-4433 . T) (-4444 . T)) NIL (-432 S A R B) ((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-433 R -3508) +(-433 R -3514) ((|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 (-434 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"))) -((-4424 -12 (|has| |#1| (-6 -4424)) (|has| |#2| (-6 -4424))) (-4431 . T) (-4432 . T) (-4434 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4424)) (|HasAttribute| |#2| (QUOTE -4424)))) -(-435 R -3508) +((-4430 -12 (|has| |#1| (-6 -4430)) (|has| |#2| (-6 -4430))) (-4437 . T) (-4438 . T) (-4440 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4430)) (|HasAttribute| |#2| (QUOTE -4430)))) +(-435 R -3514) ((|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 -(-436 R -3508) +(-436 R -3514) ((|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 -(-437 R -3508) +(-437 R -3514) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-438 R -3508) +(-438 R -3514) ((|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 @@ -1688,7 +1688,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-440 R -3508 UP) +(-440 R -3514 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 -1044) (QUOTE (-48))))) @@ -1720,7 +1720,7 @@ 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 -(-448 R UP -3508) +(-448 R UP -3514) ((|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 @@ -1758,16 +1758,16 @@ NIL NIL (-457) ((|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}."))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-458 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"))) -((-4434 |has| (-412 (-952 |#1|)) (-562)) (-4432 . T) (-4431 . T)) +((-4440 |has| (-412 (-952 |#1|)) (-562)) (-4438 . T) (-4437 . T)) ((|HasCategory| (-412 (-952 |#1|)) (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-412 (-952 |#1|)) (QUOTE (-562)))) (-459 |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"))) -(((-4439 "*") |has| |#2| (-173)) (-4430 |has| |#2| (-562)) (-4435 |has| |#2| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4435)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4445 "*") |has| |#2| (-173)) (-4436 |has| |#2| (-562)) (-4441 |has| |#2| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . 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A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1794,7 +1794,7 @@ NIL NIL (-466 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . T)) NIL (-467 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1802,7 +1802,7 @@ NIL NIL (-468 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-868))))) (-469 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}."))) @@ -1832,7 +1832,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-476 |lv| -3508 R) +(-476 |lv| -3514 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 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A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2264) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-481 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)}"))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-868))))) (-482) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-483) ((|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'."))) @@ -1866,29 +1866,29 @@ NIL NIL (-484 |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."))) -((-4437 . T) (-4438 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2264) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-485) ((|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 (-486 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) -(-490 -3508 UP UPUP R) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +(-490 -3514 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 @@ -1898,12 +1898,12 @@ NIL NIL (-492) ((|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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3972 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3978 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3978 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) (-493 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 -4437)) (|HasAttribute| |#1| (QUOTE -4438)) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) +((|HasAttribute| |#1| (QUOTE -4443)) (|HasAttribute| |#1| (QUOTE -4444)) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (-494 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1924,33 +1924,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-499 -3508 UP |AlExt| |AlPol|) +(-499 -3514 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-500) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-551))))) (-501 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-502 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."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-503 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 -(-504 R UP -3508) +(-504 R UP -3514) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-505 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1107))) (|HasCategory| (-112) (LIST (QUOTE -312) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-112) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-112) (QUOTE (-1107))) (|HasCategory| (-112) (LIST (QUOTE -618) (QUOTE (-868))))) (-506 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)}."))) @@ -1964,7 +1964,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-509 -3508 |Expon| |VarSet| |DPoly|) +(-509 -3514 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-1183))))) @@ -2014,36 +2014,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-797)))) (-521 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-522) ((|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 (-523 |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}."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((-3972 (|HasCategory| (-586 |#1|) (QUOTE (-145))) (|HasCategory| (-586 |#1|) (QUOTE (-372)))) (|HasCategory| (-586 |#1|) (QUOTE (-147))) (|HasCategory| (-586 |#1|) (QUOTE (-372))) (|HasCategory| (-586 |#1|) (QUOTE (-145)))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3978 (|HasCategory| (-586 |#1|) (QUOTE (-145))) (|HasCategory| (-586 |#1|) (QUOTE (-372)))) (|HasCategory| (-586 |#1|) (QUOTE (-147))) (|HasCategory| (-586 |#1|) (QUOTE (-372))) (|HasCategory| (-586 |#1|) (QUOTE (-145)))) (-524 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}."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-525 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."))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-526 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 -4438))) +((|HasAttribute| |#3| (QUOTE -4444))) (-527 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 -4438))) +((|HasAttribute| |#7| (QUOTE -4444))) (-528 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."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4439 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4445 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-529) ((|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 @@ -2076,7 +2076,7 @@ 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 -(-537 K -3508 |Par|) +(-537 K -3514 |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 @@ -2100,7 +2100,7 @@ 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 -(-543 K -3508 |Par|) +(-543 K -3514 |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 @@ -2130,11 +2130,11 @@ NIL NIL (-550) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4435 . T) (-4436 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4441 . T) (-4442 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-551) ((|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."))) -((-4419 . T) (-4425 . T) (-4429 . T) (-4424 . T) (-4435 . T) (-4436 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4425 . T) (-4431 . T) (-4435 . T) (-4430 . T) (-4441 . T) (-4442 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-552) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2154,13 +2154,13 @@ NIL NIL (-556 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) -(-557 R -3508) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2264) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) +(-557 R -3514) ((|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 -(-558 R0 -3508 UP UPUP R) +(-558 R0 -3514 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 @@ -2170,7 +2170,7 @@ NIL NIL (-560 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."))) -((-4213 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4219 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-561 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."))) @@ -2178,9 +2178,9 @@ NIL NIL (-562) ((|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."))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL -(-563 R -3508) +(-563 R -3514) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2192,7 +2192,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="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| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) "\\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| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) "\\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 -(-566 R -3508 L) +(-566 R -3514 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| #1#)) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -663) (|devaluate| |#2|)))) @@ -2200,11 +2200,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-568 -3508 UP UPUP R) +(-568 -3514 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 -(-569 -3508 UP) +(-569 -3514 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 @@ -2212,15 +2212,15 @@ NIL ((|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 -(-571 R -3508 L) +(-571 R -3514 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -663) (|devaluate| |#2|)))) -(-572 R -3508) +(-572 R -3514) ((|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 -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-1145)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-635))))) -(-573 -3508 UP) +(-573 -3514 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2228,27 +2228,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-575 -3508) +(-575 -3514) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-576 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."))) -((-4213 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4219 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-577) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-578 R -3508) +(-578 R -3514) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-287))) (|HasCategory| |#2| (QUOTE (-635))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-287)))) (|HasCategory| |#1| (QUOTE (-562)))) -(-579 -3508 UP) +(-579 -3514 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-580 R -3508) +(-580 R -3514) ((|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 @@ -2270,30 +2270,30 @@ NIL NIL (-585 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-586 |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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-372)))) (-587) ((|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 -(-588 -3508) +(-588 -3514) ((|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}."))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . T)) ((|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1183))))) -(-589 E -3508) +(-589 E -3514) ((|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 -(-590 R -3508) +(-590 R -3514) ((|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 (-591) -((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator."))) +((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL (-592 I) @@ -2322,22 +2322,22 @@ NIL NIL (-598 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-3972 (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-3978 (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-599 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 (-600 |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}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-551)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-551)) (|devaluate| |#1|)))) (|HasCategory| (-551) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-551)))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-551)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-551)) (|devaluate| |#1|)))) (|HasCategory| (-551) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4396) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-551)))))) (-601 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4439 "*") |has| |#1| (-562)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-562)) (-4436 |has| |#1| (-562)) (-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| |#1| (QUOTE (-562)))) (-602) -((|constructor| (NIL "This domain provides representations for internal type form.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) +((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) NIL NIL (-603 A B) @@ -2348,7 +2348,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-605 R -3508 FG) +(-605 R -3514 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2358,12 +2358,12 @@ NIL NIL (-607 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-608 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 -4438)) (|HasCategory| |#2| (QUOTE (-855))) (|HasAttribute| |#1| (QUOTE -4437)) (|HasCategory| |#3| (QUOTE (-1107)))) +((|HasAttribute| |#1| (QUOTE -4444)) (|HasCategory| |#2| (QUOTE (-855))) (|HasAttribute| |#1| (QUOTE -4443)) (|HasCategory| |#3| (QUOTE (-1107)))) (-609 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2378,19 +2378,19 @@ NIL NIL (-612 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4434 -3972 (-3268 (|has| |#2| (-371 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4432 . T) (-4431 . T)) -((-3972 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) +((-4440 -3978 (-3274 (|has| |#2| (-371 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4438 . T) (-4437 . T)) +((-3978 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-613 |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."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2264) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-614 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 (-615 |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}."))) -((-4438 . T)) +((-4444 . T)) NIL (-616 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."))) @@ -2408,7 +2408,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-620 -3508 UP) +(-620 -3514 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2426,7 +2426,7 @@ NIL NIL (-624 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}."))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| |#1| (QUOTE (-853)))) (-625 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."))) @@ -2434,15 +2434,15 @@ NIL NIL (-626 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."))) -((-4434 . T)) +((-4440 . T)) NIL -(-627 R -3508) +(-627 R -3514) ((|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 (-628 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"))) -((-4432 . T) (-4431 . T) ((-4439 "*") . T) (-4430 . T) (-4434 . T)) +((-4438 . T) (-4437 . T) ((-4445 "*") . T) (-4436 . T) (-4440 . T)) ((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (-629 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."))) @@ -2458,13 +2458,13 @@ NIL NIL (-632 |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}}."))) -((-4434 . T)) +((-4440 . T)) NIL (-633 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 -(-634 R -3508) +(-634 R -3514) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL @@ -2472,25 +2472,25 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-636 |lv| -3508) +(-636 |lv| -3514) ((|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 (-637) ((|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."))) -((-4438 . T)) -((-12 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2263) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-1165) (QUOTE (-855))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) +((-4444 . T)) +((-12 (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2264) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) (QUOTE (-1107)))) (-3978 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) (QUOTE (-1107)))) (-3978 (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-1165) (QUOTE (-855))) (-3978 (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) (QUOTE (-1107)))) (-638 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)."))) -((-4434 -3972 (-3268 (|has| |#2| (-371 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4432 . T) (-4431 . T)) -((-3972 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) +((-4440 -3978 (-3274 (|has| |#2| (-371 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4438 . T) (-4437 . T)) +((-3978 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-639 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-640 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#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) (-4432 . T) (-4431 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4438 . T) (-4437 . T)) NIL (-641 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) @@ -2503,10 +2503,10 @@ NIL (-643 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 -((-3758 (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-367)))) +((-3764 (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-367)))) (-644 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4434 . T)) +((-4440 . T)) NIL (-645 R) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2514,8 +2514,8 @@ NIL NIL (-646 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-647 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 @@ -2538,8 +2538,8 @@ NIL NIL (-652 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."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-653 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2551,30 +2551,30 @@ NIL (-655 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 -4438))) +((|HasAttribute| |#1| (QUOTE -4444))) (-656 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 (-657 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}."))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . T)) ((|HasCategory| |#1| (QUOTE (-796)))) -(-658 R -3508 L) +(-658 R -3514 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 -(-659 A -2832) +(-659 A -2838) ((|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}}"))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-660 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}}"))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-661 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-662 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2582,9 +2582,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-663 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}."))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) NIL -(-664 -3508 UP) +(-664 -3514 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)))) @@ -2606,7 +2606,7 @@ NIL NIL (-669 |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) (-4432 . T) (-4431 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4438 . T) (-4437 . T)) ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-173)))) (-670 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}."))) @@ -2614,13 +2614,13 @@ NIL NIL (-671 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}."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL -(-672 -3508 |Row| |Col| M) +(-672 -3514 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-673 -3508) +(-673 -3514) ((|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|) #1="failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2630,8 +2630,8 @@ NIL NIL (-675 |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."))) -((-4434 . T) (-4437 . T) (-4431 . T) (-4432 . T)) -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4439 #1="*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-562))) (-3972 (|HasAttribute| |#2| (QUOTE (-4439 #1#))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) +((-4440 . T) (-4443 . T) (-4437 . T) (-4438 . T)) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4445 #1="*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3978 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-562))) (-3978 (|HasAttribute| |#2| (QUOTE (-4445 #1#))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) (-676) ((|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 @@ -2651,7 +2651,7 @@ NIL (-680 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 -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-681) ((|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 @@ -2691,10 +2691,10 @@ NIL (-690 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4439 "*"))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-562)))) +((|HasAttribute| |#2| (QUOTE (-4445 "*"))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-562)))) (-691 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4437 . T) (-4438 . T)) +((-4443 . T) (-4444 . T)) NIL (-692 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}."))) @@ -2706,8 +2706,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562)))) (-694 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."))) -((-4437 . T) (-4438 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4439 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4443 . T) (-4444 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4445 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-695 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 @@ -2716,7 +2716,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-697 S -3508 FLAF FLAS) +(-697 S -3514 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 @@ -2726,11 +2726,11 @@ NIL NIL (-699) ((|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"))) -((-4430 . T) (-4435 |has| (-704) (-367)) (-4429 |has| (-704) (-367)) (-1466 . T) (-4436 |has| (-704) (-6 -4436)) (-4433 |has| (-704) (-6 -4433)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . 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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}."))) -((-4438 . T)) +((-4444 . T)) NIL (-701 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}."))) @@ -2740,13 +2740,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-703 OV E -3508 PG) +(-703 OV E -3514 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 (-704) ((|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}"))) -((-4213 . T) (-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4219 . T) (-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-705 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."))) @@ -2754,7 +2754,7 @@ NIL NIL (-706) ((|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}"))) -((-4436 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4442 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-707 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"))) @@ -2772,7 +2772,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-711 S -3084 I) +(-711 S -3090 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 @@ -2782,7 +2782,7 @@ NIL NIL (-713 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)}.}"))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) NIL (-714 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}."))) @@ -2792,25 +2792,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-716 R |Mod| -2224 -3953 |exactQuo|) +(-716 R |Mod| -2225 -3959 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-717 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4433 |has| |#1| (-367)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4439 |has| |#1| (-367)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3978 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-718 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-719 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) (-4434 . T)) +((-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) (-4440 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-720 R |Mod| -2224 -3953 |exactQuo|) +(-720 R |Mod| -2225 -3959 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4434 . T)) +((-4440 . T)) NIL (-721 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2818,11 +2818,11 @@ NIL NIL (-722 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . T)) NIL -(-723 -3508) +(-723 -3514) ((|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]]}."))) -((-4434 . T)) +((-4440 . T)) NIL (-724 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."))) @@ -2846,7 +2846,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-372)))) (-729 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."))) -((-4430 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 |has| |#1| (-367)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-730 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."))) @@ -2856,7 +2856,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-732 -3508 UP) +(-732 -3514 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 @@ -2874,8 +2874,8 @@ NIL NIL (-736 |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."))) -(((-4439 "*") |has| |#2| (-173)) (-4430 |has| |#2| (-562)) (-4435 |has| |#2| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4435)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4445 "*") |has| |#2| (-173)) (-4436 |has| |#2| (-562)) (-4441 |has| |#2| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (-3978 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3978 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3978 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (-3978 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3978 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4441)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) (-737 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2890,15 +2890,15 @@ NIL NIL (-740 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) (-4434 . T)) +((-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) (-4440 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-855)))) (-741 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}."))) -((-4437 . T) (-4427 . T) (-4438 . T)) +((-4443 . T) (-4433 . T) (-4444 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-742 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4427 . T) (-4438 . T)) +((-4433 . T) (-4444 . T)) NIL (-743) ((|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."))) @@ -2910,7 +2910,7 @@ NIL NIL (-745 |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}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4432 . T) (-4431 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4438 . T) (-4437 . T) (-4440 . T)) NIL (-746 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"))) @@ -2926,7 +2926,7 @@ NIL NIL (-749 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}."))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . T)) NIL (-750) ((|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}."))) @@ -3008,11 +3008,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-770 -3508) +(-770 -3514) ((|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 -(-771 P -3508) +(-771 P -3514) ((|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 @@ -3020,7 +3020,7 @@ NIL NIL NIL NIL -(-773 UP -3508) +(-773 UP -3514) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3034,9 +3034,9 @@ NIL NIL (-776) ((|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."))) -(((-4439 "*") . T)) +(((-4445 "*") . T)) NIL -(-777 R -3508) +(-777 R -3514) ((|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 @@ -3056,7 +3056,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-782 -3508 |ExtF| |SUEx| |ExtP| |n|) +(-782 -3514 |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 @@ -3070,12 +3070,12 @@ NIL NIL (-785 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."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . 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(|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) 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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 @@ -3086,7 +3086,7 @@ NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551)))))) (-789 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.}"))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL (-790 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}."))) @@ -3134,7 +3134,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-372)))) (-801 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) NIL (-802) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) @@ -3142,9 +3142,9 @@ NIL NIL (-803 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-3972 (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) -(-804 -3972 R OS S) +((-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-3978 (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3978 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) +(-804 -3978 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 @@ -3152,11 +3152,11 @@ NIL ((|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 -(-806 R -3508 L) +(-806 R -3514 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-807 R -3508) +(-807 R -3514) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| #1="failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| #1#) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2="failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2#) (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3164,7 +3164,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-809 R -3508) +(-809 R -3514) ((|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 @@ -3172,11 +3172,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-811 -3508 UP UPUP R) +(-811 -3514 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 -(-812 -3508 UP L LQ) +(-812 -3514 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 @@ -3184,41 +3184,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-814 -3508 UP L LQ) +(-814 -3514 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-815 -3508 UP) +(-815 -3514 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1="failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\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|) #1#)) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-816 -3508 L UP A LO) +(-816 -3514 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 -(-817 -3508 UP) +(-817 -3514 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-818 -3508 LO) +(-818 -3514 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-819 -3508 LODO) +(-819 -3514 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) NIL NIL -(-820 -3033 S |f|) +(-820 -3039 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4431 |has| |#2| (-1055)) (-4432 |has| |#2| (-1055)) (-4434 |has| |#2| (-6 -4434)) ((-4439 "*") |has| |#2| (-173)) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-853))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST 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T)) +((|HasCategory| |#1| (QUOTE (-916))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3978 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-822 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4439 "*") |has| |#2| (-367)) (-4430 |has| |#2| (-367)) (-4435 |has| |#2| (-367)) (-4429 |has| |#2| (-367)) (-4434 . T) (-4432 . T) (-4431 . T)) +(((-4445 "*") |has| |#2| (-367)) (-4436 |has| |#2| (-367)) (-4441 |has| |#2| (-367)) (-4435 |has| |#2| (-367)) (-4440 . T) (-4438 . T) (-4437 . T)) ((|HasCategory| |#2| (QUOTE (-367)))) (-823 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}))."))) @@ -3230,7 +3230,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-855)))) (-825) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-826) ((|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|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3262,7 +3262,7 @@ NIL NIL (-833 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-234)))) (-834) ((|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."))) @@ -3270,7 +3270,7 @@ NIL NIL (-835 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4437 . T) (-4427 . T) (-4438 . T)) +((-4443 . T) (-4433 . T) (-4444 . T)) NIL (-836) ((|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."))) @@ -3278,15 +3278,15 @@ NIL NIL (-837 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."))) -((-4434 |has| |#1| (-853))) -((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3972 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4440 |has| |#1| (-853))) +((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-3978 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3978 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-550)))) (-838 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 (-839 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) (-4434 . T)) +((-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) (-4440 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) (-840 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) @@ -3318,8 +3318,8 @@ NIL NIL (-847 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4434 |has| |#1| (-853))) -((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3972 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4440 |has| |#1| (-853))) +((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-3978 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3978 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-550)))) (-848 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3328,7 +3328,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-850 -3033 S) +(-850 -3039 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3342,7 +3342,7 @@ NIL NIL (-853) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4434 . T)) +((-4440 . T)) NIL (-854 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3358,19 +3358,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173)))) (-857 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) NIL (-858 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 (-367))) (|HasCategory| |#1| (QUOTE (-562)))) -(-859 R |sigma| -3677) +(-859 R |sigma| -3683) ((|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."))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) -(-860 |x| R |sigma| -3677) +(-860 |x| R |sigma| -3683) ((|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}."))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-367)))) (-861 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..)}."))) @@ -3414,7 +3414,7 @@ NIL NIL (-871 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)"))) -((-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) (-4434 . T)) +((-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) (-4440 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (-872 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)."))) @@ -3426,24 +3426,24 @@ NIL NIL (-874 |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)."))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-875 |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}."))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-876 |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)."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| (-874 |#1|) (QUOTE (-916))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-874 |#1|) (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-147))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-874 |#1|) (QUOTE (-1026))) (|HasCategory| (-874 |#1|) (QUOTE (-825))) (-3972 (|HasCategory| (-874 |#1|) (QUOTE (-825))) (|HasCategory| (-874 |#1|) (QUOTE (-855)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (QUOTE (-1157))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (QUOTE (-234))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -874) (|devaluate| |#1|)) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (QUOTE (-310))) (|HasCategory| (-874 |#1|) (QUOTE (-550))) (|HasCategory| (-874 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-916)))) (|HasCategory| (-874 |#1|) (QUOTE (-145))))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| (-874 |#1|) (QUOTE (-916))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-874 |#1|) (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-147))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-874 |#1|) (QUOTE (-1026))) (|HasCategory| (-874 |#1|) (QUOTE (-825))) (-3978 (|HasCategory| (-874 |#1|) (QUOTE (-825))) (|HasCategory| (-874 |#1|) (QUOTE (-855)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (QUOTE (-1157))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (QUOTE (-234))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -874) (|devaluate| |#1|)) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (QUOTE (-310))) (|HasCategory| (-874 |#1|) (QUOTE (-550))) (|HasCategory| (-874 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-916)))) (-3978 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-916)))) (|HasCategory| (-874 |#1|) (QUOTE (-145))))) (-877 |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)}."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-825))) (-3972 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -289) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-855))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-825))) (-3978 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -289) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-855))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) (-878 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 (-1107))) (|HasCategory| |#2| (QUOTE (-1107)))) (-3972 (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-1107))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-1107)))) (-3978 (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-1107))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))))) (-879) ((|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 @@ -3503,7 +3503,7 @@ NIL (-893 |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 (-3758 (|HasCategory| |#2| (QUOTE (-1055)))) (-3758 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (-3758 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183))))) +((-12 (-3764 (|HasCategory| |#2| (QUOTE (-1055)))) (-3764 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (-3764 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183))))) (-894 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 @@ -3516,7 +3516,7 @@ NIL ((|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 -(-897 R -3084) +(-897 R -3090) ((|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 @@ -3536,7 +3536,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-902 UP -3508) +(-902 UP -3514) ((|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 @@ -3554,23 +3554,23 @@ NIL NIL (-906 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}."))) -((-4434 . T)) +((-4440 . T)) NIL (-907 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 (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-908 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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4434 . T)) -((-3972 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) +((-4440 . T)) +((-3978 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (-909 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 (-910 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."))) -((-4434 . T)) +((-4440 . T)) NIL (-911 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}."))) @@ -3578,7 +3578,7 @@ NIL NIL (-912 |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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-372)))) (-913 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) @@ -3594,9 +3594,9 @@ NIL ((|HasCategory| |#1| (QUOTE (-145)))) (-916) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL -(-917 R0 -3508 UP UPUP R) +(-917 R0 -3514 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 @@ -3610,7 +3610,7 @@ NIL NIL (-920 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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-921 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."))) @@ -3624,13 +3624,13 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-924 -3508) +(-924 -3514) ((|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 (-925) ((|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}."))) -(((-4439 "*") . T)) +(((-4445 "*") . T)) NIL (-926 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})."))) @@ -3638,13 +3638,13 @@ NIL NIL (-927) ((|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)}"))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL -(-928 |xx| -3508) +(-928 |xx| -3514) ((|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 -(-929 -3508 P) +(-929 -3514 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3672,7 +3672,7 @@ NIL ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-936 R -3508) +(-936 R -3514) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3680,7 +3680,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-938 S R -3508) +(-938 S R -3514) ((|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 @@ -3700,11 +3700,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -892) (|devaluate| |#1|)))) -(-943 -3084) +(-943 -3090) ((|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 -(-944 R -3508 -3084) +(-944 R -3514 -3090) ((|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 @@ -3726,8 +3726,8 @@ NIL NIL (-949 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-950 |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 @@ -3738,8 +3738,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-853)))) (-952 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}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1183) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1183) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3978 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-953 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 @@ -3751,12 +3751,12 @@ NIL (-955 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 (-916))) (|HasAttribute| |#2| (QUOTE -4435)) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasAttribute| |#2| (QUOTE -4441)) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540))))) (-956 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}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) NIL -(-957 E V R P -3508) +(-957 E V R P -3514) ((|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 @@ -3764,7 +3764,7 @@ NIL ((|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 -(-959 E V R P -3508) +(-959 E V R P -3514) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-457)))) @@ -3778,16 +3778,16 @@ NIL NIL (-962 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4435))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-6 -4441)) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3978 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4441))) (-963 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 (-964 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"))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-965 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 @@ -3796,7 +3796,7 @@ NIL ((|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 -(-967 -3508) +(-967 -3514) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3810,8 +3810,8 @@ NIL NIL (-970 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"))) -((-4434 -12 (|has| |#2| (-478)) (|has| |#1| (-478)))) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) +((-4440 -12 (|has| |#2| (-478)) (|has| |#1| (-478)))) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) (-971) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3826,7 +3826,7 @@ NIL NIL (-974 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4437 . T) (-4438 . T)) +((-4443 . T) (-4444 . T)) NIL (-975 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}}"))) @@ -3846,7 +3846,7 @@ NIL NIL (-979 |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}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-980) ((|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}."))) @@ -3858,7 +3858,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-562)))) (-982 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."))) -((-4437 . T)) +((-4443 . T)) NIL (-983 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."))) @@ -3874,7 +3874,7 @@ NIL NIL (-986 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}."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL (-987 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) @@ -3892,7 +3892,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-991 K R UP -3508) +(-991 K R UP -3514) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -3918,7 +3918,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-1157)))) (-997 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}."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-998 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}."))) @@ -3934,19 +3934,19 @@ NIL NIL (-1001 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."))) -((-4437 . T) (-4438 . T)) +((-4443 . T) (-4444 . T)) NIL (-1002 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.}"))) -((-4430 |has| |#1| (-293)) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4436 |has| |#1| (-293)) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-367))) (-3978 (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550)))) (-1003 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 (-550))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-293)))) (-1004 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-4430 |has| |#1| (-293)) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 |has| |#1| (-293)) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1005 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) @@ -3954,8 +3954,8 @@ NIL NIL (-1006 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-1007 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3964,14 +3964,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1009 -3508 UP UPUP |radicnd| |n|) +(-1009 -3514 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4430 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) (-4429 |has| (-412 |#2|) (-367)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-354))) (-3972 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-3972 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (-3972 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-354))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-551)))) (-3972 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) +((-4436 |has| (-412 |#2|) (-367)) (-4441 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-354))) (-3978 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-3978 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (-3978 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-354))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-551)))) (-3978 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) (-1010 |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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3972 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3978 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3978 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) (-1011) ((|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 @@ -3991,7 +3991,7 @@ NIL (-1015 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 -4438)) (|HasCategory| |#2| (QUOTE (-1107)))) +((|HasAttribute| |#1| (QUOTE -4444)) (|HasCategory| |#2| (QUOTE (-1107)))) (-1016 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 @@ -4002,21 +4002,21 @@ NIL NIL (-1018) ((|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}}"))) -((-4430 . T) (-4435 . T) (-4429 . T) (-4432 . T) (-4431 . T) ((-4439 "*") . T) (-4434 . T)) +((-4436 . T) (-4441 . T) (-4435 . T) (-4438 . T) (-4437 . T) ((-4445 "*") . T) (-4440 . T)) NIL -(-1019 R -3508) +(-1019 R -3514) ((|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 -(-1020 R -3508) +(-1020 R -3514) ((|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 -(-1021 -3508 UP) +(-1021 -3514 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 -(-1022 -3508 UP) +(-1022 -3514 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 @@ -4050,9 +4050,9 @@ NIL NIL (-1030 |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"))) -((-4430 . T) (-4435 . T) (-4429 . T) (-4432 . T) (-4431 . T) ((-4439 "*") . T) (-4434 . T)) -((-3972 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (QUOTE (-551))))) -(-1031 -3508 L) +((-4436 . T) (-4441 . T) (-4435 . T) (-4438 . T) (-4437 . T) ((-4445 "*") . T) (-4440 . T)) +((-3978 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (QUOTE (-551))))) +(-1031 -3514 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4062,7 +4062,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1107)))) (-1033 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."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-868))))) (-1034) ((|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."))) @@ -4071,7 +4071,7 @@ NIL (-1035 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4439 "*")))) +((|HasAttribute| |#1| (QUOTE (-4445 "*")))) (-1036 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 @@ -4088,14 +4088,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1040 -3508 |Expon| |VarSet| |FPol| |LFPol|) +(-1040 -3514 |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"))) -(((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1041) ((|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.}"))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2263) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-51) (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2264) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (QUOTE (-1107)))) (-3978 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (QUOTE (-1107)))) (-3978 (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (QUOTE (-1107))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-51) (QUOTE (-1107))) (-3978 (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (LIST (QUOTE -618) (QUOTE (-868))))) (-1042) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4138,7 +4138,7 @@ NIL NIL (-1052 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}."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) ((-12 (|HasCategory| (-785 |#1| (-869 |#2|)) (QUOTE (-1107))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -785) (|devaluate| |#1|) (LIST (QUOTE -869) (|devaluate| |#2|)))))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-785 |#1| (-869 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-869 |#2|) (QUOTE (-372))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-1053) ((|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"))) @@ -4150,9 +4150,9 @@ NIL NIL (-1055) ((|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."))) -((-4434 . T)) +((-4440 . T)) NIL -(-1056 |xx| -3508) +(-1056 |xx| -3514) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4166,12 +4166,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-310))) (|HasCategory| |#4| (QUOTE (-367))) (|HasCategory| |#4| (QUOTE (-562))) (|HasCategory| |#4| (QUOTE (-173)))) (-1059 |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"))) -((-4437 . T) (-4432 . T) (-4431 . T)) +((-4443 . T) (-4438 . T) (-4437 . T)) NIL (-1060 |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}."))) -((-4437 . T) (-4432 . T) (-4431 . T)) -((|HasCategory| |#3| (QUOTE (-173))) (-3972 (-12 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-367)))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (QUOTE (-310))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4438 . T) (-4437 . T)) +((|HasCategory| |#3| (QUOTE (-173))) (-3978 (-12 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-367)))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (QUOTE (-310))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-868))))) (-1061 |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 @@ -4194,7 +4194,7 @@ NIL NIL (-1066) ((|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."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1067 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4202,19 +4202,19 @@ NIL NIL (-1068) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4425 . T) (-4429 . T) (-4424 . T) (-4435 . T) (-4436 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4431 . T) (-4435 . T) (-4430 . T) (-4441 . T) (-4442 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1069) ((|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}"))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2263) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-51) (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2264) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (QUOTE (-1107)))) (-3978 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (QUOTE (-1107)))) (-3978 (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (QUOTE (-1107))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-51) (QUOTE (-1107))) (-3978 (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 (-1183)) (|:| -2264 (-51))) (LIST (QUOTE -618) (QUOTE (-868))))) (-1070 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -997) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-1183))))) (-1071 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) NIL (-1072) ((|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'."))) @@ -4238,7 +4238,7 @@ NIL NIL (-1077 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL (-1078 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."))) @@ -4252,7 +4252,7 @@ NIL ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1081 |Base| R -3508) +(-1081 |Base| R -3514) ((|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 @@ -4260,7 +4260,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1083 |Base| R -3508) +(-1083 |Base| R -3514) ((|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 @@ -4270,8 +4270,8 @@ NIL NIL (-1085 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."))) -((-4430 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-354))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-354)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))))) +((-4436 |has| |#1| (-367)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-354))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-354)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))))) (-1086 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 @@ -4302,8 +4302,8 @@ NIL NIL (-1093 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"))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3978 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1094 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 @@ -4342,15 +4342,15 @@ NIL NIL (-1103 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)}}"))) -((-4437 . T) (-4427 . T) (-4438 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4443 . T) (-4433 . T) (-4444 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-1104 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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL (-1105 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4427 . T)) +((-4433 . T)) NIL (-1106 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4390,7 +4390,7 @@ NIL NIL (-1115 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.}"))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL (-1116) ((|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 pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4406,8 +4406,8 @@ NIL NIL (-1119 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4431 |has| |#3| (-1055)) (-4432 |has| |#3| (-1055)) (-4434 |has| |#3| (-6 -4434)) ((-4439 "*") |has| |#3| (-173)) (-4437 . 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(|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-853))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551)))))) (|HasCategory| (-551) (QUOTE (-855))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-234))) (|HasCategory| |#3| (QUOTE (-1055)))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3978 (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#3| (QUOTE (-1055)))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasAttribute| |#3| (QUOTE -4440)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (-1120 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 @@ -4420,7 +4420,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1123 R -3508) +(-1123 R -3514) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) #1#) |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4434,19 +4434,19 @@ NIL NIL (-1126) ((|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."))) -((-4425 . T) (-4429 . T) (-4424 . T) (-4435 . T) (-4436 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4431 . T) (-4435 . T) (-4430 . T) (-4441 . T) (-4442 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1127 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4437 . T) (-4438 . T)) +((-4443 . T) (-4444 . T)) NIL (-1128 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-367))) (|HasAttribute| |#3| (QUOTE (-4439 "*"))) (|HasCategory| |#3| (QUOTE (-173)))) +((|HasCategory| |#3| (QUOTE (-367))) (|HasAttribute| |#3| (QUOTE (-4445 "*"))) (|HasCategory| |#3| (QUOTE (-173)))) (-1129 |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."))) -((-4437 . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4443 . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1130 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}."))) @@ -4454,17 +4454,17 @@ NIL NIL (-1131 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."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3978 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1132 |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}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-367)))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-367)))) (-1133 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}"))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL -(-1134 UP -3508) +(-1134 UP -3514) ((|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 @@ -4518,19 +4518,19 @@ NIL NIL (-1147 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107))) (-3972 (-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107)))) (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107))) (-3978 (-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107)))) (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-868))))) (-1148 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4434 . T) (-4426 |has| |#2| (-6 (-4439 "*"))) (-4437 . T) (-4431 . T) (-4432 . T)) -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4439 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-367))) (-3972 (|HasAttribute| |#2| (QUOTE (-4439 "*"))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) +((-4440 . T) (-4432 |has| |#2| (-6 (-4445 "*"))) (-4443 . T) (-4437 . T) (-4438 . T)) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4445 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3978 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-367))) (-3978 (|HasAttribute| |#2| (QUOTE (-4445 "*"))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) (-1149 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1150) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL (-1151 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.}"))) @@ -4538,12 +4538,12 @@ NIL NIL (-1152 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."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-868))))) (-1153 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}."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-1154 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 @@ -4554,8 +4554,8 @@ NIL NIL (-1156 |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."))) -((-4438 . T)) -((-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) +((-4444 . T)) +((-12 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2264) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-1157) ((|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 @@ -4570,8 +4570,8 @@ NIL NIL (-1160 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."))) -((-4438 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-1161 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 @@ -4586,16 +4586,16 @@ NIL NIL (-1164) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL (-1165) NIL -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-1166 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2264) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (QUOTE (-1107)))) (-3978 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (QUOTE (-1107)))) (-3978 (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (QUOTE (-1107))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-1167 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4626,9 +4626,9 @@ NIL NIL (-1174 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4439 "*") -3972 (-3268 (|has| |#1| (-367)) (|has| (-1181 |#1| |#2| |#3|) (-825))) (|has| |#1| (-173)) (-3268 (|has| |#1| (-367)) (|has| (-1181 |#1| |#2| |#3|) (-916)))) (-4430 -3972 (-3268 (|has| |#1| (-367)) (|has| (-1181 |#1| |#2| |#3|) (-825))) (|has| |#1| (-562)) (-3268 (|has| |#1| (-367)) (|has| (-1181 |#1| |#2| |#3|) (-916)))) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . 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T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4439 |has| |#1| (-367)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3978 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1178 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4650,12 +4650,12 @@ NIL NIL (-1180 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4256) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4396) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4262) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3503) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-1181 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|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}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4256) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -4396) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4262) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3503) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-1182) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4670,8 +4670,8 @@ NIL NIL (-1185 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-977) (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4435))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-6 -4441)) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3978 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-977) (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4441))) (-1186) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4710,8 +4710,8 @@ NIL NIL (-1195 |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}"))) -((-4437 . T) (-4438 . T)) -((-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4443 . T) (-4444 . T)) +((-12 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4310) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2264) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3978 (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-1196 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 @@ -4726,7 +4726,7 @@ NIL NIL (-1199 |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})}."))) -((-4438 . T)) +((-4444 . T)) NIL (-1200 |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."))) @@ -4766,8 +4766,8 @@ NIL NIL (-1209 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4438 . T) (-4437 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4444 . T) (-4443 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-1210 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4776,7 +4776,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1212 R -3508) +(-1212 R -3514) ((|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 @@ -4784,21 +4784,21 @@ NIL ((|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 -(-1214 R -3508) +(-1214 R -3514) ((|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 -619) (LIST (QUOTE -896) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -892) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -892) (|devaluate| |#1|))))) (-1215 |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}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-367)))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-367)))) (-1216 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 (-372)))) (-1217 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL (-1218 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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}."))) @@ -4812,7 +4812,7 @@ NIL ((|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 (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) -(-1221 -3508) +(-1221 -3514) ((|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 @@ -4838,7 +4838,7 @@ NIL NIL (-1227) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1228) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4858,15 +4858,15 @@ NIL NIL (-1232 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4439 "*") -3972 (-3268 (|has| |#1| (-367)) (|has| (-1262 |#1| |#2| |#3|) (-825))) (|has| |#1| (-173)) (-3268 (|has| |#1| (-367)) (|has| (-1262 |#1| |#2| |#3|) (-916)))) (-4430 -3972 (-3268 (|has| |#1| (-367)) (|has| (-1262 |#1| |#2| |#3|) (-825))) (|has| |#1| (-562)) (-3268 (|has| |#1| (-367)) (|has| (-1262 |#1| |#2| |#3|) (-916)))) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . 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((|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 (-1234 |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."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1235 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)}."))) @@ -4874,12 +4874,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-1236 |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)}. 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(|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4262) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3503) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-855)))) (|HasCategory| |#2| (QUOTE (-916))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-310)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-145)))))) (-1238 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4894,8 +4894,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-853)))) (-1241 |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}"))) -(((-4439 "*") |has| |#2| (-173)) (-4430 |has| |#2| (-562)) (-4433 |has| |#2| (-367)) (-4435 |has| |#2| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE -4435)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4445 "*") |has| |#2| (-173)) (-4436 |has| |#2| (-562)) (-4439 |has| |#2| (-367)) (-4441 |has| |#2| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (-3978 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3978 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3978 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3978 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3978 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE -4441)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3978 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1242 |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 @@ -4922,7 +4922,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-1157)))) (-1248 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}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4433 |has| |#1| (-367)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4439 |has| |#1| (-367)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) NIL (-1249 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."))) @@ -4931,10 +4931,10 @@ NIL (-1250 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 -906) (QUOTE (-1183)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1118))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4390) (LIST (|devaluate| |#2|) (QUOTE (-1183)))))) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1118))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4396) (LIST (|devaluate| |#2|) (QUOTE (-1183)))))) (-1251 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1252 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4942,15 +4942,15 @@ NIL NIL (-1253 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4256) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4396) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4262) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3503) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-1254 |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 (-1255 |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."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1256 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)}."))) @@ -4958,28 +4958,28 @@ NIL NIL (-1257 |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)}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1258 |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)}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4256) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551)))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3978 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4396) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4262) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3503) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551)))))) (-1259 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))}."))) -(((-4439 "*") |has| (-1253 |#2| |#3| |#4|) (-173)) (-4430 |has| (-1253 |#2| |#3| |#4|) (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-173))) (-3972 (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-367))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-457))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-562)))) +(((-4445 "*") |has| (-1253 |#2| |#3| |#4|) (-173)) (-4436 |has| (-1253 |#2| |#3| |#4|) (-562)) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-173))) (-3978 (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-367))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-457))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-562)))) (-1260 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4438))) +((|HasAttribute| |#1| (QUOTE -4444))) (-1261 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL (-1262 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|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}."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4256) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4437 . T) (-4438 . T) (-4440 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3978 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -4396) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4262) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3503) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-1263 |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 @@ -4987,16 +4987,16 @@ NIL (-1264 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 (-551)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasSignature| |#2| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4256) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasSignature| |#2| (LIST (QUOTE -3503) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4262) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367)))) (-1265 |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."))) -(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-562)) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1266 |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 -(-1267 -3508 UP L UTS) +(-1267 -3514 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 (-562)))) @@ -5014,12 +5014,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-1008))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1271 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) NIL (-1272 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4438 . T) (-4437 . T)) -((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4443 . T)) +((-3978 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3978 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3978 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-1273 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 @@ -5050,13 +5050,13 @@ NIL NIL (-1280 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}."))) -((-4432 . T) (-4431 . T)) +((-4438 . T) (-4437 . T)) NIL (-1281 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 -(-1282 K R UP -3508) +(-1282 K R UP -3514) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5070,56 +5070,56 @@ NIL NIL (-1285 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)"))) -((-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) (-4434 . T)) +((-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) (-4440 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (-1286 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}}."))) -((-4438 . T) (-4437 . T)) +((-4444 . T) (-4443 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-868))))) (-1287 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})"))) -((-4431 . T) (-4432 . T) (-4434 . T)) +((-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1288 |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."))) -((-4434 . T) (-4430 |has| |#2| (-6 -4430)) (-4432 . T) (-4431 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4430))) +((-4440 . T) (-4436 |has| |#2| (-6 -4436)) (-4438 . T) (-4437 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4436))) (-1289 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 -(-1290 S -3508) +(-1290 S -3514) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1291 -3508) +(-1291 -3514) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) -((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL (-1292 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4430 |has| |#2| (-6 -4430)) (-4432 . T) (-4431 . T) (-4434 . T)) +((-4436 |has| |#2| (-6 -4436)) (-4438 . T) (-4437 . T) (-4440 . T)) NIL (-1293 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4430 |has| |#2| (-6 -4430)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -722) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasAttribute| |#2| (QUOTE -4430))) +((-4436 |has| |#2| (-6 -4436)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -722) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasAttribute| |#2| (QUOTE -4436))) (-1294 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."))) -((-4430 |has| |#1| (-6 -4430)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasAttribute| |#1| (QUOTE -4430))) +((-4436 |has| |#1| (-6 -4436)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasAttribute| |#1| (QUOTE -4436))) (-1295 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4430 |has| |#2| (-6 -4430)) (-4432 . T) (-4431 . T) (-4434 . T)) +((-4436 |has| |#2| (-6 -4436)) (-4438 . T) (-4437 . T) (-4440 . T)) NIL (-1296 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4434 . T) (-4435 |has| |#1| (-6 -4435)) (-4430 |has| |#1| (-6 -4430)) (-4432 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4434)) (|HasAttribute| |#1| (QUOTE -4435)) (|HasAttribute| |#1| (QUOTE -4430))) +((-4440 . T) (-4441 |has| |#1| (-6 -4441)) (-4436 |has| |#1| (-6 -4436)) (-4438 . T) (-4437 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4440)) (|HasAttribute| |#1| (QUOTE -4441)) (|HasAttribute| |#1| (QUOTE -4436))) (-1297 |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."))) -((-4430 |has| |#2| (-6 -4430)) (-4432 . T) (-4431 . T) (-4434 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4430))) +((-4436 |has| |#2| (-6 -4436)) (-4438 . T) (-4437 . T) (-4440 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4436))) (-1298 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 @@ -5134,7 +5134,7 @@ NIL NIL (-1301 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +(((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) NIL NIL NIL @@ -5152,4 +5152,4 @@ NIL NIL NIL NIL -((-3 NIL 2265121 2265126 2265131 2265136) (-2 NIL 2265101 2265106 2265111 2265116) (-1 NIL 2265081 2265086 2265091 2265096) (0 NIL 2265061 2265066 2265071 2265076) (-1301 "ZMOD.spad" 2264870 2264883 2264999 2265056) (-1300 "ZLINDEP.spad" 2263936 2263947 2264860 2264865) (-1299 "ZDSOLVE.spad" 2253881 2253903 2263926 2263931) (-1298 "YSTREAM.spad" 2253376 2253387 2253871 2253876) (-1297 "XRPOLY.spad" 2252596 2252616 2253232 2253301) (-1296 "XPR.spad" 2250391 2250404 2252314 2252413) (-1295 "XPOLYC.spad" 2249710 2249726 2250317 2250386) (-1294 "XPOLY.spad" 2249265 2249276 2249566 2249635) (-1293 "XPBWPOLY.spad" 2247702 2247722 2249045 2249114) (-1292 "XFALG.spad" 2244750 2244766 2247628 2247697) (-1291 "XF.spad" 2243213 2243228 2244652 2244745) (-1290 "XF.spad" 2241656 2241673 2243097 2243102) (-1289 "XEXPPKG.spad" 2240907 2240933 2241646 2241651) (-1288 "XDPOLY.spad" 2240521 2240537 2240763 2240832) (-1287 "XALG.spad" 2240181 2240192 2240477 2240516) (-1286 "WUTSET.spad" 2236020 2236037 2239827 2239854) (-1285 "WP.spad" 2235219 2235263 2235878 2235945) (-1284 "WHILEAST.spad" 2235017 2235026 2235209 2235214) (-1283 "WHEREAST.spad" 2234688 2234697 2235007 2235012) (-1282 "WFFINTBS.spad" 2232351 2232373 2234678 2234683) (-1281 "WEIER.spad" 2230573 2230584 2232341 2232346) (-1280 "VSPACE.spad" 2230246 2230257 2230541 2230568) (-1279 "VSPACE.spad" 2229939 2229952 2230236 2230241) (-1278 "VOID.spad" 2229616 2229625 2229929 2229934) (-1277 "VIEWDEF.spad" 2224817 2224826 2229606 2229611) (-1276 "VIEW3D.spad" 2208778 2208787 2224807 2224812) (-1275 "VIEW2D.spad" 2196669 2196678 2208768 2208773) (-1274 "VIEW.spad" 2194349 2194358 2196659 2196664) (-1273 "VECTOR2.spad" 2192988 2193001 2194339 2194344) (-1272 "VECTOR.spad" 2191662 2191673 2191913 2191940) (-1271 "VECTCAT.spad" 2189566 2189577 2191630 2191657) (-1270 "VECTCAT.spad" 2187277 2187290 2189343 2189348) (-1269 "VARIABLE.spad" 2187057 2187072 2187267 2187272) (-1268 "UTYPE.spad" 2186701 2186710 2187047 2187052) (-1267 "UTSODETL.spad" 2185996 2186020 2186657 2186662) (-1266 "UTSODE.spad" 2184212 2184232 2185986 2185991) (-1265 "UTSCAT.spad" 2181691 2181707 2184110 2184207) (-1264 "UTSCAT.spad" 2178814 2178832 2181235 2181240) (-1263 "UTS2.spad" 2178409 2178444 2178804 2178809) (-1262 "UTS.spad" 2173213 2173241 2176876 2176973) (-1261 "URAGG.spad" 2167886 2167897 2173203 2173208) (-1260 "URAGG.spad" 2162523 2162536 2167842 2167847) (-1259 "UPXSSING.spad" 2160168 2160194 2161604 2161737) (-1258 "UPXSCONS.spad" 2157927 2157947 2158300 2158449) (-1257 "UPXSCCA.spad" 2156498 2156518 2157773 2157922) (-1256 "UPXSCCA.spad" 2155211 2155233 2156488 2156493) (-1255 "UPXSCAT.spad" 2153800 2153816 2155057 2155206) (-1254 "UPXS2.spad" 2153343 2153396 2153790 2153795) (-1253 "UPXS.spad" 2150497 2150525 2151475 2151624) (-1252 "UPSQFREE.spad" 2148912 2148926 2150487 2150492) (-1251 "UPSCAT.spad" 2146523 2146547 2148810 2148907) (-1250 "UPSCAT.spad" 2143840 2143866 2146129 2146134) (-1249 "UPOLYC2.spad" 2143311 2143330 2143830 2143835) (-1248 "UPOLYC.spad" 2138351 2138362 2143153 2143306) (-1247 "UPOLYC.spad" 2133283 2133296 2138087 2138092) (-1246 "UPMP.spad" 2132183 2132196 2133273 2133278) (-1245 "UPDIVP.spad" 2131748 2131762 2132173 2132178) (-1244 "UPDECOMP.spad" 2129993 2130007 2131738 2131743) (-1243 "UPCDEN.spad" 2129202 2129218 2129983 2129988) (-1242 "UP2.spad" 2128566 2128587 2129192 2129197) (-1241 "UP.spad" 2125765 2125780 2126152 2126305) (-1240 "UNISEG2.spad" 2125262 2125275 2125721 2125726) (-1239 "UNISEG.spad" 2124615 2124626 2125181 2125186) (-1238 "UNIFACT.spad" 2123718 2123730 2124605 2124610) (-1237 "ULSCONS.spad" 2116114 2116134 2116484 2116633) (-1236 "ULSCCAT.spad" 2113851 2113871 2115960 2116109) (-1235 "ULSCCAT.spad" 2111696 2111718 2113807 2113812) (-1234 "ULSCAT.spad" 2109928 2109944 2111542 2111691) (-1233 "ULS2.spad" 2109442 2109495 2109918 2109923) (-1232 "ULS.spad" 2100000 2100028 2101087 2101516) (-1231 "UINT8.spad" 2099877 2099886 2099990 2099995) (-1230 "UINT64.spad" 2099753 2099762 2099867 2099872) (-1229 "UINT32.spad" 2099629 2099638 2099743 2099748) (-1228 "UINT16.spad" 2099505 2099514 2099619 2099624) (-1227 "UFD.spad" 2098570 2098579 2099431 2099500) (-1226 "UFD.spad" 2097697 2097708 2098560 2098565) (-1225 "UDVO.spad" 2096578 2096587 2097687 2097692) (-1224 "UDPO.spad" 2094071 2094082 2096534 2096539) (-1223 "TYPEAST.spad" 2093990 2093999 2094061 2094066) (-1222 "TYPE.spad" 2093922 2093931 2093980 2093985) (-1221 "TWOFACT.spad" 2092574 2092589 2093912 2093917) (-1220 "TUPLE.spad" 2092060 2092071 2092473 2092478) (-1219 "TUBETOOL.spad" 2088927 2088936 2092050 2092055) (-1218 "TUBE.spad" 2087574 2087591 2088917 2088922) (-1217 "TSETCAT.spad" 2074701 2074718 2087542 2087569) (-1216 "TSETCAT.spad" 2061814 2061833 2074657 2074662) (-1215 "TS.spad" 2060413 2060429 2061379 2061476) (-1214 "TRMANIP.spad" 2054779 2054796 2060119 2060124) (-1213 "TRIMAT.spad" 2053742 2053767 2054769 2054774) (-1212 "TRIGMNIP.spad" 2052269 2052286 2053732 2053737) (-1211 "TRIGCAT.spad" 2051781 2051790 2052259 2052264) (-1210 "TRIGCAT.spad" 2051291 2051302 2051771 2051776) (-1209 "TREE.spad" 2049866 2049877 2050898 2050925) (-1208 "TRANFUN.spad" 2049705 2049714 2049856 2049861) (-1207 "TRANFUN.spad" 2049542 2049553 2049695 2049700) (-1206 "TOPSP.spad" 2049216 2049225 2049532 2049537) (-1205 "TOOLSIGN.spad" 2048879 2048890 2049206 2049211) (-1204 "TEXTFILE.spad" 2047440 2047449 2048869 2048874) (-1203 "TEX1.spad" 2046996 2047007 2047430 2047435) (-1202 "TEX.spad" 2044142 2044151 2046986 2046991) (-1201 "TEMUTL.spad" 2043697 2043706 2044132 2044137) (-1200 "TBCMPPK.spad" 2041790 2041813 2043687 2043692) (-1199 "TBAGG.spad" 2040840 2040863 2041770 2041785) (-1198 "TBAGG.spad" 2039898 2039923 2040830 2040835) (-1197 "TANEXP.spad" 2039306 2039317 2039888 2039893) (-1196 "TABLEAU.spad" 2038787 2038798 2039296 2039301) (-1195 "TABLE.spad" 2037198 2037221 2037468 2037495) (-1194 "TABLBUMP.spad" 2034001 2034012 2037188 2037193) (-1193 "SYSTEM.spad" 2033229 2033238 2033991 2033996) (-1192 "SYSSOLP.spad" 2030712 2030723 2033219 2033224) (-1191 "SYSPTR.spad" 2030611 2030620 2030702 2030707) (-1190 "SYSNNI.spad" 2029793 2029804 2030601 2030606) (-1189 "SYSINT.spad" 2029197 2029208 2029783 2029788) (-1188 "SYNTAX.spad" 2025403 2025412 2029187 2029192) (-1187 "SYMTAB.spad" 2023471 2023480 2025393 2025398) (-1186 "SYMS.spad" 2019500 2019509 2023461 2023466) (-1185 "SYMPOLY.spad" 2018507 2018518 2018589 2018716) (-1184 "SYMFUNC.spad" 2018008 2018019 2018497 2018502) (-1183 "SYMBOL.spad" 2015511 2015520 2017998 2018003) (-1182 "SWITCH.spad" 2012282 2012291 2015501 2015506) (-1181 "SUTS.spad" 2009187 2009215 2010749 2010846) (-1180 "SUPXS.spad" 2006328 2006356 2007319 2007468) (-1179 "SUPFRACF.spad" 2005433 2005451 2006318 2006323) (-1178 "SUP2.spad" 2004825 2004838 2005423 2005428) (-1177 "SUP.spad" 2001638 2001649 2002411 2002564) (-1176 "SUMRF.spad" 2000612 2000623 2001628 2001633) (-1175 "SUMFS.spad" 2000249 2000266 2000602 2000607) (-1174 "SULS.spad" 1990794 1990822 1991894 1992323) (-1173 "SUCHTAST.spad" 1990563 1990572 1990784 1990789) (-1172 "SUCH.spad" 1990245 1990260 1990553 1990558) (-1171 "SUBSPACE.spad" 1982360 1982375 1990235 1990240) (-1170 "SUBRESP.spad" 1981530 1981544 1982316 1982321) (-1169 "STTFNC.spad" 1977998 1978014 1981520 1981525) (-1168 "STTF.spad" 1974097 1974113 1977988 1977993) (-1167 "STTAYLOR.spad" 1966732 1966743 1973978 1973983) (-1166 "STRTBL.spad" 1965237 1965254 1965386 1965413) (-1165 "STRING.spad" 1964646 1964655 1964660 1964687) (-1164 "STRICAT.spad" 1964434 1964443 1964614 1964641) (-1163 "STREAM3.spad" 1964007 1964022 1964424 1964429) (-1162 "STREAM2.spad" 1963135 1963148 1963997 1964002) (-1161 "STREAM1.spad" 1962841 1962852 1963125 1963130) (-1160 "STREAM.spad" 1959759 1959770 1962366 1962381) (-1159 "STINPROD.spad" 1958695 1958711 1959749 1959754) (-1158 "STEPAST.spad" 1957929 1957938 1958685 1958690) (-1157 "STEP.spad" 1957130 1957139 1957919 1957924) (-1156 "STBL.spad" 1955656 1955684 1955823 1955838) (-1155 "STAGG.spad" 1954731 1954742 1955646 1955651) (-1154 "STAGG.spad" 1953804 1953817 1954721 1954726) (-1153 "STACK.spad" 1953161 1953172 1953411 1953438) (-1152 "SREGSET.spad" 1950865 1950882 1952807 1952834) (-1151 "SRDCMPK.spad" 1949426 1949446 1950855 1950860) (-1150 "SRAGG.spad" 1944569 1944578 1949394 1949421) (-1149 "SRAGG.spad" 1939732 1939743 1944559 1944564) (-1148 "SQMATRIX.spad" 1937348 1937366 1938264 1938351) (-1147 "SPLTREE.spad" 1931900 1931913 1936784 1936811) (-1146 "SPLNODE.spad" 1928488 1928501 1931890 1931895) (-1145 "SPFCAT.spad" 1927297 1927306 1928478 1928483) (-1144 "SPECOUT.spad" 1925849 1925858 1927287 1927292) (-1143 "SPADXPT.spad" 1917444 1917453 1925839 1925844) (-1142 "spad-parser.spad" 1916909 1916918 1917434 1917439) (-1141 "SPADAST.spad" 1916610 1916619 1916899 1916904) (-1140 "SPACEC.spad" 1900809 1900820 1916600 1916605) (-1139 "SPACE3.spad" 1900585 1900596 1900799 1900804) (-1138 "SORTPAK.spad" 1900134 1900147 1900541 1900546) (-1137 "SOLVETRA.spad" 1897897 1897908 1900124 1900129) (-1136 "SOLVESER.spad" 1896425 1896436 1897887 1897892) (-1135 "SOLVERAD.spad" 1892451 1892462 1896415 1896420) (-1134 "SOLVEFOR.spad" 1890913 1890931 1892441 1892446) (-1133 "SNTSCAT.spad" 1890513 1890530 1890881 1890908) (-1132 "SMTS.spad" 1888785 1888811 1890078 1890175) (-1131 "SMP.spad" 1886260 1886280 1886650 1886777) (-1130 "SMITH.spad" 1885105 1885130 1886250 1886255) (-1129 "SMATCAT.spad" 1883215 1883245 1885049 1885100) (-1128 "SMATCAT.spad" 1881257 1881289 1883093 1883098) (-1127 "SKAGG.spad" 1880220 1880231 1881225 1881252) (-1126 "SINT.spad" 1879052 1879061 1880086 1880215) (-1125 "SIMPAN.spad" 1878780 1878789 1879042 1879047) (-1124 "SIGNRF.spad" 1877905 1877916 1878770 1878775) (-1123 "SIGNEF.spad" 1877191 1877208 1877895 1877900) (-1122 "SIGAST.spad" 1876576 1876585 1877181 1877186) (-1121 "SIG.spad" 1875906 1875915 1876566 1876571) (-1120 "SHP.spad" 1873834 1873849 1875862 1875867) (-1119 "SHDP.spad" 1863545 1863572 1864054 1864185) (-1118 "SGROUP.spad" 1863153 1863162 1863535 1863540) (-1117 "SGROUP.spad" 1862759 1862770 1863143 1863148) (-1116 "SGCF.spad" 1855922 1855931 1862749 1862754) (-1115 "SFRTCAT.spad" 1854852 1854869 1855890 1855917) (-1114 "SFRGCD.spad" 1853915 1853935 1854842 1854847) (-1113 "SFQCMPK.spad" 1848552 1848572 1853905 1853910) (-1112 "SFORT.spad" 1847991 1848005 1848542 1848547) (-1111 "SEXOF.spad" 1847834 1847874 1847981 1847986) (-1110 "SEXCAT.spad" 1845435 1845475 1847824 1847829) (-1109 "SEX.spad" 1845327 1845336 1845425 1845430) (-1108 "SETMN.spad" 1843779 1843796 1845317 1845322) (-1107 "SETCAT.spad" 1843101 1843110 1843769 1843774) (-1106 "SETCAT.spad" 1842421 1842432 1843091 1843096) (-1105 "SETAGG.spad" 1838970 1838981 1842401 1842416) (-1104 "SETAGG.spad" 1835527 1835540 1838960 1838965) (-1103 "SET.spad" 1833851 1833862 1834948 1834987) (-1102 "SEQAST.spad" 1833554 1833563 1833841 1833846) (-1101 "SEGXCAT.spad" 1832710 1832723 1833544 1833549) (-1100 "SEGCAT.spad" 1831635 1831646 1832700 1832705) (-1099 "SEGBIND2.spad" 1831333 1831346 1831625 1831630) (-1098 "SEGBIND.spad" 1831091 1831102 1831280 1831285) (-1097 "SEGAST.spad" 1830805 1830814 1831081 1831086) (-1096 "SEG2.spad" 1830240 1830253 1830761 1830766) (-1095 "SEG.spad" 1830053 1830064 1830159 1830164) (-1094 "SDVAR.spad" 1829329 1829340 1830043 1830048) (-1093 "SDPOL.spad" 1826755 1826766 1827046 1827173) (-1092 "SCPKG.spad" 1824844 1824855 1826745 1826750) (-1091 "SCOPE.spad" 1823997 1824006 1824834 1824839) (-1090 "SCACHE.spad" 1822693 1822704 1823987 1823992) (-1089 "SASTCAT.spad" 1822602 1822611 1822683 1822688) (-1088 "SAOS.spad" 1822474 1822483 1822592 1822597) (-1087 "SAERFFC.spad" 1822187 1822207 1822464 1822469) (-1086 "SAEFACT.spad" 1821888 1821908 1822177 1822182) (-1085 "SAE.spad" 1820063 1820079 1820674 1820809) (-1084 "RURPK.spad" 1817722 1817738 1820053 1820058) (-1083 "RULESET.spad" 1817175 1817199 1817712 1817717) (-1082 "RULECOLD.spad" 1817027 1817040 1817165 1817170) (-1081 "RULE.spad" 1815267 1815291 1817017 1817022) (-1080 "RTVALUE.spad" 1815002 1815011 1815257 1815262) (-1079 "RSTRCAST.spad" 1814719 1814728 1814992 1814997) (-1078 "RSETGCD.spad" 1811097 1811117 1814709 1814714) (-1077 "RSETCAT.spad" 1801033 1801050 1811065 1811092) (-1076 "RSETCAT.spad" 1790989 1791008 1801023 1801028) (-1075 "RSDCMPK.spad" 1789441 1789461 1790979 1790984) (-1074 "RRCC.spad" 1787825 1787855 1789431 1789436) (-1073 "RRCC.spad" 1786207 1786239 1787815 1787820) (-1072 "RPTAST.spad" 1785909 1785918 1786197 1786202) (-1071 "RPOLCAT.spad" 1765269 1765284 1785777 1785904) (-1070 "RPOLCAT.spad" 1744343 1744360 1764853 1764858) (-1069 "ROUTINE.spad" 1740226 1740235 1742990 1743017) (-1068 "ROMAN.spad" 1739554 1739563 1740092 1740221) (-1067 "ROIRC.spad" 1738634 1738666 1739544 1739549) (-1066 "RNS.spad" 1737537 1737546 1738536 1738629) (-1065 "RNS.spad" 1736526 1736537 1737527 1737532) (-1064 "RNGBIND.spad" 1735686 1735700 1736481 1736486) (-1063 "RNG.spad" 1735421 1735430 1735676 1735681) (-1062 "RMODULE.spad" 1735186 1735197 1735411 1735416) (-1061 "RMCAT2.spad" 1734606 1734663 1735176 1735181) (-1060 "RMATRIX.spad" 1733430 1733449 1733773 1733812) (-1059 "RMATCAT.spad" 1729009 1729040 1733386 1733425) (-1058 "RMATCAT.spad" 1724478 1724511 1728857 1728862) (-1057 "RLINSET.spad" 1723872 1723883 1724468 1724473) (-1056 "RINTERP.spad" 1723760 1723780 1723862 1723867) (-1055 "RING.spad" 1723230 1723239 1723740 1723755) (-1054 "RING.spad" 1722708 1722719 1723220 1723225) (-1053 "RIDIST.spad" 1722100 1722109 1722698 1722703) (-1052 "RGCHAIN.spad" 1720683 1720699 1721585 1721612) (-1051 "RGBCSPC.spad" 1720464 1720476 1720673 1720678) (-1050 "RGBCMDL.spad" 1719994 1720006 1720454 1720459) (-1049 "RFFACTOR.spad" 1719456 1719467 1719984 1719989) (-1048 "RFFACT.spad" 1719191 1719203 1719446 1719451) (-1047 "RFDIST.spad" 1718187 1718196 1719181 1719186) (-1046 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1546002) (-953 "POLY2.spad" 1545056 1545068 1545449 1545454) (-952 "POLY.spad" 1542391 1542401 1542906 1543033) (-951 "POLUTIL.spad" 1541332 1541361 1542347 1542352) (-950 "POLTOPOL.spad" 1540080 1540095 1541322 1541327) (-949 "POINT.spad" 1538918 1538928 1539005 1539032) (-948 "PNTHEORY.spad" 1535620 1535628 1538908 1538913) (-947 "PMTOOLS.spad" 1534395 1534409 1535610 1535615) (-946 "PMSYM.spad" 1533944 1533954 1534385 1534390) (-945 "PMQFCAT.spad" 1533535 1533549 1533934 1533939) (-944 "PMPREDFS.spad" 1532989 1533011 1533525 1533530) (-943 "PMPRED.spad" 1532468 1532482 1532979 1532984) (-942 "PMPLCAT.spad" 1531548 1531566 1532400 1532405) (-941 "PMLSAGG.spad" 1531133 1531147 1531538 1531543) (-940 "PMKERNEL.spad" 1530712 1530724 1531123 1531128) (-939 "PMINS.spad" 1530292 1530302 1530702 1530707) (-938 "PMFS.spad" 1529869 1529887 1530282 1530287) (-937 "PMDOWN.spad" 1529159 1529173 1529859 1529864) (-936 "PMASSFS.spad" 1528126 1528142 1529149 1529154) (-935 "PMASS.spad" 1527136 1527144 1528116 1528121) (-934 "PLOTTOOL.spad" 1526916 1526924 1527126 1527131) (-933 "PLOT3D.spad" 1523380 1523388 1526906 1526911) (-932 "PLOT1.spad" 1522537 1522547 1523370 1523375) (-931 "PLOT.spad" 1517460 1517468 1522527 1522532) (-930 "PLEQN.spad" 1504750 1504777 1517450 1517455) (-929 "PINTERPA.spad" 1504534 1504550 1504740 1504745) (-928 "PINTERP.spad" 1504156 1504175 1504524 1504529) (-927 "PID.spad" 1503126 1503134 1504082 1504151) (-926 "PICOERCE.spad" 1502783 1502793 1503116 1503121) (-925 "PI.spad" 1502392 1502400 1502757 1502778) (-924 "PGROEB.spad" 1500993 1501007 1502382 1502387) (-923 "PGE.spad" 1492610 1492618 1500983 1500988) (-922 "PGCD.spad" 1491500 1491517 1492600 1492605) (-921 "PFRPAC.spad" 1490649 1490659 1491490 1491495) (-920 "PFR.spad" 1487312 1487322 1490551 1490644) (-919 "PFOTOOLS.spad" 1486570 1486586 1487302 1487307) (-918 "PFOQ.spad" 1485940 1485958 1486560 1486565) (-917 "PFO.spad" 1485359 1485386 1485930 1485935) (-916 "PFECAT.spad" 1483041 1483049 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(-822 "ODR.spad" 1347291 1347317 1347459 1347608) (-821 "ODPOL.spad" 1344673 1344683 1345013 1345140) (-820 "ODP.spad" 1334520 1334540 1334893 1335024) (-819 "ODETOOLS.spad" 1333169 1333188 1334510 1334515) (-818 "ODESYS.spad" 1330863 1330880 1333159 1333164) (-817 "ODERTRIC.spad" 1326872 1326889 1330820 1330825) (-816 "ODERED.spad" 1326271 1326295 1326862 1326867) (-815 "ODERAT.spad" 1323888 1323905 1326261 1326266) (-814 "ODEPRRIC.spad" 1320925 1320947 1323878 1323883) (-813 "ODEPROB.spad" 1320182 1320190 1320915 1320920) (-812 "ODEPRIM.spad" 1317516 1317538 1320172 1320177) (-811 "ODEPAL.spad" 1316902 1316926 1317506 1317511) (-810 "ODEPACK.spad" 1303568 1303576 1316892 1316897) (-809 "ODEINT.spad" 1303003 1303019 1303558 1303563) (-808 "ODEIFTBL.spad" 1300398 1300406 1302993 1302998) (-807 "ODEEF.spad" 1295893 1295909 1300388 1300393) (-806 "ODECONST.spad" 1295430 1295448 1295883 1295888) (-805 "ODECAT.spad" 1294028 1294036 1295420 1295425) (-804 "OCTCT2.spad" 1293674 1293695 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1109114) (-709 "MKFUNC.spad" 1108130 1108140 1108713 1108718) (-708 "MKFLCFN.spad" 1107098 1107108 1108120 1108125) (-707 "MKBCFUNC.spad" 1106593 1106611 1107088 1107093) (-706 "MINT.spad" 1106032 1106040 1106495 1106588) (-705 "MHROWRED.spad" 1104543 1104553 1106022 1106027) (-704 "MFLOAT.spad" 1103063 1103071 1104433 1104538) (-703 "MFINFACT.spad" 1102463 1102485 1103053 1103058) (-702 "MESH.spad" 1100250 1100258 1102453 1102458) (-701 "MDDFACT.spad" 1098461 1098471 1100240 1100245) (-700 "MDAGG.spad" 1097752 1097762 1098441 1098456) (-699 "MCMPLX.spad" 1093763 1093771 1094377 1094578) (-698 "MCDEN.spad" 1092973 1092985 1093753 1093758) (-697 "MCALCFN.spad" 1090095 1090121 1092963 1092968) (-696 "MAYBE.spad" 1089379 1089390 1090085 1090090) (-695 "MATSTOR.spad" 1086687 1086697 1089369 1089374) (-694 "MATRIX.spad" 1085391 1085401 1085875 1085902) (-693 "MATLIN.spad" 1082735 1082759 1085275 1085280) (-692 "MATCAT2.spad" 1082017 1082065 1082725 1082730) (-691 "MATCAT.spad" 1073746 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(-613 "KAFILE.spad" 974662 974678 974897 974924) (-612 "JORDAN.spad" 972491 972503 973952 974097) (-611 "JOINAST.spad" 972185 972193 972481 972486) (-610 "JAVACODE.spad" 972051 972059 972175 972180) (-609 "IXAGG.spad" 970184 970208 972041 972046) (-608 "IXAGG.spad" 968172 968198 970031 970036) (-607 "IVECTOR.spad" 966942 966957 967097 967124) (-606 "ITUPLE.spad" 966103 966113 966932 966937) (-605 "ITRIGMNP.spad" 964942 964961 966093 966098) (-604 "ITFUN3.spad" 964448 964462 964932 964937) (-603 "ITFUN2.spad" 964192 964204 964438 964443) (-602 "ITFORM.spad" 963779 963787 964182 964187) (-601 "ITAYLOR.spad" 961773 961788 963643 963740) (-600 "ISUPS.spad" 954210 954225 960747 960844) (-599 "ISUMP.spad" 953711 953727 954200 954205) (-598 "ISTRING.spad" 952799 952812 952880 952907) (-597 "ISAST.spad" 952518 952526 952789 952794) (-596 "IRURPK.spad" 951235 951254 952508 952513) (-595 "IRSN.spad" 949239 949247 951225 951230) (-594 "IRRF2F.spad" 947724 947734 949195 949200) (-593 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160088 160096 160315 160330) (-144 "CHAR.spad" 157962 157970 160078 160083) (-143 "CFCAT.spad" 157290 157298 157952 157957) (-142 "CDEN.spad" 156486 156500 157280 157285) (-141 "CCLASS.spad" 154635 154643 155897 155936) (-140 "CATEGORY.spad" 153677 153685 154625 154630) (-139 "CATCTOR.spad" 153568 153576 153667 153672) (-138 "CATAST.spad" 153186 153194 153558 153563) (-137 "CASEAST.spad" 152900 152908 153176 153181) (-136 "CARTEN2.spad" 152290 152317 152890 152895) (-135 "CARTEN.spad" 147577 147601 152280 152285) (-134 "CARD.spad" 144872 144880 147551 147572) (-133 "CAPSLAST.spad" 144646 144654 144862 144867) (-132 "CACHSET.spad" 144270 144278 144636 144641) (-131 "CABMON.spad" 143825 143833 144260 144265) (-130 "BYTEORD.spad" 143500 143508 143815 143820) (-129 "BYTEBUF.spad" 141359 141367 142669 142696) (-128 "BYTE.spad" 140786 140794 141349 141354) (-127 "BTREE.spad" 139859 139869 140393 140420) (-126 "BTOURN.spad" 138864 138874 139466 139493) (-125 "BTCAT.spad" 138256 138266 138832 138859) (-124 "BTCAT.spad" 137668 137680 138246 138251) (-123 "BTAGG.spad" 136796 136804 137636 137663) (-122 "BTAGG.spad" 135944 135954 136786 136791) (-121 "BSTREE.spad" 134685 134695 135551 135578) (-120 "BRILL.spad" 132882 132893 134675 134680) (-119 "BRAGG.spad" 131822 131832 132872 132877) (-118 "BRAGG.spad" 130726 130738 131778 131783) (-117 "BPADICRT.spad" 128707 128719 128962 129055) (-116 "BPADIC.spad" 128371 128383 128633 128702) (-115 "BOUNDZRO.spad" 128027 128044 128361 128366) (-114 "BOP1.spad" 125493 125503 128017 128022) (-113 "BOP.spad" 120675 120683 125483 125488) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP80.spad" 96764 96777 97432 97437) (-87 "ASP8.spad" 95807 95820 96754 96759) (-86 "ASP78.spad" 95258 95271 95797 95802) (-85 "ASP77.spad" 94627 94640 95248 95253) (-84 "ASP74.spad" 93719 93732 94617 94622) (-83 "ASP73.spad" 92990 93003 93709 93714) (-82 "ASP7.spad" 92150 92163 92980 92985) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP49.spad" 86342 86355 87333 87338) (-77 "ASP42.spad" 84749 84788 86332 86337) (-76 "ASP41.spad" 83328 83367 84739 84744) (-75 "ASP4.spad" 82623 82636 83318 83323) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP19.spad" 61377 61390 66681 66686) (-63 "ASP12.spad" 60791 60804 61367 61372) (-62 "ASP10.spad" 60062 60075 60781 60786) (-61 "ASP1.spad" 59443 59456 60052 60057) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY12.spad" 57516 57527 58793 58798) (-58 "ARRAY1.spad" 56353 56362 56699 56726) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY1.spad" 45243 45252 46162 46167) (-51 "ANY.spad" 44102 44109 45233 45238) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2265877 2265882 2265887 2265892) (-2 NIL 2265857 2265862 2265867 2265872) (-1 NIL 2265837 2265842 2265847 2265852) (0 NIL 2265817 2265822 2265827 2265832) (-1301 "ZMOD.spad" 2265626 2265639 2265755 2265812) (-1300 "ZLINDEP.spad" 2264692 2264703 2265616 2265621) (-1299 "ZDSOLVE.spad" 2254637 2254659 2264682 2264687) (-1298 "YSTREAM.spad" 2254132 2254143 2254627 2254632) (-1297 "XRPOLY.spad" 2253352 2253372 2253988 2254057) (-1296 "XPR.spad" 2251147 2251160 2253070 2253169) (-1295 "XPOLYC.spad" 2250466 2250482 2251073 2251142) (-1294 "XPOLY.spad" 2250021 2250032 2250322 2250391) (-1293 "XPBWPOLY.spad" 2248458 2248478 2249801 2249870) (-1292 "XFALG.spad" 2245506 2245522 2248384 2248453) (-1291 "XF.spad" 2243969 2243984 2245408 2245501) (-1290 "XF.spad" 2242412 2242429 2243853 2243858) (-1289 "XEXPPKG.spad" 2241663 2241689 2242402 2242407) (-1288 "XDPOLY.spad" 2241277 2241293 2241519 2241588) (-1287 "XALG.spad" 2240937 2240948 2241233 2241272) (-1286 "WUTSET.spad" 2236776 2236793 2240583 2240610) (-1285 "WP.spad" 2235975 2236019 2236634 2236701) (-1284 "WHILEAST.spad" 2235773 2235782 2235965 2235970) (-1283 "WHEREAST.spad" 2235444 2235453 2235763 2235768) (-1282 "WFFINTBS.spad" 2233107 2233129 2235434 2235439) (-1281 "WEIER.spad" 2231329 2231340 2233097 2233102) (-1280 "VSPACE.spad" 2231002 2231013 2231297 2231324) (-1279 "VSPACE.spad" 2230695 2230708 2230992 2230997) (-1278 "VOID.spad" 2230372 2230381 2230685 2230690) (-1277 "VIEWDEF.spad" 2225573 2225582 2230362 2230367) (-1276 "VIEW3D.spad" 2209534 2209543 2225563 2225568) (-1275 "VIEW2D.spad" 2197425 2197434 2209524 2209529) (-1274 "VIEW.spad" 2195105 2195114 2197415 2197420) (-1273 "VECTOR2.spad" 2193744 2193757 2195095 2195100) (-1272 "VECTOR.spad" 2192418 2192429 2192669 2192696) (-1271 "VECTCAT.spad" 2190322 2190333 2192386 2192413) (-1270 "VECTCAT.spad" 2188033 2188046 2190099 2190104) (-1269 "VARIABLE.spad" 2187813 2187828 2188023 2188028) (-1268 "UTYPE.spad" 2187457 2187466 2187803 2187808) (-1267 "UTSODETL.spad" 2186752 2186776 2187413 2187418) (-1266 "UTSODE.spad" 2184968 2184988 2186742 2186747) (-1265 "UTSCAT.spad" 2182447 2182463 2184866 2184963) (-1264 "UTSCAT.spad" 2179570 2179588 2181991 2181996) (-1263 "UTS2.spad" 2179165 2179200 2179560 2179565) (-1262 "UTS.spad" 2173969 2173997 2177632 2177729) (-1261 "URAGG.spad" 2168642 2168653 2173959 2173964) (-1260 "URAGG.spad" 2163279 2163292 2168598 2168603) (-1259 "UPXSSING.spad" 2160924 2160950 2162360 2162493) (-1258 "UPXSCONS.spad" 2158683 2158703 2159056 2159205) (-1257 "UPXSCCA.spad" 2157254 2157274 2158529 2158678) (-1256 "UPXSCCA.spad" 2155967 2155989 2157244 2157249) (-1255 "UPXSCAT.spad" 2154556 2154572 2155813 2155962) (-1254 "UPXS2.spad" 2154099 2154152 2154546 2154551) (-1253 "UPXS.spad" 2151253 2151281 2152231 2152380) (-1252 "UPSQFREE.spad" 2149668 2149682 2151243 2151248) (-1251 "UPSCAT.spad" 2147279 2147303 2149566 2149663) (-1250 "UPSCAT.spad" 2144596 2144622 2146885 2146890) (-1249 "UPOLYC2.spad" 2144067 2144086 2144586 2144591) (-1248 "UPOLYC.spad" 2139107 2139118 2143909 2144062) (-1247 "UPOLYC.spad" 2134039 2134052 2138843 2138848) (-1246 "UPMP.spad" 2132939 2132952 2134029 2134034) (-1245 "UPDIVP.spad" 2132504 2132518 2132929 2132934) (-1244 "UPDECOMP.spad" 2130749 2130763 2132494 2132499) (-1243 "UPCDEN.spad" 2129958 2129974 2130739 2130744) (-1242 "UP2.spad" 2129322 2129343 2129948 2129953) (-1241 "UP.spad" 2126521 2126536 2126908 2127061) (-1240 "UNISEG2.spad" 2126018 2126031 2126477 2126482) (-1239 "UNISEG.spad" 2125371 2125382 2125937 2125942) (-1238 "UNIFACT.spad" 2124474 2124486 2125361 2125366) (-1237 "ULSCONS.spad" 2116870 2116890 2117240 2117389) (-1236 "ULSCCAT.spad" 2114607 2114627 2116716 2116865) (-1235 "ULSCCAT.spad" 2112452 2112474 2114563 2114568) (-1234 "ULSCAT.spad" 2110684 2110700 2112298 2112447) (-1233 "ULS2.spad" 2110198 2110251 2110674 2110679) (-1232 "ULS.spad" 2100756 2100784 2101843 2102272) (-1231 "UINT8.spad" 2100633 2100642 2100746 2100751) (-1230 "UINT64.spad" 2100509 2100518 2100623 2100628) (-1229 "UINT32.spad" 2100385 2100394 2100499 2100504) (-1228 "UINT16.spad" 2100261 2100270 2100375 2100380) (-1227 "UFD.spad" 2099326 2099335 2100187 2100256) (-1226 "UFD.spad" 2098453 2098464 2099316 2099321) (-1225 "UDVO.spad" 2097334 2097343 2098443 2098448) (-1224 "UDPO.spad" 2094827 2094838 2097290 2097295) (-1223 "TYPEAST.spad" 2094746 2094755 2094817 2094822) (-1222 "TYPE.spad" 2094678 2094687 2094736 2094741) (-1221 "TWOFACT.spad" 2093330 2093345 2094668 2094673) (-1220 "TUPLE.spad" 2092816 2092827 2093229 2093234) (-1219 "TUBETOOL.spad" 2089683 2089692 2092806 2092811) (-1218 "TUBE.spad" 2088330 2088347 2089673 2089678) (-1217 "TSETCAT.spad" 2075457 2075474 2088298 2088325) (-1216 "TSETCAT.spad" 2062570 2062589 2075413 2075418) (-1215 "TS.spad" 2061169 2061185 2062135 2062232) (-1214 "TRMANIP.spad" 2055535 2055552 2060875 2060880) (-1213 "TRIMAT.spad" 2054498 2054523 2055525 2055530) (-1212 "TRIGMNIP.spad" 2053025 2053042 2054488 2054493) (-1211 "TRIGCAT.spad" 2052537 2052546 2053015 2053020) (-1210 "TRIGCAT.spad" 2052047 2052058 2052527 2052532) (-1209 "TREE.spad" 2050622 2050633 2051654 2051681) (-1208 "TRANFUN.spad" 2050461 2050470 2050612 2050617) (-1207 "TRANFUN.spad" 2050298 2050309 2050451 2050456) (-1206 "TOPSP.spad" 2049972 2049981 2050288 2050293) (-1205 "TOOLSIGN.spad" 2049635 2049646 2049962 2049967) (-1204 "TEXTFILE.spad" 2048196 2048205 2049625 2049630) (-1203 "TEX1.spad" 2047752 2047763 2048186 2048191) (-1202 "TEX.spad" 2044898 2044907 2047742 2047747) (-1201 "TEMUTL.spad" 2044453 2044462 2044888 2044893) (-1200 "TBCMPPK.spad" 2042546 2042569 2044443 2044448) (-1199 "TBAGG.spad" 2041596 2041619 2042526 2042541) (-1198 "TBAGG.spad" 2040654 2040679 2041586 2041591) (-1197 "TANEXP.spad" 2040062 2040073 2040644 2040649) (-1196 "TABLEAU.spad" 2039543 2039554 2040052 2040057) (-1195 "TABLE.spad" 2037954 2037977 2038224 2038251) (-1194 "TABLBUMP.spad" 2034757 2034768 2037944 2037949) (-1193 "SYSTEM.spad" 2033985 2033994 2034747 2034752) (-1192 "SYSSOLP.spad" 2031468 2031479 2033975 2033980) (-1191 "SYSPTR.spad" 2031367 2031376 2031458 2031463) (-1190 "SYSNNI.spad" 2030549 2030560 2031357 2031362) (-1189 "SYSINT.spad" 2029953 2029964 2030539 2030544) (-1188 "SYNTAX.spad" 2026159 2026168 2029943 2029948) (-1187 "SYMTAB.spad" 2024227 2024236 2026149 2026154) (-1186 "SYMS.spad" 2020256 2020265 2024217 2024222) (-1185 "SYMPOLY.spad" 2019263 2019274 2019345 2019472) (-1184 "SYMFUNC.spad" 2018764 2018775 2019253 2019258) (-1183 "SYMBOL.spad" 2016267 2016276 2018754 2018759) (-1182 "SWITCH.spad" 2013038 2013047 2016257 2016262) (-1181 "SUTS.spad" 2009943 2009971 2011505 2011602) (-1180 "SUPXS.spad" 2007084 2007112 2008075 2008224) (-1179 "SUPFRACF.spad" 2006189 2006207 2007074 2007079) (-1178 "SUP2.spad" 2005581 2005594 2006179 2006184) (-1177 "SUP.spad" 2002394 2002405 2003167 2003320) (-1176 "SUMRF.spad" 2001368 2001379 2002384 2002389) (-1175 "SUMFS.spad" 2001005 2001022 2001358 2001363) (-1174 "SULS.spad" 1991550 1991578 1992650 1993079) (-1173 "SUCHTAST.spad" 1991319 1991328 1991540 1991545) (-1172 "SUCH.spad" 1991001 1991016 1991309 1991314) (-1171 "SUBSPACE.spad" 1983116 1983131 1990991 1990996) (-1170 "SUBRESP.spad" 1982286 1982300 1983072 1983077) (-1169 "STTFNC.spad" 1978754 1978770 1982276 1982281) (-1168 "STTF.spad" 1974853 1974869 1978744 1978749) (-1167 "STTAYLOR.spad" 1967488 1967499 1974734 1974739) (-1166 "STRTBL.spad" 1965993 1966010 1966142 1966169) (-1165 "STRING.spad" 1965402 1965411 1965416 1965443) (-1164 "STRICAT.spad" 1965190 1965199 1965370 1965397) (-1163 "STREAM3.spad" 1964763 1964778 1965180 1965185) (-1162 "STREAM2.spad" 1963891 1963904 1964753 1964758) (-1161 "STREAM1.spad" 1963597 1963608 1963881 1963886) (-1160 "STREAM.spad" 1960515 1960526 1963122 1963137) (-1159 "STINPROD.spad" 1959451 1959467 1960505 1960510) (-1158 "STEPAST.spad" 1958685 1958694 1959441 1959446) (-1157 "STEP.spad" 1957886 1957895 1958675 1958680) (-1156 "STBL.spad" 1956412 1956440 1956579 1956594) (-1155 "STAGG.spad" 1955487 1955498 1956402 1956407) (-1154 "STAGG.spad" 1954560 1954573 1955477 1955482) (-1153 "STACK.spad" 1953917 1953928 1954167 1954194) (-1152 "SREGSET.spad" 1951621 1951638 1953563 1953590) (-1151 "SRDCMPK.spad" 1950182 1950202 1951611 1951616) (-1150 "SRAGG.spad" 1945325 1945334 1950150 1950177) (-1149 "SRAGG.spad" 1940488 1940499 1945315 1945320) (-1148 "SQMATRIX.spad" 1938104 1938122 1939020 1939107) (-1147 "SPLTREE.spad" 1932656 1932669 1937540 1937567) (-1146 "SPLNODE.spad" 1929244 1929257 1932646 1932651) (-1145 "SPFCAT.spad" 1928053 1928062 1929234 1929239) (-1144 "SPECOUT.spad" 1926605 1926614 1928043 1928048) (-1143 "SPADXPT.spad" 1918200 1918209 1926595 1926600) (-1142 "spad-parser.spad" 1917665 1917674 1918190 1918195) (-1141 "SPADAST.spad" 1917366 1917375 1917655 1917660) (-1140 "SPACEC.spad" 1901565 1901576 1917356 1917361) (-1139 "SPACE3.spad" 1901341 1901352 1901555 1901560) (-1138 "SORTPAK.spad" 1900890 1900903 1901297 1901302) (-1137 "SOLVETRA.spad" 1898653 1898664 1900880 1900885) (-1136 "SOLVESER.spad" 1897181 1897192 1898643 1898648) (-1135 "SOLVERAD.spad" 1893207 1893218 1897171 1897176) (-1134 "SOLVEFOR.spad" 1891669 1891687 1893197 1893202) (-1133 "SNTSCAT.spad" 1891269 1891286 1891637 1891664) (-1132 "SMTS.spad" 1889541 1889567 1890834 1890931) (-1131 "SMP.spad" 1887016 1887036 1887406 1887533) (-1130 "SMITH.spad" 1885861 1885886 1887006 1887011) (-1129 "SMATCAT.spad" 1883971 1884001 1885805 1885856) (-1128 "SMATCAT.spad" 1882013 1882045 1883849 1883854) (-1127 "SKAGG.spad" 1880976 1880987 1881981 1882008) (-1126 "SINT.spad" 1879808 1879817 1880842 1880971) (-1125 "SIMPAN.spad" 1879536 1879545 1879798 1879803) (-1124 "SIGNRF.spad" 1878661 1878672 1879526 1879531) (-1123 "SIGNEF.spad" 1877947 1877964 1878651 1878656) (-1122 "SIGAST.spad" 1877332 1877341 1877937 1877942) (-1121 "SIG.spad" 1876662 1876671 1877322 1877327) (-1120 "SHP.spad" 1874590 1874605 1876618 1876623) (-1119 "SHDP.spad" 1864301 1864328 1864810 1864941) (-1118 "SGROUP.spad" 1863909 1863918 1864291 1864296) (-1117 "SGROUP.spad" 1863515 1863526 1863899 1863904) (-1116 "SGCF.spad" 1856678 1856687 1863505 1863510) (-1115 "SFRTCAT.spad" 1855608 1855625 1856646 1856673) (-1114 "SFRGCD.spad" 1854671 1854691 1855598 1855603) (-1113 "SFQCMPK.spad" 1849308 1849328 1854661 1854666) (-1112 "SFORT.spad" 1848747 1848761 1849298 1849303) (-1111 "SEXOF.spad" 1848590 1848630 1848737 1848742) (-1110 "SEXCAT.spad" 1846191 1846231 1848580 1848585) (-1109 "SEX.spad" 1846083 1846092 1846181 1846186) (-1108 "SETMN.spad" 1844535 1844552 1846073 1846078) (-1107 "SETCAT.spad" 1843857 1843866 1844525 1844530) (-1106 "SETCAT.spad" 1843177 1843188 1843847 1843852) (-1105 "SETAGG.spad" 1839726 1839737 1843157 1843172) (-1104 "SETAGG.spad" 1836283 1836296 1839716 1839721) (-1103 "SET.spad" 1834607 1834618 1835704 1835743) (-1102 "SEQAST.spad" 1834310 1834319 1834597 1834602) (-1101 "SEGXCAT.spad" 1833466 1833479 1834300 1834305) (-1100 "SEGCAT.spad" 1832391 1832402 1833456 1833461) (-1099 "SEGBIND2.spad" 1832089 1832102 1832381 1832386) (-1098 "SEGBIND.spad" 1831847 1831858 1832036 1832041) (-1097 "SEGAST.spad" 1831561 1831570 1831837 1831842) (-1096 "SEG2.spad" 1830996 1831009 1831517 1831522) (-1095 "SEG.spad" 1830809 1830820 1830915 1830920) (-1094 "SDVAR.spad" 1830085 1830096 1830799 1830804) (-1093 "SDPOL.spad" 1827511 1827522 1827802 1827929) (-1092 "SCPKG.spad" 1825600 1825611 1827501 1827506) (-1091 "SCOPE.spad" 1824753 1824762 1825590 1825595) (-1090 "SCACHE.spad" 1823449 1823460 1824743 1824748) (-1089 "SASTCAT.spad" 1823358 1823367 1823439 1823444) (-1088 "SAOS.spad" 1823230 1823239 1823348 1823353) (-1087 "SAERFFC.spad" 1822943 1822963 1823220 1823225) (-1086 "SAEFACT.spad" 1822644 1822664 1822933 1822938) (-1085 "SAE.spad" 1820819 1820835 1821430 1821565) (-1084 "RURPK.spad" 1818478 1818494 1820809 1820814) (-1083 "RULESET.spad" 1817931 1817955 1818468 1818473) (-1082 "RULECOLD.spad" 1817783 1817796 1817921 1817926) (-1081 "RULE.spad" 1816023 1816047 1817773 1817778) (-1080 "RTVALUE.spad" 1815758 1815767 1816013 1816018) (-1079 "RSTRCAST.spad" 1815475 1815484 1815748 1815753) (-1078 "RSETGCD.spad" 1811853 1811873 1815465 1815470) (-1077 "RSETCAT.spad" 1801789 1801806 1811821 1811848) (-1076 "RSETCAT.spad" 1791745 1791764 1801779 1801784) (-1075 "RSDCMPK.spad" 1790197 1790217 1791735 1791740) (-1074 "RRCC.spad" 1788581 1788611 1790187 1790192) (-1073 "RRCC.spad" 1786963 1786995 1788571 1788576) (-1072 "RPTAST.spad" 1786665 1786674 1786953 1786958) (-1071 "RPOLCAT.spad" 1766025 1766040 1786533 1786660) (-1070 "RPOLCAT.spad" 1745099 1745116 1765609 1765614) (-1069 "ROUTINE.spad" 1740982 1740991 1743746 1743773) (-1068 "ROMAN.spad" 1740310 1740319 1740848 1740977) (-1067 "ROIRC.spad" 1739390 1739422 1740300 1740305) (-1066 "RNS.spad" 1738293 1738302 1739292 1739385) (-1065 "RNS.spad" 1737282 1737293 1738283 1738288) (-1064 "RNGBIND.spad" 1736442 1736456 1737237 1737242) (-1063 "RNG.spad" 1736177 1736186 1736432 1736437) (-1062 "RMODULE.spad" 1735942 1735953 1736167 1736172) (-1061 "RMCAT2.spad" 1735362 1735419 1735932 1735937) (-1060 "RMATRIX.spad" 1734186 1734205 1734529 1734568) (-1059 "RMATCAT.spad" 1729765 1729796 1734142 1734181) (-1058 "RMATCAT.spad" 1725234 1725267 1729613 1729618) (-1057 "RLINSET.spad" 1724628 1724639 1725224 1725229) (-1056 "RINTERP.spad" 1724516 1724536 1724618 1724623) (-1055 "RING.spad" 1723986 1723995 1724496 1724511) (-1054 "RING.spad" 1723464 1723475 1723976 1723981) (-1053 "RIDIST.spad" 1722856 1722865 1723454 1723459) (-1052 "RGCHAIN.spad" 1721439 1721455 1722341 1722368) (-1051 "RGBCSPC.spad" 1721220 1721232 1721429 1721434) (-1050 "RGBCMDL.spad" 1720750 1720762 1721210 1721215) (-1049 "RFFACTOR.spad" 1720212 1720223 1720740 1720745) (-1048 "RFFACT.spad" 1719947 1719959 1720202 1720207) (-1047 "RFDIST.spad" 1718943 1718952 1719937 1719942) (-1046 "RF.spad" 1716585 1716596 1718933 1718938) (-1045 "RETSOL.spad" 1716004 1716017 1716575 1716580) (-1044 "RETRACT.spad" 1715432 1715443 1715994 1715999) (-1043 "RETRACT.spad" 1714858 1714871 1715422 1715427) (-1042 "RETAST.spad" 1714670 1714679 1714848 1714853) (-1041 "RESULT.spad" 1712730 1712739 1713317 1713344) (-1040 "RESRING.spad" 1712077 1712124 1712668 1712725) (-1039 "RESLATC.spad" 1711401 1711412 1712067 1712072) (-1038 "REPSQ.spad" 1711132 1711143 1711391 1711396) (-1037 "REPDB.spad" 1710839 1710850 1711122 1711127) (-1036 "REP2.spad" 1700497 1700508 1710681 1710686) (-1035 "REP1.spad" 1694693 1694704 1700447 1700452) (-1034 "REP.spad" 1692247 1692256 1694683 1694688) (-1033 "REGSET.spad" 1690044 1690061 1691893 1691920) (-1032 "REF.spad" 1689379 1689390 1689999 1690004) (-1031 "REDORDER.spad" 1688585 1688602 1689369 1689374) (-1030 "RECLOS.spad" 1687368 1687388 1688072 1688165) (-1029 "REALSOLV.spad" 1686508 1686517 1687358 1687363) (-1028 "REAL0Q.spad" 1683806 1683821 1686498 1686503) (-1027 "REAL0.spad" 1680650 1680665 1683796 1683801) (-1026 "REAL.spad" 1680522 1680531 1680640 1680645) (-1025 "RDUCEAST.spad" 1680243 1680252 1680512 1680517) (-1024 "RDIV.spad" 1679898 1679923 1680233 1680238) (-1023 "RDIST.spad" 1679465 1679476 1679888 1679893) (-1022 "RDETRS.spad" 1678329 1678347 1679455 1679460) (-1021 "RDETR.spad" 1676468 1676486 1678319 1678324) (-1020 "RDEEFS.spad" 1675567 1675584 1676458 1676463) (-1019 "RDEEF.spad" 1674577 1674594 1675557 1675562) (-1018 "RCFIELD.spad" 1671763 1671772 1674479 1674572) (-1017 "RCFIELD.spad" 1669035 1669046 1671753 1671758) (-1016 "RCAGG.spad" 1666963 1666974 1669025 1669030) (-1015 "RCAGG.spad" 1664818 1664831 1666882 1666887) (-1014 "RATRET.spad" 1664178 1664189 1664808 1664813) (-1013 "RATFACT.spad" 1663870 1663882 1664168 1664173) (-1012 "RANDSRC.spad" 1663189 1663198 1663860 1663865) (-1011 "RADUTIL.spad" 1662945 1662954 1663179 1663184) (-1010 "RADIX.spad" 1659866 1659880 1661412 1661505) (-1009 "RADFF.spad" 1658279 1658316 1658398 1658554) (-1008 "RADCAT.spad" 1657874 1657883 1658269 1658274) (-1007 "RADCAT.spad" 1657467 1657478 1657864 1657869) (-1006 "QUEUE.spad" 1656815 1656826 1657074 1657101) (-1005 "QUATCT2.spad" 1656435 1656454 1656805 1656810) (-1004 "QUATCAT.spad" 1654605 1654616 1656365 1656430) (-1003 "QUATCAT.spad" 1652526 1652539 1654288 1654293) (-1002 "QUAT.spad" 1651107 1651118 1651450 1651515) (-1001 "QUAGG.spad" 1649934 1649945 1651075 1651102) (-1000 "QQUTAST.spad" 1649702 1649711 1649924 1649929) (-999 "QFORM.spad" 1649167 1649181 1649692 1649697) (-998 "QFCAT2.spad" 1648860 1648876 1649157 1649162) (-997 "QFCAT.spad" 1647563 1647573 1648762 1648855) (-996 "QFCAT.spad" 1645857 1645869 1647058 1647063) (-995 "QEQUAT.spad" 1645416 1645424 1645847 1645852) (-994 "QCMPACK.spad" 1640163 1640182 1645406 1645411) (-993 "QALGSET2.spad" 1638159 1638177 1640153 1640158) (-992 "QALGSET.spad" 1634240 1634272 1638073 1638078) (-991 "PWFFINTB.spad" 1631656 1631677 1634230 1634235) (-990 "PUSHVAR.spad" 1630995 1631014 1631646 1631651) (-989 "PTRANFN.spad" 1627123 1627133 1630985 1630990) (-988 "PTPACK.spad" 1624211 1624221 1627113 1627118) (-987 "PTFUNC2.spad" 1624034 1624048 1624201 1624206) (-986 "PTCAT.spad" 1623289 1623299 1624002 1624029) (-985 "PSQFR.spad" 1622596 1622620 1623279 1623284) (-984 "PSEUDLIN.spad" 1621482 1621492 1622586 1622591) (-983 "PSETPK.spad" 1606915 1606931 1621360 1621365) (-982 "PSETCAT.spad" 1600835 1600858 1606895 1606910) (-981 "PSETCAT.spad" 1594729 1594754 1600791 1600796) (-980 "PSCURVE.spad" 1593712 1593720 1594719 1594724) (-979 "PSCAT.spad" 1592495 1592524 1593610 1593707) (-978 "PSCAT.spad" 1591368 1591399 1592485 1592490) (-977 "PRTITION.spad" 1590329 1590337 1591358 1591363) (-976 "PRTDAST.spad" 1590048 1590056 1590319 1590324) (-975 "PRS.spad" 1579610 1579627 1590004 1590009) (-974 "PRQAGG.spad" 1579045 1579055 1579578 1579605) (-973 "PROPLOG.spad" 1578344 1578352 1579035 1579040) (-972 "PROPFRML.spad" 1576912 1576923 1578334 1578339) (-971 "PROPERTY.spad" 1576400 1576408 1576902 1576907) (-970 "PRODUCT.spad" 1574082 1574094 1574366 1574421) (-969 "PRINT.spad" 1573834 1573842 1574072 1574077) (-968 "PRIMES.spad" 1572087 1572097 1573824 1573829) (-967 "PRIMELT.spad" 1570168 1570182 1572077 1572082) (-966 "PRIMCAT.spad" 1569795 1569803 1570158 1570163) (-965 "PRIMARR2.spad" 1568562 1568574 1569785 1569790) (-964 "PRIMARR.spad" 1567567 1567577 1567745 1567772) (-963 "PREASSOC.spad" 1566949 1566961 1567557 1567562) (-962 "PR.spad" 1565341 1565353 1566040 1566167) (-961 "PPCURVE.spad" 1564478 1564486 1565331 1565336) (-960 "PORTNUM.spad" 1564253 1564261 1564468 1564473) (-959 "POLYROOT.spad" 1563102 1563124 1564209 1564214) (-958 "POLYLIFT.spad" 1562367 1562390 1563092 1563097) (-957 "POLYCATQ.spad" 1560485 1560507 1562357 1562362) (-956 "POLYCAT.spad" 1553955 1553976 1560353 1560480) (-955 "POLYCAT.spad" 1546763 1546786 1553163 1553168) (-954 "POLY2UP.spad" 1546215 1546229 1546753 1546758) (-953 "POLY2.spad" 1545812 1545824 1546205 1546210) (-952 "POLY.spad" 1543147 1543157 1543662 1543789) (-951 "POLUTIL.spad" 1542088 1542117 1543103 1543108) (-950 "POLTOPOL.spad" 1540836 1540851 1542078 1542083) (-949 "POINT.spad" 1539674 1539684 1539761 1539788) (-948 "PNTHEORY.spad" 1536376 1536384 1539664 1539669) (-947 "PMTOOLS.spad" 1535151 1535165 1536366 1536371) (-946 "PMSYM.spad" 1534700 1534710 1535141 1535146) (-945 "PMQFCAT.spad" 1534291 1534305 1534690 1534695) (-944 "PMPREDFS.spad" 1533745 1533767 1534281 1534286) (-943 "PMPRED.spad" 1533224 1533238 1533735 1533740) (-942 "PMPLCAT.spad" 1532304 1532322 1533156 1533161) (-941 "PMLSAGG.spad" 1531889 1531903 1532294 1532299) (-940 "PMKERNEL.spad" 1531468 1531480 1531879 1531884) (-939 "PMINS.spad" 1531048 1531058 1531458 1531463) (-938 "PMFS.spad" 1530625 1530643 1531038 1531043) (-937 "PMDOWN.spad" 1529915 1529929 1530615 1530620) (-936 "PMASSFS.spad" 1528882 1528898 1529905 1529910) (-935 "PMASS.spad" 1527892 1527900 1528872 1528877) (-934 "PLOTTOOL.spad" 1527672 1527680 1527882 1527887) (-933 "PLOT3D.spad" 1524136 1524144 1527662 1527667) (-932 "PLOT1.spad" 1523293 1523303 1524126 1524131) (-931 "PLOT.spad" 1518216 1518224 1523283 1523288) (-930 "PLEQN.spad" 1505506 1505533 1518206 1518211) (-929 "PINTERPA.spad" 1505290 1505306 1505496 1505501) (-928 "PINTERP.spad" 1504912 1504931 1505280 1505285) (-927 "PID.spad" 1503882 1503890 1504838 1504907) (-926 "PICOERCE.spad" 1503539 1503549 1503872 1503877) (-925 "PI.spad" 1503148 1503156 1503513 1503534) (-924 "PGROEB.spad" 1501749 1501763 1503138 1503143) (-923 "PGE.spad" 1493366 1493374 1501739 1501744) (-922 "PGCD.spad" 1492256 1492273 1493356 1493361) (-921 "PFRPAC.spad" 1491405 1491415 1492246 1492251) (-920 "PFR.spad" 1488068 1488078 1491307 1491400) (-919 "PFOTOOLS.spad" 1487326 1487342 1488058 1488063) (-918 "PFOQ.spad" 1486696 1486714 1487316 1487321) (-917 "PFO.spad" 1486115 1486142 1486686 1486691) (-916 "PFECAT.spad" 1483797 1483805 1486041 1486110) (-915 "PFECAT.spad" 1481507 1481517 1483753 1483758) (-914 "PFBRU.spad" 1479395 1479407 1481497 1481502) (-913 "PFBR.spad" 1476955 1476978 1479385 1479390) (-912 "PF.spad" 1476529 1476541 1476760 1476853) (-911 "PERMGRP.spad" 1471291 1471301 1476519 1476524) (-910 "PERMCAT.spad" 1469849 1469859 1471271 1471286) (-909 "PERMAN.spad" 1468381 1468395 1469839 1469844) (-908 "PERM.spad" 1464066 1464076 1468211 1468226) (-907 "PENDTREE.spad" 1463407 1463417 1463695 1463700) (-906 "PDRING.spad" 1461958 1461968 1463387 1463402) (-905 "PDRING.spad" 1460517 1460529 1461948 1461953) (-904 "PDEPROB.spad" 1459532 1459540 1460507 1460512) (-903 "PDEPACK.spad" 1453572 1453580 1459522 1459527) (-902 "PDECOMP.spad" 1453042 1453059 1453562 1453567) (-901 "PDECAT.spad" 1451398 1451406 1453032 1453037) (-900 "PCOMP.spad" 1451251 1451264 1451388 1451393) (-899 "PBWLB.spad" 1449839 1449856 1451241 1451246) (-898 "PATTERN2.spad" 1449577 1449589 1449829 1449834) (-897 "PATTERN1.spad" 1447913 1447929 1449567 1449572) (-896 "PATTERN.spad" 1442452 1442462 1447903 1447908) (-895 "PATRES2.spad" 1442124 1442138 1442442 1442447) (-894 "PATRES.spad" 1439699 1439711 1442114 1442119) (-893 "PATMATCH.spad" 1437896 1437927 1439407 1439412) (-892 "PATMAB.spad" 1437325 1437335 1437886 1437891) (-891 "PATLRES.spad" 1436411 1436425 1437315 1437320) (-890 "PATAB.spad" 1436175 1436185 1436401 1436406) (-889 "PARTPERM.spad" 1433575 1433583 1436165 1436170) (-888 "PARSURF.spad" 1433009 1433037 1433565 1433570) (-887 "PARSU2.spad" 1432806 1432822 1432999 1433004) (-886 "script-parser.spad" 1432326 1432334 1432796 1432801) (-885 "PARSCURV.spad" 1431760 1431788 1432316 1432321) (-884 "PARSC2.spad" 1431551 1431567 1431750 1431755) (-883 "PARPCURV.spad" 1431013 1431041 1431541 1431546) (-882 "PARPC2.spad" 1430804 1430820 1431003 1431008) (-881 "PARAMAST.spad" 1429932 1429940 1430794 1430799) (-880 "PAN2EXPR.spad" 1429344 1429352 1429922 1429927) (-879 "PALETTE.spad" 1428314 1428322 1429334 1429339) (-878 "PAIR.spad" 1427301 1427314 1427902 1427907) (-877 "PADICRC.spad" 1424635 1424653 1425806 1425899) (-876 "PADICRAT.spad" 1422650 1422662 1422871 1422964) (-875 "PADICCT.spad" 1421199 1421211 1422576 1422645) (-874 "PADIC.spad" 1420894 1420906 1421125 1421194) (-873 "PADEPAC.spad" 1419583 1419602 1420884 1420889) (-872 "PADE.spad" 1418335 1418351 1419573 1419578) (-871 "OWP.spad" 1417575 1417605 1418193 1418260) (-870 "OVERSET.spad" 1417148 1417156 1417565 1417570) (-869 "OVAR.spad" 1416929 1416952 1417138 1417143) (-868 "OUTFORM.spad" 1406321 1406329 1416919 1416924) (-867 "OUTBFILE.spad" 1405739 1405747 1406311 1406316) (-866 "OUTBCON.spad" 1404745 1404753 1405729 1405734) (-865 "OUTBCON.spad" 1403749 1403759 1404735 1404740) (-864 "OUT.spad" 1402835 1402843 1403739 1403744) (-863 "OSI.spad" 1402310 1402318 1402825 1402830) (-862 "OSGROUP.spad" 1402228 1402236 1402300 1402305) (-861 "ORTHPOL.spad" 1400713 1400723 1402145 1402150) (-860 "OREUP.spad" 1400166 1400194 1400393 1400432) (-859 "ORESUP.spad" 1399467 1399491 1399846 1399885) (-858 "OREPCTO.spad" 1397324 1397336 1399387 1399392) (-857 "OREPCAT.spad" 1391471 1391481 1397280 1397319) (-856 "OREPCAT.spad" 1385508 1385520 1391319 1391324) (-855 "ORDSET.spad" 1384680 1384688 1385498 1385503) (-854 "ORDSET.spad" 1383850 1383860 1384670 1384675) (-853 "ORDRING.spad" 1383240 1383248 1383830 1383845) (-852 "ORDRING.spad" 1382638 1382648 1383230 1383235) (-851 "ORDMON.spad" 1382493 1382501 1382628 1382633) (-850 "ORDFUNS.spad" 1381625 1381641 1382483 1382488) (-849 "ORDFIN.spad" 1381445 1381453 1381615 1381620) (-848 "ORDCOMP2.spad" 1380738 1380750 1381435 1381440) (-847 "ORDCOMP.spad" 1379203 1379213 1380285 1380314) (-846 "OPTPROB.spad" 1377841 1377849 1379193 1379198) (-845 "OPTPACK.spad" 1370250 1370258 1377831 1377836) (-844 "OPTCAT.spad" 1367929 1367937 1370240 1370245) (-843 "OPSIG.spad" 1367583 1367591 1367919 1367924) (-842 "OPQUERY.spad" 1367132 1367140 1367573 1367578) (-841 "OPERCAT.spad" 1366598 1366608 1367122 1367127) (-840 "OPERCAT.spad" 1366062 1366074 1366588 1366593) (-839 "OP.spad" 1365804 1365814 1365884 1365951) (-838 "ONECOMP2.spad" 1365228 1365240 1365794 1365799) (-837 "ONECOMP.spad" 1363973 1363983 1364775 1364804) (-836 "OMSERVER.spad" 1362979 1362987 1363963 1363968) (-835 "OMSAGG.spad" 1362767 1362777 1362935 1362974) (-834 "OMPKG.spad" 1361383 1361391 1362757 1362762) (-833 "OMLO.spad" 1360808 1360820 1361269 1361308) (-832 "OMEXPR.spad" 1360642 1360652 1360798 1360803) (-831 "OMERRK.spad" 1359676 1359684 1360632 1360637) (-830 "OMERR.spad" 1359221 1359229 1359666 1359671) (-829 "OMENC.spad" 1358565 1358573 1359211 1359216) (-828 "OMDEV.spad" 1352874 1352882 1358555 1358560) (-827 "OMCONN.spad" 1352283 1352291 1352864 1352869) (-826 "OM.spad" 1351256 1351264 1352273 1352278) (-825 "OINTDOM.spad" 1351019 1351027 1351182 1351251) (-824 "OFMONOID.spad" 1349142 1349152 1350975 1350980) (-823 "ODVAR.spad" 1348403 1348413 1349132 1349137) (-822 "ODR.spad" 1348047 1348073 1348215 1348364) (-821 "ODPOL.spad" 1345429 1345439 1345769 1345896) (-820 "ODP.spad" 1335276 1335296 1335649 1335780) (-819 "ODETOOLS.spad" 1333925 1333944 1335266 1335271) (-818 "ODESYS.spad" 1331619 1331636 1333915 1333920) (-817 "ODERTRIC.spad" 1327628 1327645 1331576 1331581) (-816 "ODERED.spad" 1327027 1327051 1327618 1327623) (-815 "ODERAT.spad" 1324644 1324661 1327017 1327022) (-814 "ODEPRRIC.spad" 1321681 1321703 1324634 1324639) (-813 "ODEPROB.spad" 1320938 1320946 1321671 1321676) (-812 "ODEPRIM.spad" 1318272 1318294 1320928 1320933) (-811 "ODEPAL.spad" 1317658 1317682 1318262 1318267) (-810 "ODEPACK.spad" 1304324 1304332 1317648 1317653) (-809 "ODEINT.spad" 1303759 1303775 1304314 1304319) (-808 "ODEIFTBL.spad" 1301154 1301162 1303749 1303754) (-807 "ODEEF.spad" 1296649 1296665 1301144 1301149) (-806 "ODECONST.spad" 1296186 1296204 1296639 1296644) (-805 "ODECAT.spad" 1294784 1294792 1296176 1296181) (-804 "OCTCT2.spad" 1294430 1294451 1294774 1294779) (-803 "OCT.spad" 1292566 1292576 1293280 1293319) (-802 "OCAMON.spad" 1292414 1292422 1292556 1292561) (-801 "OC.spad" 1290210 1290220 1292370 1292409) (-800 "OC.spad" 1287731 1287743 1289893 1289898) (-799 "OASGP.spad" 1287546 1287554 1287721 1287726) (-798 "OAMONS.spad" 1287068 1287076 1287536 1287541) (-797 "OAMON.spad" 1286929 1286937 1287058 1287063) (-796 "OAGROUP.spad" 1286791 1286799 1286919 1286924) (-795 "NUMTUBE.spad" 1286382 1286398 1286781 1286786) (-794 "NUMQUAD.spad" 1274358 1274366 1286372 1286377) (-793 "NUMODE.spad" 1265712 1265720 1274348 1274353) (-792 "NUMINT.spad" 1263278 1263286 1265702 1265707) (-791 "NUMFMT.spad" 1262118 1262126 1263268 1263273) (-790 "NUMERIC.spad" 1254232 1254242 1261923 1261928) (-789 "NTSCAT.spad" 1252740 1252756 1254200 1254227) (-788 "NTPOLFN.spad" 1252291 1252301 1252657 1252662) (-787 "NSUP2.spad" 1251683 1251695 1252281 1252286) (-786 "NSUP.spad" 1244729 1244739 1249269 1249422) (-785 "NSMP.spad" 1240960 1240979 1241268 1241395) (-784 "NREP.spad" 1239338 1239352 1240950 1240955) (-783 "NPCOEF.spad" 1238584 1238604 1239328 1239333) (-782 "NORMRETR.spad" 1238182 1238221 1238574 1238579) (-781 "NORMPK.spad" 1236084 1236103 1238172 1238177) (-780 "NORMMA.spad" 1235772 1235798 1236074 1236079) (-779 "NONE1.spad" 1235448 1235458 1235762 1235767) (-778 "NONE.spad" 1235189 1235197 1235438 1235443) (-777 "NODE1.spad" 1234676 1234692 1235179 1235184) (-776 "NNI.spad" 1233571 1233579 1234650 1234671) (-775 "NLINSOL.spad" 1232197 1232207 1233561 1233566) (-774 "NIPROB.spad" 1230738 1230746 1232187 1232192) (-773 "NFINTBAS.spad" 1228298 1228315 1230728 1230733) (-772 "NETCLT.spad" 1228272 1228283 1228288 1228293) (-771 "NCODIV.spad" 1226488 1226504 1228262 1228267) (-770 "NCNTFRAC.spad" 1226130 1226144 1226478 1226483) (-769 "NCEP.spad" 1224296 1224310 1226120 1226125) (-768 "NASRING.spad" 1223892 1223900 1224286 1224291) (-767 "NASRING.spad" 1223486 1223496 1223882 1223887) (-766 "NARNG.spad" 1222838 1222846 1223476 1223481) (-765 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(-746 "MULTFACT.spad" 1148081 1148098 1148688 1148693) (-745 "MTSCAT.spad" 1146175 1146196 1147979 1148076) (-744 "MTHING.spad" 1145834 1145844 1146165 1146170) (-743 "MSYSCMD.spad" 1145268 1145276 1145824 1145829) (-742 "MSETAGG.spad" 1145113 1145123 1145236 1145263) (-741 "MSET.spad" 1143071 1143081 1144819 1144858) (-740 "MRING.spad" 1140048 1140060 1142779 1142846) (-739 "MRF2.spad" 1139618 1139632 1140038 1140043) (-738 "MRATFAC.spad" 1139164 1139181 1139608 1139613) (-737 "MPRFF.spad" 1137204 1137223 1139154 1139159) (-736 "MPOLY.spad" 1134675 1134690 1135034 1135161) (-735 "MPCPF.spad" 1133939 1133958 1134665 1134670) (-734 "MPC3.spad" 1133756 1133796 1133929 1133934) (-733 "MPC2.spad" 1133402 1133435 1133746 1133751) (-732 "MONOTOOL.spad" 1131753 1131770 1133392 1133397) (-731 "MONOID.spad" 1131072 1131080 1131743 1131748) (-730 "MONOID.spad" 1130389 1130399 1131062 1131067) (-729 "MONOGEN.spad" 1129137 1129150 1130249 1130384) (-728 "MONOGEN.spad" 1127907 1127922 1129021 1129026) (-727 "MONADWU.spad" 1125937 1125945 1127897 1127902) (-726 "MONADWU.spad" 1123965 1123975 1125927 1125932) (-725 "MONAD.spad" 1123125 1123133 1123955 1123960) (-724 "MONAD.spad" 1122283 1122293 1123115 1123120) (-723 "MOEBIUS.spad" 1121019 1121033 1122263 1122278) (-722 "MODULE.spad" 1120889 1120899 1120987 1121014) (-721 "MODULE.spad" 1120779 1120791 1120879 1120884) (-720 "MODRING.spad" 1120114 1120153 1120759 1120774) (-719 "MODOP.spad" 1118779 1118791 1119936 1120003) (-718 "MODMONOM.spad" 1118510 1118528 1118769 1118774) (-717 "MODMON.spad" 1115305 1115321 1116024 1116177) (-716 "MODFIELD.spad" 1114667 1114706 1115207 1115300) (-715 "MMLFORM.spad" 1113527 1113535 1114657 1114662) (-714 "MMAP.spad" 1113269 1113303 1113517 1113522) (-713 "MLO.spad" 1111728 1111738 1113225 1113264) (-712 "MLIFT.spad" 1110340 1110357 1111718 1111723) (-711 "MKUCFUNC.spad" 1109875 1109893 1110330 1110335) (-710 "MKRECORD.spad" 1109479 1109492 1109865 1109870) (-709 "MKFUNC.spad" 1108886 1108896 1109469 1109474) (-708 "MKFLCFN.spad" 1107854 1107864 1108876 1108881) (-707 "MKBCFUNC.spad" 1107349 1107367 1107844 1107849) (-706 "MINT.spad" 1106788 1106796 1107251 1107344) (-705 "MHROWRED.spad" 1105299 1105309 1106778 1106783) (-704 "MFLOAT.spad" 1103819 1103827 1105189 1105294) (-703 "MFINFACT.spad" 1103219 1103241 1103809 1103814) (-702 "MESH.spad" 1101006 1101014 1103209 1103214) (-701 "MDDFACT.spad" 1099217 1099227 1100996 1101001) (-700 "MDAGG.spad" 1098508 1098518 1099197 1099212) (-699 "MCMPLX.spad" 1094519 1094527 1095133 1095334) (-698 "MCDEN.spad" 1093729 1093741 1094509 1094514) (-697 "MCALCFN.spad" 1090851 1090877 1093719 1093724) (-696 "MAYBE.spad" 1090135 1090146 1090841 1090846) (-695 "MATSTOR.spad" 1087443 1087453 1090125 1090130) (-694 "MATRIX.spad" 1086147 1086157 1086631 1086658) (-693 "MATLIN.spad" 1083491 1083515 1086031 1086036) (-692 "MATCAT2.spad" 1082773 1082821 1083481 1083486) (-691 "MATCAT.spad" 1074502 1074524 1082741 1082768) (-690 "MATCAT.spad" 1066103 1066127 1074344 1074349) (-689 "MAPPKG3.spad" 1065018 1065032 1066093 1066098) (-688 "MAPPKG2.spad" 1064356 1064368 1065008 1065013) (-687 "MAPPKG1.spad" 1063184 1063194 1064346 1064351) (-686 "MAPPAST.spad" 1062499 1062507 1063174 1063179) (-685 "MAPHACK3.spad" 1062311 1062325 1062489 1062494) (-684 "MAPHACK2.spad" 1062080 1062092 1062301 1062306) (-683 "MAPHACK1.spad" 1061724 1061734 1062070 1062075) (-682 "MAGMA.spad" 1059514 1059531 1061714 1061719) (-681 "MACROAST.spad" 1059093 1059101 1059504 1059509) (-680 "M3D.spad" 1056813 1056823 1058471 1058476) (-679 "LZSTAGG.spad" 1054051 1054061 1056803 1056808) (-678 "LZSTAGG.spad" 1051287 1051299 1054041 1054046) (-677 "LWORD.spad" 1047992 1048009 1051277 1051282) (-676 "LSTAST.spad" 1047776 1047784 1047982 1047987) (-675 "LSQM.spad" 1046003 1046017 1046397 1046448) (-674 "LSPP.spad" 1045538 1045555 1045993 1045998) (-673 "LSMP1.spad" 1043373 1043387 1045528 1045533) (-672 "LSMP.spad" 1042230 1042258 1043363 1043368) (-671 "LSAGG.spad" 1041899 1041909 1042198 1042225) (-670 "LSAGG.spad" 1041588 1041600 1041889 1041894) (-669 "LPOLY.spad" 1040542 1040561 1041444 1041513) (-668 "LPEFRAC.spad" 1039813 1039823 1040532 1040537) (-667 "LOGIC.spad" 1039415 1039423 1039803 1039808) (-666 "LOGIC.spad" 1039015 1039025 1039405 1039410) (-665 "LODOOPS.spad" 1037945 1037957 1039005 1039010) (-664 "LODOF.spad" 1036991 1037008 1037902 1037907) (-663 "LODOCAT.spad" 1035657 1035667 1036947 1036986) (-662 "LODOCAT.spad" 1034321 1034333 1035613 1035618) (-661 "LODO2.spad" 1033594 1033606 1034001 1034040) (-660 "LODO1.spad" 1032994 1033004 1033274 1033313) (-659 "LODO.spad" 1032378 1032394 1032674 1032713) (-658 "LODEEF.spad" 1031180 1031198 1032368 1032373) (-657 "LO.spad" 1030581 1030595 1031114 1031141) (-656 "LNAGG.spad" 1026413 1026423 1030571 1030576) (-655 "LNAGG.spad" 1022209 1022221 1026369 1026374) (-654 "LMOPS.spad" 1018977 1018994 1022199 1022204) (-653 "LMODULE.spad" 1018745 1018755 1018967 1018972) (-652 "LMDICT.spad" 1018032 1018042 1018296 1018323) (-651 "LLINSET.spad" 1017429 1017439 1018022 1018027) (-650 "LITERAL.spad" 1017335 1017346 1017419 1017424) (-649 "LIST3.spad" 1016646 1016660 1017325 1017330) (-648 "LIST2MAP.spad" 1013549 1013561 1016636 1016641) (-647 "LIST2.spad" 1012251 1012263 1013539 1013544) (-646 "LIST.spad" 1009986 1009996 1011398 1011425) (-645 "LINSET.spad" 1009608 1009618 1009976 1009981) (-644 "LINEXP.spad" 1009042 1009052 1009588 1009603) (-643 "LINDEP.spad" 1007851 1007863 1008954 1008959) (-642 "LIMITRF.spad" 1005798 1005808 1007841 1007846) (-641 "LIMITPS.spad" 1004708 1004721 1005788 1005793) (-640 "LIECAT.spad" 1004184 1004194 1004634 1004703) (-639 "LIECAT.spad" 1003688 1003700 1004140 1004145) (-638 "LIE.spad" 1001704 1001716 1002978 1003123) (-637 "LIB.spad" 999754 999762 1000363 1000378) (-636 "LGROBP.spad" 997107 997126 999744 999749) (-635 "LFCAT.spad" 996166 996174 997097 997102) (-634 "LF.spad" 995121 995137 996156 996161) (-633 "LEXTRIPK.spad" 990624 990639 995111 995116) (-632 "LEXP.spad" 988627 988654 990604 990619) (-631 "LETAST.spad" 988326 988334 988617 988622) (-630 "LEADCDET.spad" 986724 986741 988316 988321) (-629 "LAZM3PK.spad" 985428 985450 986714 986719) (-628 "LAUPOL.spad" 984121 984134 985021 985090) (-627 "LAPLACE.spad" 983704 983720 984111 984116) (-626 "LALG.spad" 983480 983490 983684 983699) (-625 "LALG.spad" 983264 983276 983470 983475) (-624 "LA.spad" 982704 982718 983186 983225) (-623 "KVTFROM.spad" 982439 982449 982694 982699) (-622 "KTVLOGIC.spad" 981951 981959 982429 982434) (-621 "KRCFROM.spad" 981689 981699 981941 981946) (-620 "KOVACIC.spad" 980412 980429 981679 981684) (-619 "KONVERT.spad" 980134 980144 980402 980407) (-618 "KOERCE.spad" 979871 979881 980124 980129) (-617 "KERNEL2.spad" 979574 979586 979861 979866) (-616 "KERNEL.spad" 978229 978239 979358 979363) (-615 "KDAGG.spad" 977338 977360 978209 978224) (-614 "KDAGG.spad" 976455 976479 977328 977333) (-613 "KAFILE.spad" 975418 975434 975653 975680) (-612 "JORDAN.spad" 973247 973259 974708 974853) (-611 "JOINAST.spad" 972941 972949 973237 973242) (-610 "JAVACODE.spad" 972807 972815 972931 972936) (-609 "IXAGG.spad" 970940 970964 972797 972802) (-608 "IXAGG.spad" 968928 968954 970787 970792) (-607 "IVECTOR.spad" 967698 967713 967853 967880) (-606 "ITUPLE.spad" 966859 966869 967688 967693) (-605 "ITRIGMNP.spad" 965698 965717 966849 966854) (-604 "ITFUN3.spad" 965204 965218 965688 965693) (-603 "ITFUN2.spad" 964948 964960 965194 965199) (-602 "ITFORM.spad" 964303 964311 964938 964943) (-601 "ITAYLOR.spad" 962297 962312 964167 964264) (-600 "ISUPS.spad" 954734 954749 961271 961368) (-599 "ISUMP.spad" 954235 954251 954724 954729) (-598 "ISTRING.spad" 953323 953336 953404 953431) (-597 "ISAST.spad" 953042 953050 953313 953318) (-596 "IRURPK.spad" 951759 951778 953032 953037) (-595 "IRSN.spad" 949763 949771 951749 951754) (-594 "IRRF2F.spad" 948248 948258 949719 949724) (-593 "IRREDFFX.spad" 947849 947860 948238 948243) (-592 "IROOT.spad" 946188 946198 947839 947844) (-591 "IRFORM.spad" 945512 945520 946178 946183) (-590 "IR2F.spad" 944718 944734 945502 945507) (-589 "IR2.spad" 943746 943762 944708 944713) (-588 "IR.spad" 941547 941561 943601 943628) (-587 "IPRNTPK.spad" 941307 941315 941537 941542) (-586 "IPF.spad" 940872 940884 941112 941205) (-585 "IPADIC.spad" 940633 940659 940798 940867) (-584 "IP4ADDR.spad" 940190 940198 940623 940628) (-583 "IOMODE.spad" 939811 939819 940180 940185) (-582 "IOBFILE.spad" 939172 939180 939801 939806) (-581 "IOBCON.spad" 939037 939045 939162 939167) (-580 "INVLAPLA.spad" 938686 938702 939027 939032) (-579 "INTTR.spad" 932080 932097 938676 938681) (-578 "INTTOOLS.spad" 929835 929851 931654 931659) (-577 "INTSLPE.spad" 929155 929163 929825 929830) (-576 "INTRVL.spad" 928721 928731 929069 929150) (-575 "INTRF.spad" 927145 927159 928711 928716) (-574 "INTRET.spad" 926577 926587 927135 927140) (-573 "INTRAT.spad" 925304 925321 926567 926572) (-572 "INTPM.spad" 923689 923705 924947 924952) (-571 "INTPAF.spad" 921560 921578 923621 923626) (-570 "INTPACK.spad" 911934 911942 921550 921555) (-569 "INTHERTR.spad" 911208 911225 911924 911929) (-568 "INTHERAL.spad" 910878 910902 911198 911203) (-567 "INTHEORY.spad" 907317 907325 910868 910873) (-566 "INTG0.spad" 901068 901086 907249 907254) (-565 "INTFTBL.spad" 896522 896530 901058 901063) (-564 "INTFACT.spad" 895581 895591 896512 896517) (-563 "INTEF.spad" 893968 893984 895571 895576) (-562 "INTDOM.spad" 892591 892599 893894 893963) (-561 "INTDOM.spad" 891276 891286 892581 892586) (-560 "INTCAT.spad" 889535 889545 891190 891271) (-559 "INTBIT.spad" 889042 889050 889525 889530) (-558 "INTALG.spad" 888230 888257 889032 889037) (-557 "INTAF.spad" 887730 887746 888220 888225) (-556 "INTABL.spad" 886248 886279 886411 886438) (-555 "INT8.spad" 886128 886136 886238 886243) (-554 "INT64.spad" 886007 886015 886118 886123) (-553 "INT32.spad" 885886 885894 885997 886002) (-552 "INT16.spad" 885765 885773 885876 885881) (-551 "INT.spad" 885213 885221 885619 885760) (-550 "INS.spad" 882716 882724 885115 885208) (-549 "INS.spad" 880305 880315 882706 882711) (-548 "INPSIGN.spad" 879775 879788 880295 880300) (-547 "INPRODPF.spad" 878871 878890 879765 879770) (-546 "INPRODFF.spad" 877959 877983 878861 878866) (-545 "INNMFACT.spad" 876934 876951 877949 877954) (-544 "INMODGCD.spad" 876422 876452 876924 876929) (-543 "INFSP.spad" 874719 874741 876412 876417) (-542 "INFPROD0.spad" 873799 873818 874709 874714) (-541 "INFORM1.spad" 873424 873434 873789 873794) (-540 "INFORM.spad" 870623 870631 873414 873419) (-539 "INFINITY.spad" 870175 870183 870613 870618) (-538 "INETCLTS.spad" 870152 870160 870165 870170) (-537 "INEP.spad" 868690 868712 870142 870147) (-536 "INDE.spad" 868419 868436 868680 868685) (-535 "INCRMAPS.spad" 867840 867850 868409 868414) (-534 "INBFILE.spad" 866912 866920 867830 867835) (-533 "INBFF.spad" 862706 862717 866902 866907) (-532 "INBCON.spad" 860996 861004 862696 862701) (-531 "INBCON.spad" 859284 859294 860986 860991) (-530 "INAST.spad" 858945 858953 859274 859279) (-529 "IMPTAST.spad" 858653 858661 858935 858940) (-528 "IMATRIX.spad" 857598 857624 858110 858137) (-527 "IMATQF.spad" 856692 856736 857554 857559) (-526 "IMATLIN.spad" 855297 855321 856648 856653) (-525 "ILIST.spad" 853955 853970 854480 854507) (-524 "IIARRAY2.spad" 853343 853381 853562 853589) (-523 "IFF.spad" 852753 852769 853024 853117) (-522 "IFAST.spad" 852367 852375 852743 852748) (-521 "IFARRAY.spad" 849860 849875 851550 851577) (-520 "IFAMON.spad" 849722 849739 849816 849821) (-519 "IEVALAB.spad" 849127 849139 849712 849717) (-518 "IEVALAB.spad" 848530 848544 849117 849122) (-517 "IDPOAMS.spad" 848286 848298 848520 848525) (-516 "IDPOAM.spad" 848006 848018 848276 848281) (-515 "IDPO.spad" 847804 847816 847996 848001) (-514 "IDPC.spad" 846742 846754 847794 847799) (-513 "IDPAM.spad" 846487 846499 846732 846737) (-512 "IDPAG.spad" 846234 846246 846477 846482) (-511 "IDENT.spad" 845884 845892 846224 846229) (-510 "IDECOMP.spad" 843123 843141 845874 845879) (-509 "IDEAL.spad" 838072 838111 843058 843063) (-508 "ICDEN.spad" 837261 837277 838062 838067) (-507 "ICARD.spad" 836452 836460 837251 837256) (-506 "IBPTOOLS.spad" 835059 835076 836442 836447) (-505 "IBITS.spad" 834262 834275 834695 834722) (-504 "IBATOOL.spad" 831239 831258 834252 834257) (-503 "IBACHIN.spad" 829746 829761 831229 831234) (-502 "IARRAY2.spad" 828734 828760 829353 829380) (-501 "IARRAY1.spad" 827779 827794 827917 827944) (-500 "IAN.spad" 826002 826010 827595 827688) (-499 "IALGFACT.spad" 825605 825638 825992 825997) (-498 "HYPCAT.spad" 825029 825037 825595 825600) (-497 "HYPCAT.spad" 824451 824461 825019 825024) (-496 "HOSTNAME.spad" 824259 824267 824441 824446) (-495 "HOMOTOP.spad" 824002 824012 824249 824254) (-494 "HOAGG.spad" 821284 821294 823992 823997) (-493 "HOAGG.spad" 818341 818353 821051 821056) (-492 "HEXADEC.spad" 816443 816451 816808 816901) (-491 "HEUGCD.spad" 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index dad40acb..9ed0db09 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,5 +1,5 @@ -(188581 . 3477435927) +(188581 . 3477490105) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -43,26 +43,26 @@ (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) ((((-868)) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) (((|#1| |#2|) . T)) -((((-551) (-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T) ((|#1| |#2|) . T)) -((((-551) (-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T) ((|#1| |#2|) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T) ((|#2|) . 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T)) +(((#1=(-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) #1#) |has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-312 (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107)))) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) |has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-312 (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)))) ((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107)))) +((((-551) (-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1| |#2|) . T)) ((((-169 (-382))) . T) (((-226)) . T) (((-382)) . T)) ((((-412 (-551))) . T) (((-551)) . T)) @@ -93,11 +93,11 @@ (((|#1|) . T)) (|has| |#1| (-855)) (((|#1|) . T)) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) ((((-551) |#1|) . T)) @@ -110,13 +110,13 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1| (-58 |#1|) (-58 |#1|)) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) -((((-694 (-343 (-3965) (-3965 (QUOTE X) (QUOTE HESS)) (-704)))) . T)) +((((-694 (-343 (-3971) (-3971 (QUOTE X) (QUOTE HESS)) (-704)))) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -133,7 +133,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) -((((-1272 (-343 (-3965) (-3965 (QUOTE X)) (-704)))) . T)) +((((-1272 (-343 (-3971) (-3971 (QUOTE X)) (-704)))) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -144,7 +144,7 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (|has| |#1| (-1107)) @@ -163,7 +163,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) . T)) (((|#1|) . T)) ((((-868)) . T)) @@ -240,7 +240,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -249,7 +249,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -258,7 +258,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) . T)) (((|#1|) . T)) ((((-144)) . T)) @@ -327,20 +327,20 @@ ((((-868)) . T) (((-1188)) . T)) ((((-1188)) . T)) (|has| |#1| (-826)) -(-3972 (|has| |#1| (-145)) (|has| |#1| (-354))) +(-3978 (|has| |#1| (-145)) (|has| |#1| (-354))) ((((-868)) . T)) (|has| |#1| (-147)) (((|#1|) . 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T)) (((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107)))) @@ -1430,10 +1430,10 @@ ((((-551) |#2|) . T)) ((((-551) |#2|) . T)) (|has| |#2| (-798)) -(-3972 (|has| |#2| (-798)) (|has| |#2| (-853))) -(-3972 (|has| |#2| (-798)) (|has| |#2| (-853))) -(-3972 (|has| |#2| (-798)) (|has| |#2| (-853))) -(-3972 (|has| |#2| (-798)) (|has| |#2| (-853))) +(-3978 (|has| |#2| (-798)) (|has| |#2| (-853))) +(-3978 (|has| |#2| (-798)) (|has| |#2| (-853))) +(-3978 (|has| |#2| (-798)) (|has| |#2| (-853))) +(-3978 (|has| |#2| (-798)) (|has| |#2| (-853))) (|has| |#2| (-853)) (|has| |#2| (-853)) (((|#2|) |has| |#2| (-367))) @@ -1442,7 +1442,7 @@ ((((-868)) . T) (((-1188)) . T)) ((((-1188)) . T)) (((|#1|) . T)) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (|has| |#1| (-1107)) @@ -1491,11 +1491,11 @@ (((|#1|) . T)) (|has| |#1| (-855)) (((|#1|) . T)) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) ((((-551) |#1|) . T)) @@ -1508,7 +1508,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1| (-501 |#1| |#3|) (-501 |#1| |#2|)) . T)) ((((-112)) . T)) ((((-112)) . T)) @@ -1542,11 +1542,11 @@ (((|#1|) . T)) (|has| |#1| (-855)) (((|#1|) . T)) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) ((((-551) |#1|) . T)) @@ -1577,15 +1577,15 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1| |#4| |#5|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) ((((-551) |#1|) . T)) @@ -1599,7 +1599,7 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1| (-607 |#1| |#3|) (-607 |#1| |#2|)) . T)) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (|has| |#1| (-1107)) @@ -1644,13 +1644,13 @@ (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -(((|#2|) . T) (((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) ((#1=(-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) #1#) |has| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (-312 (-2 (|:| -4304 |#1|) (|:| -2263 |#2|))))) -(((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) (((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) |has| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (-312 (-2 (|:| -4304 |#1|) (|:| -2263 |#2|))))) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +(((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) ((#1=(-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) #1#) |has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-312 (-2 (|:| -4310 |#1|) (|:| -2264 |#2|))))) +(((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) (((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) |has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-312 (-2 (|:| -4310 |#1|) (|:| -2264 |#2|))))) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) +((((-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T)) (((|#1| |#2|) . T)) ((($) . T)) ((($ $) . T)) @@ -1728,10 +1728,10 @@ ((($) . T) (((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) . T)) (|has| |#1| (-145)) (|has| |#1| (-147)) -(-3972 (|has| |#1| (-173)) (|has| |#1| (-562))) -((((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) . T) (($) -3972 (|has| |#1| (-173)) (|has| |#1| (-562)))) -((((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) . T) (($) -3972 (|has| |#1| (-173)) (|has| |#1| (-562)))) -(((#1=(-412 (-551)) #1#) |has| |#1| (-38 (-412 (-551)))) ((|#1| |#1|) . T) (($ $) -3972 (|has| |#1| (-173)) (|has| |#1| (-562)))) +(-3978 (|has| |#1| (-173)) (|has| |#1| (-562))) +((((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) . T) (($) -3978 (|has| |#1| (-173)) (|has| |#1| (-562)))) +((((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) . T) (($) -3978 (|has| |#1| (-173)) (|has| |#1| (-562)))) +(((#1=(-412 (-551)) #1#) |has| |#1| (-38 (-412 (-551)))) ((|#1| |#1|) . T) (($ $) -3978 (|has| |#1| (-173)) (|has| |#1| (-562)))) (|has| |#1| (-562)) (|has| |#1| (-562)) ((((-551)) . T) (((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) |has| |#1| (-173)) (($) |has| |#1| (-562))) @@ -1764,11 +1764,11 @@ ((((-551) |#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) (((|#1|) . T)) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) . T)) (|has| |#1| (-855)) (((|#1|) . T)) @@ -1779,7 +1779,7 @@ ((((-1188)) . T)) ((((-1223)) . T) (((-868)) . T) (((-1188)) . T)) ((((-1188)) . T)) -(((|#1|) -3972 (|has| |#2| (-371 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -3978 (|has| |#2| (-371 |#1|)) (|has| |#2| (-423 |#1|)))) (((|#1|) |has| |#2| (-423 |#1|))) (((|#1|) . T)) (((|#1|) . T)) @@ -1794,16 +1794,16 @@ ((((-1165) |#1|) . T)) ((((-1165) |#1|) . T)) ((((-1165) |#1|) . T)) -((((-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))) . T)) -((((-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))) . T)) -(((|#1|) . T) (((-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) ((#1=(-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) #1#) |has| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (-312 (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))))) -(((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) (((-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))) |has| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (-312 (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))))) -((((-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))) . T)) -((((-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))) . T)) +((((-2 (|:| -4310 (-1165)) (|:| -2264 |#1|))) . T)) +((((-2 (|:| -4310 (-1165)) (|:| -2264 |#1|))) . T)) +(((|#1|) . T) (((-2 (|:| -4310 (-1165)) (|:| -2264 |#1|))) . T)) +(((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) ((#1=(-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) #1#) |has| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (-312 (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|))))) +(((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) (((-2 (|:| -4310 (-1165)) (|:| -2264 |#1|))) |has| (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|)) (-312 (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|))))) +((((-2 (|:| -4310 (-1165)) (|:| -2264 |#1|))) . T)) +((((-2 (|:| -4310 (-1165)) (|:| -2264 |#1|))) . T)) ((((-1165) |#1|) . T)) ((((-868)) . T)) -((((-393) (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))) . T)) +((((-393) (-2 (|:| -4310 (-1165)) (|:| -2264 |#1|))) . T)) ((((-540)) |has| |#1| (-619 (-540))) (((-896 (-382))) |has| |#1| (-619 (-896 (-382)))) (((-896 (-551))) |has| |#1| (-619 (-896 (-551))))) (((|#1|) . T)) ((((-868)) . T)) @@ -1854,15 +1854,15 @@ ((((-1165) (-51)) . T)) ((((-1165) (-51)) . T)) ((((-1165) (-51)) . T)) -((((-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))) . T)) -((((-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))) . T)) -(((#1=(-51)) . T) (((-2 (|:| -4304 (-1165)) (|:| -2263 #1#))) . T)) -(((#1=(-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) #1#) |has| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (-312 (-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))))) -((((-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))) |has| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (-312 (-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))))) -((((-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))) . T)) -((((-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))) . T)) +((((-2 (|:| -4310 (-1165)) (|:| -2264 (-51)))) . T)) +((((-2 (|:| -4310 (-1165)) (|:| -2264 (-51)))) . T)) +(((#1=(-51)) . T) (((-2 (|:| -4310 (-1165)) (|:| -2264 #1#))) . T)) +(((#1=(-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) #1#) |has| (-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) (-312 (-2 (|:| -4310 (-1165)) (|:| -2264 (-51)))))) +((((-2 (|:| -4310 (-1165)) (|:| -2264 (-51)))) |has| (-2 (|:| -4310 (-1165)) (|:| -2264 (-51))) (-312 (-2 (|:| -4310 (-1165)) (|:| -2264 (-51)))))) +((((-2 (|:| -4310 (-1165)) (|:| -2264 (-51)))) . T)) +((((-2 (|:| -4310 (-1165)) (|:| -2264 (-51)))) . T)) ((((-1165) (-51)) . T)) -(((|#1|) -3972 (|has| |#2| (-371 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -3978 (|has| |#2| (-371 |#1|)) (|has| |#2| (-423 |#1|)))) (((|#1|) |has| |#2| (-423 |#1|))) (((|#1|) . T)) (((|#1|) . T)) @@ -1876,11 +1876,11 @@ (|has| |#1| (-826)) (((|#1|) . T)) (((|#1|) . T)) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) ((((-551) |#1|) . T)) @@ -1904,7 +1904,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -1984,7 +1984,7 @@ (((|#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) -(((|#2|) |has| |#2| (-6 (-4439 "*")))) +(((|#2|) |has| |#2| (-6 (-4445 "*")))) (((|#2| |#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2012,7 +2012,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-868)) . T)) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (|has| |#1| (-1107)) @@ -2029,7 +2029,7 @@ ((((-1188)) . T)) ((((-540)) |has| |#1| (-619 (-540)))) (((|#1| (-1272 |#1|) (-1272 |#1|)) . T)) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (|has| |#1| (-1107)) @@ -2106,10 +2106,10 @@ ((((-868)) . T)) ((((-412 $) (-412 $)) |has| |#1| (-562)) (($ $) . T) ((|#1| |#1|) . 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T) (((-551)) . T) (($) . T)) (((|#1|) . T) (((-412 (-551))) . T) (((-551)) . T) (($) . T)) (((|#1|) . T) (((-412 (-551))) . T)) -(((|#1|) . T) (((-551)) -3972 (|has| |#1| (-1044 (-551))) (|has| (-412 (-551)) (-1044 (-551)))) (((-412 (-551))) . T)) +(((|#1|) . T) (((-551)) -3978 (|has| |#1| (-1044 (-551))) (|has| (-412 (-551)) (-1044 (-551)))) (((-412 (-551))) . T)) (|has| |#1| (-1107)) ((((-868)) |has| |#1| (-1107))) (|has| |#1| (-1107)) @@ -2882,13 +2882,13 @@ ((((-1183) (-51)) . T)) ((((-1183) (-51)) . T)) ((((-1183) (-51)) . T)) -((((-2 (|:| -4304 (-1183)) (|:| -2263 (-51)))) . T)) -((((-2 (|:| -4304 (-1183)) (|:| -2263 (-51)))) . T)) -(((#1=(-51)) . T) (((-2 (|:| -4304 (-1183)) (|:| -2263 #1#))) . 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T)) +((((-2 (|:| -4310 (-1183)) (|:| -2264 (-51)))) . T)) ((((-1183) (-51)) . T)) ((((-1188)) . T)) ((((-868)) . T) (((-1188)) . T)) @@ -2913,8 +2913,8 @@ (((|#3|) . T)) (((|#3| |#3|) -12 (|has| |#3| (-312 |#3|)) (|has| |#3| (-1107)))) (((|#3|) -12 (|has| |#3| (-312 |#3|)) (|has| |#3| (-1107)))) -(((|#3|) -3972 (|has| |#3| (-173)) (|has| |#3| (-367)))) -(((|#3|) -3972 (|has| |#3| (-173)) (|has| |#3| (-367)))) +(((|#3|) -3978 (|has| |#3| (-173)) (|has| |#3| (-367)))) +(((|#3|) -3978 (|has| |#3| (-173)) (|has| |#3| (-367)))) (((|#1| |#2| |#3| (-240 |#2| |#3|) (-240 |#1| |#3|)) . T)) (|has| |#1| (-1107)) ((((-868)) |has| |#1| (-1107))) @@ -2941,13 +2941,13 @@ ((((-1183) (-51)) . T)) ((((-1183) (-51)) . T)) ((((-1183) (-51)) . T)) -((((-2 (|:| -4304 (-1183)) (|:| -2263 (-51)))) . T)) -((((-2 (|:| -4304 (-1183)) (|:| -2263 (-51)))) . T)) -(((#1=(-51)) . T) (((-2 (|:| -4304 (-1183)) (|:| -2263 #1#))) . 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T) (($) -3972 (|has| |#1| (-367)) (|has| |#1| (-562)))) -(-3972 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) -(-3972 (|has| |#1| (-367)) (|has| |#1| (-562))) +(((|#1|) |has| |#1| (-173)) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (($) -3978 (|has| |#1| (-367)) (|has| |#1| (-562)))) +(((|#1|) |has| |#1| (-173)) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (($) -3978 (|has| |#1| (-367)) (|has| |#1| (-562)))) +(((|#1|) |has| |#1| (-173)) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (($) -3978 (|has| |#1| (-367)) (|has| |#1| (-562)))) +((((-1269 |#2|)) . T) (((-1262 |#1| |#2| |#3|)) . T) (((-1232 |#1| |#2| |#3|)) . T) ((|#1|) |has| |#1| (-173)) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (((-551)) . T) (($) -3978 (|has| |#1| (-367)) (|has| |#1| (-562)))) +(-3978 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) +(-3978 (|has| |#1| (-367)) (|has| |#1| (-562))) (|has| |#1| (-367)) (|has| |#1| (-367)) (|has| |#1| (-367)) @@ -3746,21 +3746,21 @@ (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367)) -(-3972 (|has| |#1| (-367)) (|has| |#1| (-562))) +(-3978 (|has| |#1| (-367)) (|has| |#1| (-562))) ((((-868)) . T)) -(((|#1|) . T) (($) -3972 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) (((-412 (-551))) -3972 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367)))) -(((|#1|) . T) (($) -3972 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) (((-412 (-551))) -3972 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367)))) -(((|#1| |#1|) . T) (($ $) -3972 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) ((#1=(-412 (-551)) #1#) -3972 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367)))) -(((|#1|) . T) (((-412 (-551))) -3972 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (((-551)) . T) (($) . T)) -(((|#1|) . T) (((-412 (-551))) -3972 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (($) . T)) +(((|#1|) . T) (($) -3978 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367)))) +(((|#1|) . T) (($) -3978 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367)))) +(((|#1| |#1|) . T) (($ $) -3978 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) ((#1=(-412 (-551)) #1#) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367)))) +(((|#1|) . T) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (((-551)) . T) (($) . T)) +(((|#1|) . T) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (($) . 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T) (($) -3972 (|has| |#1| (-367)) (|has| |#1| (-562)))) -(-3972 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) -(-3972 (|has| |#1| (-367)) (|has| |#1| (-562))) +(((|#1|) |has| |#1| (-173)) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (($) -3978 (|has| |#1| (-367)) (|has| |#1| (-562)))) +(((|#1|) |has| |#1| (-173)) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (($) -3978 (|has| |#1| (-367)) (|has| |#1| (-562)))) +(((|#1|) |has| |#1| (-173)) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (($) -3978 (|has| |#1| (-367)) (|has| |#1| (-562)))) +(((|#2|) . T) ((|#1|) |has| |#1| (-173)) (((-412 (-551))) -3978 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367))) (((-551)) . T) (($) -3978 (|has| |#1| (-367)) (|has| |#1| (-562)))) +(-3978 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) +(-3978 (|has| |#1| (-367)) (|has| |#1| (-562))) (|has| |#1| (-367)) (|has| |#1| (-367)) (|has| |#1| (-367)) @@ -3792,14 +3792,14 @@ (((|#1| (-776)) . T)) (|has| |#1| (-562)) (|has| |#1| (-562)) -(-3972 (|has| |#1| (-173)) (|has| |#1| (-562))) +(-3978 (|has| |#1| (-173)) (|has| |#1| (-562))) (|has| |#1| (-147)) (|has| |#1| (-145)) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-173)) (((-412 (-551))) |has| |#1| (-38 (-412 (-551))))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-173)) (((-412 (-551))) |has| |#1| (-38 (-412 (-551))))) -((($) -3972 (|has| |#1| (-173)) (|has| |#1| (-562))) ((|#1|) . T) (((-412 (-551))) |has| |#1| (-38 (-412 (-551))))) -((($) -3972 (|has| |#1| (-173)) (|has| |#1| (-562))) ((|#1|) . T) (((-412 (-551))) |has| |#1| (-38 (-412 (-551))))) -((($ $) -3972 (|has| |#1| (-173)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#1=(-412 (-551)) #1#) |has| |#1| (-38 (-412 (-551))))) +((($) -3978 (|has| |#1| (-173)) (|has| |#1| (-562))) ((|#1|) . T) (((-412 (-551))) |has| |#1| (-38 (-412 (-551))))) +((($) -3978 (|has| |#1| (-173)) (|has| |#1| (-562))) ((|#1|) . T) (((-412 (-551))) |has| |#1| (-38 (-412 (-551))))) +((($ $) -3978 (|has| |#1| (-173)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#1=(-412 (-551)) #1#) |has| |#1| (-38 (-412 (-551))))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-173)) (((-412 (-551))) |has| |#1| (-38 (-412 (-551))))) (((|#1| (-776) (-1088)) . T)) ((((-1183)) -12 (|has| |#1| (-906 (-1183))) (|has| |#1| (-15 * (|#1| (-776) |#1|))))) @@ -3818,11 +3818,11 @@ ((((-551) |#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) (((|#1|) . T)) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3978 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3978 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) . T)) (|has| |#1| (-855)) (((|#1|) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 0bf572b7..62afc8e1 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3477435920) -(4440 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3477490098) +(4446 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| @@ -452,14 +452,14 @@ |clipParametric| |clipWithRanges| |numberOfHues| |yellow| |iifact| |iibinom| |iiperm| |iipow| |iidsum| |iidprod| |ipow| |factorial| |multinomial| |permutation| |stirling1| |stirling2| |summation| |factorials| |mkcomm| - |polarCoordinates| |complex| |imaginary| |elaborate| |macroExpand| |solid| - |solid?| |denominators| |numerators| |convergents| |approximants| - |reducedForm| |partialQuotients| |partialDenominators| |partialNumerators| - |reducedContinuedFraction| |push| |bindings| |cartesian| |polar| |cylindrical| - |spherical| |parabolic| |parabolicCylindrical| |paraboloidal| - |ellipticCylindrical| |prolateSpheroidal| |oblateSpheroidal| |bipolar| - |bipolarCylindrical| |toroidal| |conical| |modTree| |multiEuclideanTree| - |complexZeros| |divisorCascade| |graeffe| |pleskenSplit| + |polarCoordinates| |complex| |imaginary| |elaborateFile| |elaborate| + |macroExpand| |solid| |solid?| |denominators| |numerators| |convergents| + |approximants| |reducedForm| |partialQuotients| |partialDenominators| + |partialNumerators| |reducedContinuedFraction| |push| |bindings| |cartesian| + |polar| |cylindrical| |spherical| |parabolic| |parabolicCylindrical| + |paraboloidal| |ellipticCylindrical| |prolateSpheroidal| |oblateSpheroidal| + |bipolar| |bipolarCylindrical| |toroidal| |conical| |modTree| + |multiEuclideanTree| |complexZeros| |divisorCascade| |graeffe| |pleskenSplit| |reciprocalPolynomial| |rootRadius| |schwerpunkt| |setErrorBound| |startPolynomial| |cycleElt| |computeCycleLength| |computeCycleEntry| |findConstructor| |arguments| |operations| |dualSignature| |kind| |package| @@ -625,30 +625,31 @@ |primlimitedint| |explimitedint| |primextintfrac| |primlimintfrac| |primintfldpoly| |expintfldpoly| |monomialIntegrate| |monomialIntPoly| |inverseLaplace| |inputOutputBinaryFile| |bothWays| |input| |resolve| |bytes| - |ip4Address| |iprint| |elem?| |notelem| |logpart| |ratpart| |mkAnswer| - |perfectNthPower?| |perfectNthRoot| |approxNthRoot| |perfectSquare?| - |perfectSqrt| |approxSqrt| |generateIrredPoly| |complexExpand| - |complexIntegrate| |dimensionOfIrreducibleRepresentation| + |ip4Address| |iprint| |elem?| |notelem| |logpart| |ratpart| |mkAnswer| |irDef| + |irCtor| |irVar| |perfectNthPower?| |perfectNthRoot| |approxNthRoot| + |perfectSquare?| |perfectSqrt| |approxSqrt| |generateIrredPoly| + |complexExpand| |complexIntegrate| |dimensionOfIrreducibleRepresentation| |irreducibleRepresentation| |checkRur| |cAcsch| |cAsech| |cAcoth| |cAtanh| |cAcosh| |cAsinh| |cCsch| |cSech| |cCoth| |cTanh| |cCosh| |cSinh| |cAcsc| |cAsec| |cAcot| |cAtan| |cAcos| |cAsin| |cCsc| |cSec| |cCot| |cTan| |cCos| |cSin| |cLog| |cExp| |cRationalPower| |cPower| |seriesToOutputForm| |iCompose| - |taylorQuoByVar| |iExquo| |getStream| |getRef| |makeSeries| |voidMode| - |noValueMode| |jokerMode| GF2FG FG2F F2FG |explogs2trigs| |trigs2explogs| - |swap!| |fill!| |minIndex| |maxIndex| |entry?| |indices| |index?| |entries| - |categories| |search| |key?| |symbolIfCan| |kernel| |argument| - |constantKernel| |constantIfCan| |kovacic| |unknown| |laplace| - |trailingCoefficient| |normalizeIfCan| |polCase| |distFact| |identification| - |LyndonCoordinates| |LyndonBasis| |zeroDimensional?| |fglmIfCan| |groebner| - |lexTriangular| |squareFreeLexTriangular| |belong?| |erf| |dilog| |li| |Ci| - |Si| |Ei| |linGenPos| |groebgen| |totolex| |minPol| |computeBasis| |coord| - |anticoord| |intcompBasis| |choosemon| |transform| |pack!| |library| - |complexLimit| |limit| |linearlyDependent?| |linearDependence| |solveLinear| - |reducedSystem| |setDifference| |setIntersection| |setUnion| |append| |null| - |nil| |substitute| |duplicates?| |mapGen| |mapExpon| |commutativeEquality| - |leftMult| |rightMult| |makeUnit| |reverse!| |reverse| |nthFactor| |nthExpon| - |makeMulti| |makeTerm| |listOfMonoms| |insert| |delete| |symmetricSquare| - |factor1| |symmetricProduct| |symmetricPower| |directSum| |\\/| |/\\| ~ + |taylorQuoByVar| |iExquo| |getStream| |getRef| |makeSeries| |mappingMode| + |categoryMode| |voidMode| |noValueMode| |jokerMode| GF2FG FG2F F2FG + |explogs2trigs| |trigs2explogs| |swap!| |fill!| |minIndex| |maxIndex| |entry?| + |indices| |index?| |entries| |categories| |search| |key?| |symbolIfCan| + |kernel| |argument| |constantKernel| |constantIfCan| |kovacic| |unknown| + |laplace| |trailingCoefficient| |normalizeIfCan| |polCase| |distFact| + |identification| |LyndonCoordinates| |LyndonBasis| |zeroDimensional?| + |fglmIfCan| |groebner| |lexTriangular| |squareFreeLexTriangular| |belong?| + |erf| |dilog| |li| |Ci| |Si| |Ei| |linGenPos| |groebgen| |totolex| |minPol| + |computeBasis| |coord| |anticoord| |intcompBasis| |choosemon| |transform| + |pack!| |library| |complexLimit| |limit| |linearlyDependent?| + |linearDependence| |solveLinear| |reducedSystem| |setDifference| + |setIntersection| |setUnion| |append| |null| |nil| |substitute| |duplicates?| + |mapGen| |mapExpon| |commutativeEquality| |leftMult| |rightMult| |makeUnit| + |reverse!| |reverse| |nthFactor| |nthExpon| |makeMulti| |makeTerm| + |listOfMonoms| |insert| |delete| |symmetricSquare| |factor1| + |symmetricProduct| |symmetricPower| |directSum| |\\/| |/\\| ~ |solveLinearPolynomialEquationByFractions| |hasSolution?| |linSolve| |LyndonWordsList| |LyndonWordsList1| |lyndonIfCan| |lyndon| |lyndon?| |numberOfComputedEntries| |rst| |frst| |lazyEvaluate| |lazy?| 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T) ((-107 #1=(-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T) ((-102) -3978 (|has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-1107)) (|has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-855)) (|has| |#2| (-1107))) ((-618 (-868)) -3978 (|has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-1107)) (|has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-855)) (|has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-618 (-868))) (|has| |#2| (-1107)) (|has| |#2| (-618 (-868)))) ((-151 #2=(-2 (|:| -4310 |#1|) (|:| -2264 |#2|))) . T) ((-619 (-540)) |has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-619 (-540))) ((-230 #1#) . T) ((-236 #1#) . T) ((-289 #3=(-551) #2#) . T) ((-289 |#1| |#2|) . T) ((-291 #3# #2#) . T) ((-291 |#1| |#2|) . T) ((-312 #2#) -12 (|has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-312 (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)))) (|has| (-2 (|:| -4310 |#1|) (|:| -2264 |#2|)) (-1107))) ((-312 |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) ((-285 #2#) . T) ((-376 #2#) . T) ((-494 #2#) . T) ((-494 |#2|) . 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T) ((-38 |#2|) |has| |#2| (-173)) ((-102) -3978 (|has| |#2| (-1107)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3978 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-111 $ $) |has| |#2| (-173)) ((-131) -3978 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131))) ((-621 #1=(-412 (-551))) -12 (|has| |#2| (-1044 (-412 (-551)))) (|has| |#2| (-1107))) ((-621 (-551)) -3978 (|has| |#2| (-1055)) (-12 (|has| |#2| (-1044 (-551))) (|has| |#2| (-1107))) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-621 |#2|) -3978 (|has| |#2| (-1107)) (|has| |#2| (-173))) ((-618 (-868)) -3978 (|has| |#2| (-1107)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-618 (-868))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-618 (-1272 |#2|)) . T) ((-173) |has| |#2| (-173)) ((-232 |#2|) |has| |#2| (-1055)) ((-234) -12 (|has| |#2| (-234)) (|has| |#2| (-1055))) ((-289 #2=(-551) |#2|) . T) ((-291 #2# |#2|) . T) ((-312 |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) ((-372) |has| |#2| (-372)) ((-381 |#2|) |has| |#2| (-1055)) ((-417 |#2|) |has| |#2| (-1107)) ((-494 |#2|) . T) ((-609 #2# |#2|) . T) ((-519 |#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) ((-651 (-551)) -3978 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 |#2|) -3978 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 $) -3978 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-653 |#2|) -3978 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-653 $) -3978 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-645 |#2|) -3978 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-644 (-551)) -12 (|has| |#2| (-644 (-551))) (|has| |#2| (-1055))) ((-644 |#2|) |has| |#2| (-1055)) ((-722 |#2|) -3978 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-731) -3978 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-796) |has| |#2| (-853)) ((-797) -3978 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-798) |has| |#2| (-798)) ((-799) -3978 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-802) -3978 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-853) |has| |#2| (-853)) ((-855) -3978 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-906 (-1183)) -12 (|has| |#2| (-906 (-1183))) (|has| |#2| (-1055))) ((-1044 #1#) -12 (|has| |#2| (-1044 (-412 (-551)))) (|has| |#2| (-1107))) ((-1044 (-551)) -12 (|has| |#2| (-1044 (-551))) (|has| |#2| (-1107))) ((-1044 |#2|) |has| |#2| (-1107)) ((-1057 |#2|) -3978 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1057 $) |has| |#2| (-173)) ((-1062 |#2|) -3978 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1062 $) |has| |#2| (-173)) ((-1055) -3978 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1063) -3978 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1118) -3978 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-1107) -3978 (|has| |#2| (-1107)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1222) . T) ((-1280 |#2|) |has| |#2| (-367))) +((-2986 (((-112) $ $) NIL (|has| |#2| (-1107)))) (-3626 (((-112) $) NIL (|has| |#2| (-131)))) (-4157 (($ (-925)) 65 (|has| |#2| (-1055)))) (-2390 (((-1278) $ (-551) (-551)) NIL (|has| $ (-6 -4444)))) (-2823 (($ $ $) 70 (|has| |#2| (-798)))) (-1410 (((-3 $ "failed") $ $) 57 (|has| |#2| (-131)))) (-1312 (((-112) $ (-776)) 17)) (-3558 (((-776)) NIL (|has| |#2| (-372)))) (-4073 (((-551) $) NIL (|has| |#2| (-853)))) (-4237 ((|#2| $ (-551) |#2|) NIL (|has| $ (-6 -4444)))) (-4174 (($) NIL T CONST)) (-3595 (((-3 (-551) #1="failed") $) NIL (-12 (|has| |#2| (-1044 (-551))) (|has| |#2| (-1107)))) (((-3 (-412 (-551)) #1#) $) NIL (-12 (|has| |#2| (-1044 (-412 (-551)))) (|has| |#2| (-1107)))) (((-3 |#2| #1#) $) 34 (|has| |#2| (-1107)))) (-3594 (((-551) $) NIL (-12 (|has| |#2| (-1044 (-551))) (|has| |#2| (-1107)))) (((-412 (-551)) $) NIL (-12 (|has| |#2| (-1044 (-412 (-551)))) (|has| |#2| (-1107)))) ((|#2| $) 32 (|has| |#2| (-1107)))) (-2445 (((-694 (-551)) (-694 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T) ((-173) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-619 (-540)) -12 (|has| |#1| (-619 (-540))) (|has| |#3| (-619 (-540)))) ((-619 (-896 (-382))) -12 (|has| |#1| (-619 (-896 (-382)))) (|has| |#3| (-619 (-896 (-382))))) ((-619 (-896 (-551))) -12 (|has| |#1| (-619 (-896 (-551)))) (|has| |#3| (-619 (-896 (-551))))) ((-232 |#1|) . T) ((-234) |has| |#1| (-234)) ((-293) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-312 $) . T) ((-329 |#1| |#4|) . T) ((-381 |#1|) . T) ((-417 |#1|) . T) ((-457) -3972 (|has| |#1| (-916)) (|has| |#1| (-457))) ((-519 |#2| |#1|) |has| |#1| (-234)) ((-519 |#2| $) |has| |#1| (-234)) ((-519 |#3| |#1|) . T) ((-519 |#3| $) . T) ((-519 $ $) . T) ((-562) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-651 #1#) |has| |#1| (-38 (-412 (-551)))) ((-651 (-551)) . T) ((-651 |#1|) . T) ((-651 $) . T) ((-653 #1#) |has| |#1| (-38 (-412 (-551)))) ((-653 |#1|) . T) ((-653 $) . T) ((-645 #1#) |has| |#1| (-38 (-412 (-551)))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-644 (-551)) |has| |#1| (-644 (-551))) ((-644 |#1|) . T) ((-722 #1#) |has| |#1| (-38 (-412 (-551)))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-731) . T) ((-906 (-1183)) |has| |#1| (-906 (-1183))) ((-906 |#3|) . T) ((-892 (-382)) -12 (|has| |#1| (-892 (-382))) (|has| |#3| (-892 (-382)))) ((-892 (-551)) -12 (|has| |#1| (-892 (-551))) (|has| |#3| (-892 (-551)))) ((-956 |#1| |#4| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1044 (-412 (-551))) |has| |#1| (-1044 (-412 (-551)))) ((-1044 (-551)) |has| |#1| (-1044 (-551))) ((-1044 |#1|) . T) ((-1044 |#2|) . T) ((-1044 |#3|) . T) ((-1057 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1057 |#1|) . T) ((-1057 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1062 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1062 |#1|) . T) ((-1062 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1055) . T) ((-1063) . T) ((-1118) . T) ((-1107) . T) ((-1227) |has| |#1| (-916))) -((-2980 (((-112) $ $) 19 (|has| |#1| (-1107)))) (-1601 ((|#1| $) 55)) (-3760 ((|#1| $) 45)) (-1312 (((-112) $ (-776)) 8)) (-4168 (($) 7 T CONST)) (-3415 (($ $) 61)) (-2454 (($ $) 49)) (-3762 ((|#1| |#1| $) 47)) (-3761 ((|#1| $) 46)) (-2133 (((-646 |#1|) $) 31 (|has| $ (-6 -4437)))) (-4163 (((-112) $ (-776)) 9)) (-3020 (((-646 |#1|) $) 30 (|has| $ (-6 -4437)))) (-3678 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1107)) (|has| $ (-6 -4437))))) (-2137 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4438)))) (-4402 (($ (-1 |#1| |#1|) $) 36)) (-4160 (((-112) $ (-776)) 10)) (-4277 (((-776) $) 62)) (-3675 (((-1165) $) 22 (|has| |#1| (-1107)))) (-1372 ((|#1| $) 40)) (-1599 ((|#1| |#1| $) 53)) (-1598 ((|#1| |#1| $) 52)) (-4051 (($ |#1| $) 41)) (-3015 (((-776) $) 56)) (-3676 (((-1126) $) 21 (|has| |#1| (-1107)))) (-3414 ((|#1| $) 63)) (-1597 ((|#1| $) 51)) (-1596 ((|#1| $) 50)) (-1373 ((|#1| $) 42)) (-2135 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4437)))) (-4211 (($ $ (-646 (-296 |#1|))) 27 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (($ $ (-296 |#1|)) 26 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (($ $ (-646 |#1|) (-646 |#1|)) 24 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))))) (-1313 (((-112) $ $) 14)) (-3417 ((|#1| |#1| $) 59)) (-3839 (((-112) $) 11)) (-4008 (($) 12)) (-3416 ((|#1| $) 60)) (-1602 (($) 58) (($ (-646 |#1|)) 57)) (-3759 (((-776) $) 44)) (-2134 (((-776) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4437))) (((-776) |#1| $) 29 (-12 (|has| |#1| (-1107)) (|has| $ (-6 -4437))))) (-3836 (($ $) 13)) (-4390 (((-868) $) 18 (|has| |#1| (-618 (-868))))) (-1600 ((|#1| $) 54)) (-3674 (((-112) $ $) 23 (|has| |#1| (-1107)))) (-1374 (($ (-646 |#1|)) 43)) (-3413 ((|#1| $) 64)) (-2136 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4437)))) (-3467 (((-112) $ $) 20 (|has| |#1| (-1107)))) (-4401 (((-776) $) 6 (|has| $ (-6 -4437))))) +((-1630 (*1 *2 *3) (-12 (-4 *4 (-1055)) (-4 *3 (-855)) (-4 *5 (-268 *3)) (-4 *6 (-798)) (-5 *2 (-1 *1 (-776))) (-4 *1 (-255 *4 *3 *5 *6)))) (-1596 (*1 *2 *1) (-12 (-4 *1 (-255 *3 *4 *5 *6)) (-4 *3 (-1055)) (-4 *4 (-855)) (-4 *5 (-268 *4)) (-4 *6 (-798)) (-5 *2 (-646 *4)))) (-4221 (*1 *2 *1 *3) (-12 (-4 *1 (-255 *4 *3 *5 *6)) (-4 *4 (-1055)) (-4 *3 (-855)) (-4 *5 (-268 *3)) (-4 *6 (-798)) (-5 *2 (-776)))) (-4221 (*1 *2 *1) (-12 (-4 *1 (-255 *3 *4 *5 *6)) (-4 *3 (-1055)) (-4 *4 (-855)) (-4 *5 (-268 *4)) (-4 *6 (-798)) (-5 *2 (-776)))) (-4398 (*1 *2 *1 *3) (-12 (-4 *1 (-255 *4 *3 *5 *6)) (-4 *4 (-1055)) (-4 *3 (-855)) (-4 *5 (-268 *3)) (-4 *6 (-798)) (-5 *2 (-776)))) (-1595 (*1 *2 *1) (-12 (-4 *1 (-255 *3 *4 *5 *6)) (-4 *3 (-1055)) (-4 *4 (-855)) (-4 *5 (-268 *4)) (-4 *6 (-798)) (-5 *2 (-646 (-776))))) (-1629 (*1 *2 *1) (-12 (-4 *1 (-255 *3 *4 *5 *6)) (-4 *3 (-1055)) (-4 *4 (-855)) (-4 *5 (-268 *4)) (-4 *6 (-798)) (-5 *2 (-776)))) (-1595 (*1 *2 *1 *3) (-12 (-4 *1 (-255 *4 *3 *5 *6)) (-4 *4 (-1055)) (-4 *3 (-855)) (-4 *5 (-268 *3)) (-4 *6 (-798)) (-5 *2 (-646 (-776))))) (-1629 (*1 *2 *1 *3) (-12 (-4 *1 (-255 *4 *3 *5 *6)) (-4 *4 (-1055)) (-4 *3 (-855)) (-4 *5 (-268 *3)) (-4 *6 (-798)) (-5 *2 (-776)))) (-1594 (*1 *2 *1) (-12 (-4 *1 (-255 *3 *4 *5 *6)) (-4 *3 (-1055)) (-4 *4 (-855)) (-4 *5 (-268 *4)) (-4 *6 (-798)) (-5 *2 (-112)))) (-1593 (*1 *2 *1) (-12 (-4 *1 (-255 *3 *4 *2 *5)) (-4 *3 (-1055)) (-4 *4 (-855)) (-4 *5 (-798)) (-4 *2 (-268 *4)))) (-1592 (*1 *1 *1) (-12 (-4 *1 (-255 *2 *3 *4 *5)) (-4 *2 (-1055)) (-4 *3 (-855)) (-4 *4 (-268 *3)) (-4 *5 (-798)))) (-1591 (*1 *1 *1) (-12 (-4 *1 (-255 *2 *3 *4 *5)) (-4 *2 (-1055)) (-4 *3 (-855)) (-4 *4 (-268 *3)) (-4 *5 (-798)))) (-1630 (*1 *2 *1) (-12 (-4 *3 (-234)) (-4 *3 (-1055)) (-4 *4 (-855)) (-4 *5 (-268 *4)) (-4 *6 (-798)) (-5 *2 (-1 *1 (-776))) (-4 *1 (-255 *3 *4 *5 *6))))) +(-13 (-956 |t#1| |t#4| |t#3|) (-232 |t#1|) (-1044 |t#2|) (-10 -8 (-15 -1630 ((-1 $ (-776)) |t#2|)) (-15 -1596 ((-646 |t#2|) $)) (-15 -4221 ((-776) $ |t#2|)) (-15 -4221 ((-776) $)) (-15 -4398 ((-776) $ |t#2|)) (-15 -1595 ((-646 (-776)) $)) (-15 -1629 ((-776) $)) (-15 -1595 ((-646 (-776)) $ |t#2|)) (-15 -1629 ((-776) $ |t#2|)) (-15 -1594 ((-112) $)) (-15 -1593 (|t#3| $)) (-15 -1592 ($ $)) (-15 -1591 ($ $)) (IF (|has| |t#1| (-234)) (PROGN (-6 (-519 |t#2| |t#1|)) (-6 (-519 |t#2| $)) (-6 (-312 $)) (-15 -1630 ((-1 $ (-776)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #1=(-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((-38 |#1|) |has| |#1| (-173)) ((-38 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-412 (-551)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-621 #1#) -3978 (|has| |#1| (-1044 (-412 (-551)))) (|has| |#1| (-38 (-412 (-551))))) ((-621 (-551)) . T) ((-621 |#1|) . T) ((-621 |#2|) . T) ((-621 |#3|) . T) ((-621 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-618 (-868)) . T) ((-173) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-619 (-540)) -12 (|has| |#1| (-619 (-540))) (|has| |#3| (-619 (-540)))) ((-619 (-896 (-382))) -12 (|has| |#1| (-619 (-896 (-382)))) (|has| |#3| (-619 (-896 (-382))))) ((-619 (-896 (-551))) -12 (|has| |#1| (-619 (-896 (-551)))) (|has| |#3| (-619 (-896 (-551))))) ((-232 |#1|) . T) ((-234) |has| |#1| (-234)) ((-293) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-312 $) . T) ((-329 |#1| |#4|) . T) ((-381 |#1|) . T) ((-417 |#1|) . T) ((-457) -3978 (|has| |#1| (-916)) (|has| |#1| (-457))) ((-519 |#2| |#1|) |has| |#1| (-234)) ((-519 |#2| $) |has| |#1| (-234)) ((-519 |#3| |#1|) . T) ((-519 |#3| $) . T) ((-519 $ $) . T) ((-562) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-651 #1#) |has| |#1| (-38 (-412 (-551)))) ((-651 (-551)) . T) ((-651 |#1|) . T) ((-651 $) . T) ((-653 #1#) |has| |#1| (-38 (-412 (-551)))) ((-653 |#1|) . T) ((-653 $) . T) ((-645 #1#) |has| |#1| (-38 (-412 (-551)))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-644 (-551)) |has| |#1| (-644 (-551))) ((-644 |#1|) . T) ((-722 #1#) |has| |#1| (-38 (-412 (-551)))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-731) . T) ((-906 (-1183)) |has| |#1| (-906 (-1183))) ((-906 |#3|) . T) ((-892 (-382)) -12 (|has| |#1| (-892 (-382))) (|has| |#3| (-892 (-382)))) ((-892 (-551)) -12 (|has| |#1| (-892 (-551))) (|has| |#3| (-892 (-551)))) ((-956 |#1| |#4| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1044 (-412 (-551))) |has| |#1| (-1044 (-412 (-551)))) ((-1044 (-551)) |has| |#1| (-1044 (-551))) ((-1044 |#1|) . T) ((-1044 |#2|) . T) ((-1044 |#3|) . T) ((-1057 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1057 |#1|) . T) ((-1057 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1062 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1062 |#1|) . T) ((-1062 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1055) . T) ((-1063) . T) ((-1118) . T) ((-1107) . T) ((-1227) |has| |#1| (-916))) +((-2986 (((-112) $ $) 19 (|has| |#1| (-1107)))) (-1602 ((|#1| $) 55)) (-3766 ((|#1| $) 45)) (-1312 (((-112) $ (-776)) 8)) (-4174 (($) 7 T CONST)) (-3421 (($ $) 61)) (-2460 (($ $) 49)) (-3768 ((|#1| |#1| $) 47)) (-3767 ((|#1| $) 46)) (-2134 (((-646 |#1|) $) 31 (|has| $ (-6 -4443)))) (-4169 (((-112) $ (-776)) 9)) (-3026 (((-646 |#1|) $) 30 (|has| $ (-6 -4443)))) (-3684 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1107)) (|has| $ (-6 -4443))))) (-2138 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4444)))) (-4408 (($ (-1 |#1| |#1|) $) 36)) (-4166 (((-112) $ (-776)) 10)) (-4283 (((-776) $) 62)) (-3681 (((-1165) $) 22 (|has| |#1| (-1107)))) (-1372 ((|#1| $) 40)) (-1600 ((|#1| |#1| $) 53)) (-1599 ((|#1| |#1| $) 52)) (-4057 (($ |#1| $) 41)) (-3021 (((-776) $) 56)) (-3682 (((-1126) $) 21 (|has| |#1| (-1107)))) (-3420 ((|#1| $) 63)) (-1598 ((|#1| $) 51)) (-1597 ((|#1| $) 50)) (-1373 ((|#1| $) 42)) (-2136 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4443)))) (-4217 (($ $ (-646 (-296 |#1|))) 27 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (($ $ (-296 |#1|)) 26 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (($ $ (-646 |#1|) (-646 |#1|)) 24 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))))) (-1313 (((-112) $ $) 14)) (-3423 ((|#1| |#1| $) 59)) (-3845 (((-112) $) 11)) (-4014 (($) 12)) (-3422 ((|#1| $) 60)) (-1603 (($) 58) (($ (-646 |#1|)) 57)) (-3765 (((-776) $) 44)) (-2135 (((-776) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4443))) (((-776) |#1| $) 29 (-12 (|has| |#1| (-1107)) (|has| $ (-6 -4443))))) (-3842 (($ $) 13)) (-4396 (((-868) $) 18 (|has| |#1| (-618 (-868))))) (-1601 ((|#1| $) 54)) (-3680 (((-112) $ $) 23 (|has| |#1| (-1107)))) (-1374 (($ (-646 |#1|)) 43)) (-3419 ((|#1| $) 64)) (-2137 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4443)))) (-3473 (((-112) $ $) 20 (|has| |#1| (-1107)))) (-4407 (((-776) $) 6 (|has| $ (-6 -4443))))) (((-256 |#1|) (-140) (-1222)) (T -256)) -((-1602 (*1 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1602 (*1 *1 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-1222)) (-4 *1 (-256 *3)))) (-3015 (*1 *2 *1) (-12 (-4 *1 (-256 *3)) (-4 *3 (-1222)) (-5 *2 (-776)))) (-1601 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1600 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1599 (*1 *2 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1598 (*1 *2 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1597 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1596 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-2454 (*1 *1 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222))))) -(-13 (-1127 |t#1|) (-1001 |t#1|) (-10 -8 (-15 -1602 ($)) (-15 -1602 ($ (-646 |t#1|))) (-15 -3015 ((-776) $)) (-15 -1601 (|t#1| $)) (-15 -1600 (|t#1| $)) (-15 -1599 (|t#1| |t#1| $)) (-15 -1598 (|t#1| |t#1| $)) (-15 -1597 (|t#1| $)) (-15 -1596 (|t#1| $)) (-15 -2454 ($ $)))) -(((-34) . T) ((-107 |#1|) . T) ((-102) |has| |#1| (-1107)) ((-618 (-868)) -3972 (|has| |#1| (-1107)) (|has| |#1| (-618 (-868)))) ((-312 |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) ((-494 |#1|) . T) ((-519 |#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) ((-1001 |#1|) . T) ((-1107) |has| |#1| (-1107)) ((-1127 |#1|) . T) ((-1222) . T)) -((-1603 (((-1139 (-226)) (-888 |#1|) (-1098 (-382)) (-1098 (-382))) 75) (((-1139 (-226)) (-888 |#1|) (-1098 (-382)) (-1098 (-382)) (-646 (-263))) 74) (((-1139 (-226)) |#1| (-1098 (-382)) (-1098 (-382))) 65) (((-1139 (-226)) |#1| (-1098 (-382)) (-1098 (-382)) (-646 (-263))) 64) (((-1139 (-226)) (-885 |#1|) (-1098 (-382))) 56) (((-1139 (-226)) (-885 |#1|) (-1098 (-382)) (-646 (-263))) 55)) (-1610 (((-1276) (-888 |#1|) (-1098 (-382)) (-1098 (-382))) 78) (((-1276) (-888 |#1|) (-1098 (-382)) (-1098 (-382)) (-646 (-263))) 77) (((-1276) |#1| (-1098 (-382)) (-1098 (-382))) 68) (((-1276) |#1| (-1098 (-382)) (-1098 (-382)) (-646 (-263))) 67) (((-1276) (-885 |#1|) (-1098 (-382))) 60) (((-1276) (-885 |#1|) (-1098 (-382)) (-646 (-263))) 59) (((-1275) (-883 |#1|) (-1098 (-382))) 47) (((-1275) (-883 |#1|) (-1098 (-382)) (-646 (-263))) 46) (((-1275) |#1| (-1098 (-382))) 38) (((-1275) |#1| (-1098 (-382)) (-646 (-263))) 36))) -(((-257 |#1|) (-10 -7 (-15 -1610 ((-1275) |#1| (-1098 (-382)) (-646 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T) ((-653 #1#) |has| |#1| (-38 (-412 (-551)))) ((-653 |#1|) . T) ((-653 $) . T) ((-645 #1#) |has| |#1| (-38 (-412 (-551)))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-644 (-551)) |has| |#1| (-644 (-551))) ((-644 |#1|) . T) ((-722 #1#) |has| |#1| (-38 (-412 (-551)))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-731) . T) ((-906 |#3|) . T) ((-892 (-382)) -12 (|has| |#1| (-892 (-382))) (|has| |#3| (-892 (-382)))) ((-892 (-551)) -12 (|has| |#1| (-892 (-551))) (|has| |#3| (-892 (-551)))) ((-956 |#1| |#2| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1044 (-412 (-551))) |has| |#1| (-1044 (-412 (-551)))) ((-1044 (-551)) |has| |#1| (-1044 (-551))) ((-1044 |#1|) . T) ((-1044 |#3|) . T) ((-1057 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1057 |#1|) . T) ((-1057 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1062 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1062 |#1|) . T) ((-1062 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1055) . T) ((-1063) . T) ((-1118) . T) ((-1107) . T) ((-1227) |has| |#1| (-916))) +((-2986 (((-112) $ $) NIL)) (-3681 (((-1165) $) NIL)) (-3619 (((-646 (-1141)) $) 18)) (-3682 (((-1126) $) NIL)) (-4396 (((-868) $) 27) (($ (-1188)) NIL) (((-1188) $) NIL)) (-3671 (((-1141) $) 20)) (-3680 (((-112) $ $) NIL)) (-3473 (((-112) $ $) NIL))) +(((-1072) (-13 (-1089) (-10 -8 (-15 -3619 ((-646 (-1141)) $)) (-15 -3671 ((-1141) $))))) (T -1072)) +((-3619 (*1 *2 *1) (-12 (-5 *2 (-646 (-1141))) (-5 *1 (-1072)))) (-3671 (*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-1072))))) +(-13 (-1089) (-10 -8 (-15 -3619 ((-646 (-1141)) $)) (-15 -3671 ((-1141) $)))) +((-3626 (((-112) |#3| $) 15)) (-3621 (((-3 $ "failed") |#3| (-925)) 29)) (-3908 (((-3 |#3| "failed") |#3| $) 45)) (-3624 (((-112) |#3| $) 19)) (-3625 (((-112) |#3| $) 17))) +(((-1073 |#1| |#2| |#3|) (-10 -8 (-15 -3621 ((-3 |#1| "failed") |#3| (-925))) (-15 -3908 ((-3 |#3| "failed") |#3| |#1|)) (-15 -3624 ((-112) |#3| |#1|)) (-15 -3625 ((-112) |#3| |#1|)) (-15 -3626 ((-112) |#3| |#1|))) (-1074 |#2| |#3|) (-13 (-853) (-367)) (-1248 |#2|)) (T -1073)) +NIL +(-10 -8 (-15 -3621 ((-3 |#1| "failed") |#3| (-925))) (-15 -3908 ((-3 |#3| "failed") |#3| |#1|)) (-15 -3624 ((-112) |#3| |#1|)) (-15 -3625 ((-112) |#3| |#1|)) (-15 -3626 ((-112) |#3| |#1|))) +((-2986 (((-112) $ $) 7)) (-3626 (((-112) |#2| $) 22)) (-4073 (((-551) |#2| $) 23)) (-3621 (((-3 $ "failed") |#2| (-925)) 16)) (-3620 ((|#1| |#2| $ |#1|) 14)) (-3908 (((-3 |#2| "failed") |#2| $) 19)) (-3624 (((-112) |#2| $) 20)) (-3625 (((-112) |#2| $) 21)) (-3681 (((-1165) $) 10)) (-3682 (((-1126) $) 11)) (-3623 ((|#2| $) 18)) (-4396 (((-868) $) 12)) (-3680 (((-112) $ $) 9)) (-4219 ((|#1| |#2| $ |#1|) 15)) (-3622 (((-646 $) |#2|) 17)) (-3473 (((-112) $ $) 6))) (((-1074 |#1| |#2|) (-140) (-13 (-853) (-367)) (-1248 |t#1|)) (T -1074)) -((-4067 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-551)))) (-3620 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3619 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3618 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3902 (*1 *2 *2 *1) (|partial| -12 (-4 *1 (-1074 *3 *2)) (-4 *3 (-13 (-853) (-367))) (-4 *2 (-1248 *3)))) (-3617 (*1 *2 *1) (-12 (-4 *1 (-1074 *3 *2)) (-4 *3 (-13 (-853) (-367))) (-4 *2 (-1248 *3)))) (-3616 (*1 *2 *3) (-12 (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-646 *1)) (-4 *1 (-1074 *4 *3)))) (-3615 (*1 *1 *2 *3) (|partial| -12 (-5 *3 (-925)) (-4 *4 (-13 (-853) (-367))) (-4 *1 (-1074 *4 *2)) (-4 *2 (-1248 *4)))) (-4213 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1074 *2 *3)) (-4 *2 (-13 (-853) (-367))) (-4 *3 (-1248 *2)))) (-3614 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1074 *2 *3)) (-4 *2 (-13 (-853) (-367))) (-4 *3 (-1248 *2))))) -(-13 (-1107) (-10 -8 (-15 -4067 ((-551) |t#2| $)) (-15 -3620 ((-112) |t#2| $)) (-15 -3619 ((-112) |t#2| $)) (-15 -3618 ((-112) |t#2| $)) (-15 -3902 ((-3 |t#2| "failed") |t#2| $)) (-15 -3617 (|t#2| $)) (-15 -3616 ((-646 $) |t#2|)) (-15 -3615 ((-3 $ "failed") |t#2| (-925))) (-15 -4213 (|t#1| |t#2| $ |t#1|)) (-15 -3614 (|t#1| |t#2| $ |t#1|)))) +((-4073 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-551)))) (-3626 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3625 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3624 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3908 (*1 *2 *2 *1) (|partial| -12 (-4 *1 (-1074 *3 *2)) (-4 *3 (-13 (-853) (-367))) (-4 *2 (-1248 *3)))) (-3623 (*1 *2 *1) (-12 (-4 *1 (-1074 *3 *2)) (-4 *3 (-13 (-853) (-367))) (-4 *2 (-1248 *3)))) (-3622 (*1 *2 *3) (-12 (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-646 *1)) (-4 *1 (-1074 *4 *3)))) (-3621 (*1 *1 *2 *3) (|partial| -12 (-5 *3 (-925)) (-4 *4 (-13 (-853) (-367))) (-4 *1 (-1074 *4 *2)) (-4 *2 (-1248 *4)))) (-4219 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1074 *2 *3)) (-4 *2 (-13 (-853) (-367))) (-4 *3 (-1248 *2)))) (-3620 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1074 *2 *3)) (-4 *2 (-13 (-853) (-367))) (-4 *3 (-1248 *2))))) +(-13 (-1107) (-10 -8 (-15 -4073 ((-551) |t#2| $)) (-15 -3626 ((-112) |t#2| $)) (-15 -3625 ((-112) |t#2| $)) (-15 -3624 ((-112) |t#2| $)) (-15 -3908 ((-3 |t#2| "failed") |t#2| $)) (-15 -3623 (|t#2| $)) (-15 -3622 ((-646 $) |t#2|)) (-15 -3621 ((-3 $ "failed") |t#2| (-925))) (-15 -4219 (|t#1| |t#2| $ |t#1|)) (-15 -3620 (|t#1| |t#2| $ |t#1|)))) (((-102) . 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T) ((-23) . T) ((-47 |#1| #1=(-551)) . T) ((-25) . T) ((-38 #2=(-412 (-551))) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-38 |#1|) |has| |#1| (-173)) ((-38 |#2|) |has| |#1| (-367)) ((-38 $) -3972 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-35) |has| |#1| (-38 (-412 (-551)))) ((-95) |has| |#1| (-38 (-412 (-551)))) ((-102) . T) ((-111 #2# #2#) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-367)) ((-111 $ $) -3972 (|has| |#1| (-562)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) -3972 (-12 (|has| |#1| (-367)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -3972 (-12 (|has| |#1| (-367)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-621 #2#) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-621 (-551)) . T) ((-621 #3=(-1183)) -12 (|has| |#1| (-367)) (|has| |#2| (-1044 (-1183)))) ((-621 |#1|) |has| |#1| (-173)) ((-621 |#2|) . 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T) ((-651 |#1|) . T) ((-651 |#2|) |has| |#1| (-367)) ((-651 $) . T) ((-653 #2#) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-653 |#1|) . T) ((-653 |#2|) |has| |#1| (-367)) ((-653 $) . T) ((-645 #2#) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-645 |#1|) |has| |#1| (-173)) ((-645 |#2|) |has| |#1| (-367)) ((-645 $) -3972 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-644 (-551)) -12 (|has| |#1| (-367)) (|has| |#2| (-644 (-551)))) ((-644 |#2|) |has| |#1| (-367)) ((-722 #2#) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-722 |#1|) |has| |#1| (-173)) ((-722 |#2|) |has| |#1| (-367)) ((-722 $) -3972 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-731) . 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T) ((-23) . T) ((-47 |#1| #1=(-551)) . T) ((-25) . T) ((-38 #2=(-412 (-551))) -3978 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-38 |#1|) |has| |#1| (-173)) ((-38 |#2|) |has| |#1| (-367)) ((-38 $) -3978 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-35) |has| |#1| (-38 (-412 (-551)))) ((-95) |has| |#1| (-38 (-412 (-551)))) ((-102) . T) ((-111 #2# #2#) -3978 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-367)) ((-111 $ $) -3978 (|has| |#1| (-562)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) -3978 (-12 (|has| |#1| (-367)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -3978 (-12 (|has| |#1| (-367)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-621 #2#) -3978 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-621 (-551)) . T) ((-621 #3=(-1183)) -12 (|has| |#1| (-367)) (|has| |#2| (-1044 (-1183)))) ((-621 |#1|) |has| |#1| (-173)) ((-621 |#2|) . 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T) ((-651 |#1|) . T) ((-651 |#2|) |has| |#1| (-367)) ((-651 $) . T) ((-653 #2#) -3978 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-653 |#1|) . T) ((-653 |#2|) |has| |#1| (-367)) ((-653 $) . T) ((-645 #2#) -3978 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-645 |#1|) |has| |#1| (-173)) ((-645 |#2|) |has| |#1| (-367)) ((-645 $) -3978 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-644 (-551)) -12 (|has| |#1| (-367)) (|has| |#2| (-644 (-551)))) ((-644 |#2|) |has| |#1| (-367)) ((-722 #2#) -3978 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-722 |#1|) |has| |#1| (-173)) ((-722 |#2|) |has| |#1| (-367)) ((-722 $) -3978 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-731) . 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T) ((-23) . T) ((-47 |#1| #1=(-776)) . T) ((-25) . T) ((-38 #2=(-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((-38 |#1|) |has| |#1| (-173)) ((-38 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-102) . T) ((-111 #2# #2#) |has| |#1| (-38 (-412 (-551)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-621 #2#) -3972 (|has| |#1| (-1044 (-412 (-551)))) (|has| |#1| (-38 (-412 (-551))))) ((-621 (-551)) . T) ((-621 #3=(-1088)) . T) ((-621 |#1|) . T) ((-621 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-618 (-868)) . 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T) ((-1057 #2#) |has| |#1| (-38 (-412 (-551)))) ((-1057 |#1|) . T) ((-1057 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1062 #2#) |has| |#1| (-38 (-412 (-551)))) ((-1062 |#1|) . T) ((-1062 $) -3978 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1055) . T) ((-1063) . T) ((-1118) . T) ((-1107) . 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3178243 3178347 3178552 "XEXPPKG" 3179002 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1288 3176352 3178093 3178189 "XDPOLY" 3178194 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1287 3175159 3175759 3175802 "XALG" 3175807 NIL XALG (NIL T) -9 NIL 3175918 NIL) (-1286 3168628 3173136 3173630 "WUTSET" 3174751 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1285 3166884 3167680 3168003 "WP" 3168439 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1284 3166486 3166706 3166776 "WHILEAST" 3166836 T WHILEAST (NIL) -8 NIL NIL NIL) (-1283 3165958 3166203 3166297 "WHEREAST" 3166414 T WHEREAST (NIL) -8 NIL NIL NIL) (-1282 3164844 3165042 3165337 "WFFINTBS" 3165755 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1281 3162748 3163175 3163637 "WEIER" 3164416 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1280 3161794 3162244 3162286 "VSPACE" 3162422 NIL VSPACE (NIL T) -9 NIL 3162496 NIL) (-1279 3161632 3161659 3161750 "VSPACE-" 3161755 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1278 3161441 3161483 3161551 "VOID" 3161586 T VOID (NIL) -8 NIL NIL NIL) (-1277 3157865 3158504 3159241 "VIEWDEF" 3160726 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1276 3147169 3149413 3151586 "VIEW3D" 3155714 T VIEW3D (NIL) -8 NIL NIL NIL) (-1275 3139420 3141080 3142659 "VIEW2D" 3145612 T VIEW2D (NIL) -8 NIL NIL NIL) (-1274 3137556 3137915 3138321 "VIEW" 3139036 T VIEW (NIL) -7 NIL NIL NIL) (-1273 3136133 3136392 3136710 "VECTOR2" 3137286 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1272 3131486 3135903 3135995 "VECTOR" 3136076 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1271 3124960 3129267 3129310 "VECTCAT" 3130305 NIL VECTCAT (NIL T) -9 NIL 3130892 NIL) (-1270 3123974 3124228 3124618 "VECTCAT-" 3124623 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1269 3123428 3123625 3123745 "VARIABLE" 3123889 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1268 3123361 3123366 3123396 "UTYPE" 3123401 T UTYPE (NIL) -9 NIL NIL NIL) (-1267 3122191 3122345 3122607 "UTSODETL" 3123187 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1266 3119631 3120091 3120615 "UTSODE" 3121732 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1265 3110505 3115872 3115915 "UTSCAT" 3117027 NIL UTSCAT (NIL T) -9 NIL 3117785 NIL) (-1264 3107852 3108575 3109564 "UTSCAT-" 3109569 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1263 3107479 3107522 3107655 "UTS2" 3107803 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1262 3099316 3105105 3105594 "UTS" 3107048 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3093543 3096154 3096197 "URAGG" 3098267 NIL URAGG (NIL T) -9 NIL 3098990 NIL) (-1260 3090485 3091347 3092469 "URAGG-" 3092474 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1259 3086201 3089120 3089585 "UPXSSING" 3090149 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1258 3079276 3086105 3086177 "UPXSCONS" 3086182 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1257 3069023 3075814 3075876 "UPXSCCA" 3076450 NIL UPXSCCA (NIL T T) -9 NIL 3076683 NIL) (-1256 3068661 3068746 3068920 "UPXSCCA-" 3068925 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1255 3058260 3064824 3064867 "UPXSCAT" 3065515 NIL UPXSCAT (NIL T) -9 NIL 3066124 NIL) (-1254 3057690 3057769 3057948 "UPXS2" 3058175 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1253 3049760 3056937 3057210 "UPXS" 3057475 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1252 3048417 3048669 3049019 "UPSQFREE" 3049504 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1251 3041838 3044895 3044950 "UPSCAT" 3046111 NIL UPSCAT (NIL T T) -9 NIL 3046885 NIL) (-1250 3041042 3041249 3041576 "UPSCAT-" 3041581 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1249 3040669 3040712 3040845 "UPOLYC2" 3040993 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1248 3026357 3034092 3034135 "UPOLYC" 3036236 NIL UPOLYC (NIL T) -9 NIL 3037457 NIL) (-1247 3017721 3020135 3023270 "UPOLYC-" 3023275 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1246 3017060 3017167 3017331 "UPMP" 3017610 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1245 3016613 3016694 3016833 "UPDIVP" 3016973 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1244 3015181 3015430 3015746 "UPDECOMP" 3016362 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1243 3014416 3014528 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2931295 2931814 2932353 "TUBETOOL" 2933087 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1218 2930144 2930349 2930590 "TUBE" 2931088 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1217 2918784 2922903 2923000 "TSETCAT" 2928269 NIL TSETCAT (NIL T T T T) -9 NIL 2929800 NIL) (-1216 2913516 2915116 2917007 "TSETCAT-" 2917012 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1215 2908245 2912488 2912771 "TS" 2913268 NIL TS (NIL T) -8 NIL NIL NIL) (-1214 2902884 2903731 2904660 "TRMANIP" 2907381 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1213 2902325 2902388 2902551 "TRIMAT" 2902816 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1212 2900191 2900428 2900785 "TRIGMNIP" 2902074 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1211 2899711 2899824 2899854 "TRIGCAT" 2900067 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1210 2899380 2899459 2899600 "TRIGCAT-" 2899605 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1209 2896226 2898238 2898519 "TREE" 2899134 NIL TREE (NIL T) -8 NIL NIL NIL) (-1208 2895500 2896028 2896058 "TRANFUN" 2896093 T TRANFUN (NIL) -9 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NIL NIL NIL) (-1195 2867097 2873562 2873655 "TABLE" 2873660 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1194 2861705 2862925 2864173 "TABLBUMP" 2865883 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1193 2860927 2861074 2861255 "SYSTEM" 2861546 T SYSTEM (NIL) -8 NIL NIL NIL) (-1192 2857386 2858085 2858868 "SYSSOLP" 2860178 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1191 2857184 2857341 2857372 "SYSPTR" 2857377 T SYSPTR (NIL) -8 NIL NIL NIL) (-1190 2856228 2856733 2856852 "SYSNNI" 2857038 NIL SYSNNI (NIL NIL) -8 NIL NIL 2857123) (-1189 2855535 2855994 2856073 "SYSINT" 2856133 NIL SYSINT (NIL NIL) -8 NIL NIL 2856178) (-1188 2851879 2852813 2853523 "SYNTAX" 2854847 T SYNTAX (NIL) -8 NIL NIL NIL) (-1187 2849037 2849639 2850271 "SYMTAB" 2851269 T SYMTAB (NIL) -8 NIL NIL NIL) (-1186 2844310 2845206 2846183 "SYMS" 2848082 T SYMS (NIL) -8 NIL NIL NIL) (-1185 2841555 2843771 2844001 "SYMPOLY" 2844118 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1184 2841072 2841147 2841270 "SYMFUNC" 2841467 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1183 2837092 2838384 2839197 "SYMBOL" 2840281 T SYMBOL (NIL) -8 NIL NIL NIL) (-1182 2830631 2832320 2834040 "SWITCH" 2835394 T SWITCH (NIL) -8 NIL NIL NIL) (-1181 2823865 2829452 2829755 "SUTS" 2830386 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1180 2815935 2823112 2823385 "SUPXS" 2823650 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1179 2815094 2815221 2815438 "SUPFRACF" 2815803 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1178 2814715 2814774 2814887 "SUP2" 2815029 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1177 2806514 2814333 2814459 "SUP" 2814624 NIL SUP (NIL T) -8 NIL NIL NIL) (-1176 2804962 2805236 2805592 "SUMRF" 2806213 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1175 2804297 2804363 2804555 "SUMFS" 2804883 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1174 2788280 2803474 2803725 "SULS" 2804104 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1173 2787882 2788102 2788172 "SUCHTAST" 2788232 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1172 2787177 2787407 2787547 "SUCH" 2787790 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1171 2781043 2782083 2783042 "SUBSPACE" 2786265 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1170 2780473 2780563 2780727 "SUBRESP" 2780931 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1169 2774646 2775766 2776913 "STTFNC" 2779373 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1168 2768012 2769311 2770622 "STTF" 2773382 NIL STTF (NIL T) -7 NIL NIL NIL) (-1167 2759323 2761194 2762988 "STTAYLOR" 2766253 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1166 2752455 2759187 2759270 "STRTBL" 2759275 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1165 2747819 2752410 2752441 "STRING" 2752446 T STRING (NIL) -8 NIL NIL NIL) (-1164 2742680 2747192 2747222 "STRICAT" 2747281 T STRICAT (NIL) -9 NIL 2747343 NIL) (-1163 2742190 2742267 2742411 "STREAM3" 2742597 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1162 2741172 2741355 2741590 "STREAM2" 2742003 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1161 2740860 2740912 2741005 "STREAM1" 2741114 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1160 2733615 2738479 2739090 "STREAM" 2740284 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1159 2732631 2732812 2733043 "STINPROD" 2733431 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1158 2731818 2732120 2732268 "STEPAST" 2732505 T STEPAST (NIL) -8 NIL NIL NIL) (-1157 2731370 2731580 2731610 "STEP" 2731690 T STEP (NIL) -9 NIL 2731768 NIL) (-1156 2724804 2731269 2731346 "STBL" 2731351 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1155 2719932 2724025 2724068 "STAGG" 2724221 NIL STAGG (NIL T) -9 NIL 2724310 NIL) (-1154 2717640 2718240 2719110 "STAGG-" 2719115 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1153 2715787 2717410 2717502 "STACK" 2717583 NIL STACK (NIL T) -8 NIL NIL NIL) (-1152 2708509 2713928 2714384 "SREGSET" 2715417 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1151 2700934 2702303 2703816 "SRDCMPK" 2707115 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1150 2693851 2698374 2698404 "SRAGG" 2699707 T SRAGG (NIL) -9 NIL 2700315 NIL) (-1149 2692868 2693123 2693502 "SRAGG-" 2693507 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1148 2687332 2691815 2692236 "SQMATRIX" 2692494 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1147 2681018 2684050 2684777 "SPLTREE" 2686677 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1146 2676981 2677674 2678320 "SPLNODE" 2680444 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1145 2676028 2676261 2676291 "SPFCAT" 2676735 T SPFCAT (NIL) -9 NIL NIL NIL) (-1144 2674765 2674975 2675239 "SPECOUT" 2675786 T SPECOUT (NIL) -7 NIL NIL NIL) (-1143 2665875 2667747 2667777 "SPADXPT" 2672453 T SPADXPT (NIL) -9 NIL 2674617 NIL) (-1142 2665636 2665676 2665745 "SPADPRSR" 2665828 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1141 2663685 2665591 2665622 "SPADAST" 2665627 T SPADAST (NIL) -8 NIL NIL NIL) (-1140 2655630 2657403 2657446 "SPACEC" 2661819 NIL SPACEC (NIL T) -9 NIL 2663635 NIL) (-1139 2653760 2655562 2655611 "SPACE3" 2655616 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1138 2652512 2652683 2652974 "SORTPAK" 2653565 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1137 2650604 2650907 2651319 "SOLVETRA" 2652176 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1136 2649654 2649876 2650137 "SOLVESER" 2650377 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1135 2644958 2645846 2646841 "SOLVERAD" 2648706 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1134 2640773 2641382 2642111 "SOLVEFOR" 2644325 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1133 2635070 2640122 2640219 "SNTSCAT" 2640224 NIL SNTSCAT (NIL T T T T) -9 NIL 2640294 NIL) (-1132 2629176 2633393 2633784 "SMTS" 2634760 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1131 2623887 2629064 2629141 "SMP" 2629146 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1130 2622046 2622347 2622745 "SMITH" 2623584 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1129 2614757 2618949 2619052 "SMATCAT" 2620406 NIL SMATCAT (NIL NIL T T T) -9 NIL 2620956 NIL) (-1128 2611718 2612534 2613705 "SMATCAT-" 2613710 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1127 2609384 2610954 2610997 "SKAGG" 2611258 NIL SKAGG (NIL T) -9 NIL 2611393 NIL) (-1126 2605697 2608800 2608995 "SINT" 2609182 T SINT (NIL) -8 NIL NIL 2609355) (-1125 2605469 2605507 2605573 "SIMPAN" 2605653 T SIMPAN (NIL) -7 NIL NIL NIL) (-1124 2604328 2604542 2604810 "SIGNRF" 2605235 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1123 2603182 2603326 2603603 "SIGNEF" 2604164 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1122 2602488 2602765 2602889 "SIGAST" 2603080 T SIGAST (NIL) -8 NIL NIL NIL) (-1121 2601767 2602023 2602163 "SIG" 2602370 T SIG (NIL) -8 NIL NIL NIL) (-1120 2599457 2599911 2600417 "SHP" 2601308 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1119 2593316 2599358 2599434 "SHDP" 2599439 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1118 2592889 2593081 2593111 "SGROUP" 2593204 T SGROUP (NIL) -9 NIL 2593266 NIL) (-1117 2592747 2592773 2592846 "SGROUP-" 2592851 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1116 2589582 2590280 2591003 "SGCF" 2592046 T SGCF (NIL) -7 NIL NIL NIL) (-1115 2583977 2589029 2589126 "SFRTCAT" 2589131 NIL SFRTCAT (NIL T T T T) -9 NIL 2589170 NIL) (-1114 2577398 2578416 2579552 "SFRGCD" 2582960 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1113 2570524 2571597 2572783 "SFQCMPK" 2576331 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1112 2570144 2570233 2570344 "SFORT" 2570465 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1111 2569262 2569984 2570105 "SEXOF" 2570110 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1110 2564775 2565490 2565585 "SEXCAT" 2568522 NIL SEXCAT (NIL T T T T T) -9 NIL 2569100 NIL) (-1109 2563882 2564656 2564724 "SEX" 2564729 T SEX (NIL) -8 NIL NIL NIL) (-1108 2562112 2562599 2562902 "SETMN" 2563625 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1107 2561608 2561760 2561790 "SETCAT" 2561966 T SETCAT (NIL) -9 NIL 2562076 NIL) (-1106 2561300 2561378 2561508 "SETCAT-" 2561513 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1105 2557661 2559761 2559804 "SETAGG" 2560674 NIL SETAGG (NIL T) -9 NIL 2561014 NIL) (-1104 2557119 2557235 2557472 "SETAGG-" 2557477 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1103 2554272 2557053 2557101 "SET" 2557106 NIL SET (NIL T) -8 NIL NIL NIL) (-1102 2553715 2553968 2554069 "SEQAST" 2554193 T SEQAST (NIL) -8 NIL NIL NIL) (-1101 2552914 2553208 2553269 "SEGXCAT" 2553555 NIL SEGXCAT (NIL T T) -9 NIL 2553675 NIL) (-1100 2551893 2552107 2552150 "SEGCAT" 2552672 NIL SEGCAT (NIL T) -9 NIL 2552893 NIL) (-1099 2551514 2551573 2551686 "SEGBIND2" 2551828 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1098 2550446 2550877 2551085 "SEGBIND" 2551341 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1097 2550019 2550247 2550324 "SEGAST" 2550391 T SEGAST (NIL) -8 NIL NIL NIL) (-1096 2549238 2549364 2549568 "SEG2" 2549863 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1095 2548244 2548904 2549086 "SEG" 2549091 NIL SEG (NIL T) -8 NIL NIL NIL) (-1094 2547654 2548179 2548226 "SDVAR" 2548231 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1093 2540222 2547424 2547554 "SDPOL" 2547559 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1092 2538815 2539081 2539400 "SCPKG" 2539937 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1091 2537979 2538151 2538343 "SCOPE" 2538645 T SCOPE (NIL) -8 NIL NIL NIL) (-1090 2537199 2537333 2537512 "SCACHE" 2537834 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1089 2536845 2537031 2537061 "SASTCAT" 2537066 T SASTCAT (NIL) -9 NIL 2537079 NIL) (-1088 2536332 2536680 2536756 "SAOS" 2536791 T SAOS (NIL) -8 NIL NIL NIL) (-1087 2535897 2535932 2536105 "SAERFFC" 2536291 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1086 2535490 2535525 2535684 "SAEFACT" 2535856 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1085 2529438 2535387 2535467 "SAE" 2535472 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1084 2527759 2528073 2528474 "RURPK" 2529104 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1083 2526396 2526702 2527007 "RULESET" 2527593 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1082 2526008 2526190 2526273 "RULECOLD" 2526348 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1081 2523231 2523761 2524219 "RULE" 2525689 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1080 2523021 2523049 2523120 "RTVALUE" 2523182 T RTVALUE (NIL) -8 NIL NIL NIL) (-1079 2522492 2522738 2522832 "RSTRCAST" 2522949 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1078 2517340 2518135 2519055 "RSETGCD" 2521691 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1077 2506597 2511649 2511746 "RSETCAT" 2515865 NIL RSETCAT (NIL T T T T) -9 NIL 2516962 NIL) (-1076 2504524 2505063 2505887 "RSETCAT-" 2505892 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1075 2496910 2498286 2499806 "RSDCMPK" 2503123 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1074 2494889 2495356 2495430 "RRCC" 2496516 NIL RRCC (NIL T T) -9 NIL 2496860 NIL) (-1073 2494240 2494414 2494693 "RRCC-" 2494698 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1072 2493683 2493936 2494037 "RPTAST" 2494161 T RPTAST (NIL) -8 NIL NIL NIL) (-1071 2467565 2476891 2476958 "RPOLCAT" 2487622 NIL RPOLCAT (NIL T T T) -9 NIL 2490781 NIL) (-1070 2459099 2461427 2464537 "RPOLCAT-" 2464542 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1069 2450032 2457310 2457792 "ROUTINE" 2458639 T ROUTINE (NIL) -8 NIL NIL NIL) (-1068 2446832 2449658 2449798 "ROMAN" 2449914 T ROMAN (NIL) -8 NIL NIL NIL) (-1067 2445078 2445692 2445952 "ROIRC" 2446637 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1066 2441314 2443594 2443624 "RNS" 2443928 T RNS (NIL) -9 NIL 2444202 NIL) (-1065 2439823 2440206 2440740 "RNS-" 2440815 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1064 2438826 2439188 2439390 "RNGBIND" 2439674 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1063 2438229 2438637 2438667 "RNG" 2438672 T RNG (NIL) -9 NIL 2438693 NIL) (-1062 2437628 2438016 2438059 "RMODULE" 2438064 NIL RMODULE (NIL T) -9 NIL 2438091 NIL) (-1061 2436464 2436558 2436894 "RMCAT2" 2437529 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1060 2433314 2435810 2436107 "RMATRIX" 2436226 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1059 2426141 2428401 2428516 "RMATCAT" 2431875 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2432857 NIL) (-1058 2425516 2425663 2425970 "RMATCAT-" 2425975 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1057 2424917 2425138 2425181 "RLINSET" 2425375 NIL RLINSET (NIL T) -9 NIL 2425466 NIL) (-1056 2424484 2424559 2424687 "RINTERP" 2424836 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1055 2423542 2424096 2424126 "RING" 2424182 T RING (NIL) -9 NIL 2424274 NIL) (-1054 2423334 2423378 2423475 "RING-" 2423480 NIL RING- (NIL T) -8 NIL NIL NIL) (-1053 2422175 2422412 2422670 "RIDIST" 2423098 T RIDIST (NIL) -7 NIL NIL NIL) (-1052 2413491 2421643 2421849 "RGCHAIN" 2422023 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1051 2412841 2413247 2413288 "RGBCSPC" 2413346 NIL RGBCSPC (NIL T) -9 NIL 2413398 NIL) (-1050 2411999 2412380 2412421 "RGBCMDL" 2412653 NIL RGBCMDL (NIL T) -9 NIL 2412767 NIL) (-1049 2411645 2411708 2411811 "RFFACTOR" 2411930 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1048 2411370 2411405 2411502 "RFFACT" 2411604 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1047 2409487 2409851 2410233 "RFDIST" 2411010 T RFDIST (NIL) -7 NIL NIL NIL) (-1046 2406481 2407095 2407765 "RF" 2408851 NIL RF (NIL T) -7 NIL NIL NIL) (-1045 2405934 2406026 2406189 "RETSOL" 2406383 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1044 2405570 2405650 2405693 "RETRACT" 2405826 NIL RETRACT (NIL T) -9 NIL 2405913 NIL) (-1043 2405419 2405444 2405531 "RETRACT-" 2405536 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1042 2405021 2405241 2405311 "RETAST" 2405371 T RETAST (NIL) -8 NIL NIL NIL) (-1041 2397761 2404674 2404801 "RESULT" 2404916 T RESULT (NIL) -8 NIL NIL NIL) (-1040 2396352 2397030 2397229 "RESRING" 2397664 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1039 2395988 2396037 2396135 "RESLATC" 2396289 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1038 2395693 2395728 2395835 "REPSQ" 2395947 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1037 2395390 2395425 2395536 "REPDB" 2395652 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1036 2389290 2390679 2391902 "REP2" 2394202 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1035 2385667 2386348 2387156 "REP1" 2388517 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1034 2383089 2383669 2384271 "REP" 2385087 T REP (NIL) -7 NIL NIL NIL) (-1033 2375812 2381230 2381686 "REGSET" 2382719 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1032 2374577 2374960 2375210 "REF" 2375597 NIL REF (NIL T) -8 NIL NIL NIL) (-1031 2373954 2374057 2374224 "REDORDER" 2374461 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1030 2369953 2373167 2373394 "RECLOS" 2373782 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1029 2369005 2369186 2369401 "REALSOLV" 2369760 T REALSOLV (NIL) -7 NIL NIL NIL) (-1028 2365488 2366290 2367174 "REAL0Q" 2368170 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1027 2361089 2362077 2363138 "REAL0" 2364469 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1026 2360935 2360976 2361006 "REAL" 2361011 T REAL (NIL) -9 NIL 2361046 NIL) (-1025 2360406 2360652 2360746 "RDUCEAST" 2360863 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1024 2359811 2359883 2360090 "RDIV" 2360328 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1023 2358879 2359053 2359266 "RDIST" 2359633 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1022 2357476 2357763 2358135 "RDETRS" 2358587 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1021 2355288 2355742 2356280 "RDETR" 2357018 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1020 2353913 2354191 2354588 "RDEEFS" 2355004 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1019 2352422 2352728 2353153 "RDEEF" 2353601 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1018 2346492 2349403 2349433 "RCFIELD" 2350728 T RCFIELD (NIL) -9 NIL 2351459 NIL) (-1017 2344556 2345060 2345756 "RCFIELD-" 2345831 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1016 2340825 2342657 2342700 "RCAGG" 2343784 NIL RCAGG (NIL T) -9 NIL 2344249 NIL) (-1015 2340453 2340547 2340710 "RCAGG-" 2340715 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1014 2339788 2339900 2340065 "RATRET" 2340337 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1013 2339341 2339408 2339529 "RATFACT" 2339716 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1012 2338649 2338769 2338921 "RANDSRC" 2339211 T RANDSRC (NIL) -7 NIL NIL NIL) (-1011 2338383 2338427 2338500 "RADUTIL" 2338598 T RADUTIL (NIL) -7 NIL NIL NIL) (-1010 2331520 2337216 2337526 "RADIX" 2338107 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1009 2323150 2331362 2331492 "RADFF" 2331497 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1008 2322797 2322872 2322902 "RADCAT" 2323062 T RADCAT (NIL) -9 NIL NIL NIL) (-1007 2322579 2322627 2322727 "RADCAT-" 2322732 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1006 2320677 2322349 2322441 "QUEUE" 2322522 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1005 2320308 2320351 2320482 "QUATCT2" 2320628 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1004 2313764 2317102 2317144 "QUATCAT" 2317935 NIL QUATCAT (NIL T) -9 NIL 2318701 NIL) (-1003 2309924 2310954 2312337 "QUATCAT-" 2312433 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1002 2306468 2309857 2309905 "QUAT" 2309910 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1001 2303933 2305544 2305587 "QUAGG" 2305968 NIL QUAGG (NIL T) -9 NIL 2306143 NIL) (-1000 2303535 2303755 2303825 "QQUTAST" 2303885 T QQUTAST (NIL) -8 NIL NIL NIL) (-999 2302433 2302933 2303105 "QFORM" 2303407 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-998 2302071 2302114 2302241 "QFCAT2" 2302384 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-997 2293092 2298315 2298355 "QFCAT" 2299013 NIL QFCAT (NIL T) -9 NIL 2300014 NIL) (-996 2288700 2289889 2291468 "QFCAT-" 2291562 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-995 2288160 2288270 2288400 "QEQUAT" 2288590 T QEQUAT (NIL) -8 NIL NIL NIL) (-994 2281306 2282379 2283563 "QCMPACK" 2287093 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-993 2280551 2280725 2280957 "QALGSET2" 2281126 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-992 2278106 2278552 2278978 "QALGSET" 2280208 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-991 2276796 2277020 2277337 "PWFFINTB" 2277879 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-990 2274995 2275163 2275517 "PUSHVAR" 2276610 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-989 2270913 2271967 2272008 "PTRANFN" 2273892 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-988 2269315 2269606 2269928 "PTPACK" 2270624 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-987 2268947 2269004 2269113 "PTFUNC2" 2269252 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-986 2263424 2267819 2267860 "PTCAT" 2268156 NIL PTCAT (NIL T) -9 NIL 2268309 NIL) (-985 2263082 2263117 2263241 "PSQFR" 2263383 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-984 2261677 2261975 2262309 "PSEUDLIN" 2262780 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-983 2248440 2250811 2253135 "PSETPK" 2259437 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-982 2241458 2244198 2244294 "PSETCAT" 2247315 NIL PSETCAT (NIL T T T T) -9 NIL 2248129 NIL) (-981 2239294 2239928 2240749 "PSETCAT-" 2240754 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-980 2238643 2238808 2238836 "PSCURVE" 2239104 T PSCURVE (NIL) -9 NIL 2239271 NIL) (-979 2234641 2236157 2236222 "PSCAT" 2237066 NIL PSCAT (NIL T T T) -9 NIL 2237306 NIL) (-978 2233704 2233920 2234320 "PSCAT-" 2234325 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2232409 2233069 2233274 "PRTITION" 2233519 T PRTITION (NIL) -8 NIL NIL NIL) (-976 2231884 2232130 2232222 "PRTDAST" 2232337 T PRTDAST (NIL) -8 NIL NIL NIL) (-975 2220974 2223188 2225376 "PRS" 2229746 NIL PRS (NIL T T) -7 NIL NIL NIL) (-974 2218785 2220324 2220364 "PRQAGG" 2220547 NIL PRQAGG (NIL T) -9 NIL 2220649 NIL) (-973 2217989 2218294 2218322 "PROPLOG" 2218569 T PROPLOG (NIL) -9 NIL 2218735 NIL) (-972 2216170 2216736 2217033 "PROPFRML" 2217725 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-971 2215639 2215746 2215874 "PROPERTY" 2216062 T PROPERTY (NIL) -8 NIL NIL NIL) (-970 2209697 2213805 2214625 "PRODUCT" 2214865 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-969 2209493 2209525 2209584 "PRINT" 2209658 T PRINT (NIL) -7 NIL NIL NIL) (-968 2208833 2208950 2209102 "PRIMES" 2209373 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-967 2206898 2207299 2207765 "PRIMELT" 2208412 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-966 2206627 2206676 2206704 "PRIMCAT" 2206828 T PRIMCAT (NIL) -9 NIL NIL NIL) (-965 2205634 2205812 2206040 "PRIMARR2" 2206445 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-964 2201749 2205572 2205617 "PRIMARR" 2205622 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-963 2201392 2201448 2201559 "PREASSOC" 2201687 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-962 2198677 2200850 2201084 "PR" 2201203 NIL PR (NIL T T) -8 NIL NIL NIL) (-961 2198152 2198285 2198313 "PPCURVE" 2198518 T PPCURVE (NIL) -9 NIL 2198654 NIL) (-960 2197747 2197947 2198030 "PORTNUM" 2198089 T PORTNUM (NIL) -8 NIL NIL NIL) (-959 2195106 2195505 2196097 "POLYROOT" 2197328 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-958 2194489 2194547 2194781 "POLYLIFT" 2195042 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-957 2190764 2191213 2191842 "POLYCATQ" 2194034 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-956 2177490 2182604 2182669 "POLYCAT" 2186183 NIL POLYCAT (NIL T T T) -9 NIL 2188061 NIL) (-955 2170996 2172839 2175204 "POLYCAT-" 2175209 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-954 2170583 2170651 2170771 "POLY2UP" 2170922 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-953 2170215 2170272 2170381 "POLY2" 2170520 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-952 2164428 2169819 2169979 "POLY" 2170088 NIL POLY (NIL T) -8 NIL NIL NIL) (-951 2163113 2163352 2163628 "POLUTIL" 2164202 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-950 2161468 2161745 2162076 "POLTOPOL" 2162835 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-949 2156933 2161404 2161450 "POINT" 2161455 NIL POINT (NIL T) -8 NIL NIL NIL) (-948 2155120 2155477 2155852 "PNTHEORY" 2156578 T PNTHEORY (NIL) -7 NIL NIL NIL) (-947 2153578 2153875 2154274 "PMTOOLS" 2154818 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-946 2153171 2153249 2153366 "PMSYM" 2153494 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-945 2152681 2152750 2152924 "PMQFCAT" 2153096 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-944 2152074 2152160 2152322 "PMPREDFS" 2152582 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-943 2151429 2151539 2151695 "PMPRED" 2151951 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-942 2150093 2150301 2150679 "PMPLCAT" 2151191 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-941 2149625 2149704 2149856 "PMLSAGG" 2150008 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-940 2149098 2149174 2149356 "PMKERNEL" 2149543 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-939 2148715 2148790 2148903 "PMINS" 2149017 NIL PMINS (NIL T) -7 NIL NIL NIL) (-938 2148157 2148226 2148435 "PMFS" 2148640 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-937 2147385 2147503 2147708 "PMDOWN" 2148034 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-936 2146658 2146768 2146931 "PMASSFS" 2147272 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-935 2145825 2145983 2146164 "PMASS" 2146497 T PMASS (NIL) -7 NIL NIL NIL) (-934 2145480 2145548 2145642 "PLOTTOOL" 2145751 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-933 2141284 2142328 2143249 "PLOT3D" 2144579 T PLOT3D (NIL) -8 NIL NIL NIL) (-932 2140196 2140373 2140608 "PLOT1" 2141088 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-931 2134803 2136007 2137155 "PLOT" 2139068 T PLOT (NIL) -8 NIL NIL NIL) (-930 2110192 2114869 2119720 "PLEQN" 2130069 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-929 2109885 2109932 2110035 "PINTERPA" 2110139 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-928 2109203 2109325 2109505 "PINTERP" 2109750 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-927 2107500 2108475 2108503 "PID" 2108685 T PID (NIL) -9 NIL 2108819 NIL) (-926 2107251 2107288 2107363 "PICOERCE" 2107457 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-925 2106472 2107020 2107107 "PI" 2107147 T PI (NIL) -8 NIL NIL 2107214) (-924 2105792 2105931 2106107 "PGROEB" 2106328 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-923 2101379 2102193 2103098 "PGE" 2104907 T PGE (NIL) -7 NIL NIL NIL) (-922 2099502 2099749 2100115 "PGCD" 2101096 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-921 2098840 2098943 2099104 "PFRPAC" 2099386 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-920 2095482 2097388 2097741 "PFR" 2098519 NIL PFR (NIL T) -8 NIL NIL NIL) (-919 2093871 2094115 2094440 "PFOTOOLS" 2095229 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-918 2092404 2092643 2092994 "PFOQ" 2093628 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-917 2090905 2091117 2091473 "PFO" 2092188 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-916 2088239 2089510 2089538 "PFECAT" 2090123 T PFECAT (NIL) -9 NIL 2090507 NIL) (-915 2087684 2087838 2088052 "PFECAT-" 2088057 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-914 2086287 2086539 2086840 "PFBRU" 2087433 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-913 2084153 2084505 2084937 "PFBR" 2085938 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-912 2080708 2084042 2084111 "PF" 2084116 NIL PF (NIL NIL) -8 NIL NIL NIL) (-911 2075942 2076915 2077785 "PERMGRP" 2079871 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-910 2074048 2075005 2075046 "PERMCAT" 2075492 NIL PERMCAT (NIL T) -9 NIL 2075797 NIL) (-909 2073701 2073742 2073866 "PERMAN" 2074001 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-908 2069583 2071077 2071753 "PERM" 2073058 NIL PERM (NIL T) -8 NIL NIL NIL) (-907 2067073 2069248 2069370 "PENDTREE" 2069494 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-906 2065097 2065865 2065906 "PDRING" 2066563 NIL PDRING (NIL T) -9 NIL 2066849 NIL) (-905 2064200 2064418 2064780 "PDRING-" 2064785 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-904 2061415 2062193 2062861 "PDEPROB" 2063552 T PDEPROB (NIL) -8 NIL NIL NIL) (-903 2058960 2059464 2060019 "PDEPACK" 2060880 T PDEPACK (NIL) -7 NIL NIL NIL) (-902 2057872 2058062 2058313 "PDECOMP" 2058759 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-901 2055451 2056294 2056322 "PDECAT" 2057109 T PDECAT (NIL) -9 NIL 2057822 NIL) (-900 2055202 2055235 2055325 "PCOMP" 2055412 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-899 2053380 2054003 2054300 "PBWLB" 2054931 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-898 2053012 2053069 2053178 "PATTERN2" 2053317 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2050769 2051157 2051614 "PATTERN1" 2052601 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2043244 2044842 2046180 "PATTERN" 2049452 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-895 2042808 2042875 2043007 "PATRES2" 2043171 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2040176 2040757 2041238 "PATRES" 2042373 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-893 2038059 2038464 2038871 "PATMATCH" 2039843 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-892 2037569 2037778 2037819 "PATMAB" 2037926 NIL PATMAB (NIL T) -9 NIL 2038009 NIL) (-891 2036087 2036423 2036681 "PATLRES" 2037374 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-890 2035633 2035756 2035797 "PATAB" 2035802 NIL PATAB (NIL T) -9 NIL 2035974 NIL) (-889 2033114 2033646 2034219 "PARTPERM" 2035080 T PARTPERM (NIL) -7 NIL NIL NIL) (-888 2032735 2032798 2032900 "PARSURF" 2033045 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-887 2032367 2032424 2032533 "PARSU2" 2032672 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-886 2032131 2032171 2032238 "PARSER" 2032320 T PARSER (NIL) -7 NIL NIL NIL) (-885 2031752 2031815 2031917 "PARSCURV" 2032062 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-884 2031384 2031441 2031550 "PARSC2" 2031689 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-883 2031023 2031081 2031178 "PARPCURV" 2031320 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-882 2030655 2030712 2030821 "PARPC2" 2030960 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-881 2029716 2030028 2030210 "PARAMAST" 2030493 T PARAMAST (NIL) -8 NIL NIL NIL) (-880 2029236 2029322 2029441 "PAN2EXPR" 2029617 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-879 2028013 2028357 2028585 "PALETTE" 2029028 T PALETTE (NIL) -8 NIL NIL NIL) (-878 2026406 2027018 2027378 "PAIR" 2027699 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-877 2020297 2025665 2025859 "PADICRC" 2026261 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-876 2013547 2019643 2019827 "PADICRAT" 2020145 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-875 2010659 2012221 2012261 "PADICCT" 2012842 NIL PADICCT (NIL NIL) -9 NIL 2013124 NIL) (-874 2008976 2010596 2010641 "PADIC" 2010646 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-873 2007933 2008133 2008401 "PADEPAC" 2008763 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-872 2007145 2007278 2007484 "PADE" 2007795 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-871 2005532 2006353 2006633 "OWP" 2006949 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-870 2005025 2005238 2005335 "OVERSET" 2005455 T OVERSET (NIL) -8 NIL NIL NIL) (-869 2004071 2004630 2004802 "OVAR" 2004893 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-868 1992943 1995180 1997380 "OUTFORM" 2001891 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 1992279 1992540 1992667 "OUTBFILE" 1992836 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 1991586 1991751 1991779 "OUTBCON" 1992097 T OUTBCON (NIL) -9 NIL 1992263 NIL) (-865 1991187 1991299 1991456 "OUTBCON-" 1991461 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 1990451 1990572 1990733 "OUT" 1991046 T OUT (NIL) -7 NIL NIL NIL) (-863 1989831 1990180 1990269 "OSI" 1990382 T OSI (NIL) -8 NIL NIL NIL) (-862 1989361 1989699 1989727 "OSGROUP" 1989732 T OSGROUP (NIL) -9 NIL 1989754 NIL) (-861 1988106 1988333 1988618 "ORTHPOL" 1989108 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-860 1985671 1987941 1988062 "OREUP" 1988067 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-859 1983088 1985362 1985489 "ORESUP" 1985613 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-858 1980616 1981116 1981677 "OREPCTO" 1982577 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-857 1974309 1976503 1976544 "OREPCAT" 1978892 NIL OREPCAT (NIL T) -9 NIL 1979996 NIL) (-856 1971477 1972252 1973303 "OREPCAT-" 1973308 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-855 1970628 1970926 1970954 "ORDSET" 1971263 T ORDSET (NIL) -9 NIL 1971427 NIL) (-854 1970059 1970207 1970431 "ORDSET-" 1970436 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-853 1968624 1969415 1969443 "ORDRING" 1969645 T ORDRING (NIL) -9 NIL 1969770 NIL) (-852 1968269 1968363 1968507 "ORDRING-" 1968512 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-851 1967649 1968112 1968140 "ORDMON" 1968145 T ORDMON (NIL) -9 NIL 1968166 NIL) (-850 1966811 1966958 1967153 "ORDFUNS" 1967498 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-849 1966149 1966568 1966596 "ORDFIN" 1966661 T ORDFIN (NIL) -9 NIL 1966735 NIL) (-848 1965415 1965542 1965728 "ORDCOMP2" 1966009 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1961981 1964001 1964410 "ORDCOMP" 1965039 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-846 1958562 1959472 1960286 "OPTPROB" 1961187 T OPTPROB (NIL) -8 NIL NIL NIL) (-845 1955364 1956003 1956707 "OPTPACK" 1957878 T OPTPACK (NIL) -7 NIL NIL NIL) (-844 1953051 1953817 1953845 "OPTCAT" 1954664 T OPTCAT (NIL) -9 NIL 1955314 NIL) (-843 1952435 1952728 1952833 "OPSIG" 1952966 T OPSIG (NIL) -8 NIL NIL NIL) (-842 1952203 1952242 1952308 "OPQUERY" 1952389 T OPQUERY (NIL) -7 NIL NIL NIL) (-841 1951577 1951803 1951844 "OPERCAT" 1952056 NIL OPERCAT (NIL T) -9 NIL 1952153 NIL) (-840 1951332 1951388 1951505 "OPERCAT-" 1951510 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1948465 1949643 1950147 "OP" 1950861 NIL OP (NIL T) -8 NIL NIL NIL) (-838 1947770 1947885 1948059 "ONECOMP2" 1948337 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1944590 1946567 1946936 "ONECOMP" 1947434 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-836 1944009 1944115 1944245 "OMSERVER" 1944480 T OMSERVER (NIL) -7 NIL NIL NIL) (-835 1940871 1943449 1943489 "OMSAGG" 1943550 NIL OMSAGG (NIL T) -9 NIL 1943614 NIL) (-834 1939494 1939757 1940039 "OMPKG" 1940609 T OMPKG (NIL) -7 NIL NIL NIL) (-833 1938041 1939043 1939212 "OMLO" 1939375 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1937001 1937148 1937368 "OMEXPR" 1937867 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1936152 1936422 1936582 "OMERRK" 1936861 T OMERRK (NIL) -8 NIL NIL NIL) (-830 1935443 1935698 1935834 "OMERR" 1936036 T OMERR (NIL) -8 NIL NIL NIL) (-829 1934894 1935120 1935228 "OMENC" 1935355 T OMENC (NIL) -8 NIL NIL NIL) (-828 1928789 1929974 1931145 "OMDEV" 1933743 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1927858 1928029 1928223 "OMCONN" 1928615 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1927288 1927391 1927419 "OM" 1927718 T OM (NIL) -9 NIL NIL NIL) (-825 1925809 1926785 1926813 "OINTDOM" 1926818 T OINTDOM (NIL) -9 NIL 1926839 NIL) (-824 1923154 1924497 1924834 "OFMONOID" 1925504 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-823 1922565 1923091 1923136 "ODVAR" 1923141 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-822 1919990 1922310 1922465 "ODR" 1922470 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-821 1912612 1919766 1919892 "ODPOL" 1919897 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-820 1906441 1912484 1912589 "ODP" 1912594 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-819 1905207 1905422 1905697 "ODETOOLS" 1906215 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-818 1902174 1902832 1903548 "ODESYS" 1904540 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-817 1897056 1897964 1898989 "ODERTRIC" 1901249 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-816 1896482 1896564 1896758 "ODERED" 1896968 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-815 1893378 1893924 1894599 "ODERAT" 1895907 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-814 1890335 1890802 1891399 "ODEPRRIC" 1892907 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-813 1888278 1888874 1889360 "ODEPROB" 1889869 T ODEPROB (NIL) -8 NIL NIL NIL) (-812 1884798 1885283 1885930 "ODEPRIM" 1887757 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-811 1884047 1884149 1884409 "ODEPAL" 1884690 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-810 1880209 1881000 1881864 "ODEPACK" 1883203 T ODEPACK (NIL) -7 NIL NIL NIL) (-809 1879270 1879377 1879599 "ODEINT" 1880098 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-808 1873371 1874796 1876243 "ODEIFTBL" 1877843 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-807 1868783 1869565 1870513 "ODEEF" 1872534 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-806 1868132 1868221 1868444 "ODECONST" 1868688 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-805 1866257 1866918 1866946 "ODECAT" 1867551 T ODECAT (NIL) -9 NIL 1868082 NIL) (-804 1865895 1865938 1866065 "OCTCT2" 1866208 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1862762 1865600 1865722 "OCT" 1865805 NIL OCT (NIL T) -8 NIL NIL NIL) (-802 1862114 1862582 1862610 "OCAMON" 1862615 T OCAMON (NIL) -9 NIL 1862636 NIL) (-801 1856770 1859198 1859238 "OC" 1860335 NIL OC (NIL T) -9 NIL 1861193 NIL) (-800 1854018 1854759 1855742 "OC-" 1855836 NIL OC- (NIL T T) -8 NIL NIL NIL) (-799 1853549 1853890 1853918 "OASGP" 1853923 T OASGP (NIL) -9 NIL 1853943 NIL) (-798 1852810 1853299 1853327 "OAMONS" 1853367 T OAMONS (NIL) -9 NIL 1853410 NIL) (-797 1852224 1852657 1852685 "OAMON" 1852690 T OAMON (NIL) -9 NIL 1852710 NIL) (-796 1851482 1852000 1852028 "OAGROUP" 1852033 T OAGROUP (NIL) -9 NIL 1852053 NIL) (-795 1851172 1851222 1851310 "NUMTUBE" 1851426 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-794 1844745 1846263 1847799 "NUMQUAD" 1849656 T NUMQUAD (NIL) -7 NIL NIL NIL) (-793 1840501 1841489 1842514 "NUMODE" 1843740 T NUMODE (NIL) -7 NIL NIL NIL) (-792 1837856 1838736 1838764 "NUMINT" 1839687 T NUMINT (NIL) -9 NIL 1840451 NIL) (-791 1836804 1837001 1837219 "NUMFMT" 1837658 T NUMFMT (NIL) -7 NIL NIL NIL) (-790 1823163 1826108 1828640 "NUMERIC" 1834311 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-789 1817560 1822612 1822707 "NTSCAT" 1822712 NIL NTSCAT (NIL T T T T) -9 NIL 1822751 NIL) (-788 1816754 1816919 1817112 "NTPOLFN" 1817399 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-787 1816386 1816443 1816552 "NSUP2" 1816691 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804508 1813211 1814023 "NSUP" 1815607 NIL NSUP (NIL T) -8 NIL NIL NIL) (-785 1794784 1804282 1804415 "NSMP" 1804420 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-784 1793216 1793517 1793874 "NREP" 1794472 NIL NREP (NIL T) -7 NIL NIL NIL) (-783 1791807 1792059 1792417 "NPCOEF" 1792959 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-782 1790873 1790988 1791204 "NORMRETR" 1791688 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-781 1788914 1789204 1789613 "NORMPK" 1790581 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-780 1788599 1788627 1788751 "NORMMA" 1788880 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-779 1788388 1788417 1788486 "NONE1" 1788563 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1788188 1788345 1788374 "NONE" 1788379 T NONE (NIL) -8 NIL NIL NIL) (-777 1787685 1787747 1787926 "NODE1" 1788120 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-776 1785970 1786821 1787076 "NNI" 1787423 T NNI (NIL) -8 NIL NIL 1787658) (-775 1784390 1784703 1785067 "NLINSOL" 1785638 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-774 1780631 1781626 1782525 "NIPROB" 1783511 T NIPROB (NIL) -8 NIL NIL NIL) (-773 1779388 1779622 1779924 "NFINTBAS" 1780393 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-772 1778562 1779038 1779079 "NETCLT" 1779251 NIL NETCLT (NIL T) -9 NIL 1779333 NIL) (-771 1777270 1777501 1777782 "NCODIV" 1778330 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-770 1777032 1777069 1777144 "NCNTFRAC" 1777227 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-769 1775212 1775576 1775996 "NCEP" 1776657 NIL NCEP (NIL T) -7 NIL NIL NIL) (-768 1774070 1774836 1774864 "NASRING" 1774974 T NASRING (NIL) -9 NIL 1775054 NIL) (-767 1773865 1773909 1774003 "NASRING-" 1774008 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-766 1772972 1773497 1773525 "NARNG" 1773642 T NARNG (NIL) -9 NIL 1773733 NIL) (-765 1772664 1772731 1772865 "NARNG-" 1772870 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-764 1771543 1771750 1771985 "NAGSP" 1772449 T NAGSP (NIL) -7 NIL NIL NIL) (-763 1762815 1764499 1766172 "NAGS" 1769890 T NAGS (NIL) -7 NIL NIL NIL) (-762 1761363 1761671 1762002 "NAGF07" 1762504 T NAGF07 (NIL) -7 NIL NIL NIL) (-761 1755901 1757192 1758499 "NAGF04" 1760076 T NAGF04 (NIL) -7 NIL NIL NIL) (-760 1748869 1750483 1752116 "NAGF02" 1754288 T NAGF02 (NIL) -7 NIL NIL NIL) (-759 1744093 1745193 1746310 "NAGF01" 1747772 T NAGF01 (NIL) -7 NIL NIL NIL) (-758 1737721 1739287 1740872 "NAGE04" 1742528 T NAGE04 (NIL) -7 NIL NIL NIL) (-757 1728890 1731011 1733141 "NAGE02" 1735611 T NAGE02 (NIL) -7 NIL NIL NIL) (-756 1724843 1725790 1726754 "NAGE01" 1727946 T NAGE01 (NIL) -7 NIL NIL NIL) (-755 1722638 1723172 1723730 "NAGD03" 1724305 T NAGD03 (NIL) -7 NIL NIL NIL) (-754 1714388 1716316 1718270 "NAGD02" 1720704 T NAGD02 (NIL) -7 NIL NIL NIL) (-753 1708199 1709624 1711064 "NAGD01" 1712968 T NAGD01 (NIL) -7 NIL NIL NIL) (-752 1704408 1705230 1706067 "NAGC06" 1707382 T NAGC06 (NIL) -7 NIL NIL NIL) (-751 1702873 1703205 1703561 "NAGC05" 1704072 T NAGC05 (NIL) -7 NIL NIL NIL) (-750 1702249 1702368 1702512 "NAGC02" 1702749 T NAGC02 (NIL) -7 NIL NIL NIL) (-749 1701208 1701791 1701831 "NAALG" 1701910 NIL NAALG (NIL T) -9 NIL 1701971 NIL) (-748 1701043 1701072 1701162 "NAALG-" 1701167 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-747 1694993 1696101 1697288 "MULTSQFR" 1699939 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-746 1694312 1694387 1694571 "MULTFACT" 1694905 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-745 1687036 1690949 1691002 "MTSCAT" 1692072 NIL MTSCAT (NIL T T) -9 NIL 1692587 NIL) (-744 1686748 1686802 1686894 "MTHING" 1686976 NIL MTHING (NIL T) -7 NIL NIL NIL) (-743 1686540 1686573 1686633 "MSYSCMD" 1686708 T MSYSCMD (NIL) -7 NIL NIL NIL) (-742 1683609 1686101 1686142 "MSETAGG" 1686147 NIL MSETAGG (NIL T) -9 NIL 1686181 NIL) (-741 1679691 1682364 1682684 "MSET" 1683322 NIL MSET (NIL T) -8 NIL NIL NIL) (-740 1675534 1677070 1677815 "MRING" 1678991 NIL MRING (NIL T T) -8 NIL NIL NIL) (-739 1675100 1675167 1675298 "MRF2" 1675461 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-738 1674718 1674753 1674897 "MRATFAC" 1675059 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-737 1672330 1672625 1673056 "MPRFF" 1674423 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-736 1666653 1672184 1672281 "MPOLY" 1672286 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-735 1666143 1666178 1666386 "MPCPF" 1666612 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-734 1665657 1665700 1665884 "MPC3" 1666094 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1664852 1664933 1665154 "MPC2" 1665572 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-732 1663153 1663490 1663880 "MONOTOOL" 1664512 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-731 1662378 1662695 1662723 "MONOID" 1662942 T MONOID (NIL) -9 NIL 1663089 NIL) (-730 1661924 1662043 1662224 "MONOID-" 1662229 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-729 1652408 1658350 1658409 "MONOGEN" 1659083 NIL MONOGEN (NIL T T) -9 NIL 1659539 NIL) (-728 1649647 1650375 1651368 "MONOGEN-" 1651487 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-727 1648480 1648926 1648954 "MONADWU" 1649346 T MONADWU (NIL) -9 NIL 1649584 NIL) (-726 1647852 1648011 1648259 "MONADWU-" 1648264 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-725 1647211 1647455 1647483 "MONAD" 1647690 T MONAD (NIL) -9 NIL 1647802 NIL) (-724 1646896 1646974 1647106 "MONAD-" 1647111 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-723 1645185 1645809 1646088 "MOEBIUS" 1646649 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-722 1644463 1644867 1644907 "MODULE" 1644912 NIL MODULE (NIL T) -9 NIL 1644951 NIL) (-721 1644031 1644127 1644317 "MODULE-" 1644322 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-720 1641755 1642439 1642766 "MODRING" 1643855 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-719 1638701 1639860 1640381 "MODOP" 1641284 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-718 1637289 1637768 1638045 "MODMONOM" 1638564 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-717 1627371 1635580 1635994 "MODMON" 1636926 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-716 1624553 1626239 1626515 "MODFIELD" 1627246 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1623530 1623834 1624024 "MMLFORM" 1624383 T MMLFORM (NIL) -8 NIL NIL NIL) (-714 1623056 1623099 1623278 "MMAP" 1623481 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-713 1621135 1621902 1621943 "MLO" 1622366 NIL MLO (NIL T) -9 NIL 1622608 NIL) (-712 1618501 1619017 1619619 "MLIFT" 1620616 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-711 1617892 1617976 1618130 "MKUCFUNC" 1618412 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-710 1617491 1617561 1617684 "MKRECORD" 1617815 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-709 1616538 1616700 1616928 "MKFUNC" 1617302 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-708 1615926 1616030 1616186 "MKFLCFN" 1616421 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-707 1615203 1615305 1615490 "MKBCFUNC" 1615819 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-706 1611912 1614757 1614893 "MINT" 1615087 T MINT (NIL) -8 NIL NIL NIL) (-705 1610724 1610967 1611244 "MHROWRED" 1611667 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-704 1606113 1609259 1609664 "MFLOAT" 1610339 T MFLOAT (NIL) -8 NIL NIL NIL) (-703 1605470 1605546 1605717 "MFINFACT" 1606025 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-702 1601805 1602648 1603527 "MESH" 1604611 T MESH (NIL) -7 NIL NIL NIL) (-701 1600195 1600507 1600860 "MDDFACT" 1601492 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-700 1596990 1599354 1599395 "MDAGG" 1599650 NIL MDAGG (NIL T) -9 NIL 1599793 NIL) (-699 1586748 1596283 1596490 "MCMPLX" 1596803 T MCMPLX (NIL) -8 NIL NIL NIL) (-698 1585889 1586035 1586235 "MCDEN" 1586597 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-697 1583779 1584049 1584429 "MCALCFN" 1585619 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-696 1582704 1582944 1583177 "MAYBE" 1583585 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-695 1580316 1580839 1581401 "MATSTOR" 1582175 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-694 1576272 1579688 1579936 "MATRIX" 1580101 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-693 1572036 1572745 1573481 "MATLIN" 1575629 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-692 1570630 1570783 1571116 "MATCAT2" 1571871 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-691 1560730 1563919 1563996 "MATCAT" 1568879 NIL MATCAT (NIL T T T) -9 NIL 1570296 NIL) (-690 1557086 1558107 1559463 "MATCAT-" 1559468 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-689 1555198 1555522 1555906 "MAPPKG3" 1556761 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-688 1554179 1554352 1554574 "MAPPKG2" 1555022 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-687 1552678 1552962 1553289 "MAPPKG1" 1553885 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-686 1551757 1552084 1552261 "MAPPAST" 1552521 T MAPPAST (NIL) -8 NIL NIL NIL) (-685 1551368 1551426 1551549 "MAPHACK3" 1551693 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-684 1550960 1551021 1551135 "MAPHACK2" 1551300 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-683 1550397 1550501 1550643 "MAPHACK1" 1550851 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-682 1548476 1549097 1549401 "MAGMA" 1550125 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-681 1547955 1548200 1548291 "MACROAST" 1548405 T MACROAST (NIL) -8 NIL NIL NIL) (-680 1544373 1546194 1546655 "M3D" 1547527 NIL M3D (NIL T) -8 NIL NIL NIL) (-679 1538481 1542742 1542783 "LZSTAGG" 1543565 NIL LZSTAGG (NIL T) -9 NIL 1543860 NIL) (-678 1534438 1535612 1537069 "LZSTAGG-" 1537074 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-677 1531525 1532329 1532816 "LWORD" 1533983 NIL LWORD (NIL T) -8 NIL NIL NIL) (-676 1531101 1531329 1531404 "LSTAST" 1531470 T LSTAST (NIL) -8 NIL NIL NIL) (-675 1524298 1530872 1531006 "LSQM" 1531011 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-674 1523522 1523661 1523889 "LSPP" 1524153 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-673 1520364 1521021 1521734 "LSMP1" 1522841 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1518199 1518493 1518942 "LSMP" 1520060 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-671 1512078 1517366 1517407 "LSAGG" 1517469 NIL LSAGG (NIL T) -9 NIL 1517547 NIL) (-670 1508773 1509697 1510910 "LSAGG-" 1510915 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-669 1506372 1507917 1508166 "LPOLY" 1508568 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-668 1505954 1506039 1506162 "LPEFRAC" 1506281 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-667 1505606 1505718 1505746 "LOGIC" 1505857 T LOGIC (NIL) -9 NIL 1505938 NIL) (-666 1505468 1505491 1505562 "LOGIC-" 1505567 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1504661 1504801 1504994 "LODOOPS" 1505324 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1503199 1503434 1503787 "LODOF" 1504408 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-663 1499431 1501848 1501889 "LODOCAT" 1502327 NIL LODOCAT (NIL T) -9 NIL 1502538 NIL) (-662 1499164 1499222 1499349 "LODOCAT-" 1499354 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-661 1496498 1499005 1499123 "LODO2" 1499128 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-660 1493947 1496435 1496480 "LODO1" 1496485 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-659 1491384 1493863 1493929 "LODO" 1493934 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-658 1490265 1490430 1490735 "LODEEF" 1491207 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1488586 1489359 1489612 "LO" 1490097 NIL LO (NIL T T T) -8 NIL NIL NIL) (-656 1483825 1486716 1486757 "LNAGG" 1487704 NIL LNAGG (NIL T) -9 NIL 1488148 NIL) (-655 1482972 1483186 1483528 "LNAGG-" 1483533 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-654 1479108 1479897 1480536 "LMOPS" 1482387 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-653 1478511 1478899 1478940 "LMODULE" 1478945 NIL LMODULE (NIL T) -9 NIL 1478971 NIL) (-652 1475709 1478156 1478279 "LMDICT" 1478421 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-651 1475115 1475336 1475377 "LLINSET" 1475568 NIL LLINSET (NIL T) -9 NIL 1475659 NIL) (-650 1474814 1475023 1475083 "LITERAL" 1475088 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-649 1474339 1474413 1474552 "LIST3" 1474734 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1472473 1472785 1473184 "LIST2MAP" 1473986 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-647 1471480 1471658 1471886 "LIST2" 1472291 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-646 1464645 1470414 1470718 "LIST" 1471209 NIL LIST (NIL T) -8 NIL NIL NIL) (-645 1464241 1464478 1464519 "LINSET" 1464524 NIL LINSET (NIL T) -9 NIL 1464558 NIL) (-644 1462902 1463572 1463613 "LINEXP" 1463868 NIL LINEXP (NIL T) -9 NIL 1464017 NIL) (-643 1461549 1461809 1462106 "LINDEP" 1462654 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-642 1458387 1459087 1459845 "LIMITRF" 1460823 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-641 1456713 1457002 1457404 "LIMITPS" 1458089 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-640 1455661 1456130 1456170 "LIECAT" 1456310 NIL LIECAT (NIL T) -9 NIL 1456461 NIL) (-639 1455502 1455529 1455617 "LIECAT-" 1455622 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1449962 1455013 1455241 "LIE" 1455323 NIL LIE (NIL T T) -8 NIL NIL NIL) (-637 1442460 1449411 1449576 "LIB" 1449817 T LIB (NIL) -8 NIL NIL NIL) (-636 1438095 1438978 1439913 "LGROBP" 1441577 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-635 1436935 1437627 1437655 "LFCAT" 1437862 T LFCAT (NIL) -9 NIL 1438001 NIL) (-634 1434933 1435207 1435557 "LF" 1436656 NIL LF (NIL T T) -7 NIL NIL NIL) (-633 1431835 1432465 1433153 "LEXTRIPK" 1434297 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-632 1428579 1429405 1429908 "LEXP" 1431415 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-631 1428055 1428300 1428392 "LETAST" 1428507 T LETAST (NIL) -8 NIL NIL NIL) (-630 1426453 1426766 1427167 "LEADCDET" 1427737 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-629 1425643 1425717 1425946 "LAZM3PK" 1426374 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-628 1420574 1423720 1424258 "LAUPOL" 1425155 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-627 1420153 1420197 1420358 "LAPLACE" 1420524 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-626 1419147 1419731 1419772 "LALG" 1419834 NIL LALG (NIL T) -9 NIL 1419893 NIL) (-625 1418861 1418920 1419056 "LALG-" 1419061 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1416800 1417962 1418213 "LA" 1418694 NIL LA (NIL T T T) -8 NIL NIL NIL) (-623 1416635 1416659 1416700 "KVTFROM" 1416762 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-622 1415558 1416002 1416187 "KTVLOGIC" 1416470 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-621 1415393 1415417 1415458 "KRCFROM" 1415520 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-620 1414297 1414484 1414783 "KOVACIC" 1415193 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-619 1414132 1414156 1414197 "KONVERT" 1414259 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-618 1413967 1413991 1414032 "KOERCE" 1414094 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-617 1413463 1413544 1413676 "KERNEL2" 1413881 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1411293 1412056 1412433 "KERNEL" 1413119 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-615 1405063 1409832 1409886 "KDAGG" 1410263 NIL KDAGG (NIL T T) -9 NIL 1410469 NIL) (-614 1404592 1404716 1404921 "KDAGG-" 1404926 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-613 1397742 1404253 1404408 "KAFILE" 1404470 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-612 1392202 1397253 1397481 "JORDAN" 1397563 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-611 1391581 1391851 1391972 "JOINAST" 1392101 T JOINAST (NIL) -8 NIL NIL NIL) (-610 1391427 1391486 1391541 "JAVACODE" 1391546 T JAVACODE (NIL) -8 NIL NIL NIL) (-609 1387679 1389632 1389686 "IXAGG" 1390615 NIL IXAGG (NIL T T) -9 NIL 1391074 NIL) (-608 1386598 1386904 1387323 "IXAGG-" 1387328 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-607 1382128 1386520 1386579 "IVECTOR" 1386584 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-606 1380894 1381131 1381397 "ITUPLE" 1381895 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-605 1379396 1379573 1379868 "ITRIGMNP" 1380716 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-604 1378141 1378345 1378628 "ITFUN3" 1379172 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-603 1377773 1377830 1377939 "ITFUN2" 1378078 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-602 1377178 1377447 1377572 "ITFORM" 1377668 T ITFORM (NIL) -8 NIL NIL NIL) (-601 1375139 1376198 1376476 "ITAYLOR" 1376933 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-600 1364084 1369276 1370439 "ISUPS" 1374009 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-599 1363188 1363328 1363564 "ISUMP" 1363931 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-598 1358563 1363133 1363174 "ISTRING" 1363179 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-597 1358039 1358284 1358376 "ISAST" 1358491 T ISAST (NIL) -8 NIL NIL NIL) (-596 1357248 1357330 1357546 "IRURPK" 1357953 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-595 1356184 1356385 1356625 "IRSN" 1357028 T IRSN (NIL) -7 NIL NIL NIL) (-594 1354255 1354610 1355039 "IRRF2F" 1355822 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-593 1354002 1354040 1354116 "IRREDFFX" 1354211 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-592 1352617 1352876 1353175 "IROOT" 1353735 NIL IROOT (NIL T) -7 NIL NIL NIL) (-591 1352339 1352532 1352582 "IRFORM" 1352587 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1351439 1351552 1351766 "IR2F" 1352222 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-589 1349052 1349547 1350113 "IR2" 1350917 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-588 1345656 1346736 1347428 "IR" 1348392 NIL IR (NIL T) -8 NIL NIL NIL) (-587 1345447 1345481 1345541 "IPRNTPK" 1345616 T IPRNTPK (NIL) -7 NIL NIL NIL) (-586 1342030 1345336 1345405 "IPF" 1345410 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-585 1340359 1341955 1342012 "IPADIC" 1342017 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-584 1339671 1339919 1340049 "IP4ADDR" 1340249 T IP4ADDR (NIL) -8 NIL NIL NIL) (-583 1339144 1339375 1339485 "IOMODE" 1339581 T IOMODE (NIL) -8 NIL NIL NIL) (-582 1338217 1338741 1338868 "IOBFILE" 1339037 T IOBFILE (NIL) -8 NIL NIL NIL) (-581 1337705 1338121 1338149 "IOBCON" 1338154 T IOBCON (NIL) -9 NIL 1338175 NIL) (-580 1337216 1337274 1337457 "INVLAPLA" 1337641 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-579 1326912 1329254 1331628 "INTTR" 1334892 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-578 1323247 1323989 1324854 "INTTOOLS" 1326097 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-577 1322833 1322924 1323041 "INTSLPE" 1323150 T INTSLPE (NIL) -7 NIL NIL NIL) (-576 1320786 1322756 1322815 "INTRVL" 1322820 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-575 1318388 1318900 1319475 "INTRF" 1320271 NIL INTRF (NIL T) -7 NIL NIL NIL) (-574 1317799 1317896 1318038 "INTRET" 1318286 NIL INTRET (NIL T) -7 NIL NIL NIL) (-573 1315796 1316185 1316655 "INTRAT" 1317407 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-572 1313059 1313642 1314261 "INTPM" 1315281 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-571 1309827 1310419 1311150 "INTPAF" 1312452 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-570 1305006 1305968 1307019 "INTPACK" 1308796 T INTPACK (NIL) -7 NIL NIL NIL) (-569 1304258 1304410 1304618 "INTHERTR" 1304848 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1303697 1303777 1303965 "INTHERAL" 1304172 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1301543 1301986 1302443 "INTHEORY" 1303260 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1293007 1294610 1296364 "INTG0" 1299913 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1279280 1282645 1286030 "INTFTBL" 1289642 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278529 1278667 1278840 "INTFACT" 1279139 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275962 1276406 1276961 "INTEF" 1278085 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1274329 1275068 1275096 "INTDOM" 1275397 T INTDOM (NIL) -9 NIL 1275604 NIL) (-561 1273698 1273872 1274114 "INTDOM-" 1274119 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1270086 1272014 1272068 "INTCAT" 1272867 NIL INTCAT (NIL T) -9 NIL 1273188 NIL) (-559 1269558 1269661 1269789 "INTBIT" 1269978 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1268257 1268411 1268718 "INTALG" 1269403 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267740 1267830 1267987 "INTAF" 1268161 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1261085 1267550 1267690 "INTABL" 1267695 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260426 1260892 1260957 "INT8" 1260991 T INT8 (NIL) -8 NIL NIL 1261036) (-554 1259766 1260232 1260297 "INT64" 1260331 T INT64 (NIL) -8 NIL NIL 1260376) (-553 1259106 1259572 1259637 "INT32" 1259671 T INT32 (NIL) -8 NIL NIL 1259716) (-552 1258446 1258912 1258977 "INT16" 1259011 T INT16 (NIL) -8 NIL NIL 1259056) (-551 1255396 1258243 1258352 "INT" 1258357 T INT (NIL) -8 NIL NIL NIL) (-550 1250308 1253019 1253047 "INS" 1253981 T INS (NIL) -9 NIL 1254646 NIL) (-549 1247548 1248319 1249293 "INS-" 1249366 NIL INS- (NIL T) -8 NIL NIL NIL) (-548 1246396 1246601 1246877 "INPSIGN" 1247323 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-547 1245514 1245631 1245828 "INPRODPF" 1246276 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-546 1244408 1244525 1244762 "INPRODFF" 1245394 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-545 1243408 1243560 1243820 "INNMFACT" 1244244 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-544 1242605 1242702 1242890 "INMODGCD" 1243307 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-543 1241113 1241358 1241682 "INFSP" 1242350 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-542 1240297 1240414 1240597 "INFPROD0" 1240993 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-541 1239907 1239967 1240065 "INFORM1" 1240232 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1236762 1237972 1238487 "INFORM" 1239400 T INFORM (NIL) -8 NIL NIL NIL) (-539 1236285 1236374 1236488 "INFINITY" 1236668 T INFINITY (NIL) -7 NIL NIL NIL) (-538 1235461 1236005 1236106 "INETCLTS" 1236204 T INETCLTS (NIL) -8 NIL NIL NIL) (-537 1234077 1234327 1234648 "INEP" 1235209 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-536 1233326 1233974 1234039 "INDE" 1234044 NIL INDE (NIL T) -8 NIL NIL NIL) (-535 1232890 1232958 1233075 "INCRMAPS" 1233253 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-534 1231708 1232159 1232365 "INBFILE" 1232704 T INBFILE (NIL) -8 NIL NIL NIL) (-533 1227008 1227944 1228888 "INBFF" 1230796 NIL INBFF (NIL T) -7 NIL NIL NIL) (-532 1225916 1226185 1226213 "INBCON" 1226726 T INBCON (NIL) -9 NIL 1226992 NIL) (-531 1225168 1225391 1225667 "INBCON-" 1225672 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-530 1224647 1224892 1224983 "INAST" 1225097 T INAST (NIL) -8 NIL NIL NIL) (-529 1224074 1224326 1224432 "IMPTAST" 1224561 T IMPTAST (NIL) -8 NIL NIL NIL) (-528 1220519 1223918 1224022 "IMATRIX" 1224027 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-527 1219231 1219354 1219669 "IMATQF" 1220375 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-526 1217451 1217678 1218015 "IMATLIN" 1218987 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-525 1212031 1217375 1217433 "ILIST" 1217438 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-524 1209936 1211891 1212004 "IIARRAY2" 1212009 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-523 1205336 1209847 1209911 "IFF" 1209916 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-522 1204683 1204953 1205069 "IFAST" 1205240 T IFAST (NIL) -8 NIL NIL NIL) (-521 1199678 1203975 1204163 "IFARRAY" 1204540 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-520 1198858 1199582 1199655 "IFAMON" 1199660 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-519 1198442 1198507 1198561 "IEVALAB" 1198768 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-518 1198117 1198185 1198345 "IEVALAB-" 1198350 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-517 1197367 1198006 1198081 "IDPOAMS" 1198086 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1196674 1197256 1197331 "IDPOAM" 1197336 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1196305 1196588 1196651 "IDPO" 1196656 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-514 1195364 1195640 1195693 "IDPC" 1196106 NIL IDPC (NIL T T) -9 NIL 1196255 NIL) (-513 1194833 1195256 1195329 "IDPAM" 1195334 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-512 1194209 1194725 1194798 "IDPAG" 1194803 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-511 1193854 1194045 1194120 "IDENT" 1194154 T IDENT (NIL) -8 NIL NIL NIL) (-510 1190109 1190957 1191852 "IDECOMP" 1193011 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-509 1182947 1184032 1185079 "IDEAL" 1189145 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-508 1182111 1182223 1182422 "ICDEN" 1182831 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-507 1181182 1181591 1181738 "ICARD" 1181984 T ICARD (NIL) -8 NIL NIL NIL) (-506 1179242 1179555 1179960 "IBPTOOLS" 1180859 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-505 1174849 1178862 1178975 "IBITS" 1179161 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-504 1171572 1172148 1172843 "IBATOOL" 1174266 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-503 1169351 1169813 1170346 "IBACHIN" 1171107 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-502 1167180 1169197 1169300 "IARRAY2" 1169305 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-501 1163286 1167106 1167163 "IARRAY1" 1167168 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-500 1157404 1161698 1162179 "IAN" 1162825 T IAN (NIL) -8 NIL NIL NIL) (-499 1156915 1156972 1157145 "IALGFACT" 1157341 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-498 1156443 1156556 1156584 "HYPCAT" 1156791 T HYPCAT (NIL) -9 NIL NIL NIL) (-497 1155981 1156098 1156284 "HYPCAT-" 1156289 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-496 1155576 1155776 1155859 "HOSTNAME" 1155918 T HOSTNAME (NIL) -8 NIL NIL NIL) (-495 1155421 1155458 1155499 "HOMOTOP" 1155504 NIL HOMOTOP (NIL T) -9 NIL 1155537 NIL) (-494 1152053 1153431 1153472 "HOAGG" 1154453 NIL HOAGG (NIL T) -9 NIL 1155132 NIL) (-493 1150647 1151046 1151572 "HOAGG-" 1151577 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-492 1144672 1150242 1150391 "HEXADEC" 1150518 T HEXADEC (NIL) -8 NIL NIL NIL) (-491 1143420 1143642 1143905 "HEUGCD" 1144449 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-490 1142496 1143257 1143387 "HELLFDIV" 1143392 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-489 1140675 1142273 1142361 "HEAP" 1142440 NIL HEAP (NIL T) -8 NIL NIL NIL) (-488 1139938 1140227 1140361 "HEADAST" 1140561 T HEADAST (NIL) -8 NIL NIL NIL) (-487 1133811 1139853 1139915 "HDP" 1139920 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-486 1127830 1133446 1133598 "HDMP" 1133712 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-485 1127154 1127294 1127458 "HB" 1127686 T HB (NIL) -7 NIL NIL NIL) (-484 1120542 1127000 1127104 "HASHTBL" 1127109 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-483 1120018 1120263 1120355 "HASAST" 1120470 T HASAST (NIL) -8 NIL NIL NIL) (-482 1117800 1119640 1119822 "HACKPI" 1119856 T HACKPI (NIL) -8 NIL NIL NIL) (-481 1113495 1117653 1117766 "GTSET" 1117771 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-480 1106912 1113373 1113471 "GSTBL" 1113476 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-479 1099192 1105943 1106208 "GSERIES" 1106703 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-478 1098333 1098750 1098778 "GROUP" 1098981 T GROUP (NIL) -9 NIL 1099115 NIL) (-477 1097699 1097858 1098109 "GROUP-" 1098114 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-476 1096066 1096387 1096774 "GROEBSOL" 1097376 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-475 1094980 1095268 1095319 "GRMOD" 1095848 NIL GRMOD (NIL T T) -9 NIL 1096016 NIL) (-474 1094748 1094784 1094912 "GRMOD-" 1094917 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-473 1090038 1091102 1092102 "GRIMAGE" 1093768 T GRIMAGE (NIL) -8 NIL NIL NIL) (-472 1088504 1088765 1089089 "GRDEF" 1089734 T GRDEF (NIL) -7 NIL NIL NIL) (-471 1087948 1088064 1088205 "GRAY" 1088383 T GRAY (NIL) -7 NIL NIL NIL) (-470 1087135 1087541 1087592 "GRALG" 1087745 NIL GRALG (NIL T T) -9 NIL 1087838 NIL) (-469 1086796 1086869 1087032 "GRALG-" 1087037 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-468 1083573 1086381 1086559 "GPOLSET" 1086703 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-467 1082927 1082984 1083242 "GOSPER" 1083510 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-466 1078659 1079365 1079891 "GMODPOL" 1082626 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-465 1077664 1077848 1078086 "GHENSEL" 1078471 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-464 1071820 1072663 1073683 "GENUPS" 1076748 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-463 1071517 1071568 1071657 "GENUFACT" 1071763 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-462 1070929 1071006 1071171 "GENPGCD" 1071435 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-461 1070403 1070438 1070651 "GENMFACT" 1070888 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-460 1068969 1069226 1069533 "GENEEZ" 1070146 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-459 1063146 1068580 1068742 "GDMP" 1068892 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-458 1052510 1056917 1058023 "GCNAALG" 1062129 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-457 1050837 1051699 1051727 "GCDDOM" 1051982 T GCDDOM (NIL) -9 NIL 1052139 NIL) (-456 1050307 1050434 1050649 "GCDDOM-" 1050654 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-455 1038923 1041253 1043645 "GBINTERN" 1047998 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1036760 1037052 1037473 "GBF" 1038598 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1035541 1035706 1035973 "GBEUCLID" 1036576 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1034213 1034398 1034702 "GB" 1035320 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1033562 1033687 1033836 "GAUSSFAC" 1034084 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-450 1031929 1032231 1032545 "GALUTIL" 1033281 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-449 1030237 1030511 1030835 "GALPOLYU" 1031656 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-448 1027602 1027892 1028299 "GALFACTU" 1029934 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-447 1019407 1020907 1022515 "GALFACT" 1026034 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-446 1016795 1017453 1017481 "FVFUN" 1018637 T FVFUN (NIL) -9 NIL 1019357 NIL) (-445 1016061 1016243 1016271 "FVC" 1016562 T FVC (NIL) -9 NIL 1016745 NIL) (-444 1015704 1015886 1015954 "FUNDESC" 1016013 T FUNDESC (NIL) -8 NIL NIL NIL) (-443 1015319 1015501 1015582 "FUNCTION" 1015656 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-442 1014110 1014620 1014823 "FTEM" 1015136 T FTEM (NIL) -8 NIL NIL NIL) (-441 1011866 1012441 1012904 "FT" 1013667 T FT (NIL) -8 NIL NIL NIL) (-440 1010157 1010446 1010843 "FSUPFACT" 1011557 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-439 1008554 1008843 1009175 "FST" 1009845 T FST (NIL) -8 NIL NIL NIL) (-438 1007753 1007859 1008047 "FSRED" 1008436 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-437 1006452 1006708 1007055 "FSPRMELT" 1007468 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-436 1003758 1004196 1004682 "FSPECF" 1006015 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-435 1003286 1003340 1003510 "FSINT" 1003699 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-434 1001578 1002279 1002582 "FSERIES" 1003065 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-433 1000620 1000736 1000960 "FSCINT" 1001458 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-432 999662 999805 1000032 "FSAGG2" 1000473 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-431 995870 998606 998647 "FSAGG" 999017 NIL FSAGG (NIL T) -9 NIL 999276 NIL) (-430 993632 994233 995029 "FSAGG-" 995124 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 991314 991594 992141 "FS2UPS" 993350 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-428 990192 990363 990665 "FS2EXPXP" 991139 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-427 989826 989869 989998 "FS2" 990143 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 971493 979795 979836 "FS" 983720 NIL FS (NIL T) -9 NIL 986009 NIL) (-425 960217 963183 967213 "FS-" 967513 NIL FS- (NIL T T) -8 NIL NIL NIL) (-424 959643 959758 959910 "FRUTIL" 960097 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-423 954644 957286 957326 "FRNAALG" 958722 NIL FRNAALG (NIL T) -9 NIL 959329 NIL) (-422 950368 951427 952685 "FRNAALG-" 953435 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 950006 950049 950176 "FRNAAF2" 950319 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 948386 948860 949155 "FRMOD" 949818 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 947581 947668 947957 "FRIDEAL2" 948293 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-418 945332 945964 946281 "FRIDEAL" 947372 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-417 944472 944879 944920 "FRETRCT" 944925 NIL FRETRCT (NIL T) -9 NIL 945101 NIL) (-416 943605 943829 944173 "FRETRCT-" 944178 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 940693 941903 941962 "FRAMALG" 942844 NIL FRAMALG (NIL T T) -9 NIL 943136 NIL) (-414 938827 939282 939912 "FRAMALG-" 940135 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 938463 938520 938627 "FRAC2" 938764 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-412 932405 937938 938214 "FRAC" 938219 NIL FRAC (NIL T) -8 NIL NIL NIL) (-411 932041 932098 932205 "FR2" 932342 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 923569 927617 928948 "FR" 930742 NIL FR (NIL T) -8 NIL NIL NIL) (-409 918086 920975 921003 "FPS" 922122 T FPS (NIL) -9 NIL 922679 NIL) (-408 917535 917644 917808 "FPS-" 917954 NIL FPS- (NIL T) -8 NIL NIL NIL) (-407 914839 916506 916534 "FPC" 916759 T FPC (NIL) -9 NIL 916901 NIL) (-406 914632 914672 914769 "FPC-" 914774 NIL FPC- (NIL T) -8 NIL NIL NIL) (-405 913422 914120 914161 "FPATMAB" 914166 NIL FPATMAB (NIL T) -9 NIL 914318 NIL) (-404 911095 911598 912024 "FPARFRAC" 913059 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-403 906528 907026 907708 "FORTRAN" 910527 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-402 904204 904766 904794 "FORTFN" 905854 T FORTFN (NIL) -9 NIL 906478 NIL) (-401 903968 904018 904046 "FORTCAT" 904105 T FORTCAT (NIL) -9 NIL 904167 NIL) (-400 901684 902184 902723 "FORT" 903449 T FORT (NIL) -7 NIL NIL NIL) (-399 901472 901502 901571 "FORMULA1" 901648 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 899578 900088 900478 "FORMULA" 901102 T FORMULA (NIL) -8 NIL NIL NIL) (-397 899101 899153 899326 "FORDER" 899520 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-396 898197 898361 898554 "FOP" 898928 T FOP (NIL) -7 NIL NIL NIL) (-395 896778 897477 897651 "FNLA" 898079 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-394 895507 895922 895950 "FNCAT" 896410 T FNCAT (NIL) -9 NIL 896670 NIL) (-393 895046 895466 895494 "FNAME" 895499 T FNAME (NIL) -8 NIL NIL NIL) (-392 893609 894572 894600 "FMTC" 894605 T FMTC (NIL) -9 NIL 894641 NIL) (-391 892362 893545 893591 "FMONOID" 893596 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-390 889190 890358 890399 "FMONCAT" 891616 NIL FMONCAT (NIL T) -9 NIL 892221 NIL) (-389 886614 887260 887288 "FMFUN" 888432 T FMFUN (NIL) -9 NIL 889140 NIL) (-388 883693 884553 884607 "FMCAT" 885802 NIL FMCAT (NIL T T) -9 NIL 886297 NIL) (-387 882962 883143 883171 "FMC" 883461 T FMC (NIL) -9 NIL 883643 NIL) (-386 881828 882728 882828 "FM1" 882907 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 881020 881570 881719 "FM" 881724 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 878794 879210 879704 "FLOATRP" 880571 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-383 876232 876732 877310 "FLOATCP" 878261 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 869810 873961 874582 "FLOAT" 875631 T FLOAT (NIL) -8 NIL NIL NIL) (-381 868550 869388 869429 "FLINEXP" 869434 NIL FLINEXP (NIL T) -9 NIL 869527 NIL) (-380 867704 867939 868267 "FLINEXP-" 868272 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-379 866780 866924 867148 "FLASORT" 867556 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-378 863896 864764 864816 "FLALG" 866043 NIL FLALG (NIL T T) -9 NIL 866510 NIL) (-377 862938 863081 863308 "FLAGG2" 863749 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-376 856674 860424 860465 "FLAGG" 861727 NIL FLAGG (NIL T) -9 NIL 862379 NIL) (-375 855400 855739 856229 "FLAGG-" 856234 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-374 852251 853259 853318 "FINRALG" 854446 NIL FINRALG (NIL T T) -9 NIL 854954 NIL) (-373 851411 851640 851979 "FINRALG-" 851984 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-372 850791 851030 851058 "FINITE" 851254 T FINITE (NIL) -9 NIL 851361 NIL) (-371 843148 845335 845375 "FINAALG" 849042 NIL FINAALG (NIL T) -9 NIL 850495 NIL) (-370 838480 839530 840674 "FINAALG-" 842053 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-369 837138 837476 837530 "FILECAT" 838214 NIL FILECAT (NIL T T) -9 NIL 838430 NIL) (-368 836506 836893 836996 "FILE" 837068 NIL FILE (NIL T) -8 NIL NIL NIL) (-367 834224 835750 835778 "FIELD" 835818 T FIELD (NIL) -9 NIL 835898 NIL) (-366 832844 833229 833740 "FIELD-" 833745 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-365 830694 831479 831826 "FGROUP" 832530 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-364 829784 829948 830168 "FGLMICPK" 830526 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-363 825618 829709 829766 "FFX" 829771 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-362 825219 825280 825415 "FFSLPE" 825551 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-361 824723 824759 824968 "FFPOLY2" 825177 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 820713 821495 822291 "FFPOLY" 823959 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-359 816559 820632 820695 "FFP" 820700 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-358 811687 815902 816092 "FFNBX" 816413 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 806617 810822 811080 "FFNBP" 811541 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 801252 805901 806112 "FFNB" 806450 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 800084 800282 800597 "FFINTBAS" 801049 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 796155 798373 798401 "FFIELDC" 799021 T FFIELDC (NIL) -9 NIL 799397 NIL) (-353 794817 795188 795685 "FFIELDC-" 795690 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 794386 794432 794556 "FFHOM" 794759 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 792081 792568 793085 "FFF" 793901 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 787701 791823 791924 "FFCGX" 792024 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 783325 787433 787540 "FFCGP" 787644 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 778510 783052 783160 "FFCG" 783261 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 777921 777964 778199 "FFCAT2" 778461 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 759326 768398 768484 "FFCAT" 773649 NIL FFCAT (NIL T T T) -9 NIL 775100 NIL) (-345 754523 755571 756885 "FFCAT-" 758115 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-344 749923 754434 754498 "FF" 754503 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-343 739248 742895 744115 "FEXPR" 748775 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-342 738248 738683 738724 "FEVALAB" 738808 NIL FEVALAB (NIL T) -9 NIL 739069 NIL) (-341 737407 737617 737955 "FEVALAB-" 737960 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-340 734427 735168 735283 "FDIVCAT" 736851 NIL FDIVCAT (NIL T T T T) -9 NIL 737288 NIL) (-339 734189 734216 734386 "FDIVCAT-" 734391 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733409 733496 733773 "FDIV2" 734096 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 731975 732792 732995 "FDIV" 733308 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-336 730949 731270 731472 "FCTRDATA" 731793 T FCTRDATA (NIL) -8 NIL NIL NIL) (-335 729635 729894 730183 "FCPAK1" 730680 T FCPAK1 (NIL) -7 NIL NIL NIL) (-334 728734 729135 729276 "FCOMP" 729526 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-333 712439 715884 719422 "FC" 725216 T FC (NIL) -8 NIL NIL NIL) (-332 704804 708830 708870 "FAXF" 710672 NIL FAXF (NIL T) -9 NIL 711364 NIL) (-331 702080 702738 703563 "FAXF-" 704028 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-330 697132 701456 701632 "FARRAY" 701937 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-329 692033 694093 694146 "FAMR" 695169 NIL FAMR (NIL T T) -9 NIL 695629 NIL) (-328 690923 691225 691660 "FAMR-" 691665 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-327 690092 690845 690898 "FAMONOID" 690903 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-326 687878 688588 688641 "FAMONC" 689582 NIL FAMONC (NIL T T) -9 NIL 689968 NIL) (-325 686542 687632 687769 "FAGROUP" 687774 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-324 684337 684656 685059 "FACUTIL" 686223 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-323 683436 683621 683843 "FACTFUNC" 684147 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-322 675860 682739 682938 "EXPUPXS" 683292 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-321 673343 673883 674469 "EXPRTUBE" 675294 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-320 669614 670206 670936 "EXPRODE" 672682 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-319 664168 664755 665561 "EXPR2UPS" 668912 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 663800 663857 663966 "EXPR2" 664105 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 649346 662449 662878 "EXPR" 663404 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 640762 648499 648789 "EXPEXPAN" 649183 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-315 640242 640486 640577 "EXITAST" 640691 T EXITAST (NIL) -8 NIL NIL NIL) (-314 640042 640199 640228 "EXIT" 640233 T EXIT (NIL) -8 NIL NIL NIL) (-313 639669 639731 639844 "EVALCYC" 639974 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-312 639210 639328 639369 "EVALAB" 639539 NIL EVALAB (NIL T) -9 NIL 639643 NIL) (-311 638691 638813 639034 "EVALAB-" 639039 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-310 636059 637361 637389 "EUCDOM" 637944 T EUCDOM (NIL) -9 NIL 638294 NIL) (-309 634464 634906 635496 "EUCDOM-" 635501 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-308 634096 634153 634262 "ESTOOLS2" 634401 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 633847 633889 633969 "ESTOOLS1" 634048 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 621385 624145 626895 "ESTOOLS" 631117 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 621130 621162 621244 "ESCONT1" 621347 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-304 617504 618265 619045 "ESCONT" 620370 T ESCONT (NIL) -7 NIL NIL NIL) (-303 617179 617229 617329 "ES2" 617448 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-302 616809 616867 616976 "ES1" 617115 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-301 610846 612454 612482 "ES" 615250 T ES (NIL) -9 NIL 616660 NIL) (-300 605793 607080 608897 "ES-" 609061 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 605009 605138 605314 "ERROR" 605637 T ERROR (NIL) -7 NIL NIL NIL) (-298 598403 604868 604959 "EQTBL" 604964 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-297 598035 598092 598201 "EQ2" 598340 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 590538 593349 594798 "EQ" 596619 NIL -3971 (NIL T) -8 NIL NIL NIL) (-295 585828 586876 587969 "EP" 589477 NIL EP (NIL T) -7 NIL NIL NIL) (-294 584428 584719 585025 "ENV" 585542 T ENV (NIL) -8 NIL NIL NIL) (-293 583522 584076 584104 "ENTIRER" 584109 T ENTIRER (NIL) -9 NIL 584155 NIL) (-292 580045 581531 581901 "EMR" 583321 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-291 579189 579374 579428 "ELTAGG" 579808 NIL ELTAGG (NIL T T) -9 NIL 580019 NIL) (-290 578908 578970 579111 "ELTAGG-" 579116 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-289 578697 578726 578780 "ELTAB" 578864 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-288 577823 577969 578168 "ELFUTS" 578548 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-287 577565 577621 577649 "ELEMFUN" 577754 T ELEMFUN (NIL) -9 NIL NIL NIL) (-286 577435 577456 577524 "ELEMFUN-" 577529 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-285 572279 575535 575576 "ELAGG" 576516 NIL ELAGG (NIL T) -9 NIL 576979 NIL) (-284 570564 570998 571661 "ELAGG-" 571666 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-283 569876 570013 570169 "ELABOR" 570428 T ELABOR (NIL) -8 NIL NIL NIL) (-282 568537 568816 569110 "ELABEXPR" 569602 T ELABEXPR (NIL) -8 NIL NIL NIL) (-281 561528 563204 564031 "EFUPXS" 567813 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-280 555105 556779 557589 "EFULS" 560804 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-279 552590 552948 553420 "EFSTRUC" 554737 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-278 542381 543947 545495 "EF" 551105 NIL EF (NIL T T) -7 NIL NIL NIL) (-277 541455 541866 542015 "EAB" 542252 T EAB (NIL) -8 NIL NIL NIL) (-276 540637 541414 541442 "E04UCFA" 541447 T E04UCFA (NIL) -8 NIL NIL NIL) (-275 539819 540596 540624 "E04NAFA" 540629 T E04NAFA (NIL) -8 NIL NIL NIL) (-274 539001 539778 539806 "E04MBFA" 539811 T E04MBFA (NIL) -8 NIL NIL NIL) (-273 538183 538960 538988 "E04JAFA" 538993 T E04JAFA (NIL) -8 NIL NIL NIL) (-272 537367 538142 538170 "E04GCFA" 538175 T E04GCFA (NIL) -8 NIL NIL NIL) (-271 536551 537326 537354 "E04FDFA" 537359 T E04FDFA (NIL) -8 NIL NIL NIL) (-270 535733 536510 536538 "E04DGFA" 536543 T E04DGFA (NIL) -8 NIL NIL NIL) (-269 529906 531258 532622 "E04AGNT" 534389 T E04AGNT (NIL) -7 NIL NIL NIL) (-268 528586 529092 529132 "DVARCAT" 529607 NIL DVARCAT (NIL T) -9 NIL 529806 NIL) (-267 527790 528002 528316 "DVARCAT-" 528321 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-266 520968 527589 527718 "DSMP" 527723 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-265 520633 520692 520790 "DROPT1" 520903 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 515748 516874 518011 "DROPT0" 519516 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510529 511693 512761 "DROPT" 514700 T DROPT (NIL) -8 NIL NIL NIL) (-262 508874 509199 509585 "DRAWPT" 510163 T DRAWPT (NIL) -7 NIL NIL NIL) (-261 508507 508560 508678 "DRAWHACK" 508815 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 507238 507507 507798 "DRAWCX" 508236 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 506753 506822 506973 "DRAWCURV" 507164 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 497221 499183 501298 "DRAWCFUN" 504658 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 491808 492731 493810 "DRAW" 496195 NIL DRAW (NIL T) -7 NIL NIL NIL) (-256 488572 490501 490542 "DQAGG" 491171 NIL DQAGG (NIL T) -9 NIL 491445 NIL) (-255 476732 483165 483248 "DPOLCAT" 485100 NIL DPOLCAT (NIL T T T T) -9 NIL 485645 NIL) (-254 471619 472951 474892 "DPOLCAT-" 474897 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-253 464748 471480 471578 "DPMO" 471583 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-252 457780 464528 464695 "DPMM" 464700 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-251 457258 457472 457570 "DOMTMPLT" 457702 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-250 456691 457060 457140 "DOMCTOR" 457198 T DOMCTOR (NIL) -8 NIL NIL NIL) (-249 455903 456171 456322 "DOMAIN" 456560 T DOMAIN (NIL) -8 NIL NIL NIL) (-248 449922 455538 455690 "DMP" 455804 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-247 449522 449578 449722 "DLP" 449860 NIL DLP (NIL T) -7 NIL NIL NIL) (-246 443346 448849 449039 "DLIST" 449364 NIL DLIST (NIL T) -8 NIL NIL NIL) (-245 440144 442199 442240 "DLAGG" 442790 NIL DLAGG (NIL T) -9 NIL 443020 NIL) (-244 438820 439484 439512 "DIVRING" 439604 T DIVRING (NIL) -9 NIL 439687 NIL) (-243 438057 438247 438547 "DIVRING-" 438552 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-242 436159 436516 436922 "DISPLAY" 437671 T DISPLAY (NIL) -7 NIL NIL NIL) (-241 435007 435210 435475 "DIRPROD2" 435952 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 428902 434921 434984 "DIRPROD" 434989 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 417684 423683 423736 "DIRPCAT" 424146 NIL DIRPCAT (NIL NIL T) -9 NIL 424986 NIL) (-238 415010 415652 416533 "DIRPCAT-" 416870 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-237 414297 414457 414643 "DIOSP" 414844 T DIOSP (NIL) -7 NIL NIL NIL) (-236 410952 413209 413250 "DIOPS" 413684 NIL DIOPS (NIL T) -9 NIL 413913 NIL) (-235 410501 410615 410806 "DIOPS-" 410811 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-234 409324 409952 409980 "DIFRING" 410167 T DIFRING (NIL) -9 NIL 410277 NIL) (-233 408970 409047 409199 "DIFRING-" 409204 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-232 406706 407978 408019 "DIFEXT" 408382 NIL DIFEXT (NIL T) -9 NIL 408676 NIL) (-231 404991 405419 406085 "DIFEXT-" 406090 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-230 402266 404523 404564 "DIAGG" 404569 NIL DIAGG (NIL T) -9 NIL 404589 NIL) (-229 401650 401807 402059 "DIAGG-" 402064 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-228 397066 400609 400886 "DHMATRIX" 401419 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-227 392678 393587 394597 "DFSFUN" 396076 T DFSFUN (NIL) -7 NIL NIL NIL) (-226 387761 391609 391921 "DFLOAT" 392386 T DFLOAT (NIL) -8 NIL NIL NIL) (-225 386024 386305 386694 "DFINTTLS" 387469 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-224 383053 384045 384445 "DERHAM" 385690 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-223 380854 382828 382917 "DEQUEUE" 382997 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-222 380108 380241 380424 "DEGRED" 380716 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-221 376718 377418 378219 "DEFINTRF" 379381 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-220 374385 374826 375390 "DEFINTEF" 376265 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-219 373735 374005 374120 "DEFAST" 374290 T DEFAST (NIL) -8 NIL NIL NIL) (-218 367760 373330 373479 "DECIMAL" 373606 T DECIMAL (NIL) -8 NIL NIL NIL) (-217 365272 365730 366236 "DDFACT" 367304 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-216 364868 364911 365062 "DBLRESP" 365223 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-215 362740 363101 363461 "DBASE" 364635 NIL DBASE (NIL T) -8 NIL NIL NIL) (-214 361982 362220 362366 "DATAARY" 362639 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-213 361088 361941 361969 "D03FAFA" 361974 T D03FAFA (NIL) -8 NIL NIL NIL) (-212 360195 361047 361075 "D03EEFA" 361080 T D03EEFA (NIL) -8 NIL NIL NIL) (-211 358145 358611 359100 "D03AGNT" 359726 T D03AGNT (NIL) -7 NIL NIL NIL) (-210 357434 358104 358132 "D02EJFA" 358137 T D02EJFA (NIL) -8 NIL NIL NIL) (-209 356723 357393 357421 "D02CJFA" 357426 T D02CJFA (NIL) -8 NIL NIL NIL) (-208 356012 356682 356710 "D02BHFA" 356715 T D02BHFA (NIL) -8 NIL NIL NIL) (-207 355301 355971 355999 "D02BBFA" 356004 T D02BBFA (NIL) -8 NIL NIL NIL) (-206 348498 350087 351693 "D02AGNT" 353715 T D02AGNT (NIL) -7 NIL NIL NIL) (-205 346266 346789 347335 "D01WGTS" 347972 T D01WGTS (NIL) -7 NIL NIL NIL) (-204 345333 346225 346253 "D01TRNS" 346258 T D01TRNS (NIL) -8 NIL NIL NIL) (-203 344401 345292 345320 "D01GBFA" 345325 T D01GBFA (NIL) -8 NIL NIL NIL) (-202 343469 344360 344388 "D01FCFA" 344393 T D01FCFA (NIL) -8 NIL NIL NIL) (-201 342537 343428 343456 "D01ASFA" 343461 T D01ASFA (NIL) -8 NIL NIL NIL) (-200 341605 342496 342524 "D01AQFA" 342529 T D01AQFA (NIL) -8 NIL NIL NIL) (-199 340673 341564 341592 "D01APFA" 341597 T D01APFA (NIL) -8 NIL NIL NIL) (-198 339741 340632 340660 "D01ANFA" 340665 T D01ANFA (NIL) -8 NIL NIL NIL) (-197 338809 339700 339728 "D01AMFA" 339733 T D01AMFA (NIL) -8 NIL NIL NIL) (-196 337877 338768 338796 "D01ALFA" 338801 T D01ALFA (NIL) -8 NIL NIL NIL) (-195 336945 337836 337864 "D01AKFA" 337869 T D01AKFA (NIL) -8 NIL NIL NIL) (-194 336013 336904 336932 "D01AJFA" 336937 T D01AJFA (NIL) -8 NIL NIL NIL) (-193 329308 330861 332422 "D01AGNT" 334472 T D01AGNT (NIL) -7 NIL NIL NIL) (-192 328645 328773 328925 "CYCLOTOM" 329176 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-191 325380 326093 326820 "CYCLES" 327938 T CYCLES (NIL) -7 NIL NIL NIL) (-190 324692 324826 324997 "CVMP" 325241 NIL CVMP (NIL T) -7 NIL NIL NIL) (-189 322533 322791 323160 "CTRIGMNP" 324420 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-188 322042 322264 322365 "CTORKIND" 322452 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321333 321649 321677 "CTORCAT" 321859 T CTORCAT (NIL) -9 NIL 321972 NIL) (-186 320931 321042 321201 "CTORCAT-" 321206 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320393 320605 320713 "CTORCALL" 320855 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 319829 320187 320260 "CTOR" 320340 T CTOR (NIL) -8 NIL NIL NIL) (-183 319203 319302 319455 "CSTTOOLS" 319726 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-182 315002 315659 316417 "CRFP" 318515 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-181 314477 314723 314815 "CRCEAST" 314930 T CRCEAST (NIL) -8 NIL NIL NIL) (-180 313524 313709 313937 "CRAPACK" 314281 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-179 312908 313009 313213 "CPMATCH" 313400 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-178 312633 312661 312767 "CPIMA" 312874 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-177 308981 309653 310372 "COORDSYS" 311968 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-176 308393 308514 308656 "CONTOUR" 308859 T CONTOUR (NIL) -8 NIL NIL NIL) (-175 304286 306396 306888 "CONTFRAC" 307933 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-174 304166 304187 304215 "CONDUIT" 304252 T CONDUIT (NIL) -9 NIL NIL NIL) (-173 303254 303808 303836 "COMRING" 303841 T COMRING (NIL) -9 NIL 303893 NIL) (-172 302308 302612 302796 "COMPPROP" 303090 T COMPPROP (NIL) -8 NIL NIL NIL) (-171 301969 302004 302132 "COMPLPAT" 302267 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-170 301605 301662 301769 "COMPLEX2" 301906 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 291914 301414 301523 "COMPLEX" 301528 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291468 291545 291662 "COMPILER" 291817 T COMPILER (NIL) -8 NIL NIL NIL) (-167 291186 291221 291319 "COMPFACT" 291427 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275275 285260 285300 "COMPCAT" 286304 NIL COMPCAT (NIL T) -9 NIL 287652 NIL) (-165 264808 267728 271348 "COMPCAT-" 271704 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264537 264565 264668 "COMMUPC" 264774 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264331 264365 264424 "COMMONOP" 264498 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 263907 264135 264210 "COMMAAST" 264276 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263463 263658 263745 "COMM" 263840 T COMM (NIL) -8 NIL NIL NIL) (-160 262712 262906 262934 "COMBOPC" 263272 T COMBOPC (NIL) -9 NIL 263447 NIL) (-159 261608 261818 262060 "COMBINAT" 262502 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258065 258639 259266 "COMBF" 261030 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 256823 257181 257416 "COLOR" 257850 T COLOR (NIL) -8 NIL NIL NIL) (-156 256299 256544 256636 "COLONAST" 256751 T COLONAST (NIL) -8 NIL NIL NIL) (-155 255939 255986 256111 "CMPLXRT" 256246 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255387 255639 255738 "CLLCTAST" 255860 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 250886 251917 252997 "CLIP" 254327 T CLIP (NIL) -7 NIL NIL NIL) (-152 249232 249992 250231 "CLIF" 250713 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245407 247378 247419 "CLAGG" 248348 NIL CLAGG (NIL T) -9 NIL 248884 NIL) (-150 243829 244286 244869 "CLAGG-" 244874 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243373 243458 243598 "CINTSLPE" 243738 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 240874 241345 241893 "CHVAR" 242901 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240048 240602 240630 "CHARZ" 240635 T CHARZ (NIL) -9 NIL 240650 NIL) (-146 239802 239842 239920 "CHARPOL" 240002 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 238860 239447 239475 "CHARNZ" 239522 T CHARNZ (NIL) -9 NIL 239578 NIL) (-144 236766 237514 237867 "CHAR" 238527 T CHAR (NIL) -8 NIL NIL NIL) (-143 236492 236553 236581 "CFCAT" 236692 T CFCAT (NIL) -9 NIL NIL NIL) (-142 235737 235848 236030 "CDEN" 236376 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 231702 234890 235170 "CCLASS" 235477 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230953 231110 231287 "CATEGORY" 231545 T -10 (NIL) -8 NIL NIL NIL) (-139 230526 230872 230920 "CATCTOR" 230925 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229977 230229 230327 "CATAST" 230448 T CATAST (NIL) -8 NIL NIL NIL) (-137 229453 229698 229790 "CASEAST" 229905 T CASEAST (NIL) -8 NIL NIL NIL) (-136 228561 228709 228930 "CARTEN2" 229300 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 223570 224590 225343 "CARTEN" 227864 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 221886 222720 222977 "CARD" 223333 T CARD (NIL) -8 NIL NIL NIL) (-133 221462 221690 221765 "CAPSLAST" 221831 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220966 221174 221202 "CACHSET" 221334 T CACHSET (NIL) -9 NIL 221412 NIL) (-131 220436 220758 220786 "CABMON" 220836 T CABMON (NIL) -9 NIL 220892 NIL) (-130 219909 220140 220250 "BYTEORD" 220346 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 215259 219414 219586 "BYTEBUF" 219757 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 214241 214793 214935 "BYTE" 215098 T BYTE (NIL) -8 NIL NIL 215220) (-127 211752 213933 214040 "BTREE" 214167 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209203 211400 211522 "BTOURN" 211662 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206575 208673 208714 "BTCAT" 208782 NIL BTCAT (NIL T) -9 NIL 208859 NIL) (-124 206242 206322 206471 "BTCAT-" 206476 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201507 205385 205413 "BTAGG" 205635 T BTAGG (NIL) -9 NIL 205796 NIL) (-122 200997 201122 201328 "BTAGG-" 201333 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197994 200275 200490 "BSTREE" 200814 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197132 197258 197442 "BRILL" 197850 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193785 195858 195899 "BRAGG" 196548 NIL BRAGG (NIL T) -9 NIL 196806 NIL) (-118 192317 192722 193276 "BRAGG-" 193281 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185567 191663 191847 "BPADICRT" 192165 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183884 185504 185549 "BPADIC" 185554 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183582 183612 183726 "BOUNDZRO" 183848 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 181363 181767 182242 "BOP1" 183140 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 176591 177789 178701 "BOP" 180471 T BOP (NIL) -8 NIL NIL NIL) (-112 175416 176165 176314 "BOOLEAN" 176462 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174695 175099 175153 "BMODULE" 175158 NIL BMODULE (NIL T T) -9 NIL 175223 NIL) (-110 170496 174493 174566 "BITS" 174642 T BITS (NIL) -8 NIL NIL NIL) (-109 169917 170036 170176 "BINDING" 170376 T BINDING (NIL) -8 NIL NIL NIL) (-108 163945 169514 169662 "BINARY" 169789 T BINARY (NIL) -8 NIL NIL NIL) (-107 161725 163200 163241 "BGAGG" 163501 NIL BGAGG (NIL T) -9 NIL 163638 NIL) (-106 161556 161588 161679 "BGAGG-" 161684 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160627 160940 161145 "BFUNCT" 161371 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159311 159492 159780 "BEZOUT" 160451 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155782 158163 158493 "BBTREE" 159014 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155516 155569 155597 "BASTYPE" 155716 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155368 155397 155470 "BASTYPE-" 155475 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154802 154878 155030 "BALFACT" 155279 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153658 154217 154403 "AUTOMOR" 154647 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153384 153389 153415 "ATTREG" 153420 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151636 152081 152433 "ATTRBUT" 153050 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151244 151464 151530 "ATTRAST" 151588 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150780 150893 150919 "ATRIG" 151120 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150589 150630 150717 "ATRIG-" 150722 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150234 150420 150446 "ASTCAT" 150451 T ASTCAT (NIL) -9 NIL 150481 NIL) (-92 149961 150020 150139 "ASTCAT-" 150144 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148110 149737 149825 "ASTACK" 149904 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146615 146912 147277 "ASSOCEQ" 147792 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145669 146274 146398 "ASP9" 146522 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 144559 145274 145416 "ASP80" 145558 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 144322 144507 144546 "ASP8" 144551 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 143298 143999 144117 "ASP78" 144235 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 142289 142978 143095 "ASP77" 143212 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 141223 141927 142058 "ASP74" 142189 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 140145 140858 140990 "ASP73" 141122 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 139065 139780 139912 "ASP7" 140044 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 138191 138891 138991 "ASP6" 138996 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137158 137868 137986 "ASP55" 138104 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136129 136832 136951 "ASP50" 137070 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135239 135830 135940 "ASP49" 136050 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 134045 134778 134946 "ASP42" 135128 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 132843 133578 133748 "ASP41" 133932 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131953 132544 132654 "ASP4" 132764 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 130925 131630 131748 "ASP35" 131866 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130690 130873 130912 "ASP34" 130917 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130427 130494 130570 "ASP33" 130645 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129342 130062 130194 "ASP31" 130326 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129107 129290 129329 "ASP30" 129334 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128842 128911 128987 "ASP29" 129062 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128607 128790 128829 "ASP28" 128834 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128372 128555 128594 "ASP27" 128599 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127478 128070 128181 "ASP24" 128292 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126576 127280 127392 "ASP20" 127397 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125540 126250 126369 "ASP19" 126488 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 125277 125344 125420 "ASP12" 125495 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 124151 124876 125020 "ASP10" 125164 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 123261 123852 123962 "ASP1" 124072 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 121112 123105 123196 "ARRAY2" 123201 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 120144 120317 120538 "ARRAY12" 120935 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 115909 119792 119906 "ARRAY1" 120061 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 110221 112139 112214 "ARR2CAT" 114844 NIL ARR2CAT (NIL T T T) -9 NIL 115602 NIL) (-56 107655 108399 109353 "ARR2CAT-" 109358 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106972 107282 107407 "ARITY" 107548 T ARITY (NIL) -8 NIL NIL NIL) (-54 105748 105900 106199 "APPRULE" 106808 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105399 105447 105566 "APPLYORE" 105694 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104677 104800 104957 "ANY1" 105273 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 104031 104270 104390 "ANY" 104575 T ANY (NIL) -8 NIL NIL NIL) (-50 101561 102468 102795 "ANTISYM" 103755 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101053 101268 101364 "ANON" 101483 T ANON (NIL) -8 NIL NIL NIL) (-48 95311 99592 100046 "AN" 100617 T AN (NIL) -8 NIL NIL NIL) (-47 91209 92597 92648 "AMR" 93396 NIL AMR (NIL T T) -9 NIL 93996 NIL) (-46 90321 90542 90905 "AMR-" 90910 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74766 90238 90299 "ALIST" 90304 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71601 74360 74529 "ALGSC" 74684 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68156 68711 69318 "ALGPKG" 71041 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67433 67534 67718 "ALGMFACT" 68042 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63468 64047 64641 "ALGMANIP" 67017 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54849 63094 63244 "ALGFF" 63401 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54045 54176 54355 "ALGFACT" 54707 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52986 53586 53624 "ALGEBRA" 53629 NIL ALGEBRA (NIL T) -9 NIL 53670 NIL) (-37 52704 52763 52895 "ALGEBRA-" 52900 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34803 50706 50758 "ALAGG" 50894 NIL ALAGG (NIL T T) -9 NIL 51055 NIL) (-35 34339 34452 34478 "AHYP" 34679 T AHYP (NIL) -9 NIL NIL NIL) (-34 33270 33518 33544 "AGG" 34043 T AGG (NIL) -9 NIL 34322 NIL) (-33 32704 32866 33080 "AGG-" 33085 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30510 30933 31338 "AF" 32346 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29990 30235 30325 "ADDAST" 30438 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29258 29517 29673 "ACPLOT" 29852 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18637 26385 26423 "ACFS" 27030 NIL ACFS (NIL T) -9 NIL 27269 NIL) (-28 16664 17154 17916 "ACFS-" 17921 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14711 14737 "ACF" 15616 T ACF (NIL) -9 NIL 16029 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3216732 3216737 3216742 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3216717 3216722 3216727 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3216702 3216707 3216712 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3216687 3216692 3216697 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1301 3215830 3216562 3216639 "ZMOD" 3216644 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1300 3214940 3215104 3215313 "ZLINDEP" 3215662 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1299 3204240 3206008 3207980 "ZDSOLVE" 3213070 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1298 3203486 3203627 3203816 "YSTREAM" 3204086 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1297 3201260 3202787 3202991 "XRPOLY" 3203329 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3197813 3199131 3199706 "XPR" 3200732 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1295 3195466 3196834 3196889 "XPOLYC" 3197177 NIL XPOLYC (NIL T T) -9 NIL 3197290 NIL) (-1294 3193196 3194806 3195010 "XPOLY" 3195306 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1293 3189574 3191713 3192101 "XPBWPOLY" 3192854 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1292 3184770 3186059 3186114 "XFALG" 3188286 NIL XFALG (NIL T T) -9 NIL 3189075 NIL) (-1291 3180467 3182760 3182802 "XF" 3183423 NIL XF (NIL T) -9 NIL 3183823 NIL) (-1290 3180088 3180176 3180345 "XF-" 3180350 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1289 3179221 3179325 3179530 "XEXPPKG" 3179980 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1288 3177330 3179071 3179167 "XDPOLY" 3179172 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1287 3176137 3176737 3176780 "XALG" 3176785 NIL XALG (NIL T) -9 NIL 3176896 NIL) (-1286 3169606 3174114 3174608 "WUTSET" 3175729 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1285 3167862 3168658 3168981 "WP" 3169417 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1284 3167464 3167684 3167754 "WHILEAST" 3167814 T WHILEAST (NIL) -8 NIL NIL NIL) (-1283 3166936 3167181 3167275 "WHEREAST" 3167392 T WHEREAST (NIL) -8 NIL NIL NIL) (-1282 3165822 3166020 3166315 "WFFINTBS" 3166733 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1281 3163726 3164153 3164615 "WEIER" 3165394 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1280 3162772 3163222 3163264 "VSPACE" 3163400 NIL VSPACE (NIL T) -9 NIL 3163474 NIL) (-1279 3162610 3162637 3162728 "VSPACE-" 3162733 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1278 3162419 3162461 3162529 "VOID" 3162564 T VOID (NIL) -8 NIL NIL NIL) (-1277 3158843 3159482 3160219 "VIEWDEF" 3161704 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1276 3148147 3150391 3152564 "VIEW3D" 3156692 T VIEW3D (NIL) -8 NIL NIL NIL) (-1275 3140398 3142058 3143637 "VIEW2D" 3146590 T VIEW2D (NIL) -8 NIL NIL NIL) (-1274 3138534 3138893 3139299 "VIEW" 3140014 T VIEW (NIL) -7 NIL NIL NIL) (-1273 3137111 3137370 3137688 "VECTOR2" 3138264 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1272 3132464 3136881 3136973 "VECTOR" 3137054 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1271 3125938 3130245 3130288 "VECTCAT" 3131283 NIL VECTCAT (NIL T) -9 NIL 3131870 NIL) (-1270 3124952 3125206 3125596 "VECTCAT-" 3125601 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1269 3124406 3124603 3124723 "VARIABLE" 3124867 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1268 3124339 3124344 3124374 "UTYPE" 3124379 T UTYPE (NIL) -9 NIL NIL NIL) (-1267 3123169 3123323 3123585 "UTSODETL" 3124165 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1266 3120609 3121069 3121593 "UTSODE" 3122710 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1265 3111483 3116850 3116893 "UTSCAT" 3118005 NIL UTSCAT (NIL T) -9 NIL 3118763 NIL) (-1264 3108830 3109553 3110542 "UTSCAT-" 3110547 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1263 3108457 3108500 3108633 "UTS2" 3108781 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1262 3100294 3106083 3106572 "UTS" 3108026 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3094521 3097132 3097175 "URAGG" 3099245 NIL URAGG (NIL T) -9 NIL 3099968 NIL) (-1260 3091463 3092325 3093447 "URAGG-" 3093452 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1259 3087179 3090098 3090563 "UPXSSING" 3091127 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1258 3080254 3087083 3087155 "UPXSCONS" 3087160 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1257 3070001 3076792 3076854 "UPXSCCA" 3077428 NIL UPXSCCA (NIL T T) -9 NIL 3077661 NIL) (-1256 3069639 3069724 3069898 "UPXSCCA-" 3069903 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1255 3059238 3065802 3065845 "UPXSCAT" 3066493 NIL UPXSCAT (NIL T) -9 NIL 3067102 NIL) (-1254 3058668 3058747 3058926 "UPXS2" 3059153 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1253 3050738 3057915 3058188 "UPXS" 3058453 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1252 3049395 3049647 3049997 "UPSQFREE" 3050482 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1251 3042816 3045873 3045928 "UPSCAT" 3047089 NIL UPSCAT (NIL T T) -9 NIL 3047863 NIL) (-1250 3042020 3042227 3042554 "UPSCAT-" 3042559 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1249 3041647 3041690 3041823 "UPOLYC2" 3041971 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1248 3027335 3035070 3035113 "UPOLYC" 3037214 NIL UPOLYC (NIL T) -9 NIL 3038435 NIL) (-1247 3018699 3021113 3024248 "UPOLYC-" 3024253 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1246 3018038 3018145 3018309 "UPMP" 3018588 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1245 3017591 3017672 3017811 "UPDIVP" 3017951 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1244 3016159 3016408 3016724 "UPDECOMP" 3017340 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1243 3015394 3015506 3015691 "UPCDEN" 3016043 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1242 3014913 3014982 3015131 "UP2" 3015319 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1241 3006764 3014596 3014725 "UP" 3014832 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1240 3005979 3006106 3006311 "UNISEG2" 3006607 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1239 3004446 3005183 3005460 "UNISEG" 3005737 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1238 3003506 3003686 3003912 "UNIFACT" 3004262 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1237 2991520 3003410 3003482 "ULSCONS" 3003487 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1236 2973555 2985524 2985586 "ULSCCAT" 2986224 NIL ULSCCAT (NIL T T) -9 NIL 2986512 NIL) (-1235 2972641 2972874 2973250 "ULSCCAT-" 2973255 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1234 2962017 2968495 2968538 "ULSCAT" 2969401 NIL ULSCAT (NIL T) -9 NIL 2970132 NIL) (-1233 2961447 2961526 2961705 "ULS2" 2961932 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1232 2945395 2960624 2960875 "ULS" 2961254 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1231 2944522 2945032 2945139 "UINT8" 2945250 T UINT8 (NIL) -8 NIL NIL 2945335) (-1230 2943648 2944158 2944265 "UINT64" 2944376 T UINT64 (NIL) -8 NIL NIL 2944461) (-1229 2942774 2943284 2943391 "UINT32" 2943502 T UINT32 (NIL) -8 NIL NIL 2943587) (-1228 2941900 2942410 2942517 "UINT16" 2942628 T UINT16 (NIL) -8 NIL NIL 2942713) (-1227 2940203 2941160 2941190 "UFD" 2941402 T UFD (NIL) -9 NIL 2941516 NIL) (-1226 2939997 2940043 2940138 "UFD-" 2940143 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1225 2939079 2939262 2939478 "UDVO" 2939803 T UDVO (NIL) -7 NIL NIL NIL) (-1224 2936895 2937304 2937775 "UDPO" 2938643 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1223 2936655 2936850 2936881 "TYPEAST" 2936886 T TYPEAST (NIL) -8 NIL NIL NIL) (-1222 2936588 2936593 2936623 "TYPE" 2936628 T TYPE (NIL) -9 NIL NIL NIL) (-1221 2935559 2935761 2936001 "TWOFACT" 2936382 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1220 2934582 2934968 2935203 "TUPLE" 2935359 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1219 2932273 2932792 2933331 "TUBETOOL" 2934065 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1218 2931122 2931327 2931568 "TUBE" 2932066 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1217 2919762 2923881 2923978 "TSETCAT" 2929247 NIL TSETCAT (NIL T T T T) -9 NIL 2930778 NIL) (-1216 2914494 2916094 2917985 "TSETCAT-" 2917990 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1215 2909223 2913466 2913749 "TS" 2914246 NIL TS (NIL T) -8 NIL NIL NIL) (-1214 2903862 2904709 2905638 "TRMANIP" 2908359 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1213 2903303 2903366 2903529 "TRIMAT" 2903794 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1212 2901169 2901406 2901763 "TRIGMNIP" 2903052 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1211 2900689 2900802 2900832 "TRIGCAT" 2901045 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1210 2900358 2900437 2900578 "TRIGCAT-" 2900583 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1209 2897204 2899216 2899497 "TREE" 2900112 NIL TREE (NIL T) -8 NIL NIL NIL) (-1208 2896478 2897006 2897036 "TRANFUN" 2897071 T TRANFUN (NIL) -9 NIL 2897137 NIL) (-1207 2895757 2895948 2896228 "TRANFUN-" 2896233 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1206 2895561 2895593 2895654 "TOPSP" 2895718 T TOPSP (NIL) -7 NIL NIL NIL) (-1205 2894909 2895024 2895178 "TOOLSIGN" 2895442 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1204 2893543 2894086 2894325 "TEXTFILE" 2894692 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1203 2893324 2893355 2893427 "TEX1" 2893506 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1202 2891236 2891777 2892206 "TEX" 2892917 T TEX (NIL) -8 NIL NIL NIL) (-1201 2890884 2890947 2891037 "TEMUTL" 2891168 T TEMUTL (NIL) -7 NIL NIL NIL) (-1200 2889038 2889318 2889643 "TBCMPPK" 2890607 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1199 2880817 2887198 2887254 "TBAGG" 2887654 NIL TBAGG (NIL T T) -9 NIL 2887865 NIL) (-1198 2875887 2877375 2879129 "TBAGG-" 2879134 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1197 2875271 2875378 2875523 "TANEXP" 2875776 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1196 2874683 2874782 2874920 "TABLEAU" 2875168 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1195 2868075 2874540 2874633 "TABLE" 2874638 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1194 2862683 2863903 2865151 "TABLBUMP" 2866861 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1193 2861905 2862052 2862233 "SYSTEM" 2862524 T SYSTEM (NIL) -8 NIL NIL NIL) (-1192 2858364 2859063 2859846 "SYSSOLP" 2861156 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1191 2858162 2858319 2858350 "SYSPTR" 2858355 T SYSPTR (NIL) -8 NIL NIL NIL) (-1190 2857206 2857711 2857830 "SYSNNI" 2858016 NIL SYSNNI (NIL NIL) -8 NIL NIL 2858101) (-1189 2856513 2856972 2857051 "SYSINT" 2857111 NIL SYSINT (NIL NIL) -8 NIL NIL 2857156) (-1188 2852857 2853791 2854501 "SYNTAX" 2855825 T SYNTAX (NIL) -8 NIL NIL NIL) (-1187 2850015 2850617 2851249 "SYMTAB" 2852247 T SYMTAB (NIL) -8 NIL NIL NIL) (-1186 2845288 2846184 2847161 "SYMS" 2849060 T SYMS (NIL) -8 NIL NIL NIL) (-1185 2842533 2844749 2844979 "SYMPOLY" 2845096 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1184 2842050 2842125 2842248 "SYMFUNC" 2842445 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1183 2838070 2839362 2840175 "SYMBOL" 2841259 T SYMBOL (NIL) -8 NIL NIL NIL) (-1182 2831609 2833298 2835018 "SWITCH" 2836372 T SWITCH (NIL) -8 NIL NIL NIL) (-1181 2824843 2830430 2830733 "SUTS" 2831364 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1180 2816913 2824090 2824363 "SUPXS" 2824628 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1179 2816072 2816199 2816416 "SUPFRACF" 2816781 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1178 2815693 2815752 2815865 "SUP2" 2816007 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1177 2807492 2815311 2815437 "SUP" 2815602 NIL SUP (NIL T) -8 NIL NIL NIL) (-1176 2805940 2806214 2806570 "SUMRF" 2807191 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1175 2805275 2805341 2805533 "SUMFS" 2805861 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1174 2789258 2804452 2804703 "SULS" 2805082 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1173 2788860 2789080 2789150 "SUCHTAST" 2789210 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1172 2788155 2788385 2788525 "SUCH" 2788768 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1171 2782021 2783061 2784020 "SUBSPACE" 2787243 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1170 2781451 2781541 2781705 "SUBRESP" 2781909 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1169 2775624 2776744 2777891 "STTFNC" 2780351 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1168 2768990 2770289 2771600 "STTF" 2774360 NIL STTF (NIL T) -7 NIL NIL NIL) (-1167 2760301 2762172 2763966 "STTAYLOR" 2767231 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1166 2753433 2760165 2760248 "STRTBL" 2760253 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1165 2748797 2753388 2753419 "STRING" 2753424 T STRING (NIL) -8 NIL NIL NIL) (-1164 2743658 2748170 2748200 "STRICAT" 2748259 T STRICAT (NIL) -9 NIL 2748321 NIL) (-1163 2743168 2743245 2743389 "STREAM3" 2743575 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1162 2742150 2742333 2742568 "STREAM2" 2742981 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1161 2741838 2741890 2741983 "STREAM1" 2742092 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1160 2734593 2739457 2740068 "STREAM" 2741262 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1159 2733609 2733790 2734021 "STINPROD" 2734409 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1158 2732796 2733098 2733246 "STEPAST" 2733483 T STEPAST (NIL) -8 NIL NIL NIL) (-1157 2732348 2732558 2732588 "STEP" 2732668 T STEP (NIL) -9 NIL 2732746 NIL) (-1156 2725782 2732247 2732324 "STBL" 2732329 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1155 2720910 2725003 2725046 "STAGG" 2725199 NIL STAGG (NIL T) -9 NIL 2725288 NIL) (-1154 2718618 2719218 2720088 "STAGG-" 2720093 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1153 2716765 2718388 2718480 "STACK" 2718561 NIL STACK (NIL T) -8 NIL NIL NIL) (-1152 2709487 2714906 2715362 "SREGSET" 2716395 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1151 2701912 2703281 2704794 "SRDCMPK" 2708093 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1150 2694829 2699352 2699382 "SRAGG" 2700685 T SRAGG (NIL) -9 NIL 2701293 NIL) (-1149 2693846 2694101 2694480 "SRAGG-" 2694485 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1148 2688310 2692793 2693214 "SQMATRIX" 2693472 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1147 2681996 2685028 2685755 "SPLTREE" 2687655 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1146 2677959 2678652 2679298 "SPLNODE" 2681422 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1145 2677006 2677239 2677269 "SPFCAT" 2677713 T SPFCAT (NIL) -9 NIL NIL NIL) (-1144 2675743 2675953 2676217 "SPECOUT" 2676764 T SPECOUT (NIL) -7 NIL NIL NIL) (-1143 2666853 2668725 2668755 "SPADXPT" 2673431 T SPADXPT (NIL) -9 NIL 2675595 NIL) (-1142 2666614 2666654 2666723 "SPADPRSR" 2666806 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1141 2664663 2666569 2666600 "SPADAST" 2666605 T SPADAST (NIL) -8 NIL NIL NIL) (-1140 2656608 2658381 2658424 "SPACEC" 2662797 NIL SPACEC (NIL T) -9 NIL 2664613 NIL) (-1139 2654738 2656540 2656589 "SPACE3" 2656594 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1138 2653490 2653661 2653952 "SORTPAK" 2654543 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1137 2651582 2651885 2652297 "SOLVETRA" 2653154 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1136 2650632 2650854 2651115 "SOLVESER" 2651355 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1135 2645936 2646824 2647819 "SOLVERAD" 2649684 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1134 2641751 2642360 2643089 "SOLVEFOR" 2645303 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1133 2636048 2641100 2641197 "SNTSCAT" 2641202 NIL SNTSCAT (NIL T T T T) -9 NIL 2641272 NIL) (-1132 2630154 2634371 2634762 "SMTS" 2635738 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1131 2624865 2630042 2630119 "SMP" 2630124 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1130 2623024 2623325 2623723 "SMITH" 2624562 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1129 2615735 2619927 2620030 "SMATCAT" 2621384 NIL SMATCAT (NIL NIL T T T) -9 NIL 2621934 NIL) (-1128 2612696 2613512 2614683 "SMATCAT-" 2614688 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1127 2610362 2611932 2611975 "SKAGG" 2612236 NIL SKAGG (NIL T) -9 NIL 2612371 NIL) (-1126 2606675 2609778 2609973 "SINT" 2610160 T SINT (NIL) -8 NIL NIL 2610333) (-1125 2606447 2606485 2606551 "SIMPAN" 2606631 T SIMPAN (NIL) -7 NIL NIL NIL) (-1124 2605306 2605520 2605788 "SIGNRF" 2606213 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1123 2604160 2604304 2604581 "SIGNEF" 2605142 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1122 2603466 2603743 2603867 "SIGAST" 2604058 T SIGAST (NIL) -8 NIL NIL NIL) (-1121 2602745 2603001 2603141 "SIG" 2603348 T SIG (NIL) -8 NIL NIL NIL) (-1120 2600435 2600889 2601395 "SHP" 2602286 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1119 2594294 2600336 2600412 "SHDP" 2600417 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1118 2593867 2594059 2594089 "SGROUP" 2594182 T SGROUP (NIL) -9 NIL 2594244 NIL) (-1117 2593725 2593751 2593824 "SGROUP-" 2593829 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1116 2590560 2591258 2591981 "SGCF" 2593024 T SGCF (NIL) -7 NIL NIL NIL) (-1115 2584955 2590007 2590104 "SFRTCAT" 2590109 NIL SFRTCAT (NIL T T T T) -9 NIL 2590148 NIL) (-1114 2578376 2579394 2580530 "SFRGCD" 2583938 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1113 2571502 2572575 2573761 "SFQCMPK" 2577309 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1112 2571122 2571211 2571322 "SFORT" 2571443 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1111 2570240 2570962 2571083 "SEXOF" 2571088 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1110 2565753 2566468 2566563 "SEXCAT" 2569500 NIL SEXCAT (NIL T T T T T) -9 NIL 2570078 NIL) (-1109 2564860 2565634 2565702 "SEX" 2565707 T SEX (NIL) -8 NIL NIL NIL) (-1108 2563090 2563577 2563880 "SETMN" 2564603 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1107 2562586 2562738 2562768 "SETCAT" 2562944 T SETCAT (NIL) -9 NIL 2563054 NIL) (-1106 2562278 2562356 2562486 "SETCAT-" 2562491 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1105 2558639 2560739 2560782 "SETAGG" 2561652 NIL SETAGG (NIL T) -9 NIL 2561992 NIL) (-1104 2558097 2558213 2558450 "SETAGG-" 2558455 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1103 2555250 2558031 2558079 "SET" 2558084 NIL SET (NIL T) -8 NIL NIL NIL) (-1102 2554693 2554946 2555047 "SEQAST" 2555171 T SEQAST (NIL) -8 NIL NIL NIL) (-1101 2553892 2554186 2554247 "SEGXCAT" 2554533 NIL SEGXCAT (NIL T T) -9 NIL 2554653 NIL) (-1100 2552871 2553085 2553128 "SEGCAT" 2553650 NIL SEGCAT (NIL T) -9 NIL 2553871 NIL) (-1099 2552492 2552551 2552664 "SEGBIND2" 2552806 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1098 2551424 2551855 2552063 "SEGBIND" 2552319 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1097 2550997 2551225 2551302 "SEGAST" 2551369 T SEGAST (NIL) -8 NIL NIL NIL) (-1096 2550216 2550342 2550546 "SEG2" 2550841 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1095 2549222 2549882 2550064 "SEG" 2550069 NIL SEG (NIL T) -8 NIL NIL NIL) (-1094 2548632 2549157 2549204 "SDVAR" 2549209 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1093 2541200 2548402 2548532 "SDPOL" 2548537 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1092 2539793 2540059 2540378 "SCPKG" 2540915 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1091 2538957 2539129 2539321 "SCOPE" 2539623 T SCOPE (NIL) -8 NIL NIL NIL) (-1090 2538177 2538311 2538490 "SCACHE" 2538812 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1089 2537823 2538009 2538039 "SASTCAT" 2538044 T SASTCAT (NIL) -9 NIL 2538057 NIL) (-1088 2537310 2537658 2537734 "SAOS" 2537769 T SAOS (NIL) -8 NIL NIL NIL) (-1087 2536875 2536910 2537083 "SAERFFC" 2537269 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1086 2536468 2536503 2536662 "SAEFACT" 2536834 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1085 2530416 2536365 2536445 "SAE" 2536450 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1084 2528737 2529051 2529452 "RURPK" 2530082 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1083 2527374 2527680 2527985 "RULESET" 2528571 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1082 2526986 2527168 2527251 "RULECOLD" 2527326 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1081 2524209 2524739 2525197 "RULE" 2526667 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1080 2523999 2524027 2524098 "RTVALUE" 2524160 T RTVALUE (NIL) -8 NIL NIL NIL) (-1079 2523470 2523716 2523810 "RSTRCAST" 2523927 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1078 2518318 2519113 2520033 "RSETGCD" 2522669 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1077 2507575 2512627 2512724 "RSETCAT" 2516843 NIL RSETCAT (NIL T T T T) -9 NIL 2517940 NIL) (-1076 2505502 2506041 2506865 "RSETCAT-" 2506870 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1075 2497888 2499264 2500784 "RSDCMPK" 2504101 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1074 2495867 2496334 2496408 "RRCC" 2497494 NIL RRCC (NIL T T) -9 NIL 2497838 NIL) (-1073 2495218 2495392 2495671 "RRCC-" 2495676 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1072 2494661 2494914 2495015 "RPTAST" 2495139 T RPTAST (NIL) -8 NIL NIL NIL) (-1071 2468543 2477869 2477936 "RPOLCAT" 2488600 NIL RPOLCAT (NIL T T T) -9 NIL 2491759 NIL) (-1070 2460077 2462405 2465515 "RPOLCAT-" 2465520 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1069 2451010 2458288 2458770 "ROUTINE" 2459617 T ROUTINE (NIL) -8 NIL NIL NIL) (-1068 2447810 2450636 2450776 "ROMAN" 2450892 T ROMAN (NIL) -8 NIL NIL NIL) (-1067 2446056 2446670 2446930 "ROIRC" 2447615 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1066 2442292 2444572 2444602 "RNS" 2444906 T RNS (NIL) -9 NIL 2445180 NIL) (-1065 2440801 2441184 2441718 "RNS-" 2441793 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1064 2439804 2440166 2440368 "RNGBIND" 2440652 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1063 2439207 2439615 2439645 "RNG" 2439650 T RNG (NIL) -9 NIL 2439671 NIL) (-1062 2438606 2438994 2439037 "RMODULE" 2439042 NIL RMODULE (NIL T) -9 NIL 2439069 NIL) (-1061 2437442 2437536 2437872 "RMCAT2" 2438507 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1060 2434292 2436788 2437085 "RMATRIX" 2437204 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1059 2427119 2429379 2429494 "RMATCAT" 2432853 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2433835 NIL) (-1058 2426494 2426641 2426948 "RMATCAT-" 2426953 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1057 2425895 2426116 2426159 "RLINSET" 2426353 NIL RLINSET (NIL T) -9 NIL 2426444 NIL) (-1056 2425462 2425537 2425665 "RINTERP" 2425814 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1055 2424520 2425074 2425104 "RING" 2425160 T RING (NIL) -9 NIL 2425252 NIL) (-1054 2424312 2424356 2424453 "RING-" 2424458 NIL RING- (NIL T) -8 NIL NIL NIL) (-1053 2423153 2423390 2423648 "RIDIST" 2424076 T RIDIST (NIL) -7 NIL NIL NIL) (-1052 2414469 2422621 2422827 "RGCHAIN" 2423001 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1051 2413819 2414225 2414266 "RGBCSPC" 2414324 NIL RGBCSPC (NIL T) -9 NIL 2414376 NIL) (-1050 2412977 2413358 2413399 "RGBCMDL" 2413631 NIL RGBCMDL (NIL T) -9 NIL 2413745 NIL) (-1049 2412623 2412686 2412789 "RFFACTOR" 2412908 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1048 2412348 2412383 2412480 "RFFACT" 2412582 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1047 2410465 2410829 2411211 "RFDIST" 2411988 T RFDIST (NIL) -7 NIL NIL NIL) (-1046 2407459 2408073 2408743 "RF" 2409829 NIL RF (NIL T) -7 NIL NIL NIL) (-1045 2406912 2407004 2407167 "RETSOL" 2407361 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1044 2406548 2406628 2406671 "RETRACT" 2406804 NIL RETRACT (NIL T) -9 NIL 2406891 NIL) (-1043 2406397 2406422 2406509 "RETRACT-" 2406514 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1042 2405999 2406219 2406289 "RETAST" 2406349 T RETAST (NIL) -8 NIL NIL NIL) (-1041 2398739 2405652 2405779 "RESULT" 2405894 T RESULT (NIL) -8 NIL NIL NIL) (-1040 2397330 2398008 2398207 "RESRING" 2398642 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1039 2396966 2397015 2397113 "RESLATC" 2397267 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1038 2396671 2396706 2396813 "REPSQ" 2396925 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1037 2396368 2396403 2396514 "REPDB" 2396630 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1036 2390268 2391657 2392880 "REP2" 2395180 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1035 2386645 2387326 2388134 "REP1" 2389495 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1034 2384067 2384647 2385249 "REP" 2386065 T REP (NIL) -7 NIL NIL NIL) (-1033 2376790 2382208 2382664 "REGSET" 2383697 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1032 2375555 2375938 2376188 "REF" 2376575 NIL REF (NIL T) -8 NIL NIL NIL) (-1031 2374932 2375035 2375202 "REDORDER" 2375439 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1030 2370931 2374145 2374372 "RECLOS" 2374760 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1029 2369983 2370164 2370379 "REALSOLV" 2370738 T REALSOLV (NIL) -7 NIL NIL NIL) (-1028 2366466 2367268 2368152 "REAL0Q" 2369148 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1027 2362067 2363055 2364116 "REAL0" 2365447 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1026 2361913 2361954 2361984 "REAL" 2361989 T REAL (NIL) -9 NIL 2362024 NIL) (-1025 2361384 2361630 2361724 "RDUCEAST" 2361841 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1024 2360789 2360861 2361068 "RDIV" 2361306 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1023 2359857 2360031 2360244 "RDIST" 2360611 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1022 2358454 2358741 2359113 "RDETRS" 2359565 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1021 2356266 2356720 2357258 "RDETR" 2357996 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1020 2354891 2355169 2355566 "RDEEFS" 2355982 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1019 2353400 2353706 2354131 "RDEEF" 2354579 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1018 2347470 2350381 2350411 "RCFIELD" 2351706 T RCFIELD (NIL) -9 NIL 2352437 NIL) (-1017 2345534 2346038 2346734 "RCFIELD-" 2346809 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1016 2341803 2343635 2343678 "RCAGG" 2344762 NIL RCAGG (NIL T) -9 NIL 2345227 NIL) (-1015 2341431 2341525 2341688 "RCAGG-" 2341693 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1014 2340766 2340878 2341043 "RATRET" 2341315 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1013 2340319 2340386 2340507 "RATFACT" 2340694 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1012 2339627 2339747 2339899 "RANDSRC" 2340189 T RANDSRC (NIL) -7 NIL NIL NIL) (-1011 2339361 2339405 2339478 "RADUTIL" 2339576 T RADUTIL (NIL) -7 NIL NIL NIL) (-1010 2332498 2338194 2338504 "RADIX" 2339085 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1009 2324128 2332340 2332470 "RADFF" 2332475 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1008 2323775 2323850 2323880 "RADCAT" 2324040 T RADCAT (NIL) -9 NIL NIL NIL) (-1007 2323557 2323605 2323705 "RADCAT-" 2323710 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1006 2321655 2323327 2323419 "QUEUE" 2323500 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1005 2321286 2321329 2321460 "QUATCT2" 2321606 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1004 2314742 2318080 2318122 "QUATCAT" 2318913 NIL QUATCAT (NIL T) -9 NIL 2319679 NIL) (-1003 2310902 2311932 2313315 "QUATCAT-" 2313411 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1002 2307446 2310835 2310883 "QUAT" 2310888 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1001 2304911 2306522 2306565 "QUAGG" 2306946 NIL QUAGG (NIL T) -9 NIL 2307121 NIL) (-1000 2304513 2304733 2304803 "QQUTAST" 2304863 T QQUTAST (NIL) -8 NIL NIL NIL) (-999 2303411 2303911 2304083 "QFORM" 2304385 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-998 2303049 2303092 2303219 "QFCAT2" 2303362 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-997 2294070 2299293 2299333 "QFCAT" 2299991 NIL QFCAT (NIL T) -9 NIL 2300992 NIL) (-996 2289678 2290867 2292446 "QFCAT-" 2292540 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-995 2289138 2289248 2289378 "QEQUAT" 2289568 T QEQUAT (NIL) -8 NIL NIL NIL) (-994 2282284 2283357 2284541 "QCMPACK" 2288071 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-993 2281529 2281703 2281935 "QALGSET2" 2282104 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-992 2279084 2279530 2279956 "QALGSET" 2281186 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-991 2277774 2277998 2278315 "PWFFINTB" 2278857 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-990 2275973 2276141 2276495 "PUSHVAR" 2277588 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-989 2271891 2272945 2272986 "PTRANFN" 2274870 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-988 2270293 2270584 2270906 "PTPACK" 2271602 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-987 2269925 2269982 2270091 "PTFUNC2" 2270230 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-986 2264402 2268797 2268838 "PTCAT" 2269134 NIL PTCAT (NIL T) -9 NIL 2269287 NIL) (-985 2264060 2264095 2264219 "PSQFR" 2264361 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-984 2262655 2262953 2263287 "PSEUDLIN" 2263758 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-983 2249418 2251789 2254113 "PSETPK" 2260415 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-982 2242436 2245176 2245272 "PSETCAT" 2248293 NIL PSETCAT (NIL T T T T) -9 NIL 2249107 NIL) (-981 2240272 2240906 2241727 "PSETCAT-" 2241732 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-980 2239621 2239786 2239814 "PSCURVE" 2240082 T PSCURVE (NIL) -9 NIL 2240249 NIL) (-979 2235619 2237135 2237200 "PSCAT" 2238044 NIL PSCAT (NIL T T T) -9 NIL 2238284 NIL) (-978 2234682 2234898 2235298 "PSCAT-" 2235303 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2233387 2234047 2234252 "PRTITION" 2234497 T PRTITION (NIL) -8 NIL NIL NIL) (-976 2232862 2233108 2233200 "PRTDAST" 2233315 T PRTDAST 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2063839 "PDEPROB" 2064530 T PDEPROB (NIL) -8 NIL NIL NIL) (-903 2059938 2060442 2060997 "PDEPACK" 2061858 T PDEPACK (NIL) -7 NIL NIL NIL) (-902 2058850 2059040 2059291 "PDECOMP" 2059737 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-901 2056429 2057272 2057300 "PDECAT" 2058087 T PDECAT (NIL) -9 NIL 2058800 NIL) (-900 2056180 2056213 2056303 "PCOMP" 2056390 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-899 2054358 2054981 2055278 "PBWLB" 2055909 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-898 2053990 2054047 2054156 "PATTERN2" 2054295 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2051747 2052135 2052592 "PATTERN1" 2053579 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2044222 2045820 2047158 "PATTERN" 2050430 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-895 2043786 2043853 2043985 "PATRES2" 2044149 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2041154 2041735 2042216 "PATRES" 2043351 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-893 2039037 2039442 2039849 "PATMATCH" 2040821 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-892 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NIL) (-880 2030214 2030300 2030419 "PAN2EXPR" 2030595 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-879 2028991 2029335 2029563 "PALETTE" 2030006 T PALETTE (NIL) -8 NIL NIL NIL) (-878 2027384 2027996 2028356 "PAIR" 2028677 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-877 2021275 2026643 2026837 "PADICRC" 2027239 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-876 2014525 2020621 2020805 "PADICRAT" 2021123 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-875 2011637 2013199 2013239 "PADICCT" 2013820 NIL PADICCT (NIL NIL) -9 NIL 2014102 NIL) (-874 2009954 2011574 2011619 "PADIC" 2011624 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-873 2008911 2009111 2009379 "PADEPAC" 2009741 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-872 2008123 2008256 2008462 "PADE" 2008773 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-871 2006510 2007331 2007611 "OWP" 2007927 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-870 2006003 2006216 2006313 "OVERSET" 2006433 T OVERSET (NIL) -8 NIL NIL NIL) (-869 2005049 2005608 2005780 "OVAR" 2005871 NIL OVAR (NIL NIL) 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OPTPACK (NIL) -7 NIL NIL NIL) (-844 1954029 1954795 1954823 "OPTCAT" 1955642 T OPTCAT (NIL) -9 NIL 1956292 NIL) (-843 1953413 1953706 1953811 "OPSIG" 1953944 T OPSIG (NIL) -8 NIL NIL NIL) (-842 1953181 1953220 1953286 "OPQUERY" 1953367 T OPQUERY (NIL) -7 NIL NIL NIL) (-841 1952555 1952781 1952822 "OPERCAT" 1953034 NIL OPERCAT (NIL T) -9 NIL 1953131 NIL) (-840 1952310 1952366 1952483 "OPERCAT-" 1952488 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1949443 1950621 1951125 "OP" 1951839 NIL OP (NIL T) -8 NIL NIL NIL) (-838 1948748 1948863 1949037 "ONECOMP2" 1949315 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1945568 1947545 1947914 "ONECOMP" 1948412 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-836 1944987 1945093 1945223 "OMSERVER" 1945458 T OMSERVER (NIL) -7 NIL NIL NIL) (-835 1941849 1944427 1944467 "OMSAGG" 1944528 NIL OMSAGG (NIL T) -9 NIL 1944592 NIL) (-834 1940472 1940735 1941017 "OMPKG" 1941587 T OMPKG (NIL) -7 NIL NIL NIL) (-833 1939019 1940021 1940190 "OMLO" 1940353 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1937979 1938126 1938346 "OMEXPR" 1938845 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1937130 1937400 1937560 "OMERRK" 1937839 T OMERRK (NIL) -8 NIL NIL NIL) (-830 1936421 1936676 1936812 "OMERR" 1937014 T OMERR (NIL) -8 NIL NIL NIL) (-829 1935872 1936098 1936206 "OMENC" 1936333 T OMENC (NIL) -8 NIL NIL NIL) (-828 1929767 1930952 1932123 "OMDEV" 1934721 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1928836 1929007 1929201 "OMCONN" 1929593 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1928266 1928369 1928397 "OM" 1928696 T OM (NIL) -9 NIL NIL NIL) (-825 1926787 1927763 1927791 "OINTDOM" 1927796 T OINTDOM (NIL) -9 NIL 1927817 NIL) (-824 1924132 1925475 1925812 "OFMONOID" 1926482 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-823 1923543 1924069 1924114 "ODVAR" 1924119 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-822 1920968 1923288 1923443 "ODR" 1923448 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-821 1913590 1920744 1920870 "ODPOL" 1920875 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-820 1907419 1913462 1913567 "ODP" 1913572 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-819 1906185 1906400 1906675 "ODETOOLS" 1907193 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-818 1903152 1903810 1904526 "ODESYS" 1905518 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-817 1898034 1898942 1899967 "ODERTRIC" 1902227 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-816 1897460 1897542 1897736 "ODERED" 1897946 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-815 1894356 1894902 1895577 "ODERAT" 1896885 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-814 1891313 1891780 1892377 "ODEPRRIC" 1893885 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-813 1889256 1889852 1890338 "ODEPROB" 1890847 T ODEPROB (NIL) -8 NIL NIL NIL) (-812 1885776 1886261 1886908 "ODEPRIM" 1888735 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-811 1885025 1885127 1885387 "ODEPAL" 1885668 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-810 1881187 1881978 1882842 "ODEPACK" 1884181 T ODEPACK (NIL) -7 NIL NIL NIL) (-809 1880248 1880355 1880577 "ODEINT" 1881076 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-808 1874349 1875774 1877221 "ODEIFTBL" 1878821 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-807 1869761 1870543 1871491 "ODEEF" 1873512 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-806 1869110 1869199 1869422 "ODECONST" 1869666 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-805 1867235 1867896 1867924 "ODECAT" 1868529 T ODECAT (NIL) -9 NIL 1869060 NIL) (-804 1866873 1866916 1867043 "OCTCT2" 1867186 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1863740 1866578 1866700 "OCT" 1866783 NIL OCT (NIL T) -8 NIL NIL NIL) (-802 1863092 1863560 1863588 "OCAMON" 1863593 T OCAMON (NIL) -9 NIL 1863614 NIL) (-801 1857748 1860176 1860216 "OC" 1861313 NIL OC (NIL T) -9 NIL 1862171 NIL) (-800 1854996 1855737 1856720 "OC-" 1856814 NIL OC- (NIL T T) -8 NIL NIL NIL) (-799 1854527 1854868 1854896 "OASGP" 1854901 T OASGP (NIL) -9 NIL 1854921 NIL) (-798 1853788 1854277 1854305 "OAMONS" 1854345 T OAMONS (NIL) -9 NIL 1854388 NIL) (-797 1853202 1853635 1853663 "OAMON" 1853668 T OAMON (NIL) -9 NIL 1853688 NIL) (-796 1852460 1852978 1853006 "OAGROUP" 1853011 T OAGROUP (NIL) -9 NIL 1853031 NIL) (-795 1852150 1852200 1852288 "NUMTUBE" 1852404 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-794 1845723 1847241 1848777 "NUMQUAD" 1850634 T NUMQUAD (NIL) -7 NIL NIL NIL) (-793 1841479 1842467 1843492 "NUMODE" 1844718 T NUMODE (NIL) -7 NIL NIL NIL) (-792 1838834 1839714 1839742 "NUMINT" 1840665 T NUMINT (NIL) -9 NIL 1841429 NIL) (-791 1837782 1837979 1838197 "NUMFMT" 1838636 T NUMFMT (NIL) -7 NIL NIL NIL) (-790 1824141 1827086 1829618 "NUMERIC" 1835289 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-789 1818538 1823590 1823685 "NTSCAT" 1823690 NIL NTSCAT (NIL T T T T) -9 NIL 1823729 NIL) (-788 1817732 1817897 1818090 "NTPOLFN" 1818377 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-787 1817364 1817421 1817530 "NSUP2" 1817669 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1805486 1814189 1815001 "NSUP" 1816585 NIL NSUP (NIL T) -8 NIL NIL NIL) (-785 1795762 1805260 1805393 "NSMP" 1805398 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-784 1794194 1794495 1794852 "NREP" 1795450 NIL NREP (NIL T) -7 NIL NIL NIL) (-783 1792785 1793037 1793395 "NPCOEF" 1793937 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-782 1791851 1791966 1792182 "NORMRETR" 1792666 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-781 1789892 1790182 1790591 "NORMPK" 1791559 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-780 1789577 1789605 1789729 "NORMMA" 1789858 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-779 1789366 1789395 1789464 "NONE1" 1789541 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1789166 1789323 1789352 "NONE" 1789357 T NONE (NIL) -8 NIL NIL NIL) (-777 1788663 1788725 1788904 "NODE1" 1789098 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-776 1786948 1787799 1788054 "NNI" 1788401 T NNI (NIL) -8 NIL NIL 1788636) (-775 1785368 1785681 1786045 "NLINSOL" 1786616 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-774 1781609 1782604 1783503 "NIPROB" 1784489 T NIPROB (NIL) -8 NIL NIL NIL) (-773 1780366 1780600 1780902 "NFINTBAS" 1781371 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-772 1779540 1780016 1780057 "NETCLT" 1780229 NIL NETCLT (NIL T) -9 NIL 1780311 NIL) (-771 1778248 1778479 1778760 "NCODIV" 1779308 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-770 1778010 1778047 1778122 "NCNTFRAC" 1778205 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-769 1776190 1776554 1776974 "NCEP" 1777635 NIL NCEP (NIL T) -7 NIL NIL NIL) (-768 1775048 1775814 1775842 "NASRING" 1775952 T NASRING (NIL) -9 NIL 1776032 NIL) (-767 1774843 1774887 1774981 "NASRING-" 1774986 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-766 1773950 1774475 1774503 "NARNG" 1774620 T NARNG (NIL) -9 NIL 1774711 NIL) (-765 1773642 1773709 1773843 "NARNG-" 1773848 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-764 1772521 1772728 1772963 "NAGSP" 1773427 T NAGSP (NIL) -7 NIL NIL NIL) (-763 1763793 1765477 1767150 "NAGS" 1770868 T NAGS (NIL) -7 NIL NIL NIL) (-762 1762341 1762649 1762980 "NAGF07" 1763482 T NAGF07 (NIL) -7 NIL NIL NIL) (-761 1756879 1758170 1759477 "NAGF04" 1761054 T NAGF04 (NIL) -7 NIL NIL NIL) (-760 1749847 1751461 1753094 "NAGF02" 1755266 T NAGF02 (NIL) -7 NIL NIL NIL) (-759 1745071 1746171 1747288 "NAGF01" 1748750 T NAGF01 (NIL) -7 NIL NIL NIL) (-758 1738699 1740265 1741850 "NAGE04" 1743506 T NAGE04 (NIL) -7 NIL NIL NIL) (-757 1729868 1731989 1734119 "NAGE02" 1736589 T NAGE02 (NIL) -7 NIL NIL NIL) (-756 1725821 1726768 1727732 "NAGE01" 1728924 T NAGE01 (NIL) -7 NIL NIL NIL) (-755 1723616 1724150 1724708 "NAGD03" 1725283 T NAGD03 (NIL) -7 NIL NIL NIL) (-754 1715366 1717294 1719248 "NAGD02" 1721682 T NAGD02 (NIL) -7 NIL NIL NIL) (-753 1709177 1710602 1712042 "NAGD01" 1713946 T NAGD01 (NIL) -7 NIL NIL NIL) (-752 1705386 1706208 1707045 "NAGC06" 1708360 T NAGC06 (NIL) -7 NIL NIL NIL) (-751 1703851 1704183 1704539 "NAGC05" 1705050 T NAGC05 (NIL) -7 NIL NIL NIL) (-750 1703227 1703346 1703490 "NAGC02" 1703727 T NAGC02 (NIL) -7 NIL NIL NIL) (-749 1702186 1702769 1702809 "NAALG" 1702888 NIL NAALG (NIL T) -9 NIL 1702949 NIL) (-748 1702021 1702050 1702140 "NAALG-" 1702145 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-747 1695971 1697079 1698266 "MULTSQFR" 1700917 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-746 1695290 1695365 1695549 "MULTFACT" 1695883 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-745 1688014 1691927 1691980 "MTSCAT" 1693050 NIL MTSCAT (NIL T T) -9 NIL 1693565 NIL) (-744 1687726 1687780 1687872 "MTHING" 1687954 NIL MTHING (NIL T) -7 NIL NIL NIL) (-743 1687518 1687551 1687611 "MSYSCMD" 1687686 T MSYSCMD (NIL) -7 NIL NIL NIL) (-742 1684587 1687079 1687120 "MSETAGG" 1687125 NIL MSETAGG (NIL T) -9 NIL 1687159 NIL) (-741 1680669 1683342 1683662 "MSET" 1684300 NIL MSET (NIL T) -8 NIL NIL NIL) (-740 1676512 1678048 1678793 "MRING" 1679969 NIL MRING (NIL T T) -8 NIL NIL NIL) (-739 1676078 1676145 1676276 "MRF2" 1676439 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-738 1675696 1675731 1675875 "MRATFAC" 1676037 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-737 1673308 1673603 1674034 "MPRFF" 1675401 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-736 1667631 1673162 1673259 "MPOLY" 1673264 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-735 1667121 1667156 1667364 "MPCPF" 1667590 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-734 1666635 1666678 1666862 "MPC3" 1667072 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1665830 1665911 1666132 "MPC2" 1666550 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-732 1664131 1664468 1664858 "MONOTOOL" 1665490 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-731 1663356 1663673 1663701 "MONOID" 1663920 T MONOID (NIL) -9 NIL 1664067 NIL) (-730 1662902 1663021 1663202 "MONOID-" 1663207 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-729 1653386 1659328 1659387 "MONOGEN" 1660061 NIL MONOGEN (NIL T T) -9 NIL 1660517 NIL) (-728 1650625 1651353 1652346 "MONOGEN-" 1652465 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-727 1649458 1649904 1649932 "MONADWU" 1650324 T MONADWU (NIL) -9 NIL 1650562 NIL) (-726 1648830 1648989 1649237 "MONADWU-" 1649242 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-725 1648189 1648433 1648461 "MONAD" 1648668 T MONAD (NIL) -9 NIL 1648780 NIL) (-724 1647874 1647952 1648084 "MONAD-" 1648089 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-723 1646163 1646787 1647066 "MOEBIUS" 1647627 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-722 1645441 1645845 1645885 "MODULE" 1645890 NIL MODULE (NIL T) -9 NIL 1645929 NIL) (-721 1645009 1645105 1645295 "MODULE-" 1645300 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-720 1642733 1643417 1643744 "MODRING" 1644833 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-719 1639679 1640838 1641359 "MODOP" 1642262 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-718 1638267 1638746 1639023 "MODMONOM" 1639542 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-717 1628349 1636558 1636972 "MODMON" 1637904 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-716 1625531 1627217 1627493 "MODFIELD" 1628224 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1624508 1624812 1625002 "MMLFORM" 1625361 T MMLFORM (NIL) -8 NIL NIL NIL) (-714 1624034 1624077 1624256 "MMAP" 1624459 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-713 1622113 1622880 1622921 "MLO" 1623344 NIL MLO (NIL T) -9 NIL 1623586 NIL) (-712 1619479 1619995 1620597 "MLIFT" 1621594 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-711 1618870 1618954 1619108 "MKUCFUNC" 1619390 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-710 1618469 1618539 1618662 "MKRECORD" 1618793 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-709 1617516 1617678 1617906 "MKFUNC" 1618280 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-708 1616904 1617008 1617164 "MKFLCFN" 1617399 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-707 1616181 1616283 1616468 "MKBCFUNC" 1616797 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-706 1612890 1615735 1615871 "MINT" 1616065 T MINT (NIL) -8 NIL NIL NIL) (-705 1611702 1611945 1612222 "MHROWRED" 1612645 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-704 1607091 1610237 1610642 "MFLOAT" 1611317 T MFLOAT (NIL) -8 NIL NIL NIL) (-703 1606448 1606524 1606695 "MFINFACT" 1607003 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-702 1602783 1603626 1604505 "MESH" 1605589 T MESH (NIL) -7 NIL NIL NIL) (-701 1601173 1601485 1601838 "MDDFACT" 1602470 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-700 1597968 1600332 1600373 "MDAGG" 1600628 NIL MDAGG (NIL T) -9 NIL 1600771 NIL) (-699 1587726 1597261 1597468 "MCMPLX" 1597781 T MCMPLX (NIL) -8 NIL NIL NIL) (-698 1586867 1587013 1587213 "MCDEN" 1587575 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-697 1584757 1585027 1585407 "MCALCFN" 1586597 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-696 1583682 1583922 1584155 "MAYBE" 1584563 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-695 1581294 1581817 1582379 "MATSTOR" 1583153 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-694 1577250 1580666 1580914 "MATRIX" 1581079 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-693 1573014 1573723 1574459 "MATLIN" 1576607 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-692 1571608 1571761 1572094 "MATCAT2" 1572849 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-691 1561708 1564897 1564974 "MATCAT" 1569857 NIL MATCAT (NIL T T T) -9 NIL 1571274 NIL) (-690 1558064 1559085 1560441 "MATCAT-" 1560446 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-689 1556176 1556500 1556884 "MAPPKG3" 1557739 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-688 1555157 1555330 1555552 "MAPPKG2" 1556000 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-687 1553656 1553940 1554267 "MAPPKG1" 1554863 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-686 1552735 1553062 1553239 "MAPPAST" 1553499 T MAPPAST (NIL) -8 NIL NIL NIL) (-685 1552346 1552404 1552527 "MAPHACK3" 1552671 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-684 1551938 1551999 1552113 "MAPHACK2" 1552278 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-683 1551375 1551479 1551621 "MAPHACK1" 1551829 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-682 1549454 1550075 1550379 "MAGMA" 1551103 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-681 1548933 1549178 1549269 "MACROAST" 1549383 T MACROAST (NIL) -8 NIL NIL NIL) (-680 1545351 1547172 1547633 "M3D" 1548505 NIL M3D (NIL T) -8 NIL NIL NIL) (-679 1539459 1543720 1543761 "LZSTAGG" 1544543 NIL LZSTAGG (NIL T) -9 NIL 1544838 NIL) (-678 1535416 1536590 1538047 "LZSTAGG-" 1538052 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-677 1532503 1533307 1533794 "LWORD" 1534961 NIL LWORD (NIL T) -8 NIL NIL NIL) (-676 1532079 1532307 1532382 "LSTAST" 1532448 T LSTAST (NIL) -8 NIL NIL NIL) (-675 1525276 1531850 1531984 "LSQM" 1531989 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-674 1524500 1524639 1524867 "LSPP" 1525131 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-673 1521342 1521999 1522712 "LSMP1" 1523819 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1519177 1519471 1519920 "LSMP" 1521038 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-671 1513056 1518344 1518385 "LSAGG" 1518447 NIL LSAGG (NIL T) -9 NIL 1518525 NIL) (-670 1509751 1510675 1511888 "LSAGG-" 1511893 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-669 1507350 1508895 1509144 "LPOLY" 1509546 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-668 1506932 1507017 1507140 "LPEFRAC" 1507259 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-667 1506584 1506696 1506724 "LOGIC" 1506835 T LOGIC (NIL) -9 NIL 1506916 NIL) (-666 1506446 1506469 1506540 "LOGIC-" 1506545 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1505639 1505779 1505972 "LODOOPS" 1506302 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1504177 1504412 1504765 "LODOF" 1505386 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-663 1500409 1502826 1502867 "LODOCAT" 1503305 NIL LODOCAT (NIL T) -9 NIL 1503516 NIL) (-662 1500142 1500200 1500327 "LODOCAT-" 1500332 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-661 1497476 1499983 1500101 "LODO2" 1500106 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-660 1494925 1497413 1497458 "LODO1" 1497463 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-659 1492362 1494841 1494907 "LODO" 1494912 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-658 1491243 1491408 1491713 "LODEEF" 1492185 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1489564 1490337 1490590 "LO" 1491075 NIL LO (NIL T T T) -8 NIL NIL NIL) (-656 1484803 1487694 1487735 "LNAGG" 1488682 NIL LNAGG (NIL T) -9 NIL 1489126 NIL) (-655 1483950 1484164 1484506 "LNAGG-" 1484511 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-654 1480086 1480875 1481514 "LMOPS" 1483365 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-653 1479489 1479877 1479918 "LMODULE" 1479923 NIL LMODULE (NIL T) -9 NIL 1479949 NIL) (-652 1476687 1479134 1479257 "LMDICT" 1479399 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-651 1476093 1476314 1476355 "LLINSET" 1476546 NIL LLINSET (NIL T) -9 NIL 1476637 NIL) (-650 1475792 1476001 1476061 "LITERAL" 1476066 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-649 1475317 1475391 1475530 "LIST3" 1475712 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1473451 1473763 1474162 "LIST2MAP" 1474964 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-647 1472458 1472636 1472864 "LIST2" 1473269 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-646 1465623 1471392 1471696 "LIST" 1472187 NIL LIST (NIL T) -8 NIL NIL NIL) (-645 1465219 1465456 1465497 "LINSET" 1465502 NIL LINSET (NIL T) -9 NIL 1465536 NIL) (-644 1463880 1464550 1464591 "LINEXP" 1464846 NIL LINEXP (NIL T) -9 NIL 1464995 NIL) (-643 1462527 1462787 1463084 "LINDEP" 1463632 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-642 1459365 1460065 1460823 "LIMITRF" 1461801 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-641 1457691 1457980 1458382 "LIMITPS" 1459067 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-640 1456639 1457108 1457148 "LIECAT" 1457288 NIL LIECAT (NIL T) -9 NIL 1457439 NIL) (-639 1456480 1456507 1456595 "LIECAT-" 1456600 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1450940 1455991 1456219 "LIE" 1456301 NIL LIE (NIL T T) -8 NIL NIL NIL) (-637 1443438 1450389 1450554 "LIB" 1450795 T LIB (NIL) -8 NIL NIL NIL) (-636 1439073 1439956 1440891 "LGROBP" 1442555 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-635 1437913 1438605 1438633 "LFCAT" 1438840 T LFCAT (NIL) -9 NIL 1438979 NIL) (-634 1435911 1436185 1436535 "LF" 1437634 NIL LF (NIL T T) -7 NIL NIL NIL) (-633 1432813 1433443 1434131 "LEXTRIPK" 1435275 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-632 1429557 1430383 1430886 "LEXP" 1432393 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-631 1429033 1429278 1429370 "LETAST" 1429485 T LETAST (NIL) -8 NIL NIL NIL) (-630 1427431 1427744 1428145 "LEADCDET" 1428715 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-629 1426621 1426695 1426924 "LAZM3PK" 1427352 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-628 1421552 1424698 1425236 "LAUPOL" 1426133 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-627 1421131 1421175 1421336 "LAPLACE" 1421502 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-626 1420125 1420709 1420750 "LALG" 1420812 NIL LALG (NIL T) -9 NIL 1420871 NIL) (-625 1419839 1419898 1420034 "LALG-" 1420039 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1417778 1418940 1419191 "LA" 1419672 NIL LA (NIL T T T) -8 NIL NIL NIL) (-623 1417613 1417637 1417678 "KVTFROM" 1417740 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-622 1416536 1416980 1417165 "KTVLOGIC" 1417448 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-621 1416371 1416395 1416436 "KRCFROM" 1416498 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-620 1415275 1415462 1415761 "KOVACIC" 1416171 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-619 1415110 1415134 1415175 "KONVERT" 1415237 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-618 1414945 1414969 1415010 "KOERCE" 1415072 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-617 1414441 1414522 1414654 "KERNEL2" 1414859 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1412271 1413034 1413411 "KERNEL" 1414097 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-615 1406041 1410810 1410864 "KDAGG" 1411241 NIL KDAGG (NIL T T) -9 NIL 1411447 NIL) (-614 1405570 1405694 1405899 "KDAGG-" 1405904 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-613 1398720 1405231 1405386 "KAFILE" 1405448 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-612 1393180 1398231 1398459 "JORDAN" 1398541 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-611 1392559 1392829 1392950 "JOINAST" 1393079 T JOINAST (NIL) -8 NIL NIL NIL) (-610 1392405 1392464 1392519 "JAVACODE" 1392524 T JAVACODE (NIL) -8 NIL NIL NIL) (-609 1388657 1390610 1390664 "IXAGG" 1391593 NIL IXAGG (NIL T T) -9 NIL 1392052 NIL) (-608 1387576 1387882 1388301 "IXAGG-" 1388306 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-607 1383106 1387498 1387557 "IVECTOR" 1387562 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-606 1381872 1382109 1382375 "ITUPLE" 1382873 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-605 1380374 1380551 1380846 "ITRIGMNP" 1381694 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-604 1379119 1379323 1379606 "ITFUN3" 1380150 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-603 1378751 1378808 1378917 "ITFUN2" 1379056 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-602 1377910 1378231 1378405 "ITFORM" 1378597 T ITFORM (NIL) -8 NIL NIL NIL) (-601 1375871 1376930 1377208 "ITAYLOR" 1377665 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-600 1364816 1370008 1371171 "ISUPS" 1374741 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-599 1363920 1364060 1364296 "ISUMP" 1364663 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-598 1359295 1363865 1363906 "ISTRING" 1363911 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-597 1358771 1359016 1359108 "ISAST" 1359223 T ISAST (NIL) -8 NIL NIL NIL) (-596 1357980 1358062 1358278 "IRURPK" 1358685 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-595 1356916 1357117 1357357 "IRSN" 1357760 T IRSN (NIL) -7 NIL NIL NIL) (-594 1354987 1355342 1355771 "IRRF2F" 1356554 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-593 1354734 1354772 1354848 "IRREDFFX" 1354943 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-592 1353349 1353608 1353907 "IROOT" 1354467 NIL IROOT (NIL T) -7 NIL NIL NIL) (-591 1352554 1352842 1352993 "IRFORM" 1353218 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1351654 1351767 1351981 "IR2F" 1352437 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-589 1349267 1349762 1350328 "IR2" 1351132 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-588 1345871 1346951 1347643 "IR" 1348607 NIL IR (NIL T) -8 NIL NIL NIL) (-587 1345662 1345696 1345756 "IPRNTPK" 1345831 T IPRNTPK (NIL) -7 NIL NIL NIL) (-586 1342245 1345551 1345620 "IPF" 1345625 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-585 1340574 1342170 1342227 "IPADIC" 1342232 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-584 1339886 1340134 1340264 "IP4ADDR" 1340464 T IP4ADDR (NIL) -8 NIL NIL NIL) (-583 1339359 1339590 1339700 "IOMODE" 1339796 T IOMODE (NIL) -8 NIL NIL NIL) (-582 1338432 1338956 1339083 "IOBFILE" 1339252 T IOBFILE (NIL) -8 NIL NIL NIL) (-581 1337920 1338336 1338364 "IOBCON" 1338369 T IOBCON (NIL) -9 NIL 1338390 NIL) (-580 1337431 1337489 1337672 "INVLAPLA" 1337856 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-579 1327127 1329469 1331843 "INTTR" 1335107 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-578 1323462 1324204 1325069 "INTTOOLS" 1326312 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-577 1323048 1323139 1323256 "INTSLPE" 1323365 T INTSLPE (NIL) -7 NIL NIL NIL) (-576 1321001 1322971 1323030 "INTRVL" 1323035 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-575 1318603 1319115 1319690 "INTRF" 1320486 NIL INTRF (NIL T) -7 NIL NIL NIL) (-574 1318014 1318111 1318253 "INTRET" 1318501 NIL INTRET (NIL T) -7 NIL NIL NIL) (-573 1316011 1316400 1316870 "INTRAT" 1317622 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-572 1313274 1313857 1314476 "INTPM" 1315496 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-571 1310042 1310634 1311365 "INTPAF" 1312667 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-570 1305221 1306183 1307234 "INTPACK" 1309011 T INTPACK (NIL) -7 NIL NIL NIL) (-569 1304473 1304625 1304833 "INTHERTR" 1305063 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1303912 1303992 1304180 "INTHERAL" 1304387 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1301758 1302201 1302658 "INTHEORY" 1303475 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1293222 1294825 1296579 "INTG0" 1300128 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1279495 1282860 1286245 "INTFTBL" 1289857 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278744 1278882 1279055 "INTFACT" 1279354 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1276177 1276621 1277176 "INTEF" 1278300 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1274544 1275283 1275311 "INTDOM" 1275612 T INTDOM (NIL) -9 NIL 1275819 NIL) (-561 1273913 1274087 1274329 "INTDOM-" 1274334 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1270301 1272229 1272283 "INTCAT" 1273082 NIL INTCAT (NIL T) -9 NIL 1273403 NIL) (-559 1269773 1269876 1270004 "INTBIT" 1270193 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1268472 1268626 1268933 "INTALG" 1269618 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267955 1268045 1268202 "INTAF" 1268376 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1261300 1267765 1267905 "INTABL" 1267910 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260641 1261107 1261172 "INT8" 1261206 T INT8 (NIL) -8 NIL NIL 1261251) (-554 1259981 1260447 1260512 "INT64" 1260546 T INT64 (NIL) -8 NIL NIL 1260591) (-553 1259321 1259787 1259852 "INT32" 1259886 T INT32 (NIL) -8 NIL NIL 1259931) (-552 1258661 1259127 1259192 "INT16" 1259226 T INT16 (NIL) -8 NIL NIL 1259271) (-551 1255611 1258458 1258567 "INT" 1258572 T INT (NIL) -8 NIL NIL NIL) (-550 1250523 1253234 1253262 "INS" 1254196 T INS (NIL) -9 NIL 1254861 NIL) (-549 1247763 1248534 1249508 "INS-" 1249581 NIL INS- (NIL T) -8 NIL NIL NIL) (-548 1246611 1246816 1247092 "INPSIGN" 1247538 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-547 1245729 1245846 1246043 "INPRODPF" 1246491 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-546 1244623 1244740 1244977 "INPRODFF" 1245609 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-545 1243623 1243775 1244035 "INNMFACT" 1244459 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-544 1242820 1242917 1243105 "INMODGCD" 1243522 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-543 1241328 1241573 1241897 "INFSP" 1242565 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-542 1240512 1240629 1240812 "INFPROD0" 1241208 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-541 1240122 1240182 1240280 "INFORM1" 1240447 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1236977 1238187 1238702 "INFORM" 1239615 T INFORM (NIL) -8 NIL NIL NIL) (-539 1236500 1236589 1236703 "INFINITY" 1236883 T INFINITY (NIL) -7 NIL NIL NIL) (-538 1235676 1236220 1236321 "INETCLTS" 1236419 T INETCLTS (NIL) -8 NIL NIL NIL) (-537 1234292 1234542 1234863 "INEP" 1235424 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-536 1233541 1234189 1234254 "INDE" 1234259 NIL INDE (NIL T) -8 NIL NIL NIL) (-535 1233105 1233173 1233290 "INCRMAPS" 1233468 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-534 1231923 1232374 1232580 "INBFILE" 1232919 T INBFILE (NIL) -8 NIL NIL NIL) (-533 1227223 1228159 1229103 "INBFF" 1231011 NIL INBFF (NIL T) -7 NIL NIL NIL) (-532 1226131 1226400 1226428 "INBCON" 1226941 T INBCON (NIL) -9 NIL 1227207 NIL) (-531 1225383 1225606 1225882 "INBCON-" 1225887 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-530 1224862 1225107 1225198 "INAST" 1225312 T INAST (NIL) -8 NIL NIL NIL) (-529 1224289 1224541 1224647 "IMPTAST" 1224776 T IMPTAST (NIL) -8 NIL NIL NIL) (-528 1220734 1224133 1224237 "IMATRIX" 1224242 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-527 1219446 1219569 1219884 "IMATQF" 1220590 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-526 1217666 1217893 1218230 "IMATLIN" 1219202 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-525 1212246 1217590 1217648 "ILIST" 1217653 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-524 1210151 1212106 1212219 "IIARRAY2" 1212224 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-523 1205551 1210062 1210126 "IFF" 1210131 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-522 1204898 1205168 1205284 "IFAST" 1205455 T IFAST (NIL) -8 NIL NIL NIL) (-521 1199893 1204190 1204378 "IFARRAY" 1204755 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-520 1199073 1199797 1199870 "IFAMON" 1199875 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-519 1198657 1198722 1198776 "IEVALAB" 1198983 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-518 1198332 1198400 1198560 "IEVALAB-" 1198565 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-517 1197582 1198221 1198296 "IDPOAMS" 1198301 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1196889 1197471 1197546 "IDPOAM" 1197551 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1196520 1196803 1196866 "IDPO" 1196871 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-514 1195579 1195855 1195908 "IDPC" 1196321 NIL IDPC (NIL T T) -9 NIL 1196470 NIL) (-513 1195048 1195471 1195544 "IDPAM" 1195549 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-512 1194424 1194940 1195013 "IDPAG" 1195018 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-511 1194069 1194260 1194335 "IDENT" 1194369 T IDENT (NIL) -8 NIL NIL NIL) (-510 1190324 1191172 1192067 "IDECOMP" 1193226 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-509 1183162 1184247 1185294 "IDEAL" 1189360 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-508 1182326 1182438 1182637 "ICDEN" 1183046 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-507 1181397 1181806 1181953 "ICARD" 1182199 T ICARD (NIL) -8 NIL NIL NIL) (-506 1179457 1179770 1180175 "IBPTOOLS" 1181074 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-505 1175064 1179077 1179190 "IBITS" 1179376 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-504 1171787 1172363 1173058 "IBATOOL" 1174481 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-503 1169566 1170028 1170561 "IBACHIN" 1171322 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-502 1167395 1169412 1169515 "IARRAY2" 1169520 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-501 1163501 1167321 1167378 "IARRAY1" 1167383 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-500 1157619 1161913 1162394 "IAN" 1163040 T IAN (NIL) -8 NIL NIL NIL) (-499 1157130 1157187 1157360 "IALGFACT" 1157556 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-498 1156658 1156771 1156799 "HYPCAT" 1157006 T HYPCAT (NIL) -9 NIL NIL NIL) (-497 1156196 1156313 1156499 "HYPCAT-" 1156504 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-496 1155791 1155991 1156074 "HOSTNAME" 1156133 T HOSTNAME (NIL) -8 NIL NIL NIL) (-495 1155636 1155673 1155714 "HOMOTOP" 1155719 NIL HOMOTOP (NIL T) -9 NIL 1155752 NIL) (-494 1152268 1153646 1153687 "HOAGG" 1154668 NIL HOAGG (NIL T) -9 NIL 1155347 NIL) (-493 1150862 1151261 1151787 "HOAGG-" 1151792 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-492 1144887 1150457 1150606 "HEXADEC" 1150733 T HEXADEC (NIL) -8 NIL NIL NIL) (-491 1143635 1143857 1144120 "HEUGCD" 1144664 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-490 1142711 1143472 1143602 "HELLFDIV" 1143607 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-489 1140890 1142488 1142576 "HEAP" 1142655 NIL HEAP (NIL T) -8 NIL NIL NIL) (-488 1140153 1140442 1140576 "HEADAST" 1140776 T HEADAST (NIL) -8 NIL NIL NIL) (-487 1134026 1140068 1140130 "HDP" 1140135 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-486 1128045 1133661 1133813 "HDMP" 1133927 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-485 1127369 1127509 1127673 "HB" 1127901 T HB (NIL) -7 NIL NIL NIL) (-484 1120757 1127215 1127319 "HASHTBL" 1127324 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-483 1120233 1120478 1120570 "HASAST" 1120685 T HASAST (NIL) -8 NIL NIL NIL) (-482 1118015 1119855 1120037 "HACKPI" 1120071 T HACKPI (NIL) -8 NIL NIL NIL) (-481 1113710 1117868 1117981 "GTSET" 1117986 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-480 1107127 1113588 1113686 "GSTBL" 1113691 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-479 1099407 1106158 1106423 "GSERIES" 1106918 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-478 1098548 1098965 1098993 "GROUP" 1099196 T GROUP (NIL) -9 NIL 1099330 NIL) (-477 1097914 1098073 1098324 "GROUP-" 1098329 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-476 1096281 1096602 1096989 "GROEBSOL" 1097591 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-475 1095195 1095483 1095534 "GRMOD" 1096063 NIL GRMOD (NIL T T) -9 NIL 1096231 NIL) (-474 1094963 1094999 1095127 "GRMOD-" 1095132 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-473 1090253 1091317 1092317 "GRIMAGE" 1093983 T GRIMAGE (NIL) -8 NIL NIL NIL) (-472 1088719 1088980 1089304 "GRDEF" 1089949 T GRDEF (NIL) -7 NIL NIL NIL) (-471 1088163 1088279 1088420 "GRAY" 1088598 T GRAY (NIL) -7 NIL NIL NIL) (-470 1087350 1087756 1087807 "GRALG" 1087960 NIL GRALG (NIL T T) -9 NIL 1088053 NIL) (-469 1087011 1087084 1087247 "GRALG-" 1087252 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-468 1083788 1086596 1086774 "GPOLSET" 1086918 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-467 1083142 1083199 1083457 "GOSPER" 1083725 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-466 1078874 1079580 1080106 "GMODPOL" 1082841 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-465 1077879 1078063 1078301 "GHENSEL" 1078686 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-464 1072035 1072878 1073898 "GENUPS" 1076963 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-463 1071732 1071783 1071872 "GENUFACT" 1071978 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-462 1071144 1071221 1071386 "GENPGCD" 1071650 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-461 1070618 1070653 1070866 "GENMFACT" 1071103 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-460 1069184 1069441 1069748 "GENEEZ" 1070361 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-459 1063361 1068795 1068957 "GDMP" 1069107 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-458 1052725 1057132 1058238 "GCNAALG" 1062344 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-457 1051052 1051914 1051942 "GCDDOM" 1052197 T GCDDOM (NIL) -9 NIL 1052354 NIL) (-456 1050522 1050649 1050864 "GCDDOM-" 1050869 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-455 1039138 1041468 1043860 "GBINTERN" 1048213 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1036975 1037267 1037688 "GBF" 1038813 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1035756 1035921 1036188 "GBEUCLID" 1036791 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1034428 1034613 1034917 "GB" 1035535 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1033777 1033902 1034051 "GAUSSFAC" 1034299 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-450 1032144 1032446 1032760 "GALUTIL" 1033496 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-449 1030452 1030726 1031050 "GALPOLYU" 1031871 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-448 1027817 1028107 1028514 "GALFACTU" 1030149 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-447 1019622 1021122 1022730 "GALFACT" 1026249 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-446 1017010 1017668 1017696 "FVFUN" 1018852 T FVFUN (NIL) -9 NIL 1019572 NIL) (-445 1016276 1016458 1016486 "FVC" 1016777 T FVC (NIL) -9 NIL 1016960 NIL) (-444 1015919 1016101 1016169 "FUNDESC" 1016228 T FUNDESC (NIL) -8 NIL NIL NIL) (-443 1015534 1015716 1015797 "FUNCTION" 1015871 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-442 1014325 1014835 1015038 "FTEM" 1015351 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012081 1012656 1013119 "FT" 1013882 T FT (NIL) -8 NIL NIL NIL) (-440 1010372 1010661 1011058 "FSUPFACT" 1011772 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-439 1008769 1009058 1009390 "FST" 1010060 T FST (NIL) -8 NIL NIL NIL) (-438 1007968 1008074 1008262 "FSRED" 1008651 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-437 1006667 1006923 1007270 "FSPRMELT" 1007683 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-436 1003973 1004411 1004897 "FSPECF" 1006230 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-435 1003501 1003555 1003725 "FSINT" 1003914 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-434 1001793 1002494 1002797 "FSERIES" 1003280 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-433 1000835 1000951 1001175 "FSCINT" 1001673 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-432 999877 1000020 1000247 "FSAGG2" 1000688 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-431 996085 998821 998862 "FSAGG" 999232 NIL FSAGG (NIL T) -9 NIL 999491 NIL) (-430 993847 994448 995244 "FSAGG-" 995339 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 991529 991809 992356 "FS2UPS" 993565 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-428 990407 990578 990880 "FS2EXPXP" 991354 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-427 990041 990084 990213 "FS2" 990358 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 971708 980010 980051 "FS" 983935 NIL FS (NIL T) -9 NIL 986224 NIL) (-425 960432 963398 967428 "FS-" 967728 NIL FS- (NIL T T) -8 NIL NIL NIL) (-424 959858 959973 960125 "FRUTIL" 960312 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-423 954859 957501 957541 "FRNAALG" 958937 NIL FRNAALG (NIL T) -9 NIL 959544 NIL) (-422 950583 951642 952900 "FRNAALG-" 953650 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 950221 950264 950391 "FRNAAF2" 950534 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 948601 949075 949370 "FRMOD" 950033 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 947796 947883 948172 "FRIDEAL2" 948508 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-418 945547 946179 946496 "FRIDEAL" 947587 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-417 944687 945094 945135 "FRETRCT" 945140 NIL FRETRCT (NIL T) -9 NIL 945316 NIL) (-416 943820 944044 944388 "FRETRCT-" 944393 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 940908 942118 942177 "FRAMALG" 943059 NIL FRAMALG (NIL T T) -9 NIL 943351 NIL) (-414 939042 939497 940127 "FRAMALG-" 940350 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 938678 938735 938842 "FRAC2" 938979 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-412 932620 938153 938429 "FRAC" 938434 NIL FRAC (NIL T) -8 NIL NIL NIL) (-411 932256 932313 932420 "FR2" 932557 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 923784 927832 929163 "FR" 930957 NIL FR (NIL T) -8 NIL NIL NIL) (-409 918301 921190 921218 "FPS" 922337 T FPS (NIL) -9 NIL 922894 NIL) (-408 917750 917859 918023 "FPS-" 918169 NIL FPS- (NIL T) -8 NIL NIL NIL) (-407 915054 916721 916749 "FPC" 916974 T FPC (NIL) -9 NIL 917116 NIL) (-406 914847 914887 914984 "FPC-" 914989 NIL FPC- (NIL T) -8 NIL NIL NIL) (-405 913637 914335 914376 "FPATMAB" 914381 NIL FPATMAB (NIL T) -9 NIL 914533 NIL) (-404 911310 911813 912239 "FPARFRAC" 913274 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-403 906743 907241 907923 "FORTRAN" 910742 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-402 904419 904981 905009 "FORTFN" 906069 T FORTFN (NIL) -9 NIL 906693 NIL) (-401 904183 904233 904261 "FORTCAT" 904320 T FORTCAT (NIL) -9 NIL 904382 NIL) (-400 901899 902399 902938 "FORT" 903664 T FORT (NIL) -7 NIL NIL NIL) (-399 901687 901717 901786 "FORMULA1" 901863 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 899793 900303 900693 "FORMULA" 901317 T FORMULA (NIL) -8 NIL NIL NIL) (-397 899316 899368 899541 "FORDER" 899735 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-396 898412 898576 898769 "FOP" 899143 T FOP (NIL) -7 NIL NIL NIL) (-395 896993 897692 897866 "FNLA" 898294 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-394 895722 896137 896165 "FNCAT" 896625 T FNCAT (NIL) -9 NIL 896885 NIL) (-393 895261 895681 895709 "FNAME" 895714 T FNAME (NIL) -8 NIL NIL NIL) (-392 893824 894787 894815 "FMTC" 894820 T FMTC (NIL) -9 NIL 894856 NIL) (-391 892577 893760 893806 "FMONOID" 893811 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-390 889405 890573 890614 "FMONCAT" 891831 NIL FMONCAT (NIL T) -9 NIL 892436 NIL) (-389 886829 887475 887503 "FMFUN" 888647 T FMFUN (NIL) -9 NIL 889355 NIL) (-388 883908 884768 884822 "FMCAT" 886017 NIL FMCAT (NIL T T) -9 NIL 886512 NIL) (-387 883177 883358 883386 "FMC" 883676 T FMC (NIL) -9 NIL 883858 NIL) (-386 882043 882943 883043 "FM1" 883122 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 881235 881785 881934 "FM" 881939 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 879009 879425 879919 "FLOATRP" 880786 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-383 876447 876947 877525 "FLOATCP" 878476 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870025 874176 874797 "FLOAT" 875846 T FLOAT (NIL) -8 NIL NIL NIL) (-381 868765 869603 869644 "FLINEXP" 869649 NIL FLINEXP (NIL T) -9 NIL 869742 NIL) (-380 867919 868154 868482 "FLINEXP-" 868487 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-379 866995 867139 867363 "FLASORT" 867771 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-378 864111 864979 865031 "FLALG" 866258 NIL FLALG (NIL T T) -9 NIL 866725 NIL) (-377 863153 863296 863523 "FLAGG2" 863964 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-376 856889 860639 860680 "FLAGG" 861942 NIL FLAGG (NIL T) -9 NIL 862594 NIL) (-375 855615 855954 856444 "FLAGG-" 856449 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-374 852466 853474 853533 "FINRALG" 854661 NIL FINRALG (NIL T T) -9 NIL 855169 NIL) (-373 851626 851855 852194 "FINRALG-" 852199 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-372 851006 851245 851273 "FINITE" 851469 T FINITE (NIL) -9 NIL 851576 NIL) (-371 843363 845550 845590 "FINAALG" 849257 NIL FINAALG (NIL T) -9 NIL 850710 NIL) (-370 838695 839745 840889 "FINAALG-" 842268 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-369 837353 837691 837745 "FILECAT" 838429 NIL FILECAT (NIL T T) -9 NIL 838645 NIL) (-368 836721 837108 837211 "FILE" 837283 NIL FILE (NIL T) -8 NIL NIL NIL) (-367 834439 835965 835993 "FIELD" 836033 T FIELD (NIL) -9 NIL 836113 NIL) (-366 833059 833444 833955 "FIELD-" 833960 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-365 830909 831694 832041 "FGROUP" 832745 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-364 829999 830163 830383 "FGLMICPK" 830741 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-363 825833 829924 829981 "FFX" 829986 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-362 825434 825495 825630 "FFSLPE" 825766 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-361 824938 824974 825183 "FFPOLY2" 825392 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 820928 821710 822506 "FFPOLY" 824174 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-359 816774 820847 820910 "FFP" 820915 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-358 811902 816117 816307 "FFNBX" 816628 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 806832 811037 811295 "FFNBP" 811756 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 801467 806116 806327 "FFNB" 806665 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 800299 800497 800812 "FFINTBAS" 801264 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 796370 798588 798616 "FFIELDC" 799236 T FFIELDC (NIL) -9 NIL 799612 NIL) (-353 795032 795403 795900 "FFIELDC-" 795905 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 794601 794647 794771 "FFHOM" 794974 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 792296 792783 793300 "FFF" 794116 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 787916 792038 792139 "FFCGX" 792239 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 783540 787648 787755 "FFCGP" 787859 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 778725 783267 783375 "FFCG" 783476 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 778136 778179 778414 "FFCAT2" 778676 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 759541 768613 768699 "FFCAT" 773864 NIL FFCAT (NIL T T T) -9 NIL 775315 NIL) (-345 754738 755786 757100 "FFCAT-" 758330 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-344 750138 754649 754713 "FF" 754718 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-343 739463 743110 744330 "FEXPR" 748990 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-342 738463 738898 738939 "FEVALAB" 739023 NIL FEVALAB (NIL T) -9 NIL 739284 NIL) (-341 737622 737832 738170 "FEVALAB-" 738175 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-340 734642 735383 735498 "FDIVCAT" 737066 NIL FDIVCAT (NIL T T T T) -9 NIL 737503 NIL) (-339 734404 734431 734601 "FDIVCAT-" 734606 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733624 733711 733988 "FDIV2" 734311 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732190 733007 733210 "FDIV" 733523 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-336 731164 731485 731687 "FCTRDATA" 732008 T FCTRDATA (NIL) -8 NIL NIL NIL) (-335 729850 730109 730398 "FCPAK1" 730895 T FCPAK1 (NIL) -7 NIL NIL NIL) (-334 728949 729350 729491 "FCOMP" 729741 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-333 712654 716099 719637 "FC" 725431 T FC (NIL) -8 NIL NIL NIL) (-332 705019 709045 709085 "FAXF" 710887 NIL FAXF (NIL T) -9 NIL 711579 NIL) (-331 702295 702953 703778 "FAXF-" 704243 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-330 697347 701671 701847 "FARRAY" 702152 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-329 692248 694308 694361 "FAMR" 695384 NIL FAMR (NIL T T) -9 NIL 695844 NIL) (-328 691138 691440 691875 "FAMR-" 691880 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-327 690307 691060 691113 "FAMONOID" 691118 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-326 688093 688803 688856 "FAMONC" 689797 NIL FAMONC (NIL T T) -9 NIL 690183 NIL) (-325 686757 687847 687984 "FAGROUP" 687989 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-324 684552 684871 685274 "FACUTIL" 686438 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-323 683651 683836 684058 "FACTFUNC" 684362 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-322 676075 682954 683153 "EXPUPXS" 683507 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-321 673558 674098 674684 "EXPRTUBE" 675509 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-320 669829 670421 671151 "EXPRODE" 672897 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-319 664383 664970 665776 "EXPR2UPS" 669127 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 664015 664072 664181 "EXPR2" 664320 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 649561 662664 663093 "EXPR" 663619 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 640977 648714 649004 "EXPEXPAN" 649398 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-315 640457 640701 640792 "EXITAST" 640906 T EXITAST (NIL) -8 NIL NIL NIL) (-314 640257 640414 640443 "EXIT" 640448 T EXIT (NIL) -8 NIL NIL NIL) (-313 639884 639946 640059 "EVALCYC" 640189 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-312 639425 639543 639584 "EVALAB" 639754 NIL EVALAB (NIL T) -9 NIL 639858 NIL) (-311 638906 639028 639249 "EVALAB-" 639254 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-310 636274 637576 637604 "EUCDOM" 638159 T EUCDOM (NIL) -9 NIL 638509 NIL) (-309 634679 635121 635711 "EUCDOM-" 635716 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-308 634311 634368 634477 "ESTOOLS2" 634616 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 634062 634104 634184 "ESTOOLS1" 634263 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 621600 624360 627110 "ESTOOLS" 631332 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 621345 621377 621459 "ESCONT1" 621562 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-304 617719 618480 619260 "ESCONT" 620585 T ESCONT (NIL) -7 NIL NIL NIL) (-303 617394 617444 617544 "ES2" 617663 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-302 617024 617082 617191 "ES1" 617330 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-301 611061 612669 612697 "ES" 615465 T ES (NIL) -9 NIL 616875 NIL) (-300 606008 607295 609112 "ES-" 609276 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 605224 605353 605529 "ERROR" 605852 T ERROR (NIL) -7 NIL NIL NIL) (-298 598618 605083 605174 "EQTBL" 605179 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-297 598250 598307 598416 "EQ2" 598555 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 590753 593564 595013 "EQ" 596834 NIL -3977 (NIL T) -8 NIL NIL NIL) (-295 586043 587091 588184 "EP" 589692 NIL EP (NIL T) -7 NIL NIL NIL) (-294 584643 584934 585240 "ENV" 585757 T ENV (NIL) -8 NIL NIL NIL) (-293 583737 584291 584319 "ENTIRER" 584324 T ENTIRER (NIL) -9 NIL 584370 NIL) (-292 580260 581746 582116 "EMR" 583536 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-291 579404 579589 579643 "ELTAGG" 580023 NIL ELTAGG (NIL T T) -9 NIL 580234 NIL) (-290 579123 579185 579326 "ELTAGG-" 579331 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-289 578912 578941 578995 "ELTAB" 579079 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-288 578038 578184 578383 "ELFUTS" 578763 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-287 577780 577836 577864 "ELEMFUN" 577969 T ELEMFUN (NIL) -9 NIL NIL NIL) (-286 577650 577671 577739 "ELEMFUN-" 577744 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-285 572494 575750 575791 "ELAGG" 576731 NIL ELAGG (NIL T) -9 NIL 577194 NIL) (-284 570779 571213 571876 "ELAGG-" 571881 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-283 570091 570228 570384 "ELABOR" 570643 T ELABOR (NIL) -8 NIL NIL NIL) (-282 568752 569031 569325 "ELABEXPR" 569817 T ELABEXPR (NIL) -8 NIL NIL NIL) (-281 561743 563419 564246 "EFUPXS" 568028 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-280 555320 556994 557804 "EFULS" 561019 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-279 552805 553163 553635 "EFSTRUC" 554952 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-278 542596 544162 545710 "EF" 551320 NIL EF (NIL T T) -7 NIL NIL NIL) (-277 541670 542081 542230 "EAB" 542467 T EAB (NIL) -8 NIL NIL NIL) (-276 540852 541629 541657 "E04UCFA" 541662 T E04UCFA (NIL) -8 NIL NIL NIL) (-275 540034 540811 540839 "E04NAFA" 540844 T E04NAFA (NIL) -8 NIL NIL NIL) (-274 539216 539993 540021 "E04MBFA" 540026 T E04MBFA (NIL) -8 NIL NIL NIL) (-273 538398 539175 539203 "E04JAFA" 539208 T E04JAFA (NIL) -8 NIL NIL NIL) (-272 537582 538357 538385 "E04GCFA" 538390 T E04GCFA (NIL) -8 NIL NIL NIL) (-271 536766 537541 537569 "E04FDFA" 537574 T E04FDFA (NIL) -8 NIL NIL NIL) (-270 535948 536725 536753 "E04DGFA" 536758 T E04DGFA (NIL) -8 NIL NIL NIL) (-269 530121 531473 532837 "E04AGNT" 534604 T E04AGNT (NIL) -7 NIL NIL NIL) (-268 528801 529307 529347 "DVARCAT" 529822 NIL DVARCAT (NIL T) -9 NIL 530021 NIL) (-267 528005 528217 528531 "DVARCAT-" 528536 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-266 521183 527804 527933 "DSMP" 527938 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-265 520848 520907 521005 "DROPT1" 521118 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 515963 517089 518226 "DROPT0" 519731 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510744 511908 512976 "DROPT" 514915 T DROPT (NIL) -8 NIL NIL NIL) (-262 509089 509414 509800 "DRAWPT" 510378 T DRAWPT (NIL) -7 NIL NIL NIL) (-261 508722 508775 508893 "DRAWHACK" 509030 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 507453 507722 508013 "DRAWCX" 508451 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 506968 507037 507188 "DRAWCURV" 507379 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 497436 499398 501513 "DRAWCFUN" 504873 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 492023 492946 494025 "DRAW" 496410 NIL DRAW (NIL T) -7 NIL NIL NIL) (-256 488787 490716 490757 "DQAGG" 491386 NIL DQAGG (NIL T) -9 NIL 491660 NIL) (-255 476947 483380 483463 "DPOLCAT" 485315 NIL DPOLCAT (NIL T T T T) -9 NIL 485860 NIL) (-254 471834 473166 475107 "DPOLCAT-" 475112 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-253 464963 471695 471793 "DPMO" 471798 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-252 457995 464743 464910 "DPMM" 464915 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-251 457473 457687 457785 "DOMTMPLT" 457917 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-250 456906 457275 457355 "DOMCTOR" 457413 T DOMCTOR (NIL) -8 NIL NIL NIL) (-249 456118 456386 456537 "DOMAIN" 456775 T DOMAIN (NIL) -8 NIL NIL NIL) (-248 450137 455753 455905 "DMP" 456019 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-247 449737 449793 449937 "DLP" 450075 NIL DLP (NIL T) -7 NIL NIL NIL) (-246 443561 449064 449254 "DLIST" 449579 NIL DLIST (NIL T) -8 NIL NIL NIL) (-245 440359 442414 442455 "DLAGG" 443005 NIL DLAGG (NIL T) -9 NIL 443235 NIL) (-244 439035 439699 439727 "DIVRING" 439819 T DIVRING (NIL) -9 NIL 439902 NIL) (-243 438272 438462 438762 "DIVRING-" 438767 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-242 436374 436731 437137 "DISPLAY" 437886 T DISPLAY (NIL) -7 NIL NIL NIL) (-241 435222 435425 435690 "DIRPROD2" 436167 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 429117 435136 435199 "DIRPROD" 435204 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 417899 423898 423951 "DIRPCAT" 424361 NIL DIRPCAT (NIL NIL T) -9 NIL 425201 NIL) (-238 415225 415867 416748 "DIRPCAT-" 417085 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-237 414512 414672 414858 "DIOSP" 415059 T DIOSP (NIL) -7 NIL NIL NIL) (-236 411167 413424 413465 "DIOPS" 413899 NIL DIOPS (NIL T) -9 NIL 414128 NIL) (-235 410716 410830 411021 "DIOPS-" 411026 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-234 409539 410167 410195 "DIFRING" 410382 T DIFRING (NIL) -9 NIL 410492 NIL) (-233 409185 409262 409414 "DIFRING-" 409419 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-232 406921 408193 408234 "DIFEXT" 408597 NIL DIFEXT (NIL T) -9 NIL 408891 NIL) (-231 405206 405634 406300 "DIFEXT-" 406305 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-230 402481 404738 404779 "DIAGG" 404784 NIL DIAGG (NIL T) -9 NIL 404804 NIL) (-229 401865 402022 402274 "DIAGG-" 402279 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-228 397281 400824 401101 "DHMATRIX" 401634 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-227 392893 393802 394812 "DFSFUN" 396291 T DFSFUN (NIL) -7 NIL NIL NIL) (-226 387976 391824 392136 "DFLOAT" 392601 T DFLOAT (NIL) -8 NIL NIL NIL) (-225 386239 386520 386909 "DFINTTLS" 387684 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-224 383268 384260 384660 "DERHAM" 385905 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-223 381069 383043 383132 "DEQUEUE" 383212 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-222 380323 380456 380639 "DEGRED" 380931 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-221 376933 377633 378434 "DEFINTRF" 379596 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-220 374600 375041 375605 "DEFINTEF" 376480 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-219 373950 374220 374335 "DEFAST" 374505 T DEFAST (NIL) -8 NIL NIL NIL) (-218 367975 373545 373694 "DECIMAL" 373821 T DECIMAL (NIL) -8 NIL NIL NIL) (-217 365487 365945 366451 "DDFACT" 367519 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-216 365083 365126 365277 "DBLRESP" 365438 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-215 362955 363316 363676 "DBASE" 364850 NIL DBASE (NIL T) -8 NIL NIL NIL) (-214 362197 362435 362581 "DATAARY" 362854 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-213 361303 362156 362184 "D03FAFA" 362189 T D03FAFA (NIL) -8 NIL NIL NIL) (-212 360410 361262 361290 "D03EEFA" 361295 T D03EEFA (NIL) -8 NIL NIL NIL) (-211 358360 358826 359315 "D03AGNT" 359941 T D03AGNT (NIL) -7 NIL NIL NIL) (-210 357649 358319 358347 "D02EJFA" 358352 T D02EJFA (NIL) -8 NIL NIL NIL) (-209 356938 357608 357636 "D02CJFA" 357641 T D02CJFA (NIL) -8 NIL NIL NIL) (-208 356227 356897 356925 "D02BHFA" 356930 T D02BHFA (NIL) -8 NIL NIL NIL) (-207 355516 356186 356214 "D02BBFA" 356219 T D02BBFA (NIL) -8 NIL NIL NIL) (-206 348713 350302 351908 "D02AGNT" 353930 T D02AGNT (NIL) -7 NIL NIL NIL) (-205 346481 347004 347550 "D01WGTS" 348187 T D01WGTS (NIL) -7 NIL NIL NIL) (-204 345548 346440 346468 "D01TRNS" 346473 T D01TRNS (NIL) -8 NIL NIL NIL) (-203 344616 345507 345535 "D01GBFA" 345540 T D01GBFA (NIL) -8 NIL NIL NIL) (-202 343684 344575 344603 "D01FCFA" 344608 T D01FCFA (NIL) -8 NIL NIL NIL) (-201 342752 343643 343671 "D01ASFA" 343676 T D01ASFA (NIL) -8 NIL NIL NIL) (-200 341820 342711 342739 "D01AQFA" 342744 T D01AQFA (NIL) -8 NIL NIL NIL) (-199 340888 341779 341807 "D01APFA" 341812 T D01APFA (NIL) -8 NIL NIL NIL) (-198 339956 340847 340875 "D01ANFA" 340880 T D01ANFA (NIL) -8 NIL NIL NIL) (-197 339024 339915 339943 "D01AMFA" 339948 T D01AMFA (NIL) -8 NIL NIL NIL) (-196 338092 338983 339011 "D01ALFA" 339016 T D01ALFA (NIL) -8 NIL NIL NIL) (-195 337160 338051 338079 "D01AKFA" 338084 T D01AKFA (NIL) -8 NIL NIL NIL) (-194 336228 337119 337147 "D01AJFA" 337152 T D01AJFA (NIL) -8 NIL NIL NIL) (-193 329523 331076 332637 "D01AGNT" 334687 T D01AGNT (NIL) -7 NIL NIL NIL) (-192 328860 328988 329140 "CYCLOTOM" 329391 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-191 325595 326308 327035 "CYCLES" 328153 T CYCLES (NIL) -7 NIL NIL NIL) (-190 324907 325041 325212 "CVMP" 325456 NIL CVMP (NIL T) -7 NIL NIL NIL) (-189 322748 323006 323375 "CTRIGMNP" 324635 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-188 322257 322479 322580 "CTORKIND" 322667 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321548 321864 321892 "CTORCAT" 322074 T CTORCAT (NIL) -9 NIL 322187 NIL) (-186 321146 321257 321416 "CTORCAT-" 321421 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320608 320820 320928 "CTORCALL" 321070 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320044 320402 320475 "CTOR" 320555 T CTOR (NIL) -8 NIL NIL NIL) (-183 319418 319517 319670 "CSTTOOLS" 319941 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-182 315217 315874 316632 "CRFP" 318730 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-181 314692 314938 315030 "CRCEAST" 315145 T CRCEAST (NIL) -8 NIL NIL NIL) (-180 313739 313924 314152 "CRAPACK" 314496 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-179 313123 313224 313428 "CPMATCH" 313615 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-178 312848 312876 312982 "CPIMA" 313089 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-177 309196 309868 310587 "COORDSYS" 312183 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-176 308608 308729 308871 "CONTOUR" 309074 T CONTOUR (NIL) -8 NIL NIL NIL) (-175 304501 306611 307103 "CONTFRAC" 308148 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-174 304381 304402 304430 "CONDUIT" 304467 T CONDUIT (NIL) -9 NIL NIL NIL) (-173 303469 304023 304051 "COMRING" 304056 T COMRING (NIL) -9 NIL 304108 NIL) (-172 302523 302827 303011 "COMPPROP" 303305 T COMPPROP (NIL) -8 NIL NIL NIL) (-171 302184 302219 302347 "COMPLPAT" 302482 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-170 301820 301877 301984 "COMPLEX2" 302121 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292129 301629 301738 "COMPLEX" 301743 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291468 291589 291749 "COMPILER" 291989 T COMPILER (NIL) -8 NIL NIL NIL) (-167 291186 291221 291319 "COMPFACT" 291427 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275275 285260 285300 "COMPCAT" 286304 NIL COMPCAT (NIL T) -9 NIL 287652 NIL) (-165 264808 267728 271348 "COMPCAT-" 271704 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264537 264565 264668 "COMMUPC" 264774 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264331 264365 264424 "COMMONOP" 264498 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 263907 264135 264210 "COMMAAST" 264276 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263463 263658 263745 "COMM" 263840 T COMM (NIL) -8 NIL NIL NIL) (-160 262712 262906 262934 "COMBOPC" 263272 T COMBOPC (NIL) -9 NIL 263447 NIL) (-159 261608 261818 262060 "COMBINAT" 262502 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258065 258639 259266 "COMBF" 261030 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 256823 257181 257416 "COLOR" 257850 T COLOR (NIL) -8 NIL NIL NIL) (-156 256299 256544 256636 "COLONAST" 256751 T COLONAST (NIL) -8 NIL NIL NIL) (-155 255939 255986 256111 "CMPLXRT" 256246 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255387 255639 255738 "CLLCTAST" 255860 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 250886 251917 252997 "CLIP" 254327 T CLIP (NIL) -7 NIL NIL NIL) (-152 249232 249992 250231 "CLIF" 250713 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245407 247378 247419 "CLAGG" 248348 NIL CLAGG (NIL T) -9 NIL 248884 NIL) (-150 243829 244286 244869 "CLAGG-" 244874 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243373 243458 243598 "CINTSLPE" 243738 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 240874 241345 241893 "CHVAR" 242901 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240048 240602 240630 "CHARZ" 240635 T CHARZ (NIL) -9 NIL 240650 NIL) (-146 239802 239842 239920 "CHARPOL" 240002 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 238860 239447 239475 "CHARNZ" 239522 T CHARNZ (NIL) -9 NIL 239578 NIL) (-144 236766 237514 237867 "CHAR" 238527 T CHAR (NIL) -8 NIL NIL NIL) (-143 236492 236553 236581 "CFCAT" 236692 T CFCAT (NIL) -9 NIL NIL NIL) (-142 235737 235848 236030 "CDEN" 236376 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 231702 234890 235170 "CCLASS" 235477 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230953 231110 231287 "CATEGORY" 231545 T -10 (NIL) -8 NIL NIL NIL) (-139 230526 230872 230920 "CATCTOR" 230925 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229977 230229 230327 "CATAST" 230448 T CATAST (NIL) -8 NIL NIL NIL) (-137 229453 229698 229790 "CASEAST" 229905 T CASEAST (NIL) -8 NIL NIL NIL) (-136 228561 228709 228930 "CARTEN2" 229300 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 223570 224590 225343 "CARTEN" 227864 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 221886 222720 222977 "CARD" 223333 T CARD (NIL) -8 NIL NIL NIL) (-133 221462 221690 221765 "CAPSLAST" 221831 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220966 221174 221202 "CACHSET" 221334 T CACHSET (NIL) -9 NIL 221412 NIL) (-131 220436 220758 220786 "CABMON" 220836 T CABMON (NIL) -9 NIL 220892 NIL) (-130 219909 220140 220250 "BYTEORD" 220346 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 215259 219414 219586 "BYTEBUF" 219757 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 214241 214793 214935 "BYTE" 215098 T BYTE (NIL) -8 NIL NIL 215220) (-127 211752 213933 214040 "BTREE" 214167 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209203 211400 211522 "BTOURN" 211662 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206575 208673 208714 "BTCAT" 208782 NIL BTCAT (NIL T) -9 NIL 208859 NIL) (-124 206242 206322 206471 "BTCAT-" 206476 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201507 205385 205413 "BTAGG" 205635 T BTAGG (NIL) -9 NIL 205796 NIL) (-122 200997 201122 201328 "BTAGG-" 201333 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197994 200275 200490 "BSTREE" 200814 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197132 197258 197442 "BRILL" 197850 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193785 195858 195899 "BRAGG" 196548 NIL BRAGG (NIL T) -9 NIL 196806 NIL) (-118 192317 192722 193276 "BRAGG-" 193281 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185567 191663 191847 "BPADICRT" 192165 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183884 185504 185549 "BPADIC" 185554 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183582 183612 183726 "BOUNDZRO" 183848 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 181363 181767 182242 "BOP1" 183140 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 176591 177789 178701 "BOP" 180471 T BOP (NIL) -8 NIL NIL NIL) (-112 175416 176165 176314 "BOOLEAN" 176462 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174695 175099 175153 "BMODULE" 175158 NIL BMODULE (NIL T T) -9 NIL 175223 NIL) (-110 170496 174493 174566 "BITS" 174642 T BITS (NIL) -8 NIL NIL NIL) (-109 169917 170036 170176 "BINDING" 170376 T BINDING (NIL) -8 NIL NIL NIL) (-108 163945 169514 169662 "BINARY" 169789 T BINARY (NIL) -8 NIL NIL NIL) (-107 161725 163200 163241 "BGAGG" 163501 NIL BGAGG (NIL T) -9 NIL 163638 NIL) (-106 161556 161588 161679 "BGAGG-" 161684 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160627 160940 161145 "BFUNCT" 161371 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159311 159492 159780 "BEZOUT" 160451 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155782 158163 158493 "BBTREE" 159014 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155516 155569 155597 "BASTYPE" 155716 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155368 155397 155470 "BASTYPE-" 155475 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154802 154878 155030 "BALFACT" 155279 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153658 154217 154403 "AUTOMOR" 154647 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153384 153389 153415 "ATTREG" 153420 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151636 152081 152433 "ATTRBUT" 153050 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151244 151464 151530 "ATTRAST" 151588 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150780 150893 150919 "ATRIG" 151120 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150589 150630 150717 "ATRIG-" 150722 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150234 150420 150446 "ASTCAT" 150451 T ASTCAT (NIL) -9 NIL 150481 NIL) (-92 149961 150020 150139 "ASTCAT-" 150144 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148110 149737 149825 "ASTACK" 149904 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146615 146912 147277 "ASSOCEQ" 147792 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145669 146274 146398 "ASP9" 146522 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 144559 145274 145416 "ASP80" 145558 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 144322 144507 144546 "ASP8" 144551 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 143298 143999 144117 "ASP78" 144235 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 142289 142978 143095 "ASP77" 143212 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 141223 141927 142058 "ASP74" 142189 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 140145 140858 140990 "ASP73" 141122 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 139065 139780 139912 "ASP7" 140044 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 138191 138891 138991 "ASP6" 138996 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137158 137868 137986 "ASP55" 138104 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136129 136832 136951 "ASP50" 137070 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135239 135830 135940 "ASP49" 136050 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 134045 134778 134946 "ASP42" 135128 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 132843 133578 133748 "ASP41" 133932 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131953 132544 132654 "ASP4" 132764 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 130925 131630 131748 "ASP35" 131866 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130690 130873 130912 "ASP34" 130917 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130427 130494 130570 "ASP33" 130645 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129342 130062 130194 "ASP31" 130326 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129107 129290 129329 "ASP30" 129334 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128842 128911 128987 "ASP29" 129062 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128607 128790 128829 "ASP28" 128834 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128372 128555 128594 "ASP27" 128599 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127478 128070 128181 "ASP24" 128292 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126576 127280 127392 "ASP20" 127397 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125540 126250 126369 "ASP19" 126488 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 125277 125344 125420 "ASP12" 125495 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 124151 124876 125020 "ASP10" 125164 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 123261 123852 123962 "ASP1" 124072 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 121112 123105 123196 "ARRAY2" 123201 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 120144 120317 120538 "ARRAY12" 120935 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 115909 119792 119906 "ARRAY1" 120061 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 110221 112139 112214 "ARR2CAT" 114844 NIL ARR2CAT (NIL T T T) -9 NIL 115602 NIL) (-56 107655 108399 109353 "ARR2CAT-" 109358 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106972 107282 107407 "ARITY" 107548 T ARITY (NIL) -8 NIL NIL NIL) (-54 105748 105900 106199 "APPRULE" 106808 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105399 105447 105566 "APPLYORE" 105694 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104677 104800 104957 "ANY1" 105273 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 104031 104270 104390 "ANY" 104575 T ANY (NIL) -8 NIL NIL NIL) (-50 101561 102468 102795 "ANTISYM" 103755 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101053 101268 101364 "ANON" 101483 T ANON (NIL) -8 NIL NIL NIL) (-48 95311 99592 100046 "AN" 100617 T AN (NIL) -8 NIL NIL NIL) (-47 91209 92597 92648 "AMR" 93396 NIL AMR (NIL T T) -9 NIL 93996 NIL) (-46 90321 90542 90905 "AMR-" 90910 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74766 90238 90299 "ALIST" 90304 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71601 74360 74529 "ALGSC" 74684 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68156 68711 69318 "ALGPKG" 71041 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67433 67534 67718 "ALGMFACT" 68042 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63468 64047 64641 "ALGMANIP" 67017 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54849 63094 63244 "ALGFF" 63401 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54045 54176 54355 "ALGFACT" 54707 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52986 53586 53624 "ALGEBRA" 53629 NIL ALGEBRA (NIL T) -9 NIL 53670 NIL) (-37 52704 52763 52895 "ALGEBRA-" 52900 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34803 50706 50758 "ALAGG" 50894 NIL ALAGG (NIL T T) -9 NIL 51055 NIL) (-35 34339 34452 34478 "AHYP" 34679 T AHYP (NIL) -9 NIL NIL NIL) (-34 33270 33518 33544 "AGG" 34043 T AGG (NIL) -9 NIL 34322 NIL) (-33 32704 32866 33080 "AGG-" 33085 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30510 30933 31338 "AF" 32346 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29990 30235 30325 "ADDAST" 30438 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29258 29517 29673 "ACPLOT" 29852 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18637 26385 26423 "ACFS" 27030 NIL ACFS (NIL T) -9 NIL 27269 NIL) (-28 16664 17154 17916 "ACFS-" 17921 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14711 14737 "ACF" 15616 T ACF (NIL) -9 NIL 16029 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index d466d41c..614feeea 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,5 +1,5 @@ -(724461 . 3477435923) +(724846 . 3477490101) (((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1272 *4)) (-4 *4 (-644 (-551))) (-5 *2 (-1272 (-412 (-551)))) (-5 *1 (-1300 *4))))) @@ -38,9 +38,9 @@ (-12 (-5 *2 (-952 *3)) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *5 (-619 (-1183))) (-4 *4 (-798)) (-4 *5 (-855)))) ((*1 *1 *2) - (-3972 + (-3978 (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) - (-12 (-3758 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) + (-12 (-3764 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) @@ -51,12 +51,12 @@ (-4 *3 (-38 (-412 (-551)))) (-4 *5 (-619 (-1183))) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-646 *7)) (|:| -1717 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-646 *7)) (|:| -1718 *8))) (-4 *7 (-1071 *4 *5 *6)) (-4 *8 (-1077 *4 *5 *6 *7)) (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-5 *2 (-1165)) (-5 *1 (-1075 *4 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-646 *7)) (|:| -1717 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-646 *7)) (|:| -1718 *8))) (-4 *7 (-1071 *4 *5 *6)) (-4 *8 (-1115 *4 *5 *6 *7)) (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-5 *2 (-1165)) (-5 *1 (-1151 *4 *5 *6 *7 *8)))) @@ -105,7 +105,7 @@ ((*1 *2 *1) (-12 (-5 *2 (-410 *1)) (-4 *1 (-1227)))) ((*1 *2 *3) (-12 (-4 *4 (-562)) (-5 *2 (-410 *3)) (-5 *1 (-1252 *4 *3)) - (-4 *3 (-13 (-1248 *4) (-562) (-10 -8 (-15 -3576 ($ $ $))))))) + (-4 *3 (-13 (-1248 *4) (-562) (-10 -8 (-15 -3582 ($ $ $))))))) ((*1 *2 *3) (-12 (-5 *3 (-1052 *4 *5)) (-4 *4 (-13 (-853) (-310) (-147) (-1026))) (-14 *5 (-646 (-1183))) @@ -158,26 +158,26 @@ (((*1 *2 *3) (-12 (-5 *3 (-1052 *4 *5)) (-4 *4 (-13 (-853) (-310) (-147) (-1026))) (-14 *5 (-646 (-1183))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *4)) (|:| -3656 (-646 (-952 *4)))))) + (-5 *2 (-646 (-2 (|:| -1925 (-1177 *4)) (|:| -3662 (-646 (-952 *4)))))) (-5 *1 (-1299 *4 *5 *6)) (-14 *6 (-646 (-1183))))) ((*1 *2 *3 *4 *4 *4) (-12 (-5 *4 (-112)) (-4 *5 (-13 (-853) (-310) (-147) (-1026))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3656 (-646 (-952 *5)))))) + (-5 *2 (-646 (-2 (|:| -1925 (-1177 *5)) (|:| -3662 (-646 (-952 *5)))))) (-5 *1 (-1299 *5 *6 *7)) (-5 *3 (-646 (-952 *5))) (-14 *6 (-646 (-1183))) (-14 *7 (-646 (-1183))))) ((*1 *2 *3 *4 *4) (-12 (-5 *4 (-112)) (-4 *5 (-13 (-853) (-310) (-147) (-1026))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3656 (-646 (-952 *5)))))) + (-5 *2 (-646 (-2 (|:| -1925 (-1177 *5)) (|:| -3662 (-646 (-952 *5)))))) (-5 *1 (-1299 *5 *6 *7)) (-5 *3 (-646 (-952 *5))) (-14 *6 (-646 (-1183))) (-14 *7 (-646 (-1183))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-112)) (-4 *5 (-13 (-853) (-310) (-147) (-1026))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3656 (-646 (-952 *5)))))) + (-5 *2 (-646 (-2 (|:| -1925 (-1177 *5)) (|:| -3662 (-646 (-952 *5)))))) (-5 *1 (-1299 *5 *6 *7)) (-5 *3 (-646 (-952 *5))) (-14 *6 (-646 (-1183))) (-14 *7 (-646 (-1183))))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-853) (-310) (-147) (-1026))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *4)) (|:| -3656 (-646 (-952 *4)))))) + (-5 *2 (-646 (-2 (|:| -1925 (-1177 *4)) (|:| -3662 (-646 (-952 *4)))))) (-5 *1 (-1299 *4 *5 *6)) (-5 *3 (-646 (-952 *4))) (-14 *5 (-646 (-1183))) (-14 *6 (-646 (-1183)))))) (((*1 *2 *3 *4 *4) @@ -252,10 +252,10 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-390 *2)) (-4 *2 (-1107)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-390 *2)) (-4 *2 (-1107)))) ((*1 *1 *2 *1) - (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *6 (-239 (-4401 *3) (-776))) + (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *6 (-239 (-4407 *3) (-776))) (-14 *7 - (-1 (-112) (-2 (|:| -2575 *5) (|:| -2576 *6)) - (-2 (|:| -2575 *5) (|:| -2576 *6)))) + (-1 (-112) (-2 (|:| -2581 *5) (|:| -2582 *6)) + (-2 (|:| -2581 *5) (|:| -2582 *6)))) (-5 *1 (-466 *3 *4 *5 *6 *7 *2)) (-4 *5 (-855)) (-4 *2 (-956 *4 *6 (-869 *3))))) ((*1 *1 *1 *2) (-12 (-4 *1 (-475 *2 *3)) (-4 *2 (-173)) (-4 *3 (-23)))) @@ -323,10 +323,10 @@ (-14 *3 (-646 (-1183))))) ((*1 *1 *1) (-12 (-4 *1 (-388 *2 *3)) (-4 *2 (-1055)) (-4 *3 (-1107)))) ((*1 *1 *1) - (-12 (-14 *2 (-646 (-1183))) (-4 *3 (-173)) (-4 *5 (-239 (-4401 *2) (-776))) + (-12 (-14 *2 (-646 (-1183))) (-4 *3 (-173)) (-4 *5 (-239 (-4407 *2) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2575 *4) (|:| -2576 *5)) - (-2 (|:| -2575 *4) (|:| -2576 *5)))) + (-1 (-112) (-2 (|:| -2581 *4) (|:| -2582 *5)) + (-2 (|:| -2581 *4) (|:| -2582 *5)))) (-5 *1 (-466 *2 *3 *4 *5 *6 *7)) (-4 *4 (-855)) (-4 *7 (-956 *3 *5 (-869 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-514 *2 *3)) (-4 *2 (-1107)) (-4 *3 (-855)))) @@ -433,8 +433,8 @@ (-5 *2 (-588 *6)) (-5 *1 (-589 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -2327 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-367)) - (-4 *6 (-367)) (-5 *2 (-2 (|:| -2327 *6) (|:| |coeff| *6))) + (-5 *4 (-3 (-2 (|:| -2328 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-367)) + (-4 *6 (-367)) (-5 *2 (-2 (|:| -2328 *6) (|:| |coeff| *6))) (-5 *1 (-589 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) (-4 *5 (-367)) @@ -544,7 +544,7 @@ (-4 *6 (-798)) (-4 *2 (-13 (-1107) - (-10 -8 (-15 -4283 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-776)))))) + (-10 -8 (-15 -4289 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-776)))))) (-5 *1 (-958 *6 *7 *8 *5 *2)) (-4 *5 (-956 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-964 *5)) (-4 *5 (-1222)) (-4 *6 (-1222)) @@ -557,7 +557,7 @@ (-4 *5 (-798)) (-4 *6 (-13 (-855) - (-10 -8 (-15 -4414 ((-1183) $)) (-15 -4275 ((-3 $ "failed") (-1183)))))) + (-10 -8 (-15 -4420 ((-1183) $)) (-15 -4281 ((-3 $ "failed") (-1183)))))) (-5 *1 (-990 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-562)) (-4 *6 (-562)) (-4 *2 (-997 *6)) @@ -641,7 +641,7 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1055)) (-5 *1 (-1296 *3 *4)) (-4 *4 (-851))))) -(((*1 *2 *1) (-12 (|has| *1 (-6 -4437)) (-4 *1 (-34)) (-5 *2 (-776)))) +(((*1 *2 *1) (-12 (|has| *1 (-6 -4443)) (-4 *1 (-34)) (-5 *2 (-776)))) ((*1 *2 *1) (-12 (-5 *2 (-776)) (-5 *1 (-251)))) ((*1 *2 *1) (-12 (-4 *1 (-1110 *3 *4 *5 *6 *7)) (-4 *3 (-1107)) (-4 *4 (-1107)) @@ -684,7 +684,7 @@ (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1055)) (-4 *3 (-797)) (-4 *2 (-367)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-551)) (-5 *1 (-226)))) ((*1 *1 *1 *1) - (-3972 (-12 (-5 *1 (-296 *2)) (-4 *2 (-367)) (-4 *2 (-1222))) + (-3978 (-12 (-5 *1 (-296 *2)) (-4 *2 (-367)) (-4 *2 (-1222))) (-12 (-5 *1 (-296 *2)) (-4 *2 (-478)) (-4 *2 (-1222))))) ((*1 *1 *1 *1) (-4 *1 (-367))) ((*1 *1 *1 *2) (-12 (-5 *2 (-551)) (-5 *1 (-382)))) @@ -782,61 +782,61 @@ ((*1 *1 *2) (-12 (-5 *2 (-1131 (-551) (-616 (-48)))) (-5 *1 (-48)))) ((*1 *2 *3) (-12 (-5 *2 (-51)) (-5 *1 (-52 *3)) (-4 *3 (-1222)))) ((*1 *1 *2) - (-12 (-5 *2 (-343 (-3965 'X) (-3965) (-704))) (-5 *1 (-61 *3)) + (-12 (-5 *2 (-343 (-3971 'X) (-3971) (-704))) (-5 *1 (-61 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3965 'JINT 'X 'ELAM) (-3965) (-704)))) + (-12 (-5 *2 (-1272 (-343 (-3971 'JINT 'X 'ELAM) (-3971) (-704)))) (-5 *1 (-62 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3965) (-3965 'XC) (-704)))) (-5 *1 (-64 *3)) + (-12 (-5 *2 (-1272 (-343 (-3971) (-3971 'XC) (-704)))) (-5 *1 (-64 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-343 (-3965) (-3965 'XC) (-704))) (-5 *1 (-66 *3)) + (-12 (-5 *2 (-343 (-3971) (-3971 'XC) (-704))) (-5 *1 (-66 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3965 'X) (-3965 '-4408) (-704)))) (-5 *1 (-71 *3)) + (-12 (-5 *2 (-1272 (-343 (-3971 'X) (-3971 '-4414) (-704)))) (-5 *1 (-71 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3965) (-3965 'X) (-704)))) (-5 *1 (-74 *3)) + (-12 (-5 *2 (-1272 (-343 (-3971) (-3971 'X) (-704)))) (-5 *1 (-74 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-343 (-3965) (-3965 'X) (-704))) (-5 *1 (-75 *3)) + (-12 (-5 *2 (-343 (-3971) (-3971 'X) (-704))) (-5 *1 (-75 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3965 'X 'EPS) (-3965 '-4408) (-704)))) + (-12 (-5 *2 (-1272 (-343 (-3971 'X 'EPS) (-3971 '-4414) (-704)))) (-5 *1 (-76 *3 *4 *5)) (-14 *3 (-1183)) (-14 *4 (-1183)) (-14 *5 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3965 'EPS) (-3965 'YA 'YB) (-704)))) + (-12 (-5 *2 (-1272 (-343 (-3971 'EPS) (-3971 'YA 'YB) (-704)))) (-5 *1 (-77 *3 *4 *5)) (-14 *3 (-1183)) (-14 *4 (-1183)) (-14 *5 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-343 (-3965) (-3965 'X) (-704))) (-5 *1 (-78 *3)) + (-12 (-5 *2 (-343 (-3971) (-3971 'X) (-704))) (-5 *1 (-78 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3965) (-3965 'XC) (-704)))) (-5 *1 (-79 *3)) + (-12 (-5 *2 (-1272 (-343 (-3971) (-3971 'XC) (-704)))) (-5 *1 (-79 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3965) (-3965 'X) (-704)))) (-5 *1 (-80 *3)) + (-12 (-5 *2 (-1272 (-343 (-3971) (-3971 'X) (-704)))) (-5 *1 (-80 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3965 'X) (-3965 '-4408) (-704)))) (-5 *1 (-82 *3)) + (-12 (-5 *2 (-1272 (-343 (-3971 'X) (-3971 '-4414) (-704)))) (-5 *1 (-82 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3965 'X '-4408) (-3965) (-704)))) (-5 *1 (-83 *3)) + (-12 (-5 *2 (-1272 (-343 (-3971 'X '-4414) (-3971) (-704)))) (-5 *1 (-83 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-694 (-343 (-3965 'X '-4408) (-3965) (-704)))) (-5 *1 (-84 *3)) + (-12 (-5 *2 (-694 (-343 (-3971 'X '-4414) (-3971) (-704)))) (-5 *1 (-84 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-694 (-343 (-3965 'X) (-3965) (-704)))) (-5 *1 (-85 *3)) + (-12 (-5 *2 (-694 (-343 (-3971 'X) (-3971) (-704)))) (-5 *1 (-85 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3965 'X) (-3965) (-704)))) (-5 *1 (-86 *3)) + (-12 (-5 *2 (-1272 (-343 (-3971 'X) (-3971) (-704)))) (-5 *1 (-86 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-694 (-343 (-3965 'XL 'XR 'ELAM) (-3965) (-704)))) + (-12 (-5 *2 (-694 (-343 (-3971 'XL 'XR 'ELAM) (-3971) (-704)))) (-5 *1 (-88 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-343 (-3965 'X) (-3965 '-4408) (-704))) (-5 *1 (-89 *3)) + (-12 (-5 *2 (-343 (-3971 'X) (-3971 '-4414) (-704))) (-5 *1 (-89 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) (-12 (-5 *2 (-646 (-135 *3 *4 *5))) (-5 *1 (-135 *3 *4 *5)) (-14 *3 (-551)) @@ -884,82 +884,82 @@ (-5 *2 (-1288 *3 *4)))) ((*1 *1 *2) (-12 (-4 *1 (-378 *2 *3)) (-4 *2 (-855)) (-4 *3 (-173)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |localSymbols| (-1187)) (|:| -1787 (-646 (-333))))) + (-12 (-5 *2 (-2 (|:| |localSymbols| (-1187)) (|:| -1788 (-646 (-333))))) (-4 *1 (-387)))) ((*1 *1 *2) (-12 (-5 *2 (-333)) (-4 *1 (-387)))) ((*1 *1 *2) (-12 (-5 *2 (-646 (-333))) (-4 *1 (-387)))) ((*1 *1 *2) (-12 (-5 *2 (-694 (-704))) (-4 *1 (-387)))) ((*1 *1 *2) - 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(-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4360 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-412 (-952 (-412 *3)))) (-4 *3 (-562)) (-4 *3 (-1107)) @@ -984,13 +984,13 @@ ((*1 *1 *2) (-12 (-5 *2 (-1165)) (-5 *1 (-439)))) ((*1 *1 *2) (-12 (-5 *2 (-439)) (-5 *1 (-441)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |localSymbols| (-1187)) (|:| -1787 (-646 (-333))))) + (-12 (-5 *2 (-2 (|:| |localSymbols| (-1187)) (|:| -1788 (-646 (-333))))) (-4 *1 (-445)))) ((*1 *1 *2) (-12 (-5 *2 (-333)) (-4 *1 (-445)))) ((*1 *1 *2) (-12 (-5 *2 (-646 (-333))) (-4 *1 (-445)))) ((*1 *1 *2) (-12 (-5 *2 (-1272 (-704))) (-4 *1 (-445)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |localSymbols| (-1187)) (|:| -1787 (-646 (-333))))) + (-12 (-5 *2 (-2 (|:| |localSymbols| (-1187)) (|:| -1788 (-646 (-333))))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-333)) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-646 (-333))) (-4 *1 (-446)))) @@ -1054,7 +1054,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-646 (-2 (|:| -4398 *3) (|:| -4382 *4)))) (-4 *3 (-1055)) + (-12 (-5 *2 (-646 (-2 (|:| -4404 *3) (|:| -4388 *4)))) (-4 *3 (-1055)) (-4 *4 (-731)) (-5 *1 (-740 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-551)) (-4 *1 (-768)))) ((*1 *1 *2) @@ -1063,23 +1063,23 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (|:| |mdnia| - (-2 (|:| |fn| (-317 (-226))) (|:| -1612 (-646 (-1095 (-847 (-226))))) + (-2 (|:| |fn| (-317 (-226))) (|:| -1613 (-646 (-1095 (-847 (-226))))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))))) (-5 *1 (-774)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-317 (-226))) (|:| -1612 (-646 (-1095 (-847 (-226))))) + (-2 (|:| |fn| (-317 (-226))) (|:| -1613 (-646 (-1095 (-847 (-226))))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *1 (-774)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *1 (-774)))) ((*1 *2 *3) (-12 (-5 *2 (-778)) (-5 *1 (-779 *3)) (-4 *3 (-1222)))) @@ -1097,19 +1097,19 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3887 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (|:| |lsa| - (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))))) + (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3887 (-646 (-226))))))) (-5 *1 (-846)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))) + (-12 (-5 *2 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3887 (-646 (-226))))) (-5 *1 (-846)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3887 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (-5 *1 (-846)))) @@ -1255,7 +1255,7 @@ ((*1 *1 *1) (-4 *1 (-287))) ((*1 *2 *3) (-12 (-5 *3 (-410 *4)) (-4 *4 (-562)) - (-5 *2 (-646 (-2 (|:| -4398 (-776)) (|:| |logand| *4)))) (-5 *1 (-323 *4)))) + (-5 *2 (-646 (-2 (|:| -4404 (-776)) (|:| |logand| *4)))) (-5 *1 (-323 *4)))) ((*1 *1 *1) (-12 (-5 *1 (-343 *2 *3 *4)) (-14 *2 (-646 (-1183))) (-14 *3 (-646 (-1183))) (-4 *4 (-392)))) @@ -1399,50 +1399,50 @@ (((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-1283))))) (((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-1283))))) (((*1 *2 *3) - (-12 (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) + (-12 (-4 *3 (-13 (-310) (-10 -8 (-15 -4419 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *2 - (-2 (|:| -2199 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) + (-2 (|:| -2200 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) (-5 *1 (-355 *3 *4 *5)) (-4 *5 (-415 *3 *4)))) ((*1 *2 *3) (-12 (-5 *3 (-551)) (-4 *4 (-1248 *3)) (-5 *2 - (-2 (|:| -2199 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) + (-2 (|:| -2200 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) (-5 *1 (-773 *4 *5)) (-4 *5 (-415 *3 *4)))) ((*1 *2 *3) (-12 (-4 *4 (-354)) (-4 *3 (-1248 *4)) (-4 *5 (-1248 *3)) (-5 *2 - (-2 (|:| -2199 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) + (-2 (|:| -2200 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) (-5 *1 (-991 *4 *3 *5 *6)) (-4 *6 (-729 *3 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-354)) (-4 *3 (-1248 *4)) (-4 *5 (-1248 *3)) (-5 *2 - (-2 (|:| -2199 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) + (-2 (|:| -2200 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) (-5 *1 (-1282 *4 *3 *5 *6)) (-4 *6 (-415 *3 *5))))) (((*1 *2) (-12 (-4 *3 (-1227)) (-4 *4 (-1248 *3)) (-4 *5 (-1248 (-412 *4))) (-5 *2 (-1272 *1)) (-4 *1 (-346 *3 *4 *5)))) ((*1 *2) - (-12 (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) + (-12 (-4 *3 (-13 (-310) (-10 -8 (-15 -4419 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *2 - (-2 (|:| -2199 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) + (-2 (|:| -2200 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) (-5 *1 (-355 *3 *4 *5)) (-4 *5 (-415 *3 *4)))) ((*1 *2) (-12 (-4 *3 (-1248 (-551))) (-5 *2 - (-2 (|:| -2199 (-694 (-551))) (|:| |basisDen| (-551)) + (-2 (|:| -2200 (-694 (-551))) (|:| |basisDen| (-551)) (|:| |basisInv| (-694 (-551))))) (-5 *1 (-773 *3 *4)) (-4 *4 (-415 (-551) *3)))) ((*1 *2) (-12 (-4 *3 (-354)) (-4 *4 (-1248 *3)) (-4 *5 (-1248 *4)) (-5 *2 - (-2 (|:| -2199 (-694 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-694 *4)))) + (-2 (|:| -2200 (-694 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-694 *4)))) (-5 *1 (-991 *3 *4 *5 *6)) (-4 *6 (-729 *4 *5)))) ((*1 *2) (-12 (-4 *3 (-354)) (-4 *4 (-1248 *3)) (-4 *5 (-1248 *4)) (-5 *2 - (-2 (|:| -2199 (-694 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-694 *4)))) + (-2 (|:| -2200 (-694 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-694 *4)))) (-5 *1 (-1282 *3 *4 *5 *6)) (-4 *6 (-415 *4 *5))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-776)) (-4 *6 (-367)) (-5 *4 (-1215 *6)) @@ -1547,14 +1547,14 @@ (((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4291 (-226)) + (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4297 (-226)) (|:| |scaleX| (-226)) (|:| |scaleY| (-226)) (|:| |scaleZ| (-226)) (|:| |deltaX| (-226)) (|:| |deltaY| (-226)))) (-5 *1 (-263)))) ((*1 *2 *3 *2) (-12 (-5 *2 - (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4291 (-226)) + (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4297 (-226)) (|:| |scaleX| (-226)) (|:| |scaleY| (-226)) (|:| |scaleZ| (-226)) (|:| |deltaX| (-226)) (|:| |deltaY| (-226)))) (-5 *3 (-646 (-263))) (-5 *1 (-264)))) @@ -1565,14 +1565,14 @@ ((*1 *2 *1 *3) (-12 (-5 *3 - (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4291 (-226)) + (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4297 (-226)) (|:| |scaleX| (-226)) (|:| |scaleY| (-226)) (|:| |scaleZ| (-226)) (|:| |deltaX| (-226)) (|:| |deltaY| (-226)))) (-5 *2 (-1278)) (-5 *1 (-1276)))) ((*1 *2 *1) (-12 (-5 *2 - (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4291 (-226)) + (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4297 (-226)) (|:| |scaleX| (-226)) (|:| |scaleY| (-226)) (|:| |scaleZ| (-226)) (|:| |deltaX| (-226)) (|:| |deltaY| (-226)))) (-5 *1 (-1276)))) @@ -1636,9 +1636,9 @@ (-5 *2 (-1272 (-2 (|:| |scaleX| (-226)) (|:| |scaleY| (-226)) (|:| |deltaX| (-226)) - (|:| |deltaY| (-226)) (|:| -4294 (-551)) (|:| -4292 (-551)) - (|:| |spline| (-551)) (|:| -4323 (-551)) (|:| |axesColor| (-879)) - (|:| -4295 (-551)) (|:| |unitsColor| (-879)) (|:| |showing| (-551))))) + (|:| |deltaY| (-226)) (|:| -4300 (-551)) (|:| -4298 (-551)) + (|:| |spline| (-551)) (|:| -4329 (-551)) (|:| |axesColor| (-879)) + (|:| -4301 (-551)) (|:| |unitsColor| (-879)) (|:| |showing| (-551))))) (-5 *1 (-1275))))) (((*1 *2 *3) (-12 (-5 *2 (-1185 (-412 (-551)))) (-5 *1 (-191)) (-5 *3 (-551)))) ((*1 *2 *1) (-12 (-5 *2 (-1272 (-3 (-473) "undefined"))) (-5 *1 (-1275))))) @@ -1687,16 +1687,16 @@ (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1222)) (-4 *2 (-1222)) (-5 *1 (-59 *5 *2)))) ((*1 *2 *3 *1 *2 *2) - (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1107)) (|has| *1 (-6 -4437)) + (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1107)) (|has| *1 (-6 -4443)) (-4 *1 (-151 *2)) (-4 *2 (-1222)))) ((*1 *2 *3 *1 *2) - (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -4437)) (-4 *1 (-151 *2)) + (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -4443)) (-4 *1 (-151 *2)) (-4 *2 (-1222)))) ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -4437)) (-4 *1 (-151 *2)) + (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -4443)) (-4 *1 (-151 *2)) (-4 *2 (-1222)))) ((*1 *2 *3) - (-12 (-4 *4 (-1055)) (-5 *2 (-2 (|:| -2191 (-1177 *4)) (|:| |deg| (-925)))) + (-12 (-4 *4 (-1055)) (-5 *2 (-2 (|:| -2192 (-1177 *4)) (|:| |deg| (-925)))) (-5 *1 (-222 *4 *5)) (-5 *3 (-1177 *4)) (-4 *5 (-562)))) ((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-776)) @@ -1790,8 +1790,8 @@ (-12 (-5 *1 (-215 *2)) (-4 *2 (-13 (-855) - (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 ((-1278) $)) - (-15 -2152 ((-1278) $))))))) + (-10 -8 (-15 -4249 ((-1165) $ (-1183))) (-15 -4067 ((-1278) $)) + (-15 -2153 ((-1278) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-296 *2)) (-4 *2 (-25)) (-4 *2 (-1222)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-296 *2)) (-4 *2 (-25)) (-4 *2 (-1222)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-326 *2 *3)) (-4 *2 (-1107)) (-4 *3 (-131)))) @@ -1821,8 +1821,8 @@ (-12 (-5 *1 (-215 *2)) (-4 *2 (-13 (-855) - (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 ((-1278) $)) - (-15 -2152 ((-1278) $))))))) + (-10 -8 (-15 -4249 ((-1165) $ (-1183))) (-15 -4067 ((-1278) $)) + (-15 -2153 ((-1278) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-296 *2)) (-4 *2 (-21)) (-4 *2 (-1222)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-296 *2)) (-4 *2 (-21)) (-4 *2 (-1222)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-475 *2 *3)) (-4 *2 (-173)) (-4 *3 (-23)))) @@ -2177,13 +2177,13 @@ (-12 (-5 *2 (-1269 *4)) (-14 *4 (-1183)) (-5 *1 (-1232 *3 *4 *5)) (-4 *3 (-38 (-412 (-551)))) (-4 *3 (-1055)) (-14 *5 *3))) ((*1 *1 *1 *2) - (-3972 + (-3978 (-12 (-5 *2 (-1183)) (-4 *1 (-1234 *3)) (-4 *3 (-1055)) (-12 (-4 *3 (-29 (-551))) (-4 *3 (-966)) (-4 *3 (-1208)) (-4 *3 (-38 (-412 (-551)))))) (-12 (-5 *2 (-1183)) (-4 *1 (-1234 *3)) (-4 *3 (-1055)) - (-12 (|has| *3 (-15 -3497 ((-646 *2) *3))) - (|has| *3 (-15 -4256 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) + (-12 (|has| *3 (-15 -3503 ((-646 *2) *3))) + (|has| *3 (-15 -4262 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) ((*1 *1 *1) (-12 (-4 *1 (-1234 *2)) (-4 *2 (-1055)) (-4 *2 (-38 (-412 (-551)))))) ((*1 *1 *1) @@ -2192,26 +2192,26 @@ (-12 (-5 *2 (-1269 *4)) (-14 *4 (-1183)) (-5 *1 (-1253 *3 *4 *5)) (-4 *3 (-38 (-412 (-551)))) (-4 *3 (-1055)) (-14 *5 *3))) ((*1 *1 *1 *2) - (-3972 + (-3978 (-12 (-5 *2 (-1183)) (-4 *1 (-1255 *3)) (-4 *3 (-1055)) (-12 (-4 *3 (-29 (-551))) (-4 *3 (-966)) (-4 *3 (-1208)) (-4 *3 (-38 (-412 (-551)))))) (-12 (-5 *2 (-1183)) (-4 *1 (-1255 *3)) (-4 *3 (-1055)) - (-12 (|has| *3 (-15 -3497 ((-646 *2) *3))) - (|has| *3 (-15 -4256 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) + (-12 (|has| *3 (-15 -3503 ((-646 *2) *3))) + (|has| *3 (-15 -4262 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) ((*1 *1 *1) (-12 (-4 *1 (-1255 *2)) (-4 *2 (-1055)) (-4 *2 (-38 (-412 (-551)))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1269 *4)) (-14 *4 (-1183)) (-5 *1 (-1262 *3 *4 *5)) (-4 *3 (-38 (-412 (-551)))) (-4 *3 (-1055)) (-14 *5 *3))) ((*1 *1 *1 *2) - (-3972 + (-3978 (-12 (-5 *2 (-1183)) (-4 *1 (-1265 *3)) (-4 *3 (-1055)) (-12 (-4 *3 (-29 (-551))) (-4 *3 (-966)) (-4 *3 (-1208)) (-4 *3 (-38 (-412 (-551)))))) (-12 (-5 *2 (-1183)) (-4 *1 (-1265 *3)) (-4 *3 (-1055)) - (-12 (|has| *3 (-15 -3497 ((-646 *2) *3))) - (|has| *3 (-15 -4256 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) + (-12 (|has| *3 (-15 -3503 ((-646 *2) *3))) + (|has| *3 (-15 -4262 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) ((*1 *1 *1) (-12 (-4 *1 (-1265 *2)) (-4 *2 (-1055)) (-4 *2 (-38 (-412 (-551))))))) (((*1 *2 *1 *3) @@ -2349,14 +2349,14 @@ (-12 (-5 *3 (-1183)) (-5 *2 (-246 (-1165))) (-5 *1 (-215 *4)) (-4 *4 (-13 (-855) - (-10 -8 (-15 -4243 ((-1165) $ *3)) (-15 -4061 ((-1278) $)) - (-15 -2152 ((-1278) $))))))) + (-10 -8 (-15 -4249 ((-1165) $ *3)) (-15 -4067 ((-1278) $)) + (-15 -2153 ((-1278) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-995)) (-5 *1 (-215 *3)) (-4 *3 (-13 (-855) - (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 ((-1278) $)) - (-15 -2152 ((-1278) $))))))) + (-10 -8 (-15 -4249 ((-1165) $ (-1183))) (-15 -4067 ((-1278) $)) + (-15 -2153 ((-1278) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-776)) (-5 *1 (-246 *4)) (-4 *4 (-855)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-246 *3)) (-4 *3 (-855)))) @@ -2451,50 +2451,50 @@ (((*1 *1 *1) (-12 (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) (((*1 *2 *1) (-12 (-4 *1 (-1261 *3)) (-4 *3 (-1222)) (-5 *2 (-776))))) (((*1 *1 *1) (-12 (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-245 *2)) (-4 *2 (-1222)))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-245 *2)) (-4 *2 (-1222)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-285 *2)) (-4 *2 (-1222)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-285 *2)) (-4 *2 (-1222)))) - ((*1 *1 *1 *2) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222)))) - ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) -(((*1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) -(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) + ((*1 *1 *1 *2) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-1261 *2)) (-4 *2 (-1222)))) + ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) +(((*1 *1 *1) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) +(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-551)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1222)) (-4 *4 (-376 *2)) (-4 *5 (-376 *2)))) ((*1 *1 *1 *2 *1) - (-12 (-5 *2 "right") (|has| *1 (-6 -4438)) (-4 *1 (-119 *3)) + (-12 (-5 *2 "right") (|has| *1 (-6 -4444)) (-4 *1 (-119 *3)) (-4 *3 (-1222)))) ((*1 *1 *1 *2 *1) - (-12 (-5 *2 "left") (|has| *1 (-6 -4438)) (-4 *1 (-119 *3)) (-4 *3 (-1222)))) + (-12 (-5 *2 "left") (|has| *1 (-6 -4444)) (-4 *1 (-119 *3)) (-4 *3 (-1222)))) ((*1 *2 *1 *3 *2) - (-12 (|has| *1 (-6 -4438)) (-4 *1 (-291 *3 *2)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4444)) (-4 *1 (-291 *3 *2)) (-4 *3 (-1107)) (-4 *2 (-1222)))) ((*1 *2 *1 *3 *2) (-12 (-5 *2 (-51)) (-5 *3 (-1183)) (-5 *1 (-637)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 (-1239 (-551))) (|has| *1 (-6 -4438)) (-4 *1 (-656 *2)) + (-12 (-5 *3 (-1239 (-551))) (|has| *1 (-6 -4444)) (-4 *1 (-656 *2)) (-4 *2 (-1222)))) ((*1 *1 *1 *2 *2 *1) (-12 (-5 *2 (-646 (-551))) (-4 *1 (-691 *3 *4 *5)) (-4 *3 (-1055)) (-4 *4 (-376 *3)) (-4 *5 (-376 *3)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 "value") (|has| *1 (-6 -4438)) (-4 *1 (-1016 *2)) + (-12 (-5 *3 "value") (|has| *1 (-6 -4444)) (-4 *1 (-1016 *2)) (-4 *2 (-1222)))) ((*1 *2 *1 *2) (-12 (-5 *1 (-1032 *2)) (-4 *2 (-1222)))) ((*1 *2 *1 *3 *2) (-12 (-4 *1 (-1199 *3 *2)) (-4 *3 (-1107)) (-4 *2 (-1107)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 "last") (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) + (-12 (-5 *3 "last") (|has| *1 (-6 -4444)) (-4 *1 (-1261 *2)) (-4 *2 (-1222)))) ((*1 *1 *1 *2 *1) - (-12 (-5 *2 "rest") (|has| *1 (-6 -4438)) (-4 *1 (-1261 *3)) + (-12 (-5 *2 "rest") (|has| *1 (-6 -4444)) (-4 *1 (-1261 *3)) (-4 *3 (-1222)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 "first") (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) + (-12 (-5 *3 "first") (|has| *1 (-6 -4444)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) (((*1 *1 *1 *2 *1) (-12 (-5 *2 (-551)) (-5 *1 (-1160 *3)) (-4 *3 (-1222)))) - ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) -(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) + ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) +(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) (((*1 *1 *1 *2) - (-12 (-5 *2 (-551)) (|has| *1 (-6 -4438)) (-4 *1 (-1261 *3)) + (-12 (-5 *2 (-551)) (|has| *1 (-6 -4444)) (-4 *1 (-1261 *3)) (-4 *3 (-1222))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-13 (-1044 (-551)) (-644 (-551)) (-457))) @@ -2592,24 +2592,24 @@ (-5 *2 (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (-551)))) - (-4 *4 (-13 (-1248 *3) (-562) (-10 -8 (-15 -3576 ($ $ $))))) (-4 *3 (-562)) + (-4 *4 (-13 (-1248 *3) (-562) (-10 -8 (-15 -3582 ($ $ $))))) (-4 *3 (-562)) (-5 *1 (-1252 *3 *4))))) (((*1 *1 *1) (-12 (-4 *1 (-956 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) (-4 *4 (-855)) (-4 *2 (-457)))) ((*1 *2 *3 *1) (-12 (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *3 (-1071 *4 *5 *6)) - (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *1)))) + (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *1)))) (-4 *1 (-1077 *4 *5 *6 *3)))) ((*1 *1 *1) (-4 *1 (-1227))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-1252 *3 *2)) - (-4 *2 (-13 (-1248 *3) (-562) (-10 -8 (-15 -3576 ($ $ $)))))))) + (-4 *2 (-13 (-1248 *3) (-562) (-10 -8 (-15 -3582 ($ $ $)))))))) (((*1 *2 *1) (-12 (-4 *1 (-326 *3 *4)) (-4 *3 (-1107)) (-4 *4 (-131)) - (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4387 *4)))))) + (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4393 *4)))))) ((*1 *2 *1) - (-12 (-5 *2 (-646 (-2 (|:| -4398 *3) (|:| -4382 *4)))) (-5 *1 (-740 *3 *4)) + (-12 (-5 *2 (-646 (-2 (|:| -4404 *3) (|:| -4388 *4)))) (-5 *1 (-740 *3 *4)) (-4 *3 (-1055)) (-4 *4 (-731)))) ((*1 *2 *1) (-12 (-4 *1 (-1251 *3 *4)) (-4 *3 (-1055)) (-4 *4 (-797)) @@ -2678,7 +2678,7 @@ (-12 (-4 *1 (-1074 *2 *3)) (-4 *2 (-13 (-853) (-367))) (-4 *3 (-1248 *2)))) ((*1 *2 *1 *3) (-12 (-4 *1 (-1251 *2 *3)) (-4 *3 (-797)) (|has| *2 (-15 ** (*2 *2 *3))) - (|has| *2 (-15 -4390 (*2 (-1183)))) (-4 *2 (-1055))))) + (|has| *2 (-15 -4396 (*2 (-1183)))) (-4 *2 (-1055))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-551)) (-5 *1 (-175 *3)) (-4 *3 (-310)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-551)) (-4 *1 (-679 *3)) (-4 *3 (-1222)))) ((*1 *1 *1 *2) @@ -2795,13 +2795,13 @@ (|partial| -12 (-5 *2 (-776)) (-4 *1 (-1248 *3)) (-4 *3 (-1055))))) (((*1 *2 *1 *1 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-855)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-956 *4 *5 *3)))) + (-5 *2 (-2 (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-956 *4 *5 *3)))) ((*1 *2 *1 *1) - (-12 (-4 *3 (-1055)) (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) + (-12 (-4 *3 (-1055)) (-5 *2 (-2 (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-1248 *3))))) (((*1 *2 *1 *3) (-12 (-5 *3 (-776)) (-4 *4 (-1055)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-1248 *4))))) + (-5 *2 (-2 (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-1248 *4))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-776)) (-4 *1 (-1248 *3)) (-4 *3 (-1055))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-776)) (-4 *1 (-1248 *3)) (-4 *3 (-1055))))) (((*1 *1 *1 *1) (-12 (-4 *1 (-1248 *2)) (-4 *2 (-1055))))) @@ -2842,18 +2842,18 @@ (|partial| -12 (-4 *1 (-1248 *2)) (-4 *2 (-1055)) (-4 *2 (-562))))) (((*1 *1 *1 *1) (-12 (-4 *1 (-1248 *2)) (-4 *2 (-1055)) (-4 *2 (-562))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -4398 *4) (|:| -2161 *3) (|:| -3315 *3))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -4404 *4) (|:| -2162 *3) (|:| -3321 *3))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-1071 *3 *4 *5)))) + (-5 *2 (-2 (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-1071 *3 *4 *5)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| -4398 *3) (|:| -2161 *1) (|:| -3315 *1))) + (-5 *2 (-2 (|:| -4404 *3) (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-1248 *3))))) (((*1 *2 *3) (-12 (-4 *4 (-367)) (-4 *4 (-562)) (-4 *5 (-1248 *4)) - (-5 *2 (-2 (|:| -1948 (-628 *4 *5)) (|:| -1947 (-412 *5)))) + (-5 *2 (-2 (|:| -1949 (-628 *4 *5)) (|:| -1948 (-412 *5)))) (-5 *1 (-628 *4 *5)) (-5 *3 (-412 *5)))) ((*1 *2 *1) (-12 (-5 *2 (-646 (-1171 *3 *4))) (-5 *1 (-1171 *3 *4)) (-14 *3 (-925)) @@ -2867,14 +2867,14 @@ (((*1 *2 *2 *2) (-12 (-4 *3 (-1055)) (-5 *1 (-1246 *3 *2)) (-4 *2 (-1248 *3))))) (((*1 *2 *2 *2) (-12 (-4 *3 (-1055)) (-5 *1 (-1246 *3 *2)) (-4 *2 (-1248 *3))))) (((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) + (|partial| -12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -2162 *3) (|:| -3321 *3))) (-5 *1 (-1245 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-562) (-147))) (-5 *2 (-646 *3)) (-5 *1 (-1244 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3) (|partial| -12 (-4 *4 (-13 (-562) (-147))) - (-5 *2 (-2 (|:| -3554 *3) (|:| -3553 *3))) (-5 *1 (-1244 *4 *3)) + (-5 *2 (-2 (|:| -3560 *3) (|:| -3559 *3))) (-5 *1 (-1244 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *2 *2) (|partial| -12 (-4 *3 (-13 (-562) (-147))) (-5 *1 (-1244 *3 *2)) @@ -2898,7 +2898,7 @@ (-5 *2 (-2 (|:| |num| (-694 *4)) (|:| |den| *4))) (-5 *1 (-698 *4 *5)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *6 (-1248 *5)) - (-5 *2 (-2 (|:| -3699 *7) (|:| |rh| (-646 (-412 *6))))) + (-5 *2 (-2 (|:| -3705 *7) (|:| |rh| (-646 (-412 *6))))) (-5 *1 (-812 *5 *6 *7 *3)) (-5 *4 (-646 (-412 *6))) (-4 *7 (-663 *6)) (-4 *3 (-663 (-412 *6))))) ((*1 *2 *3) @@ -2951,13 +2951,13 @@ (-12 (-5 *4 (-112)) (-5 *2 (-2 (|:| |contp| (-551)) - (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2570 (-551))))))) + (|:| -1964 (-646 (-2 (|:| |irr| *3) (|:| -2576 (-551))))))) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-112)) (-5 *2 (-2 (|:| |contp| (-551)) - (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2570 (-551))))))) + (|:| -1964 (-646 (-2 (|:| |irr| *3) (|:| -2576 (-551))))))) (-5 *1 (-1238 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2 *3) (-12 (-4 *4 (-354)) (-5 *2 (-410 *3)) (-5 *1 (-217 *4 *3)) @@ -3023,7 +3023,7 @@ (-12 (-4 *4 (-13 (-855) - (-10 -8 (-15 -4414 ((-1183) $)) (-15 -4275 ((-3 $ "failed") (-1183)))))) + (-10 -8 (-15 -4420 ((-1183) $)) (-15 -4281 ((-3 $ "failed") (-1183)))))) (-4 *5 (-798)) (-4 *7 (-562)) (-5 *2 (-410 *3)) (-5 *1 (-461 *4 *5 *6 *7 *3)) (-4 *6 (-562)) (-4 *3 (-956 *7 *5 *4)))) ((*1 *2 *3) @@ -3067,11 +3067,11 @@ (-12 (-4 *4 (-798)) (-4 *5 (-13 (-855) - (-10 -8 (-15 -4414 ((-1183) $)) (-15 -4275 ((-3 $ "failed") (-1183)))))) + (-10 -8 (-15 -4420 ((-1183) $)) (-15 -4281 ((-3 $ "failed") (-1183)))))) (-4 *6 (-310)) (-5 *2 (-410 *3)) (-5 *1 (-735 *4 *5 *6 *3)) (-4 *3 (-956 (-952 *6) *4 *5)))) ((*1 *2 *3) - (-12 (-4 *4 (-798)) (-4 *5 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $))))) + (-12 (-4 *4 (-798)) (-4 *5 (-13 (-855) (-10 -8 (-15 -4420 ((-1183) $))))) (-4 *6 (-562)) (-5 *2 (-410 *3)) (-5 *1 (-737 *4 *5 *6 *3)) (-4 *3 (-956 (-412 (-952 *6)) *4 *5)))) ((*1 *2 *3) @@ -3188,7 +3188,7 @@ ((*1 *2 *1) (-12 (-4 *1 (-1227)) (-5 *2 (-112))))) (((*1 *2) (-12 (-5 *2 (-1278)) (-5 *1 (-1225))))) (((*1 *2) - (-12 (-5 *2 (-2 (|:| -3660 (-646 (-1183))) (|:| -3661 (-646 (-1183))))) + (-12 (-5 *2 (-2 (|:| -3666 (-646 (-1183))) (|:| -3667 (-646 (-1183))))) (-5 *1 (-1225))))) (((*1 *2 *3) (-12 (-5 *3 (-646 (-1183))) (-5 *2 (-1278)) (-5 *1 (-1225)))) ((*1 *2 *3 *3) (-12 (-5 *3 (-646 (-1183))) (-5 *2 (-1278)) (-5 *1 (-1225))))) @@ -3208,7 +3208,7 @@ (-12 (-5 *4 (-1 (-112) *3 *3)) (-4 *3 (-1107)) (-5 *2 (-112)) (-5 *1 (-1224 *3))))) (((*1 *2) - (-12 (-5 *2 (-2 (|:| -3661 (-646 *3)) (|:| -3660 (-646 *3)))) + (-12 (-5 *2 (-2 (|:| -3667 (-646 *3)) (|:| -3666 (-646 *3)))) (-5 *1 (-1224 *3)) (-4 *3 (-1107))))) (((*1 *2 *3) (-12 (-5 *3 (-646 *4)) (-4 *4 (-1107)) (-5 *2 (-1278)) (-5 *1 (-1224 *4)))) @@ -3224,7 +3224,7 @@ (-12 (-4 *4 (-354)) (-5 *2 (-410 (-1177 (-1177 *4)))) (-5 *1 (-1221 *4)) (-5 *3 (-1177 (-1177 *4)))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4437)) (-4 *1 (-151 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4443)) (-4 *1 (-151 *3)) (-4 *3 (-1222)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1222)) (-5 *1 (-606 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-679 *3)) (-4 *3 (-1222)))) @@ -3239,10 +3239,10 @@ (((*1 *1 *2) (-12 (-5 *2 (-925)) (-4 *1 (-239 *3 *4)) (-4 *4 (-1055)) (-4 *4 (-1222)))) ((*1 *1 *2) - (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *5 (-239 (-4401 *3) (-776))) + (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *5 (-239 (-4407 *3) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2575 *2) (|:| -2576 *5)) - (-2 (|:| -2575 *2) (|:| -2576 *5)))) + (-1 (-112) (-2 (|:| -2581 *2) (|:| -2582 *5)) + (-2 (|:| -2581 *2) (|:| -2582 *5)))) (-5 *1 (-466 *3 *4 *2 *5 *6 *7)) (-4 *2 (-855)) (-4 *7 (-956 *4 *5 (-869 *3))))) ((*1 *2 *2) (-12 (-5 *2 (-949 (-226))) (-5 *1 (-1219))))) @@ -3286,12 +3286,12 @@ (((*1 *2 *3 *4 *5) (|partial| -12 (-5 *4 (-1 (-112) *9)) (-5 *5 (-1 (-112) *9 *9)) (-4 *9 (-1071 *6 *7 *8)) (-4 *6 (-562)) (-4 *7 (-798)) (-4 *8 (-855)) - (-5 *2 (-2 (|:| |bas| *1) (|:| -3760 (-646 *9)))) (-5 *3 (-646 *9)) + (-5 *2 (-2 (|:| |bas| *1) (|:| -3766 (-646 *9)))) (-5 *3 (-646 *9)) (-4 *1 (-1217 *6 *7 *8 *9)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *4 (-1 (-112) *8 *8)) (-4 *8 (-1071 *5 *6 *7)) (-4 *5 (-562)) (-4 *6 (-798)) (-4 *7 (-855)) - (-5 *2 (-2 (|:| |bas| *1) (|:| -3760 (-646 *8)))) (-5 *3 (-646 *8)) + (-5 *2 (-2 (|:| |bas| *1) (|:| -3766 (-646 *8)))) (-5 *3 (-646 *8)) (-4 *1 (-1217 *5 *6 *7 *8))))) (((*1 *2 *1) (-12 (-4 *1 (-1217 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-798)) (-4 *5 (-855)) @@ -3299,7 +3299,7 @@ (((*1 *2 *1) (-12 (-4 *1 (-1217 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-798)) (-4 *5 (-855)) (-4 *6 (-1071 *3 *4 *5)) - (-5 *2 (-2 (|:| -4305 (-646 *6)) (|:| -1879 (-646 *6))))))) + (-5 *2 (-2 (|:| -4311 (-646 *6)) (|:| -1880 (-646 *6))))))) (((*1 *2 *1 *3) (-12 (-5 *3 (-646 *1)) (-4 *1 (-1071 *4 *5 *6)) (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *6 (-855)) (-5 *2 (-112)))) @@ -3422,7 +3422,7 @@ (-4 *6 (-855)) (-5 *2 (-646 *1)) (-4 *1 (-1217 *4 *5 *6 *7))))) (((*1 *2 *3) (-12 (-4 *4 (-562)) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *7 (-1071 *4 *5 *6)) - (-5 *2 (-646 (-2 (|:| -4305 *1) (|:| -1879 (-646 *7))))) (-5 *3 (-646 *7)) + (-5 *2 (-646 (-2 (|:| -4311 *1) (|:| -1880 (-646 *7))))) (-5 *3 (-646 *7)) (-4 *1 (-1217 *4 *5 *6 *7))))) (((*1 *2 *1) (-12 (-4 *1 (-1217 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-798)) (-4 *5 (-855)) @@ -3749,8 +3749,8 @@ (-12 (-5 *2 (-1278)) (-5 *1 (-215 *3)) (-4 *3 (-13 (-855) - (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 (*2 $)) - (-15 -2152 (*2 $))))))) + (-10 -8 (-15 -4249 ((-1165) $ (-1183))) (-15 -4067 (*2 $)) + (-15 -2153 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-398)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-551)) (-5 *2 (-1278)) (-5 *1 (-398)))) ((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-507)))) @@ -3794,11 +3794,11 @@ (-12 (-5 *2 (-2 - (|:| -4304 + (|:| -4310 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) - (|:| -2263 + (|:| -2264 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") @@ -3814,7 +3814,7 @@ (-3 (|:| |str| (-1160 (-226))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1612 + (|:| -1613 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -3826,12 +3826,12 @@ (-12 (-5 *2 (-2 - (|:| -4304 + (|:| -4310 (-2 (|:| |xinit| (-226)) (|:| |xend| (-226)) (|:| |fn| (-1272 (-317 (-226)))) (|:| |yinit| (-646 (-226))) (|:| |intvals| (-646 (-226))) (|:| |g| (-317 (-226))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) - (|:| -2263 + (|:| -2264 (-2 (|:| |stiffness| (-382)) (|:| |stability| (-382)) (|:| |expense| (-382)) (|:| |accuracy| (-382)) (|:| |intermediateResults| (-382)))))) @@ -3859,7 +3859,7 @@ (((*1 *2) (-12 (-5 *2 (-1278)) (-5 *1 (-1200 *3 *4)) (-4 *3 (-1107)) (-4 *4 (-1107))))) (((*1 *1 *2) - (-12 (-5 *2 (-646 (-2 (|:| -4304 *3) (|:| -2263 *4)))) (-4 *3 (-1107)) + (-12 (-5 *2 (-646 (-2 (|:| -4310 *3) (|:| -2264 *4)))) (-4 *3 (-1107)) (-4 *4 (-1107)) (-4 *1 (-1199 *3 *4)))) ((*1 *1) (-12 (-4 *1 (-1199 *2 *3)) (-4 *2 (-1107)) (-4 *3 (-1107))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-551)) (-5 *1 (-1197 *2)) (-4 *2 (-367))))) @@ -3959,7 +3959,7 @@ (|partial| -12 (-5 *5 (-1183)) (-4 *6 (-13 (-310) (-1044 (-551)) (-644 (-551)) (-147))) (-4 *4 (-13 (-29 *6) (-1208) (-966))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -2199 (-646 *4)))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -2200 (-646 *4)))) (-5 *1 (-658 *6 *4 *3)) (-4 *3 (-663 *4)))) ((*1 *2 *3 *2 *4 *2 *5) (|partial| -12 (-5 *4 (-1183)) (-5 *5 (-646 *2)) @@ -3967,39 +3967,39 @@ (-4 *6 (-13 (-310) (-1044 (-551)) (-644 (-551)) (-147))) (-5 *1 (-658 *6 *2 *3)) (-4 *3 (-663 *2)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4438)))) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4438)))) - (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2199 (-646 *4)))) + (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4444)))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4444)))) + (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2200 (-646 *4)))) (-5 *1 (-672 *5 *6 *4 *3)) (-4 *3 (-691 *5 *6 *4)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4438)))) - (-4 *7 (-13 (-376 *5) (-10 -7 (-6 -4438)))) - (-5 *2 (-646 (-2 (|:| |particular| (-3 *7 #1#)) (|:| -2199 (-646 *7))))) + (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4444)))) + (-4 *7 (-13 (-376 *5) (-10 -7 (-6 -4444)))) + (-5 *2 (-646 (-2 (|:| |particular| (-3 *7 #1#)) (|:| -2200 (-646 *7))))) (-5 *1 (-672 *5 *6 *7 *3)) (-5 *4 (-646 *7)) (-4 *3 (-691 *5 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-694 *5)) (-4 *5 (-367)) (-5 *2 (-2 (|:| |particular| (-3 (-1272 *5) #2="failed")) - (|:| -2199 (-646 (-1272 *5))))) + (|:| -2200 (-646 (-1272 *5))))) (-5 *1 (-673 *5)) (-5 *4 (-1272 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-646 (-646 *5))) (-4 *5 (-367)) (-5 *2 - (-2 (|:| |particular| (-3 (-1272 *5) #2#)) (|:| -2199 (-646 (-1272 *5))))) + (-2 (|:| |particular| (-3 (-1272 *5) #2#)) (|:| -2200 (-646 (-1272 *5))))) (-5 *1 (-673 *5)) (-5 *4 (-1272 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-694 *5)) (-4 *5 (-367)) (-5 *2 (-646 (-2 (|:| |particular| (-3 (-1272 *5) #2#)) - (|:| -2199 (-646 (-1272 *5)))))) + (|:| -2200 (-646 (-1272 *5)))))) (-5 *1 (-673 *5)) (-5 *4 (-646 (-1272 *5))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-646 (-646 *5))) (-4 *5 (-367)) (-5 *2 (-646 (-2 (|:| |particular| (-3 (-1272 *5) #2#)) - (|:| -2199 (-646 (-1272 *5)))))) + (|:| -2200 (-646 (-1272 *5)))))) (-5 *1 (-673 *5)) (-5 *4 (-646 (-1272 *5))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-646 (-952 *5))) (-5 *4 (-646 (-1183))) (-4 *5 (-562)) @@ -4015,7 +4015,7 @@ (|partial| -12 (-5 *3 (-694 *7)) (-5 *5 (-1183)) (-4 *7 (-13 (-29 *6) (-1208) (-966))) (-4 *6 (-13 (-310) (-1044 (-551)) (-644 (-551)) (-147))) - (-5 *2 (-2 (|:| |particular| (-1272 *7)) (|:| -2199 (-646 (-1272 *7))))) + (-5 *2 (-2 (|:| |particular| (-1272 *7)) (|:| -2200 (-646 (-1272 *7))))) (-5 *1 (-807 *6 *7)) (-5 *4 (-1272 *7)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-694 *6)) (-5 *4 (-1183)) @@ -4026,24 +4026,24 @@ (|partial| -12 (-5 *3 (-646 (-296 *7))) (-5 *4 (-646 (-113))) (-5 *5 (-1183)) (-4 *7 (-13 (-29 *6) (-1208) (-966))) (-4 *6 (-13 (-310) (-1044 (-551)) (-644 (-551)) (-147))) - (-5 *2 (-2 (|:| |particular| (-1272 *7)) (|:| -2199 (-646 (-1272 *7))))) + (-5 *2 (-2 (|:| |particular| (-1272 *7)) (|:| -2200 (-646 (-1272 *7))))) (-5 *1 (-807 *6 *7)))) ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *3 (-646 *7)) (-5 *4 (-646 (-113))) (-5 *5 (-1183)) (-4 *7 (-13 (-29 *6) (-1208) (-966))) (-4 *6 (-13 (-310) (-1044 (-551)) (-644 (-551)) (-147))) - (-5 *2 (-2 (|:| |particular| (-1272 *7)) (|:| -2199 (-646 (-1272 *7))))) + (-5 *2 (-2 (|:| |particular| (-1272 *7)) (|:| -2200 (-646 (-1272 *7))))) (-5 *1 (-807 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-296 *7)) (-5 *4 (-113)) (-5 *5 (-1183)) (-4 *7 (-13 (-29 *6) (-1208) (-966))) (-4 *6 (-13 (-310) (-1044 (-551)) (-644 (-551)) (-147))) - (-5 *2 (-3 (-2 (|:| |particular| *7) (|:| -2199 (-646 *7))) *7 #3="failed")) + (-5 *2 (-3 (-2 (|:| |particular| *7) (|:| -2200 (-646 *7))) *7 #3="failed")) (-5 *1 (-807 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-113)) (-5 *5 (-1183)) (-4 *6 (-13 (-310) (-1044 (-551)) (-644 (-551)) (-147))) - (-5 *2 (-3 (-2 (|:| |particular| *3) (|:| -2199 (-646 *3))) *3 #3#)) + (-5 *2 (-3 (-2 (|:| |particular| *3) (|:| -2200 (-646 *3))) *3 #3#)) (-5 *1 (-807 *6 *3)) (-4 *3 (-13 (-29 *6) (-1208) (-966))))) ((*1 *2 *3 *4 *3 *5) (|partial| -12 (-5 *3 (-296 *2)) (-5 *4 (-113)) (-5 *5 (-646 *2)) @@ -4078,9 +4078,9 @@ ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *5 - (-1 (-3 (-2 (|:| |particular| *6) (|:| -2199 (-646 *6))) "failed") *7 *6)) + (-1 (-3 (-2 (|:| |particular| *6) (|:| -2200 (-646 *6))) "failed") *7 *6)) (-4 *6 (-367)) (-4 *7 (-663 *6)) - (-5 *2 (-2 (|:| |particular| (-1272 *6)) (|:| -2199 (-694 *6)))) + (-5 *2 (-2 (|:| |particular| (-1272 *6)) (|:| -2200 (-694 *6)))) (-5 *1 (-818 *6 *7)) (-5 *3 (-694 *6)) (-5 *4 (-1272 *6)))) ((*1 *2 *3) (-12 (-5 *3 (-904)) (-5 *2 (-1041)) (-5 *1 (-903)))) ((*1 *2 *3 *4) @@ -4194,11 +4194,11 @@ (((*1 *2 *1) (|partial| -12 (-5 *2 (-646 (-282))) (-5 *1 (-282)))) ((*1 *2 *1) (-12 (-5 *2 (-646 (-1188))) (-5 *1 (-1188))))) (((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1188))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -3270)) (-5 *2 (-112)) (-5 *1 (-622)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2401)) (-5 *2 (-112)) (-5 *1 (-622)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -3269)) (-5 *2 (-112)) (-5 *1 (-622)))) +(((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -3276)) (-5 *2 (-112)) (-5 *1 (-622)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2407)) (-5 *2 (-112)) (-5 *1 (-622)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -3275)) (-5 *2 (-112)) (-5 *1 (-622)))) ((*1 *2 *1 *3) - (-12 (-5 *3 (|[\|\|]| -2528)) (-5 *2 (-112)) (-5 *1 (-696 *4)) + (-12 (-5 *3 (|[\|\|]| -2534)) (-5 *2 (-112)) (-5 *1 (-696 *4)) (-4 *4 (-618 (-868))))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| *4)) (-4 *4 (-618 (-868))) (-5 *2 (-112)) @@ -4276,8 +4276,8 @@ (-12 (-5 *3 (-439)) (-5 *2 (-646 - (-3 (|:| -3985 (-1183)) - (|:| -3657 (-646 (-3 (|:| S (-1183)) (|:| P (-952 (-551))))))))) + (-3 (|:| -3991 (-1183)) + (|:| -3663 (-646 (-3 (|:| S (-1183)) (|:| P (-952 (-551))))))))) (-5 *1 (-1187))))) (((*1 *2 *1) (-12 (-5 *2 (-646 (-1183))) (-5 *1 (-1187))))) (((*1 *2 *1) @@ -4285,14 +4285,14 @@ (-5 *2 (-646 (-646 - (-3 (|:| -3985 (-1183)) - (|:| -3657 (-646 (-3 (|:| S (-1183)) (|:| P (-952 (-551)))))))))) + (-3 (|:| -3991 (-1183)) + (|:| -3663 (-646 (-3 (|:| S (-1183)) (|:| P (-952 (-551)))))))))) (-5 *1 (-1187))))) (((*1 *2 *1) (-12 (-5 *2 (-1109)) (-5 *1 (-1187))))) (((*1 *2 *3) (-12 (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186)))) ((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-1187))))) (((*1 *1 *2) - (-12 (-5 *2 (-646 (-2 (|:| -4304 (-1183)) (|:| -2263 (-441))))) + (-12 (-5 *2 (-646 (-2 (|:| -4310 (-1183)) (|:| -2264 (-441))))) (-5 *1 (-1187))))) (((*1 *1) (-5 *1 (-1186)))) (((*1 *2 *3) (-12 (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186)))) @@ -4306,19 +4306,19 @@ ((*1 *2 *3 *4 *1) (-12 (-5 *4 (-646 (-1183))) (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186))))) (((*1 *2 *3) - (-12 (-5 *3 (-3 (|:| |fst| (-439)) (|:| -4354 #1="void"))) (-5 *2 (-1278)) + (-12 (-5 *3 (-3 (|:| |fst| (-439)) (|:| -4360 #1="void"))) (-5 *2 (-1278)) (-5 *1 (-1186)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1183)) (-5 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) + (-12 (-5 *3 (-1183)) (-5 *4 (-3 (|:| |fst| (-439)) (|:| -4360 #1#))) (-5 *2 (-1278)) (-5 *1 (-1186)))) ((*1 *2 *3 *4 *1) - (-12 (-5 *3 (-1183)) (-5 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) + (-12 (-5 *3 (-1183)) (-5 *4 (-3 (|:| |fst| (-439)) (|:| -4360 #1#))) (-5 *2 (-1278)) (-5 *1 (-1186))))) (((*1 *2) (-12 (-5 *2 (-1278)) (-5 *1 (-1186)))) ((*1 *2 *3) (-12 (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186)))) ((*1 *2 *3 *1) (-12 (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186))))) (((*1 *2 *3 *1) - (-12 (-5 *3 (-1183)) (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4354 "void"))) + (-12 (-5 *3 (-1183)) (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4360 "void"))) (-5 *1 (-1186))))) (((*1 *2 *3 *1) (-12 (-5 *2 (-646 (-1183))) (-5 *1 (-1186)) (-5 *3 (-1183))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1183)) (-5 *2 (-1187)) (-5 *1 (-1186))))) @@ -4344,15 +4344,15 @@ ((*1 *2 *1) (-12 (-5 *2 - (-2 (|:| -2996 (-646 (-868))) (|:| -2817 (-646 (-868))) - (|:| |presup| (-646 (-868))) (|:| -2994 (-646 (-868))) + (-2 (|:| -3002 (-646 (-868))) (|:| -2823 (-646 (-868))) + (|:| |presup| (-646 (-868))) (|:| -3000 (-646 (-868))) (|:| |args| (-646 (-868))))) (-5 *1 (-1183))))) (((*1 *1 *1 *2) (-12 (-5 *2 - (-2 (|:| -2996 (-646 (-868))) (|:| -2817 (-646 (-868))) - (|:| |presup| (-646 (-868))) (|:| -2994 (-646 (-868))) + (-2 (|:| -3002 (-646 (-868))) (|:| -2823 (-646 (-868))) + (|:| |presup| (-646 (-868))) (|:| -3000 (-646 (-868))) (|:| |args| (-646 (-868))))) (-5 *1 (-1183)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-646 (-646 (-868)))) (-5 *1 (-1183))))) @@ -4370,50 +4370,50 @@ (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3514 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3514 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3514 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3514 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3514 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3514 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3514 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *1) (-5 *1 (-1182))) ((*1 *1 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3514 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *2 *1 *3 *3 *4) @@ -4463,13 +4463,13 @@ ((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-1173))))) (((*1 *1 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-1222)) (-4 *1 (-151 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-646 (-2 (|:| -2576 (-776)) (|:| -4216 *4) (|:| |num| *4)))) + (-12 (-5 *2 (-646 (-2 (|:| -2582 (-776)) (|:| -4222 *4) (|:| |num| *4)))) (-4 *4 (-1248 *3)) (-4 *3 (-13 (-367) (-147))) (-5 *1 (-404 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4354 #1="void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4360 #1="void"))) (-5 *3 (-646 (-952 (-551)))) (-5 *4 (-112)) (-5 *1 (-441)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-5 *3 (-646 (-1183))) + (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4360 #1#))) (-5 *3 (-646 (-1183))) (-5 *4 (-112)) (-5 *1 (-441)))) ((*1 *2 *1) (-12 (-5 *2 (-1160 *3)) (-5 *1 (-606 *3)) (-4 *3 (-1222)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-640 *2)) (-4 *2 (-173)))) @@ -4484,23 +4484,23 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-718 *2 *3 *4)) (-4 *2 (-855)) (-4 *3 (-1107)) (-14 *4 - (-1 (-112) (-2 (|:| -2575 *2) (|:| -2576 *3)) - (-2 (|:| -2575 *2) (|:| -2576 *3)))))) + (-1 (-112) (-2 (|:| -2581 *2) (|:| -2582 *3)) + (-2 (|:| -2581 *2) (|:| -2582 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-511)) (-5 *3 (-1121)) (-5 *1 (-843)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-878 *2 *3)) (-4 *2 (-1222)) (-4 *3 (-1222)))) ((*1 *1 *2) - (-12 (-5 *2 (-646 (-2 (|:| -4304 (-1183)) (|:| -2263 *4)))) (-4 *4 (-1107)) + (-12 (-5 *2 (-646 (-2 (|:| -4310 (-1183)) (|:| -2264 *4)))) (-4 *4 (-1107)) (-5 *1 (-894 *3 *4)) (-4 *3 (-1107)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-646 *5)) (-4 *5 (-13 (-1107) (-34))) (-5 *2 (-646 (-1146 *3 *5))) (-5 *1 (-1146 *3 *5)) (-4 *3 (-13 (-1107) (-34))))) ((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| |val| *4) (|:| -1717 *5)))) + (-12 (-5 *3 (-646 (-2 (|:| |val| *4) (|:| -1718 *5)))) (-4 *4 (-13 (-1107) (-34))) (-4 *5 (-13 (-1107) (-34))) (-5 *2 (-646 (-1146 *4 *5))) (-5 *1 (-1146 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -1717 *4))) (-4 *3 (-13 (-1107) (-34))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -1718 *4))) (-4 *3 (-13 (-1107) (-34))) (-4 *4 (-13 (-1107) (-34))) (-5 *1 (-1146 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1146 *2 *3)) (-4 *2 (-13 (-1107) (-34))) @@ -4890,11 +4890,11 @@ (-12 (-5 *2 (-1160 *3)) (-4 *3 (-38 (-412 (-551)))) (-5 *1 (-1169 *3))))) (((*1 *2 *3) (-12 (-4 *4 (-38 (-412 (-551)))) - (-5 *2 (-2 (|:| -3925 (-1160 *4)) (|:| -3926 (-1160 *4)))) + (-5 *2 (-2 (|:| -3931 (-1160 *4)) (|:| -3932 (-1160 *4)))) (-5 *1 (-1168 *4)) (-5 *3 (-1160 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-38 (-412 (-551)))) - (-5 *2 (-2 (|:| -4082 (-1160 *4)) (|:| -4078 (-1160 *4)))) + (-5 *2 (-2 (|:| -4088 (-1160 *4)) (|:| -4084 (-1160 *4)))) (-5 *1 (-1168 *4)) (-5 *3 (-1160 *4))))) (((*1 *2 *3 *2) (-12 (-5 *2 (-1160 *3)) (-4 *3 (-367)) (-4 *3 (-1055)) (-5 *1 (-1167 *3))))) @@ -4986,7 +4986,7 @@ (-5 *1 (-1160 *4))))) (((*1 *2 *3 *1) (-12 - (-5 *2 (-2 (|:| |cycle?| (-112)) (|:| -3007 (-776)) (|:| |period| (-776)))) + (-5 *2 (-2 (|:| |cycle?| (-112)) (|:| -3013 (-776)) (|:| |period| (-776)))) (-5 *1 (-1160 *4)) (-4 *4 (-1222)) (-5 *3 (-776))))) (((*1 *1 *2) (-12 (-5 *2 (-1 (-1160 *3))) (-5 *1 (-1160 *3)) (-4 *3 (-1222))))) (((*1 *1 *2 *1) (-12 (-5 *1 (-646 *2)) (-4 *2 (-1222)))) @@ -5101,12 +5101,12 @@ (-5 *2 (-2 (|:| |val| (-646 *8)) (|:| |towers| (-646 (-1152 *5 *6 *7 *8))))) (-5 *1 (-1152 *5 *6 *7 *8)) (-5 *3 (-646 *8))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-646 (-2 (|:| |val| (-646 *8)) (|:| -1717 *9)))) (-5 *4 (-776)) + (-12 (-5 *3 (-646 (-2 (|:| |val| (-646 *8)) (|:| -1718 *9)))) (-5 *4 (-776)) (-4 *8 (-1071 *5 *6 *7)) (-4 *9 (-1077 *5 *6 *7 *8)) (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-5 *2 (-1278)) (-5 *1 (-1075 *5 *6 *7 *8 *9)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-646 (-2 (|:| |val| (-646 *8)) (|:| -1717 *9)))) (-5 *4 (-776)) + (-12 (-5 *3 (-646 (-2 (|:| |val| (-646 *8)) (|:| -1718 *9)))) (-5 *4 (-776)) (-4 *8 (-1071 *5 *6 *7)) (-4 *9 (-1115 *5 *6 *7 *8)) (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-5 *2 (-1278)) (-5 *1 (-1151 *5 *6 *7 *8 *9))))) @@ -5114,8 +5114,8 @@ (-12 (-5 *5 (-2 (|:| |done| (-646 *11)) - (|:| |todo| (-646 (-2 (|:| |val| *3) (|:| -1717 *11)))))) - (-5 *6 (-776)) (-5 *2 (-646 (-2 (|:| |val| (-646 *10)) (|:| -1717 *11)))) + (|:| |todo| (-646 (-2 (|:| |val| *3) (|:| -1718 *11)))))) + (-5 *6 (-776)) (-5 *2 (-646 (-2 (|:| |val| (-646 *10)) (|:| -1718 *11)))) (-5 *3 (-646 *10)) (-5 *4 (-646 *11)) (-4 *10 (-1071 *7 *8 *9)) (-4 *11 (-1077 *7 *8 *9 *10)) (-4 *7 (-457)) (-4 *8 (-798)) (-4 *9 (-855)) (-5 *1 (-1075 *7 *8 *9 *10 *11)))) @@ -5123,8 +5123,8 @@ (-12 (-5 *5 (-2 (|:| |done| (-646 *11)) - (|:| |todo| (-646 (-2 (|:| |val| *3) (|:| -1717 *11)))))) - (-5 *6 (-776)) (-5 *2 (-646 (-2 (|:| |val| (-646 *10)) (|:| -1717 *11)))) + (|:| |todo| (-646 (-2 (|:| |val| *3) (|:| -1718 *11)))))) + (-5 *6 (-776)) (-5 *2 (-646 (-2 (|:| |val| (-646 *10)) (|:| -1718 *11)))) (-5 *3 (-646 *10)) (-5 *4 (-646 *11)) (-4 *10 (-1071 *7 *8 *9)) (-4 *11 (-1115 *7 *8 *9 *10)) (-4 *7 (-457)) (-4 *8 (-798)) (-4 *9 (-855)) (-5 *1 (-1151 *7 *8 *9 *10 *11))))) @@ -5132,17 +5132,17 @@ (-12 (-4 *1 (-340 *3 *4 *5 *6)) (-4 *3 (-367)) (-4 *4 (-1248 *3)) (-4 *5 (-1248 (-412 *4))) (-4 *6 (-346 *3 *4 *5)) (-5 *2 - (-2 (|:| -2499 (-418 *4 (-412 *4) *5 *6)) (|:| |principalPart| *6))))) + (-2 (|:| -2505 (-418 *4 (-412 *4) *5 *6)) (|:| |principalPart| *6))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1248 *5)) (-4 *5 (-367)) - (-5 *2 (-2 (|:| |poly| *6) (|:| -3505 (-412 *6)) (|:| |special| (-412 *6)))) + (-5 *2 (-2 (|:| |poly| *6) (|:| -3511 (-412 *6)) (|:| |special| (-412 *6)))) (-5 *1 (-732 *5 *6)) (-5 *3 (-412 *6)))) ((*1 *2 *3) (-12 (-4 *4 (-367)) (-5 *2 (-646 *3)) (-5 *1 (-902 *3 *4)) (-4 *3 (-1248 *4)))) ((*1 *2 *3 *4 *4) (|partial| -12 (-5 *4 (-776)) (-4 *5 (-367)) - (-5 *2 (-2 (|:| -3554 *3) (|:| -3553 *3))) (-5 *1 (-902 *3 *5)) + (-5 *2 (-2 (|:| -3560 *3) (|:| -3559 *3))) (-5 *1 (-902 *3 *5)) (-4 *3 (-1248 *5)))) ((*1 *2 *3 *2 *4 *4) (-12 (-5 *2 (-646 *9)) (-5 *3 (-646 *8)) (-5 *4 (-112)) @@ -5165,79 +5165,79 @@ (-4 *9 (-855)) (-4 *3 (-1071 *7 *8 *9)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1075 *7 *8 *9 *3 *4)) (-4 *4 (-1077 *7 *8 *9 *3)))) ((*1 *2 *3 *4 *5) (-12 (-5 *5 (-776)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *3 (-1071 *6 *7 *8)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1075 *6 *7 *8 *3 *4)) (-4 *4 (-1077 *6 *7 *8 *3)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1075 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3)))) ((*1 *2 *3 *4 *5 *6) (-12 (-5 *5 (-776)) (-5 *6 (-112)) (-4 *7 (-457)) (-4 *8 (-798)) (-4 *9 (-855)) (-4 *3 (-1071 *7 *8 *9)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1151 *7 *8 *9 *3 *4)) (-4 *4 (-1115 *7 *8 *9 *3)))) ((*1 *2 *3 *4 *5) (-12 (-5 *5 (-776)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *3 (-1071 *6 *7 *8)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1151 *6 *7 *8 *3 *4)) (-4 *4 (-1115 *6 *7 *8 *3)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1151 *5 *6 *7 *3 *4)) (-4 *4 (-1115 *5 *6 *7 *3))))) (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-776)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *3 (-1071 *6 *7 *8)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1075 *6 *7 *8 *3 *4)) (-4 *4 (-1077 *6 *7 *8 *3)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1075 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3)))) ((*1 *2 *3 *4 *5) (-12 (-5 *5 (-776)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *3 (-1071 *6 *7 *8)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1151 *6 *7 *8 *3 *4)) (-4 *4 (-1115 *6 *7 *8 *3)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1151 *5 *6 *7 *3 *4)) (-4 *4 (-1115 *5 *6 *7 *3))))) (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-112)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *3 (-1071 *6 *7 *8)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1075 *6 *7 *8 *3 *4)) (-4 *4 (-1077 *6 *7 *8 *3)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) (-5 *2 (-2 (|:| |done| (-646 *4)) - (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))))) + (|:| |todo| (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))))) (-5 *1 (-1151 *5 *6 *7 *3 *4)) (-4 *4 (-1115 *5 *6 *7 *3))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-646 *8)) (-5 *4 (-646 *9)) (-4 *8 (-1071 *5 *6 *7)) @@ -5308,7 +5308,7 @@ (-4 *3 (-13 (-457) (-1044 (-551)) (-644 (-551)))) (-5 *1 (-594 *3)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1248 *5)) (-4 *5 (-367)) - (-5 *2 (-2 (|:| -3505 *3) (|:| |special| *3))) (-5 *1 (-732 *5 *3)))) + (-5 *2 (-2 (|:| -3511 *3) (|:| |special| *3))) (-5 *1 (-732 *5 *3)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1272 *5)) (-4 *5 (-367)) (-4 *5 (-1055)) (-5 *2 (-646 (-646 (-694 *5)))) (-5 *1 (-1036 *5)) @@ -5350,7 +5350,7 @@ (-12 (-5 *2 (-646 *4)) (-5 *1 (-1147 *3 *4)) (-4 *3 (-13 (-1107) (-34))) (-4 *4 (-13 (-1107) (-34)))))) (((*1 *2 *1) - (-12 (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *4)))) (-5 *1 (-1147 *3 *4)) + (-12 (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *4)))) (-5 *1 (-1147 *3 *4)) (-4 *3 (-13 (-1107) (-34))) (-4 *4 (-13 (-1107) (-34)))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1146 *4 *5)) (-4 *4 (-13 (-1107) (-34))) @@ -5360,10 +5360,10 @@ (-4 *5 (-13 (-1107) (-34))) (-4 *6 (-13 (-1107) (-34))) (-5 *2 (-112)) (-5 *1 (-1147 *5 *6))))) (((*1 *1 *2 *1) - (-12 (|has| *1 (-6 -4437)) (-4 *1 (-151 *2)) (-4 *2 (-1222)) + (-12 (|has| *1 (-6 -4443)) (-4 *1 (-151 *2)) (-4 *2 (-1222)) (-4 *2 (-1107)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4437)) (-4 *1 (-151 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4443)) (-4 *1 (-151 *3)) (-4 *3 (-1222)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-679 *3)) (-4 *3 (-1222)))) ((*1 *1 *2 *1 *3) @@ -5374,9 +5374,9 @@ (-12 (-5 *2 (-1146 *3 *4)) (-4 *3 (-13 (-1107) (-34))) (-4 *4 (-13 (-1107) (-34))) (-5 *1 (-1147 *3 *4))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4437)) (-4 *1 (-236 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4443)) (-4 *1 (-236 *3)) (-4 *3 (-1107)))) - ((*1 *1 *2 *1) (-12 (|has| *1 (-6 -4437)) (-4 *1 (-236 *2)) (-4 *2 (-1107)))) + ((*1 *1 *2 *1) (-12 (|has| *1 (-6 -4443)) (-4 *1 (-236 *2)) (-4 *2 (-1107)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-285 *2)) (-4 *2 (-1222)) (-4 *2 (-1107)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-285 *3)) (-4 *3 (-1222)))) ((*1 *2 *3 *1) @@ -5578,25 +5578,25 @@ (((*1 *2 *1) (-12 (-4 *1 (-1140 *3)) (-4 *3 (-1055)) (-5 *2 - (-2 (|:| -4294 (-776)) (|:| |curves| (-776)) (|:| |polygons| (-776)) + (-2 (|:| -4300 (-776)) (|:| |curves| (-776)) (|:| |polygons| (-776)) (|:| |constructs| (-776))))))) (((*1 *2 *3 *3) - (-12 (-5 *3 (-646 (-2 (|:| -4176 (-1177 *6)) (|:| -2576 (-551))))) + (-12 (-5 *3 (-646 (-2 (|:| -4182 (-1177 *6)) (|:| -2582 (-551))))) (-4 *6 (-310)) (-4 *4 (-798)) (-4 *5 (-855)) (-5 *2 (-112)) (-5 *1 (-747 *4 *5 *6 *7)) (-4 *7 (-956 *6 *4 *5)))) ((*1 *1 *1) (-12 (-4 *1 (-1140 *2)) (-4 *2 (-1055))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1222)) (-5 *1 (-1138 *4 *2)) - (-4 *2 (-13 (-609 (-551) *4) (-10 -7 (-6 -4437) (-6 -4438)))))) + (-4 *2 (-13 (-609 (-551) *4) (-10 -7 (-6 -4443) (-6 -4444)))))) ((*1 *2 *2) (-12 (-4 *3 (-855)) (-4 *3 (-1222)) (-5 *1 (-1138 *3 *2)) - (-4 *2 (-13 (-609 (-551) *3) (-10 -7 (-6 -4437) (-6 -4438))))))) + (-4 *2 (-13 (-609 (-551) *3) (-10 -7 (-6 -4443) (-6 -4444))))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1222)) (-5 *1 (-1138 *4 *2)) - (-4 *2 (-13 (-609 (-551) *4) (-10 -7 (-6 -4437) (-6 -4438)))))) + (-4 *2 (-13 (-609 (-551) *4) (-10 -7 (-6 -4443) (-6 -4444)))))) ((*1 *2 *2) (-12 (-4 *3 (-855)) (-4 *3 (-1222)) (-5 *1 (-1138 *3 *2)) - (-4 *2 (-13 (-609 (-551) *3) (-10 -7 (-6 -4437) (-6 -4438))))))) + (-4 *2 (-13 (-609 (-551) *3) (-10 -7 (-6 -4443) (-6 -4444))))))) (((*1 *2 *3) (-12 (-5 *3 (-1272 *4)) (-4 *4 (-1055)) (-4 *2 (-1248 *4)) (-5 *1 (-449 *4 *2)))) @@ -5692,8 +5692,8 @@ (|:| |maps| (-646 (-2 (|:| |arg| *5) (|:| |res| *5)))))) (-5 *1 (-1134 *3 *5)) (-4 *3 (-1248 *5))))) (((*1 *2 *3 *2) - (|partial| -12 (-4 *4 (-367)) (-4 *5 (-13 (-376 *4) (-10 -7 (-6 -4438)))) - (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4438)))) (-5 *1 (-672 *4 *5 *2 *3)) + (|partial| -12 (-4 *4 (-367)) (-4 *5 (-13 (-376 *4) (-10 -7 (-6 -4444)))) + (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4444)))) (-5 *1 (-672 *4 *5 *2 *3)) (-4 *3 (-691 *4 *5 *2)))) ((*1 *2 *3 *2) (|partial| -12 (-5 *2 (-1272 *4)) (-5 *3 (-694 *4)) (-4 *4 (-367)) @@ -5710,7 +5710,7 @@ (-5 *1 (-1132 *5 *6 *7))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-310)) (-4 *6 (-376 *5)) (-4 *4 (-376 *5)) - (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2199 (-646 *4)))) + (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2200 (-646 *4)))) (-5 *1 (-1130 *5 *6 *4 *3)) (-4 *3 (-691 *5 *6 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-310)) (-4 *5 (-376 *4)) (-4 *6 (-376 *4)) @@ -5757,7 +5757,7 @@ (-4 *2 (-1055))))) (((*1 *2 *3) (-12 (-5 *3 (-694 *2)) (-4 *4 (-1248 *2)) - (-4 *2 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) + (-4 *2 (-13 (-310) (-10 -8 (-15 -4419 ((-410 $) $))))) (-5 *1 (-504 *2 *4 *5)) (-4 *5 (-415 *2 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1129 *3 *2 *4 *5)) (-4 *4 (-239 *3 *2)) (-4 *5 (-239 *3 *2)) @@ -5767,22 +5767,22 @@ (-5 *1 (-526 *2 *4 *5 *3)) (-4 *3 (-691 *2 *4 *5)))) ((*1 *2 *1) (-12 (-4 *1 (-691 *2 *3 *4)) (-4 *3 (-376 *2)) (-4 *4 (-376 *2)) - (|has| *2 (-6 (-4439 "*"))) (-4 *2 (-1055)))) + (|has| *2 (-6 (-4445 "*"))) (-4 *2 (-1055)))) ((*1 *2 *3) (-12 (-4 *4 (-376 *2)) (-4 *5 (-376 *2)) (-4 *2 (-173)) (-5 *1 (-693 *2 *4 *5 *3)) (-4 *3 (-691 *2 *4 *5)))) ((*1 *2 *1) (-12 (-4 *1 (-1129 *3 *2 *4 *5)) (-4 *4 (-239 *3 *2)) (-4 *5 (-239 *3 *2)) - (|has| *2 (-6 (-4439 "*"))) (-4 *2 (-1055))))) + (|has| *2 (-6 (-4445 "*"))) (-4 *2 (-1055))))) (((*1 *2 *1) (-12 (-4 *1 (-691 *2 *3 *4)) (-4 *3 (-376 *2)) (-4 *4 (-376 *2)) - (|has| *2 (-6 (-4439 "*"))) (-4 *2 (-1055)))) + (|has| *2 (-6 (-4445 "*"))) (-4 *2 (-1055)))) ((*1 *2 *3) (-12 (-4 *4 (-376 *2)) (-4 *5 (-376 *2)) (-4 *2 (-173)) (-5 *1 (-693 *2 *4 *5 *3)) (-4 *3 (-691 *2 *4 *5)))) ((*1 *2 *1) (-12 (-4 *1 (-1129 *3 *2 *4 *5)) (-4 *4 (-239 *3 *2)) (-4 *5 (-239 *3 *2)) - (|has| *2 (-6 (-4439 "*"))) (-4 *2 (-1055))))) + (|has| *2 (-6 (-4445 "*"))) (-4 *2 (-1055))))) (((*1 *2 *2 *1) (-12 (-4 *1 (-1127 *2)) (-4 *2 (-1222))))) (((*1 *2 *1) (-12 (-4 *1 (-1127 *2)) (-4 *2 (-1222))))) (((*1 *2 *1) (-12 (-4 *1 (-1127 *2)) (-4 *2 (-1222))))) @@ -5853,7 +5853,7 @@ (-12 (-5 *3 (-646 (-551))) (-5 *2 (-694 (-551))) (-5 *1 (-1116))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *4)))) (-5 *1 (-1114 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) @@ -5864,7 +5864,7 @@ (-5 *2 (-112)) (-5 *1 (-1114 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1718 *4)))) (-5 *1 (-1114 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) @@ -5872,7 +5872,7 @@ (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1718 *4)))) (-5 *1 (-1114 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) @@ -5880,29 +5880,29 @@ (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1718 *4)))) (-5 *1 (-1114 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *4)))) (-5 *1 (-1114 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *4)))) (-5 *1 (-1114 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *3 *4 *5 *5) (-12 (-5 *5 (-112)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) - (-4 *3 (-1071 *6 *7 *8)) (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *4)))) + (-4 *3 (-1071 *6 *7 *8)) (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *4)))) (-5 *1 (-1114 *6 *7 *8 *3 *4)) (-4 *4 (-1077 *6 *7 *8 *3)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-646 (-2 (|:| |val| (-646 *8)) (|:| -1717 *9)))) (-5 *5 (-112)) + (-12 (-5 *3 (-646 (-2 (|:| |val| (-646 *8)) (|:| -1718 *9)))) (-5 *5 (-112)) (-4 *8 (-1071 *6 *7 *4)) (-4 *9 (-1077 *6 *7 *4 *8)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *4 (-855)) - (-5 *2 (-646 (-2 (|:| |val| *8) (|:| -1717 *9)))) + (-5 *2 (-646 (-2 (|:| |val| *8) (|:| -1718 *9)))) (-5 *1 (-1114 *6 *7 *4 *8 *9))))) (((*1 *2 *3 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))) (-5 *1 (-1114 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2) (-12 (-4 *3 (-457)) (-4 *4 (-798)) (-4 *5 (-855)) (-4 *6 (-1071 *3 *4 *5)) @@ -5935,41 +5935,41 @@ (((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) (|partial| -12 (-5 *5 (-112)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *9 (-1071 *6 *7 *8)) - (-5 *2 (-2 (|:| -3699 (-646 *9)) (|:| -1717 *4) (|:| |ineq| (-646 *9)))) + (-5 *2 (-2 (|:| -3705 (-646 *9)) (|:| -1718 *4) (|:| |ineq| (-646 *9)))) (-5 *1 (-994 *6 *7 *8 *9 *4)) (-5 *3 (-646 *9)) (-4 *4 (-1077 *6 *7 *8 *9)))) ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) (|partial| -12 (-5 *5 (-112)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *9 (-1071 *6 *7 *8)) - (-5 *2 (-2 (|:| -3699 (-646 *9)) (|:| -1717 *4) (|:| |ineq| (-646 *9)))) + (-5 *2 (-2 (|:| -3705 (-646 *9)) (|:| -1718 *4) (|:| |ineq| (-646 *9)))) (-5 *1 (-1113 *6 *7 *8 *9 *4)) (-5 *3 (-646 *9)) (-4 *4 (-1077 *6 *7 *8 *9))))) (((*1 *2 *3 *4 *5 *5) (-12 (-5 *4 (-646 *10)) (-5 *5 (-112)) (-4 *10 (-1077 *6 *7 *8 *9)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *9 (-1071 *6 *7 *8)) (-5 *2 - (-646 (-2 (|:| -3699 (-646 *9)) (|:| -1717 *10) (|:| |ineq| (-646 *9))))) + (-646 (-2 (|:| -3705 (-646 *9)) (|:| -1718 *10) (|:| |ineq| (-646 *9))))) (-5 *1 (-994 *6 *7 *8 *9 *10)) (-5 *3 (-646 *9)))) ((*1 *2 *3 *4 *5 *5) (-12 (-5 *4 (-646 *10)) (-5 *5 (-112)) (-4 *10 (-1077 *6 *7 *8 *9)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *9 (-1071 *6 *7 *8)) (-5 *2 - (-646 (-2 (|:| -3699 (-646 *9)) (|:| -1717 *10) (|:| |ineq| (-646 *9))))) + (-646 (-2 (|:| -3705 (-646 *9)) (|:| -1718 *10) (|:| |ineq| (-646 *9))))) (-5 *1 (-1113 *6 *7 *8 *9 *10)) (-5 *3 (-646 *9))))) (((*1 *2 *2) - (-12 (-5 *2 (-646 (-2 (|:| |val| (-646 *6)) (|:| -1717 *7)))) + (-12 (-5 *2 (-646 (-2 (|:| |val| (-646 *6)) (|:| -1718 *7)))) (-4 *6 (-1071 *3 *4 *5)) (-4 *7 (-1077 *3 *4 *5 *6)) (-4 *3 (-457)) (-4 *4 (-798)) (-4 *5 (-855)) (-5 *1 (-994 *3 *4 *5 *6 *7)))) ((*1 *2 *2) - (-12 (-5 *2 (-646 (-2 (|:| |val| (-646 *6)) (|:| -1717 *7)))) + (-12 (-5 *2 (-646 (-2 (|:| |val| (-646 *6)) (|:| -1718 *7)))) (-4 *6 (-1071 *3 *4 *5)) (-4 *7 (-1077 *3 *4 *5 *6)) (-4 *3 (-457)) (-4 *4 (-798)) (-4 *5 (-855)) (-5 *1 (-1113 *3 *4 *5 *6 *7))))) (((*1 *2 *3 *3) - (-12 (-5 *3 (-2 (|:| |val| (-646 *7)) (|:| -1717 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-646 *7)) (|:| -1718 *8))) (-4 *7 (-1071 *4 *5 *6)) (-4 *8 (-1077 *4 *5 *6 *7)) (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-5 *2 (-112)) (-5 *1 (-994 *4 *5 *6 *7 *8)))) ((*1 *2 *3 *3) - (-12 (-5 *3 (-2 (|:| |val| (-646 *7)) (|:| -1717 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-646 *7)) (|:| -1718 *8))) (-4 *7 (-1071 *4 *5 *6)) (-4 *8 (-1077 *4 *5 *6 *7)) (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-5 *2 (-112)) (-5 *1 (-1113 *4 *5 *6 *7 *8))))) @@ -6102,7 +6102,7 @@ (-12 (-4 *1 (-1110 *3 *4 *5 *6 *7)) (-4 *3 (-1107)) (-4 *4 (-1107)) (-4 *5 (-1107)) (-4 *6 (-1107)) (-4 *7 (-1107)) (-5 *2 (-112))))) (((*1 *2 *1) - (-12 (-5 *2 (-646 (-2 (|:| -4304 (-1183)) (|:| -2263 *4)))) + (-12 (-5 *2 (-646 (-2 (|:| -4310 (-1183)) (|:| -2264 *4)))) (-5 *1 (-894 *3 *4)) (-4 *3 (-1107)) (-4 *4 (-1107)))) ((*1 *2 *1) (-12 (-4 *3 (-1107)) (-4 *4 (-1107)) (-4 *5 (-1107)) (-4 *6 (-1107)) @@ -6143,7 +6143,7 @@ (-12 (-5 *2 (-1272 (-1108 *3 *4))) (-5 *1 (-1108 *3 *4)) (-14 *3 (-925)) (-14 *4 (-925))))) (((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4437)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4443)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-4 *3 (-1107)) (-5 *2 (-112)))) ((*1 *2 *3 *1) (-12 (-5 *3 (-908 *4)) (-4 *4 (-1107)) (-5 *2 (-112)) (-5 *1 (-911 *4)))) @@ -6279,15 +6279,15 @@ (-4 *3 (-1115 *5 *6 *7 *8)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-112)) (-4 *5 (-13 (-310) (-147))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3656 (-646 (-952 *5)))))) + (-5 *2 (-646 (-2 (|:| -1925 (-1177 *5)) (|:| -3662 (-646 (-952 *5)))))) (-5 *1 (-1084 *5 *6)) (-5 *3 (-646 (-952 *5))) (-14 *6 (-646 (-1183))))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-310) (-147))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *4)) (|:| -3656 (-646 (-952 *4)))))) + (-5 *2 (-646 (-2 (|:| -1925 (-1177 *4)) (|:| -3662 (-646 (-952 *4)))))) (-5 *1 (-1084 *4 *5)) (-5 *3 (-646 (-952 *4))) (-14 *5 (-646 (-1183))))) ((*1 *2 *3 *4 *4) (-12 (-5 *4 (-112)) (-4 *5 (-13 (-310) (-147))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3656 (-646 (-952 *5)))))) + (-5 *2 (-646 (-2 (|:| -1925 (-1177 *5)) (|:| -3662 (-646 (-952 *5)))))) (-5 *1 (-1084 *5 *6)) (-5 *3 (-646 (-952 *5))) (-14 *6 (-646 (-1183)))))) (((*1 *1 *2) (-12 (-5 *2 (-646 (-1081 *3 *4 *5))) (-4 *3 (-1107)) @@ -6347,7 +6347,7 @@ ((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-1079))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *4)))) (-5 *1 (-1078 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) @@ -6358,29 +6358,29 @@ (-5 *2 (-112)) (-5 *1 (-1078 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1718 *4)))) (-5 *1 (-1078 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *4)))) (-5 *1 (-1078 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *4)))) (-5 *1 (-1078 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *3 *4 *5 *5) (-12 (-5 *5 (-112)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) - (-4 *3 (-1071 *6 *7 *8)) (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *4)))) + (-4 *3 (-1071 *6 *7 *8)) (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *4)))) (-5 *1 (-1078 *6 *7 *8 *3 *4)) (-4 *4 (-1077 *6 *7 *8 *3)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-646 (-2 (|:| |val| (-646 *8)) (|:| -1717 *9)))) (-5 *5 (-112)) + (-12 (-5 *3 (-646 (-2 (|:| |val| (-646 *8)) (|:| -1718 *9)))) (-5 *5 (-112)) (-4 *8 (-1071 *6 *7 *4)) (-4 *9 (-1077 *6 *7 *4 *8)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *4 (-855)) - (-5 *2 (-646 (-2 (|:| |val| *8) (|:| -1717 *9)))) + (-5 *2 (-646 (-2 (|:| |val| *8) (|:| -1718 *9)))) (-5 *1 (-1078 *6 *7 *4 *8 *9))))) (((*1 *2 *3 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| (-646 *3)) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| (-646 *3)) (|:| -1718 *4)))) (-5 *1 (-1078 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-1077 *3 *4 *5 *6)) (-4 *3 (-457)) (-4 *4 (-798)) (-4 *5 (-855)) @@ -6405,7 +6405,7 @@ (-4 *3 (-1071 *4 *5 *6)) (-5 *2 (-112)))) ((*1 *2 *3 *1) (-12 (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *3 (-1071 *4 *5 *6)) - (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1717 *1)))) + (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1718 *1)))) (-4 *1 (-1077 *4 *5 *6 *3))))) (((*1 *2 *3 *1) (-12 (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *3 (-1071 *4 *5 *6)) @@ -6420,7 +6420,7 @@ (-4 *2 (-562)))) ((*1 *2 *3 *3 *1) (-12 (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *3 (-1071 *4 *5 *6)) - (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *1)))) + (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *1)))) (-4 *1 (-1077 *4 *5 *6 *3))))) (((*1 *2 *3 *2) (-12 (-5 *2 (-646 *1)) (-5 *3 (-646 *7)) (-4 *1 (-1077 *4 *5 *6 *7)) @@ -6530,10 +6530,10 @@ (-14 *4 (-646 (-1183))))) ((*1 *2 *1) (-12 (-4 *1 (-388 *2 *3)) (-4 *3 (-1107)) (-4 *2 (-1055)))) ((*1 *2 *1) - (-12 (-14 *3 (-646 (-1183))) (-4 *5 (-239 (-4401 *3) (-776))) + (-12 (-14 *3 (-646 (-1183))) (-4 *5 (-239 (-4407 *3) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2575 *4) (|:| -2576 *5)) - (-2 (|:| -2575 *4) (|:| -2576 *5)))) + (-1 (-112) (-2 (|:| -2581 *4) (|:| -2582 *5)) + (-2 (|:| -2581 *4) (|:| -2582 *5)))) (-4 *2 (-173)) (-5 *1 (-466 *3 *2 *4 *5 *6 *7)) (-4 *4 (-855)) (-4 *7 (-956 *2 *5 (-869 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-514 *2 *3)) (-4 *3 (-855)) (-4 *2 (-1107)))) @@ -6588,36 +6588,36 @@ (-12 (-4 *1 (-1071 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) (-4 *4 (-855))))) (((*1 *2 *1 *1 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-855)) - (-5 *2 (-2 (|:| -4398 *1) (|:| |gap| (-776)) (|:| -3315 *1))) + (-5 *2 (-2 (|:| -4404 *1) (|:| |gap| (-776)) (|:| -3321 *1))) (-4 *1 (-1071 *4 *5 *3)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -4398 *1) (|:| |gap| (-776)) (|:| -3315 *1))) + (-5 *2 (-2 (|:| -4404 *1) (|:| |gap| (-776)) (|:| -3321 *1))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *2 *1 *1) (-12 (-5 *2 - (-2 (|:| -4398 *3) (|:| |gap| (-776)) (|:| -2161 (-786 *3)) - (|:| -3315 (-786 *3)))) + (-2 (|:| -4404 *3) (|:| |gap| (-776)) (|:| -2162 (-786 *3)) + (|:| -3321 (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-1055)))) ((*1 *2 *1 *1 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-855)) - (-5 *2 (-2 (|:| -4398 *1) (|:| |gap| (-776)) (|:| -2161 *1) (|:| -3315 *1))) + (-5 *2 (-2 (|:| -4404 *1) (|:| |gap| (-776)) (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-1071 *4 *5 *3)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -4398 *1) (|:| |gap| (-776)) (|:| -2161 *1) (|:| -3315 *1))) + (-5 *2 (-2 (|:| -4404 *1) (|:| |gap| (-776)) (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *1 *1 *1) (-12 (-5 *1 (-786 *2)) (-4 *2 (-1055)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1071 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) (-4 *4 (-855))))) (((*1 *2 *1 *1) (-12 - (-5 *2 (-2 (|:| |polnum| (-786 *3)) (|:| |polden| *3) (|:| -3916 (-776)))) + (-5 *2 (-2 (|:| |polnum| (-786 *3)) (|:| |polden| *3) (|:| -3922 (-776)))) (-5 *1 (-786 *3)) (-4 *3 (-1055)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| |polnum| *1) (|:| |polden| *1) (|:| -3916 (-776)))) + (-5 *2 (-2 (|:| |polnum| *1) (|:| |polden| *1) (|:| -3922 (-776)))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-51)) (-5 *1 (-52 *2)) (-4 *2 (-1222)))) ((*1 *1 *2) @@ -6681,23 +6681,23 @@ (-4 *4 (-798)) (-4 *5 (-855)) (-4 *1 (-982 *3 *4 *5 *6)))) ((*1 *2 *1) (|partial| -12 (-4 *1 (-1044 *2)) (-4 *2 (-1222)))) ((*1 *1 *2) - (|partial| -3972 + (|partial| -3978 (-12 (-5 *2 (-952 *3)) - (-12 (-3758 (-4 *3 (-38 (-412 (-551))))) (-3758 (-4 *3 (-38 (-551)))) + (-12 (-3764 (-4 *3 (-38 (-412 (-551))))) (-3764 (-4 *3 (-38 (-551)))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 *3)) - (-12 (-3758 (-4 *3 (-550))) (-3758 (-4 *3 (-38 (-412 (-551))))) + (-12 (-3764 (-4 *3 (-550))) (-3764 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 *3)) - (-12 (-3758 (-4 *3 (-997 (-551)))) (-4 *3 (-38 (-412 (-551)))) + (-12 (-3764 (-4 *3 (-997 (-551)))) (-4 *3 (-38 (-412 (-551)))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))))) ((*1 *1 *2) - (|partial| -3972 + (|partial| -3978 (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) - (-12 (-3758 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) + (-12 (-3764 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) @@ -6758,10 +6758,10 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (|:| |mdnia| - (-2 (|:| |fn| (-317 (-226))) (|:| -1612 (-646 (-1095 (-847 (-226))))) + (-2 (|:| |fn| (-317 (-226))) (|:| -1613 (-646 (-1095 (-847 (-226))))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))))) (-5 *1 (-774)))) ((*1 *2 *1) @@ -6777,11 +6777,11 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3887 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (|:| |lsa| - (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))))) + (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3887 (-646 (-226))))))) (-5 *1 (-846)))) ((*1 *2 *1) (-12 @@ -6800,23 +6800,23 @@ (-4 *4 (-798)) (-4 *5 (-855)) (-4 *1 (-982 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1044 *2)) (-4 *2 (-1222)))) ((*1 *1 *2) - (-3972 + (-3978 (-12 (-5 *2 (-952 *3)) - (-12 (-3758 (-4 *3 (-38 (-412 (-551))))) (-3758 (-4 *3 (-38 (-551)))) + (-12 (-3764 (-4 *3 (-38 (-412 (-551))))) (-3764 (-4 *3 (-38 (-551)))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 *3)) - (-12 (-3758 (-4 *3 (-550))) (-3758 (-4 *3 (-38 (-412 (-551))))) + (-12 (-3764 (-4 *3 (-550))) (-3764 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 *3)) - (-12 (-3758 (-4 *3 (-997 (-551)))) (-4 *3 (-38 (-412 (-551)))) + (-12 (-3764 (-4 *3 (-997 (-551)))) (-4 *3 (-38 (-412 (-551)))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))))) ((*1 *1 *2) - (-3972 + (-3978 (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) - (-12 (-3758 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) + (-12 (-3764 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) @@ -6847,24 +6847,24 @@ (((*1 *2 *1 *1) (-12 (-5 *2 - (-2 (|:| -3576 (-786 *3)) (|:| |coef1| (-786 *3)) (|:| |coef2| (-786 *3)))) + (-2 (|:| -3582 (-786 *3)) (|:| |coef1| (-786 *3)) (|:| |coef2| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -3576 *1) (|:| |coef1| *1) (|:| |coef2| *1))) + (-5 *2 (-2 (|:| -3582 *1) (|:| |coef1| *1) (|:| |coef2| *1))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3576 (-786 *3)) (|:| |coef1| (-786 *3)))) + (-12 (-5 *2 (-2 (|:| -3582 (-786 *3)) (|:| |coef1| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -3576 *1) (|:| |coef1| *1))) (-4 *1 (-1071 *3 *4 *5))))) + (-5 *2 (-2 (|:| -3582 *1) (|:| |coef1| *1))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3576 (-786 *3)) (|:| |coef2| (-786 *3)))) + (-12 (-5 *2 (-2 (|:| -3582 (-786 *3)) (|:| |coef2| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -3576 *1) (|:| |coef2| *1))) (-4 *1 (-1071 *3 *4 *5))))) + (-5 *2 (-2 (|:| -3582 *1) (|:| |coef2| *1))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) (-5 *2 (-646 *1)) (-4 *1 (-1071 *3 *4 *5))))) @@ -6977,18 +6977,18 @@ ((*1 *1 *1) (-5 *1 (-933))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1095 (-226))) (-5 *1 (-933)))) ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))) + (-12 (-5 *2 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551))))) (-5 *4 (-412 (-551))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *3 *2 *2) (|partial| -12 - (-5 *2 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))) + (-5 *2 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551))))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))) + (-12 (-5 *2 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551))))) (-5 *4 (-412 (-551))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 *4)))) ((*1 *2 *3 *2 *2) (|partial| -12 - (-5 *2 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))) + (-5 *2 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551))))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 (-412 (-551)))))) ((*1 *1 *1) (-12 (-4 *2 (-13 (-853) (-367))) (-5 *1 (-1067 *2 *3)) (-4 *3 (-1248 *2))))) @@ -7188,8 +7188,8 @@ (-12 (-4 *4 (-367)) (-4 *5 (-376 *4)) (-4 *6 (-376 *4)) (-5 *2 (-776)) (-5 *1 (-526 *4 *5 *6 *3)) (-4 *3 (-691 *4 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4438)))) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4438)))) (-5 *2 (-776)) + (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4444)))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4444)))) (-5 *2 (-776)) (-5 *1 (-672 *5 *6 *4 *3)) (-4 *3 (-691 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-694 *5)) (-5 *4 (-1272 *5)) (-4 *5 (-367)) (-5 *2 (-776)) @@ -7216,10 +7216,10 @@ (-12 (-4 *1 (-1059 *3 *4 *5 *6 *7)) (-4 *5 (-1055)) (-4 *6 (-239 *4 *5)) (-4 *7 (-239 *3 *5)) (-4 *5 (-562)) (-5 *2 (-776))))) (((*1 *2 *3) - (-12 (|has| *6 (-6 -4438)) (-4 *4 (-367)) (-4 *5 (-376 *4)) (-4 *6 (-376 *4)) + (-12 (|has| *6 (-6 -4444)) (-4 *4 (-367)) (-4 *5 (-376 *4)) (-4 *6 (-376 *4)) (-5 *2 (-646 *6)) (-5 *1 (-526 *4 *5 *6 *3)) (-4 *3 (-691 *4 *5 *6)))) ((*1 *2 *3) - (-12 (|has| *9 (-6 -4438)) (-4 *4 (-562)) (-4 *5 (-376 *4)) (-4 *6 (-376 *4)) + (-12 (|has| *9 (-6 -4444)) (-4 *4 (-562)) (-4 *5 (-376 *4)) (-4 *6 (-376 *4)) (-4 *7 (-997 *4)) (-4 *8 (-376 *7)) (-4 *9 (-376 *7)) (-5 *2 (-646 *6)) (-5 *1 (-527 *4 *5 *6 *3 *7 *8 *9 *10)) (-4 *3 (-691 *4 *5 *6)) (-4 *10 (-691 *7 *8 *9)))) @@ -7297,7 +7297,7 @@ (-12 (-5 *3 (-412 (-1177 *2))) (-4 *5 (-798)) (-4 *4 (-855)) (-4 *6 (-1055)) (-4 *2 (-13 (-367) - (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $))))) + (-10 -8 (-15 -4396 ($ *7)) (-15 -3417 (*7 $)) (-15 -3416 (*7 $))))) (-5 *1 (-957 *5 *4 *6 *7 *2)) (-4 *7 (-956 *6 *5 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-412 (-1177 (-412 (-952 *5))))) (-5 *4 (-1183)) @@ -7324,12 +7324,12 @@ (-5 *2 (-412 (-1177 *3))) (-5 *1 (-957 *5 *4 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $))))))) + (-10 -8 (-15 -4396 ($ *7)) (-15 -3417 (*7 $)) (-15 -3416 (*7 $))))))) ((*1 *2 *3 *4 *2) (-12 (-5 *2 (-1177 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $))))) + (-10 -8 (-15 -4396 ($ *7)) (-15 -3417 (*7 $)) (-15 -3416 (*7 $))))) (-4 *7 (-956 *6 *5 *4)) (-4 *5 (-798)) (-4 *4 (-855)) (-4 *6 (-1055)) (-5 *1 (-957 *5 *4 *6 *7 *3)))) ((*1 *2 *3 *4) @@ -7343,12 +7343,12 @@ (-4 *2 (-855)) (-5 *1 (-957 *4 *2 *5 *6 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4390 ($ *6)) (-15 -3411 (*6 $)) (-15 -3410 (*6 $))))))) + (-10 -8 (-15 -4396 ($ *6)) (-15 -3417 (*6 $)) (-15 -3416 (*6 $))))))) ((*1 *2 *3) (|partial| -12 (-5 *3 (-412 (-952 *4))) (-4 *4 (-562)) (-5 *2 (-1183)) (-5 *1 (-1046 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))) + (-12 (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3887 (-646 (-226))))) (-5 *2 (-646 (-1183))) (-5 *1 (-269)))) ((*1 *2 *3) (-12 (-5 *3 (-1177 *7)) (-4 *7 (-956 *6 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855)) @@ -7366,7 +7366,7 @@ (-5 *2 (-646 *5)) (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $))))))) + (-10 -8 (-15 -4396 ($ *7)) (-15 -3417 (*7 $)) (-15 -3416 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-979 *3 *4 *5)) (-4 *3 (-1055)) (-4 *4 (-797)) (-4 *5 (-855)) (-5 *2 (-646 *5)))) @@ -7402,7 +7402,7 @@ (-4 *2 (-13 (-1107) (-10 -8 (-15 * ($ $ $)))))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-925)) (-5 *1 (-1037 *2)) - (-4 *2 (-13 (-1107) (-10 -8 (-15 -4283 ($ $ $)))))))) + (-4 *2 (-13 (-1107) (-10 -8 (-15 -4289 ($ $ $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-646 (-1272 *5))) (-5 *4 (-551)) (-5 *2 (-1272 *5)) (-5 *1 (-1036 *5)) (-4 *5 (-367)) (-4 *5 (-372)) (-4 *5 (-1055))))) @@ -7475,10 +7475,10 @@ (-12 (-5 *3 (-776)) (-5 *2 (-694 (-952 *4))) (-5 *1 (-1035 *4)) (-4 *4 (-1055))))) (((*1 *2 *2 *3) - (-12 (-5 *2 (-694 *4)) (-5 *3 (-925)) (|has| *4 (-6 (-4439 "*"))) + (-12 (-5 *2 (-694 *4)) (-5 *3 (-925)) (|has| *4 (-6 (-4445 "*"))) (-4 *4 (-1055)) (-5 *1 (-1035 *4)))) ((*1 *2 *2 *3) - (-12 (-5 *2 (-646 (-694 *4))) (-5 *3 (-925)) (|has| *4 (-6 (-4439 "*"))) + (-12 (-5 *2 (-646 (-694 *4))) (-5 *3 (-925)) (|has| *4 (-6 (-4445 "*"))) (-4 *4 (-1055)) (-5 *1 (-1035 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-694 (-412 (-952 (-551))))) (-5 *2 (-646 (-694 (-317 (-551))))) @@ -7511,7 +7511,7 @@ ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1032 *3)) (-4 *3 (-1222))))) (((*1 *2 *2 *3) (-12 (-4 *3 (-367)) (-5 *1 (-1031 *3 *2)) (-4 *2 (-663 *3)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-367)) (-5 *2 (-2 (|:| -3699 *3) (|:| -2914 (-646 *5)))) + (-12 (-4 *5 (-367)) (-5 *2 (-2 (|:| -3705 *3) (|:| -2920 (-646 *5)))) (-5 *1 (-1031 *5 *3)) (-5 *4 (-646 *5)) (-4 *3 (-663 *5))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-1067 (-1030 *4) (-1177 (-1030 *4)))) (-5 *3 (-868)) @@ -7520,38 +7520,38 @@ (|partial| -12 (-5 *2 (-1067 (-1030 *3) (-1177 (-1030 *3)))) (-5 *1 (-1030 *3)) (-4 *3 (-13 (-853) (-367) (-1026)))))) (((*1 *2 *3) - (-12 (-5 *2 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) + (-12 (-5 *2 (-646 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551)))))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *3 *4) - (-12 (-5 *2 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) + (-12 (-5 *2 (-646 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551)))))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))) - (-5 *4 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))))) + (-5 *4 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551))))))) ((*1 *2 *3 *4) - (-12 (-5 *2 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) + (-12 (-5 *2 (-646 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551)))))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))) (-5 *4 (-412 (-551))))) ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3554 *5) (|:| -3553 *5)))) + (-12 (-5 *5 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3560 *5) (|:| -3559 *5)))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))) - (-5 *4 (-2 (|:| -3554 *5) (|:| -3553 *5))))) + (-5 *4 (-2 (|:| -3560 *5) (|:| -3559 *5))))) ((*1 *2 *3) - (-12 (-5 *2 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) + (-12 (-5 *2 (-646 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551)))))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 (-412 (-551)))))) ((*1 *2 *3 *4) - (-12 (-5 *2 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) + (-12 (-5 *2 (-646 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551)))))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 (-412 (-551)))) - (-5 *4 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))))) + (-5 *4 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551))))))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3554 *4) (|:| -3553 *4)))) + (-12 (-5 *4 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3560 *4) (|:| -3559 *4)))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 *4)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3554 *5) (|:| -3553 *5)))) + (-12 (-5 *5 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3560 *5) (|:| -3559 *5)))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 *5)) - (-5 *4 (-2 (|:| -3554 *5) (|:| -3553 *5)))))) + (-5 *4 (-2 (|:| -3560 *5) (|:| -3559 *5)))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) + (-12 (-5 *3 (-646 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551)))))) (-5 *2 (-646 (-412 (-551)))) (-5 *1 (-1027 *4)) (-4 *4 (-1248 (-551)))))) (((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))) + (-12 (-5 *3 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551))))) (-5 *2 (-412 (-551))) (-5 *1 (-1027 *4)) (-4 *4 (-1248 (-551)))))) (((*1 *2 *2) (-12 (-5 *2 (-113)) (-4 *3 (-562)) (-5 *1 (-32 *3 *4)) (-4 *4 (-426 *3)))) @@ -7579,7 +7579,7 @@ (-12 (-5 *3 (-1272 *6)) (-5 *4 (-1272 (-551))) (-5 *5 (-551)) (-4 *6 (-1107)) (-5 *2 (-1 *6)) (-5 *1 (-1023 *6))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -3838 *4) (|:| -1628 (-551))))) (-4 *4 (-1107)) + (-12 (-5 *3 (-646 (-2 (|:| -3844 *4) (|:| -1629 (-551))))) (-4 *4 (-1107)) (-5 *2 (-1 *4)) (-5 *1 (-1023 *4))))) (((*1 *2 *3 *3 *3) (|partial| -12 (-4 *4 (-13 (-367) (-147) (-1044 (-551)))) (-4 *5 (-1248 *4)) @@ -7589,14 +7589,14 @@ (-4 *5 (-13 (-367) (-147) (-1044 (-551)))) (-5 *2 (-2 (|:| |a| *6) (|:| |b| (-412 *6)) (|:| |h| *6) (|:| |c1| (-412 *6)) - (|:| |c2| (-412 *6)) (|:| -3509 *6))) + (|:| |c2| (-412 *6)) (|:| -3515 *6))) (-5 *1 (-1022 *5 *6)) (-5 *3 (-412 *6))))) (((*1 *2 *3 *3 *3 *4 *5) (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1248 *6)) (-4 *6 (-13 (-367) (-147) (-1044 *4))) (-5 *4 (-551)) (-5 *2 (-3 (|:| |ans| (-2 (|:| |ans| *3) (|:| |nosol| (-112)))) - (|:| -3699 + (|:| -3705 (-2 (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3) (|:| |beta| *3))))) (-5 *1 (-1021 *6 *3))))) @@ -7608,7 +7608,7 @@ (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1248 *5)) (-4 *5 (-13 (-367) (-147) (-1044 (-551)))) (-5 *2 - (-2 (|:| |a| *6) (|:| |b| (-412 *6)) (|:| |c| (-412 *6)) (|:| -3509 *6))) + (-2 (|:| |a| *6) (|:| |b| (-412 *6)) (|:| |c| (-412 *6)) (|:| -3515 *6))) (-5 *1 (-1021 *5 *6)) (-5 *3 (-412 *6))))) (((*1 *2 *3 *4 *4 *4 *5 *6 *7) (|partial| -12 (-5 *5 (-1183)) @@ -7619,7 +7619,7 @@ (|:| |limitedlogs| (-646 (-2 (|:| |coeff| *4) (|:| |logand| *4))))) "failed") *4 (-646 *4))) - (-5 *7 (-1 (-3 (-2 (|:| -2327 *4) (|:| |coeff| *4)) "failed") *4 *4)) + (-5 *7 (-1 (-3 (-2 (|:| -2328 *4) (|:| |coeff| *4)) "failed") *4 *4)) (-4 *4 (-13 (-1208) (-27) (-426 *8))) (-4 *8 (-13 (-457) (-147) (-1044 *3) (-644 *3))) (-5 *3 (-551)) (-5 *2 (-646 *4)) (-5 *1 (-1020 *8 *4))))) @@ -7632,10 +7632,10 @@ (|:| |limitedlogs| (-646 (-2 (|:| |coeff| *4) (|:| |logand| *4))))) "failed") *4 (-646 *4))) - (-5 *7 (-1 (-3 (-2 (|:| -2327 *4) (|:| |coeff| *4)) "failed") *4 *4)) + (-5 *7 (-1 (-3 (-2 (|:| -2328 *4) (|:| |coeff| *4)) "failed") *4 *4)) (-4 *4 (-13 (-1208) (-27) (-426 *8))) (-4 *8 (-13 (-457) (-147) (-1044 *3) (-644 *3))) (-5 *3 (-551)) - (-5 *2 (-2 (|:| |ans| *4) (|:| -3553 *4) (|:| |sol?| (-112)))) + (-5 *2 (-2 (|:| |ans| *4) (|:| -3559 *4) (|:| |sol?| (-112)))) (-5 *1 (-1019 *8 *4))))) (((*1 *1 *1) (-12 (-5 *1 (-343 *2 *3 *4)) (-14 *2 (-646 (-1183))) (-14 *3 (-646 (-1183))) @@ -7658,9 +7658,9 @@ (((*1 *2 *1 *1) (-12 (-4 *1 (-1016 *3)) (-4 *3 (-1222)) (-4 *3 (-1107)) (-5 *2 (-112))))) (((*1 *1 *1 *2) - (-12 (-5 *2 (-646 *1)) (|has| *1 (-6 -4438)) (-4 *1 (-1016 *3)) + (-12 (-5 *2 (-646 *1)) (|has| *1 (-6 -4444)) (-4 *1 (-1016 *3)) (-4 *3 (-1222))))) -(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1016 *2)) (-4 *2 (-1222))))) +(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-1016 *2)) (-4 *2 (-1222))))) (((*1 *2 *1) (|partial| -12 (-4 *1 (-166 *3)) (-4 *3 (-173)) (-4 *3 (-550)) (-5 *2 (-412 (-551))))) @@ -7725,7 +7725,7 @@ (((*1 *1 *2 *2) (-12 (-5 *2 (-646 (-551))) (-5 *1 (-1010 *3)) (-14 *3 (-551))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-410 *5)) (-4 *5 (-562)) - (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *5) (|:| |radicand| (-646 *5)))) + (-5 *2 (-2 (|:| -2582 (-776)) (|:| -4404 *5) (|:| |radicand| (-646 *5)))) (-5 *1 (-323 *5)) (-5 *4 (-776)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1008)) (-5 *2 (-551))))) (((*1 *1 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-1107)) (-5 *1 (-1006 *3))))) @@ -7821,39 +7821,39 @@ (-12 (-4 *3 (-1248 *2)) (-4 *2 (-1248 *4)) (-5 *1 (-991 *4 *2 *3 *5)) (-4 *4 (-354)) (-4 *5 (-729 *2 *3))))) (((*1 *2 *2 *3) - (-12 (-4 *4 (-798)) (-4 *3 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $))))) + (-12 (-4 *4 (-798)) (-4 *3 (-13 (-855) (-10 -8 (-15 -4420 ((-1183) $))))) (-4 *5 (-562)) (-5 *1 (-737 *4 *3 *5 *2)) (-4 *2 (-956 (-412 (-952 *5)) *4 *3)))) ((*1 *2 *2 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-13 (-855) - (-10 -8 (-15 -4414 ((-1183) $)) - (-15 -4275 ((-3 $ #1="failed") (-1183)))))) + (-10 -8 (-15 -4420 ((-1183) $)) + (-15 -4281 ((-3 $ #1="failed") (-1183)))))) (-5 *1 (-990 *4 *5 *3 *2)) (-4 *2 (-956 (-952 *4) *5 *3)))) ((*1 *2 *2 *3) (-12 (-5 *3 (-646 *6)) (-4 *6 (-13 (-855) - (-10 -8 (-15 -4414 ((-1183) $)) (-15 -4275 ((-3 $ #1#) (-1183)))))) + (-10 -8 (-15 -4420 ((-1183) $)) (-15 -4281 ((-3 $ #1#) (-1183)))))) (-4 *4 (-1055)) (-4 *5 (-798)) (-5 *1 (-990 *4 *5 *6 *2)) (-4 *2 (-956 (-952 *4) *5 *6))))) (((*1 *2 *2 *3) - (-12 (-4 *4 (-798)) (-4 *3 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $))))) + (-12 (-4 *4 (-798)) (-4 *3 (-13 (-855) (-10 -8 (-15 -4420 ((-1183) $))))) (-4 *5 (-562)) (-5 *1 (-737 *4 *3 *5 *2)) (-4 *2 (-956 (-412 (-952 *5)) *4 *3)))) ((*1 *2 *2 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-13 (-855) - (-10 -8 (-15 -4414 ((-1183) $)) - (-15 -4275 ((-3 $ #1="failed") (-1183)))))) + (-10 -8 (-15 -4420 ((-1183) $)) + (-15 -4281 ((-3 $ #1="failed") (-1183)))))) (-5 *1 (-990 *4 *5 *3 *2)) (-4 *2 (-956 (-952 *4) *5 *3)))) ((*1 *2 *2 *3) (-12 (-5 *3 (-646 *6)) (-4 *6 (-13 (-855) - (-10 -8 (-15 -4414 ((-1183) $)) (-15 -4275 ((-3 $ #1#) (-1183)))))) + (-10 -8 (-15 -4420 ((-1183) $)) (-15 -4281 ((-3 $ #1#) (-1183)))))) (-4 *4 (-1055)) (-4 *5 (-798)) (-5 *1 (-990 *4 *5 *6 *2)) (-4 *2 (-956 (-952 *4) *5 *6))))) (((*1 *2 *2) (|partial| -12 (-4 *1 (-989 *2)) (-4 *2 (-1208))))) @@ -7953,7 +7953,7 @@ (((*1 *2 *3) (|partial| -12 (-4 *4 (-562)) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *7 (-1071 *4 *5 *6)) - (-5 *2 (-2 (|:| |bas| (-481 *4 *5 *6 *7)) (|:| -3760 (-646 *7)))) + (-5 *2 (-2 (|:| |bas| (-481 *4 *5 *6 *7)) (|:| -3766 (-646 *7)))) (-5 *1 (-983 *4 *5 *6 *7)) (-5 *3 (-646 *7))))) (((*1 *2 *2) (-12 (-5 *2 (-646 *6)) (-4 *6 (-1071 *3 *4 *5)) (-4 *3 (-562)) (-4 *4 (-798)) @@ -8062,7 +8062,7 @@ ((*1 *2 *2) (-12 (-5 *2 (-646 (-908 *3))) (-5 *1 (-908 *3)) (-4 *3 (-1107)))) ((*1 *2 *1 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-855)) (-4 *6 (-1071 *4 *5 *3)) - (-5 *2 (-2 (|:| |under| *1) (|:| -3546 *1) (|:| |upper| *1))) + (-5 *2 (-2 (|:| |under| *1) (|:| -3552 *1) (|:| |upper| *1))) (-4 *1 (-982 *4 *5 *3 *6))))) (((*1 *2 *1) (-12 (-4 *1 (-982 *3 *4 *5 *6)) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) @@ -8106,10 +8106,10 @@ (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1055)) (-4 *3 (-797)))) ((*1 *2 *1) (-12 (-4 *1 (-388 *3 *2)) (-4 *3 (-1055)) (-4 *2 (-1107)))) ((*1 *2 *1) - (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *6 (-239 (-4401 *3) (-776))) + (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *6 (-239 (-4407 *3) (-776))) (-14 *7 - (-1 (-112) (-2 (|:| -2575 *5) (|:| -2576 *6)) - (-2 (|:| -2575 *5) (|:| -2576 *6)))) + (-1 (-112) (-2 (|:| -2581 *5) (|:| -2582 *6)) + (-2 (|:| -2581 *5) (|:| -2582 *6)))) (-5 *2 (-718 *5 *6 *7)) (-5 *1 (-466 *3 *4 *5 *6 *7 *8)) (-4 *5 (-855)) (-4 *8 (-956 *4 *6 (-869 *3))))) ((*1 *2 *1) @@ -8121,10 +8121,10 @@ (-12 (-5 *3 (-646 (-925))) (-5 *1 (-152 *4 *2 *5)) (-14 *4 (-925)) (-4 *2 (-367)) (-14 *5 (-999 *4 *2)))) ((*1 *1 *2 *3) - (-12 (-5 *3 (-718 *5 *6 *7)) (-4 *5 (-855)) (-4 *6 (-239 (-4401 *4) (-776))) + (-12 (-5 *3 (-718 *5 *6 *7)) (-4 *5 (-855)) (-4 *6 (-239 (-4407 *4) (-776))) (-14 *7 - (-1 (-112) (-2 (|:| -2575 *5) (|:| -2576 *6)) - (-2 (|:| -2575 *5) (|:| -2576 *6)))) + (-1 (-112) (-2 (|:| -2581 *5) (|:| -2582 *6)) + (-2 (|:| -2581 *5) (|:| -2582 *6)))) (-14 *4 (-646 (-1183))) (-4 *2 (-173)) (-5 *1 (-466 *4 *2 *5 *6 *7 *8)) (-4 *8 (-956 *2 *6 (-869 *4))))) ((*1 *1 *2 *3) (-12 (-4 *1 (-514 *2 *3)) (-4 *2 (-1107)) (-4 *3 (-855)))) @@ -8165,11 +8165,11 @@ (-12 (-5 *2 (-646 (-646 (-551)))) (-5 *1 (-977)) (-5 *3 (-646 (-551)))))) (((*1 *2 *1) (-12 (-5 *2 (-551)) (-5 *1 (-977))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4200 *4))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4206 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4200 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4206 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *2 (-562)) (-5 *1 (-975 *2 *3)) (-4 *3 (-1248 *2))))) (((*1 *2 *2 *2 *2 *3) @@ -8179,22 +8179,22 @@ (((*1 *2 *2 *2 *3) (-12 (-5 *3 (-776)) (-4 *2 (-562)) (-5 *1 (-975 *2 *4)) (-4 *4 (-1248 *2))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-310)))) + (-12 (-5 *2 (-2 (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-310)))) ((*1 *2 *1 *1) (|partial| -12 (-4 *3 (-1107)) (-5 *2 (-2 (|:| |lm| *1) (|:| |rm| *1))) (-4 *1 (-390 *3)))) ((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -2161 (-776)) (|:| -3315 (-776)))) (-5 *1 (-776)))) + (-12 (-5 *2 (-2 (|:| -2162 (-776)) (|:| -3321 (-776)))) (-5 *1 (-776)))) ((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -2162 *3) (|:| -3321 *3))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-457)) (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| -3291 *4))) (-5 *1 (-975 *4 *3)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| -3297 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-457)) (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3291 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3297 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *2 (-562)) (-4 *2 (-457)) (-5 *1 (-975 *2 *3)) (-4 *3 (-1248 *2))))) @@ -8205,21 +8205,21 @@ (-12 (-4 *4 (-562)) (-5 *2 (-646 *3)) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4201 *4))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4207 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4201 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4207 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3576 *3))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3582 *3))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3576 *3))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3582 *3))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3576 *3))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3582 *3))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) @@ -8249,18 +8249,18 @@ (((*1 *2 *2 *2 *3) (-12 (-5 *3 (-776)) (-4 *4 (-562)) (-5 *1 (-975 *4 *2)) (-4 *2 (-1248 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -4200 *4))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -4206 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4200 *4))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4206 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4200 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4206 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *1) - (-12 (-4 *1 (-409)) (-3758 (|has| *1 (-6 -4428))) - (-3758 (|has| *1 (-6 -4420))))) + (-12 (-4 *1 (-409)) (-3764 (|has| *1 (-6 -4434))) + (-3764 (|has| *1 (-6 -4426))))) ((*1 *2 *1) (-12 (-4 *1 (-431 *2)) (-4 *2 (-1107)) (-4 *2 (-855)))) ((*1 *1) (-4 *1 (-849))) ((*1 *1 *1 *1) (-4 *1 (-855))) ((*1 *2 *1) (-12 (-4 *1 (-974 *2)) (-4 *2 (-855))))) @@ -8325,14 +8325,14 @@ (-12 (-5 *3 (-646 (-952 *5))) (-5 *4 (-646 (-1183))) (-4 *5 (-13 (-367) (-147))) (-5 *2 - (-2 (|:| -4398 (-646 (-551))) (|:| |poly| (-646 (-1177 *5))) + (-2 (|:| -4404 (-646 (-551))) (|:| |poly| (-646 (-1177 *5))) (|:| |prim| (-1177 *5)))) (-5 *1 (-967 *5)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-646 (-952 *6))) (-5 *4 (-646 (-1183))) (-5 *5 (-1183)) (-4 *6 (-13 (-367) (-147))) (-5 *2 - (-2 (|:| -4398 (-646 (-551))) (|:| |poly| (-646 (-1177 *6))) + (-2 (|:| -4404 (-646 (-551))) (|:| |poly| (-646 (-1177 *6))) (|:| |prim| (-1177 *6)))) (-5 *1 (-967 *6))))) (((*1 *1 *2 *3) @@ -8352,69 +8352,69 @@ (((*1 *1 *2) (-12 (-5 *2 (-1126)) (-5 *1 (-960))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-798)) (-4 *6 (-855)) (-4 *7 (-562)) (-4 *3 (-956 *7 *5 *6)) - (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *3) (|:| |radicand| (-646 *3)))) + (-5 *2 (-2 (|:| -2582 (-776)) (|:| -4404 *3) (|:| |radicand| (-646 *3)))) (-5 *1 (-959 *5 *6 *7 *3 *8)) (-5 *4 (-776)) (-4 *8 (-13 (-367) - (-10 -8 (-15 -4390 ($ *3)) (-15 -3411 (*3 $)) (-15 -3410 (*3 $)))))))) + (-10 -8 (-15 -4396 ($ *3)) (-15 -3417 (*3 $)) (-15 -3416 (*3 $)))))))) (((*1 *2 *3 *4) (-12 (-4 *7 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *7 (-562)) (-4 *8 (-956 *7 *5 *6)) - (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *3) (|:| |radicand| *3))) + (-5 *2 (-2 (|:| -2582 (-776)) (|:| -4404 *3) (|:| |radicand| *3))) (-5 *1 (-959 *5 *6 *7 *8 *3)) (-5 *4 (-776)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4390 ($ *8)) (-15 -3411 (*8 $)) (-15 -3410 (*8 $)))))))) + (-10 -8 (-15 -4396 ($ *8)) (-15 -3417 (*8 $)) (-15 -3416 (*8 $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-412 (-551))) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *7 (-562)) (-4 *8 (-956 *7 *5 *6)) - (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *9) (|:| |radicand| *9))) + (-5 *2 (-2 (|:| -2582 (-776)) (|:| -4404 *9) (|:| |radicand| *9))) (-5 *1 (-959 *5 *6 *7 *8 *9)) (-5 *4 (-776)) (-4 *9 (-13 (-367) - (-10 -8 (-15 -4390 ($ *8)) (-15 -3411 (*8 $)) (-15 -3410 (*8 $)))))))) + (-10 -8 (-15 -4396 ($ *8)) (-15 -3417 (*8 $)) (-15 -3416 (*8 $)))))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-798)) (-4 *6 (-855)) (-4 *3 (-562)) (-4 *7 (-956 *3 *5 *6)) - (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *8) (|:| |radicand| *8))) + (-5 *2 (-2 (|:| -2582 (-776)) (|:| -4404 *8) (|:| |radicand| *8))) (-5 *1 (-959 *5 *6 *3 *7 *8)) (-5 *4 (-776)) (-4 *8 (-13 (-367) - (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) + (-10 -8 (-15 -4396 ($ *7)) (-15 -3417 (*7 $)) (-15 -3416 (*7 $)))))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-1055)) (-4 *3 (-1107)) - (-5 *2 (-2 (|:| |val| *1) (|:| -2576 (-551)))) (-4 *1 (-426 *3)))) + (-5 *2 (-2 (|:| |val| *1) (|:| -2582 (-551)))) (-4 *1 (-426 *3)))) ((*1 *2 *1) - (|partial| -12 (-5 *2 (-2 (|:| |val| (-896 *3)) (|:| -2576 (-896 *3)))) + (|partial| -12 (-5 *2 (-2 (|:| |val| (-896 *3)) (|:| -2582 (-896 *3)))) (-5 *1 (-896 *3)) (-4 *3 (-1107)))) ((*1 *2 *3) (|partial| -12 (-4 *4 (-798)) (-4 *5 (-855)) (-4 *6 (-1055)) - (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-2 (|:| |val| *3) (|:| -2576 (-551)))) + (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-2 (|:| |val| *3) (|:| -2582 (-551)))) (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) + (-10 -8 (-15 -4396 ($ *7)) (-15 -3417 (*7 $)) (-15 -3416 (*7 $)))))))) (((*1 *2 *1 *3) (|partial| -12 (-5 *3 (-1183)) (-4 *4 (-1055)) (-4 *4 (-1107)) - (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2576 (-551)))) (-4 *1 (-426 *4)))) + (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2582 (-551)))) (-4 *1 (-426 *4)))) ((*1 *2 *1 *3) (|partial| -12 (-5 *3 (-113)) (-4 *4 (-1055)) (-4 *4 (-1107)) - (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2576 (-551)))) (-4 *1 (-426 *4)))) + (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2582 (-551)))) (-4 *1 (-426 *4)))) ((*1 *2 *1) (|partial| -12 (-4 *3 (-1118)) (-4 *3 (-1107)) - (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2576 (-551)))) (-4 *1 (-426 *3)))) + (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2582 (-551)))) (-4 *1 (-426 *3)))) ((*1 *2 *1) - (|partial| -12 (-5 *2 (-2 (|:| |val| (-896 *3)) (|:| -2576 (-776)))) + (|partial| -12 (-5 *2 (-2 (|:| |val| (-896 *3)) (|:| -2582 (-776)))) (-5 *1 (-896 *3)) (-4 *3 (-1107)))) ((*1 *2 *1) (|partial| -12 (-4 *1 (-956 *3 *4 *5)) (-4 *3 (-1055)) (-4 *4 (-798)) - (-4 *5 (-855)) (-5 *2 (-2 (|:| |var| *5) (|:| -2576 (-776)))))) + (-4 *5 (-855)) (-5 *2 (-2 (|:| |var| *5) (|:| -2582 (-776)))))) ((*1 *2 *3) (|partial| -12 (-4 *4 (-798)) (-4 *5 (-855)) (-4 *6 (-1055)) - (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-2 (|:| |var| *5) (|:| -2576 (-551)))) + (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-2 (|:| |var| *5) (|:| -2582 (-551)))) (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) + (-10 -8 (-15 -4396 ($ *7)) (-15 -3417 (*7 $)) (-15 -3416 (*7 $)))))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-1118)) (-4 *3 (-1107)) (-5 *2 (-646 *1)) (-4 *1 (-426 *3)))) @@ -8428,7 +8428,7 @@ (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-646 *3)) (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) + (-10 -8 (-15 -4396 ($ *7)) (-15 -3417 (*7 $)) (-15 -3416 (*7 $)))))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1107)) (-5 *2 (-646 *1)) (-4 *1 (-426 *3)))) @@ -8442,7 +8442,7 @@ (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-646 *3)) (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) + (-10 -8 (-15 -4396 ($ *7)) (-15 -3417 (*7 $)) (-15 -3416 (*7 $)))))))) (((*1 *2 *1) (-12 (-4 *3 (-1055)) (-4 *4 (-1107)) (-5 *2 (-646 *1)) (-4 *1 (-388 *3 *4)))) ((*1 *2 *1) @@ -8692,7 +8692,7 @@ (|:| |wcond| (-646 (-952 *9))) (|:| |bsoln| (-2 (|:| |partsol| (-1272 (-412 (-952 *9)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *9))))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *9))))))))) (-5 *1 (-930 *9 *10 *11 *12))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-694 *7)) (-5 *3 (-646 *7)) (-4 *7 (-956 *4 *6 *5)) @@ -8723,7 +8723,7 @@ (-12 (-5 *3 (-646 - (-2 (|:| -3525 (-776)) + (-2 (|:| -3531 (-776)) (|:| |eqns| (-646 (-2 (|:| |det| *7) (|:| |rows| (-646 (-551))) @@ -8736,7 +8736,7 @@ (-12 (-5 *3 (-646 - (-2 (|:| -3525 (-776)) + (-2 (|:| -3531 (-776)) (|:| |eqns| (-646 (-2 (|:| |det| *7) (|:| |rows| (-646 (-551))) @@ -8752,19 +8752,19 @@ (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| -1757 (-694 (-412 (-952 *4)))) (|:| |vec| (-646 (-412 (-952 *4)))) - (|:| -3525 (-776)) (|:| |rows| (-646 (-551))) (|:| |cols| (-646 (-551))))) + (-2 (|:| -1758 (-694 (-412 (-952 *4)))) (|:| |vec| (-646 (-412 (-952 *4)))) + (|:| -3531 (-776)) (|:| |rows| (-646 (-551))) (|:| |cols| (-646 (-551))))) (-4 *4 (-13 (-310) (-147))) (-4 *5 (-13 (-855) (-619 (-1183)))) (-4 *6 (-798)) (-5 *2 (-2 (|:| |partsol| (-1272 (-412 (-952 *4)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *4))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *4))))))) (-5 *1 (-930 *4 *5 *6 *7)) (-4 *7 (-956 *4 *6 *5))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-2 (|:| |partsol| (-1272 (-412 (-952 *4)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *4))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *4))))))) (-5 *3 (-646 *7)) (-4 *4 (-13 (-310) (-147))) (-4 *7 (-956 *4 *6 *5)) (-4 *5 (-13 (-855) (-619 (-1183)))) (-4 *6 (-798)) (-5 *1 (-930 *4 *5 *6 *7))))) @@ -8773,7 +8773,7 @@ (-4 *6 (-13 (-855) (-619 (-1183)))) (-4 *7 (-798)) (-5 *2 (-646 - (-2 (|:| -3525 (-776)) + (-2 (|:| -3531 (-776)) (|:| |eqns| (-646 (-2 (|:| |det| *8) (|:| |rows| (-646 (-551))) @@ -8818,7 +8818,7 @@ (|:| |wcond| (-646 (-952 *8))) (|:| |bsoln| (-2 (|:| |partsol| (-1272 (-412 (-952 *8)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *8)))))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *8)))))))))) (|:| |rgsz| (-551)))) (-5 *1 (-930 *8 *9 *10 *11)) (-5 *7 (-551))))) (((*1 *2 *3) @@ -8830,7 +8830,7 @@ (|:| |wcond| (-646 (-952 *4))) (|:| |bsoln| (-2 (|:| |partsol| (-1272 (-412 (-952 *4)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *4)))))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *4)))))))))) (-5 *1 (-930 *4 *5 *6 *7)) (-4 *7 (-956 *4 *6 *5))))) (((*1 *2 *3 *4) (-12 @@ -8840,7 +8840,7 @@ (|:| |wcond| (-646 (-952 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1272 (-412 (-952 *5)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *5)))))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *5)))))))))) (-5 *4 (-1165)) (-4 *5 (-13 (-310) (-147))) (-4 *8 (-956 *5 *7 *6)) (-4 *6 (-13 (-855) (-619 (-1183)))) (-4 *7 (-798)) (-5 *2 (-551)) (-5 *1 (-930 *5 *6 *7 *8))))) @@ -8853,7 +8853,7 @@ (|:| |wcond| (-646 (-952 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1272 (-412 (-952 *5)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *5)))))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *5)))))))))) (-5 *1 (-930 *5 *6 *7 *8)) (-5 *4 (-646 *8)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-694 *8)) (-5 *4 (-646 (-1183))) (-4 *8 (-956 *5 *7 *6)) @@ -8865,7 +8865,7 @@ (|:| |wcond| (-646 (-952 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1272 (-412 (-952 *5)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *5)))))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *5)))))))))) (-5 *1 (-930 *5 *6 *7 *8)))) ((*1 *2 *3) (-12 (-5 *3 (-694 *7)) (-4 *7 (-956 *4 *6 *5)) (-4 *4 (-13 (-310) (-147))) @@ -8876,7 +8876,7 @@ (|:| |wcond| (-646 (-952 *4))) (|:| |bsoln| (-2 (|:| |partsol| (-1272 (-412 (-952 *4)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *4)))))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *4)))))))))) (-5 *1 (-930 *4 *5 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-694 *9)) (-5 *5 (-925)) (-4 *9 (-956 *6 *8 *7)) @@ -8888,7 +8888,7 @@ (|:| |wcond| (-646 (-952 *6))) (|:| |bsoln| (-2 (|:| |partsol| (-1272 (-412 (-952 *6)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *6)))))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *6)))))))))) (-5 *1 (-930 *6 *7 *8 *9)) (-5 *4 (-646 *9)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-694 *9)) (-5 *4 (-646 (-1183))) (-5 *5 (-925)) @@ -8900,7 +8900,7 @@ (|:| |wcond| (-646 (-952 *6))) (|:| |bsoln| (-2 (|:| |partsol| (-1272 (-412 (-952 *6)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *6)))))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *6)))))))))) (-5 *1 (-930 *6 *7 *8 *9)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-694 *8)) (-5 *4 (-925)) (-4 *8 (-956 *5 *7 *6)) @@ -8912,7 +8912,7 @@ (|:| |wcond| (-646 (-952 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1272 (-412 (-952 *5)))) - (|:| -2199 (-646 (-1272 (-412 (-952 *5)))))))))) + (|:| -2200 (-646 (-1272 (-412 (-952 *5)))))))))) (-5 *1 (-930 *5 *6 *7 *8)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-694 *9)) (-5 *4 (-646 *9)) (-5 *5 (-1165)) @@ -8946,7 +8946,7 @@ (-12 (-5 *3 (-646 *4)) (-4 *4 (-367)) (-4 *2 (-1248 *4)) (-5 *1 (-929 *4 *2))))) (((*1 *2 *3) - (-12 (-4 *1 (-927)) (-5 *2 (-2 (|:| -4398 (-646 *1)) (|:| -2584 *1))) + (-12 (-4 *1 (-927)) (-5 *2 (-2 (|:| -4404 (-646 *1)) (|:| -2590 *1))) (-5 *3 (-646 *1))))) (((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-646 *1)) (-4 *1 (-927))))) (((*1 *2 *2 *3) @@ -9026,13 +9026,13 @@ (|partial| -12 (-5 *3 (-337 *5 *6 *7 *8)) (-4 *5 (-426 *4)) (-4 *6 (-1248 *5)) (-4 *7 (-1248 (-412 *6))) (-4 *8 (-346 *5 *6 *7)) (-4 *4 (-13 (-562) (-1044 (-551)))) - (-5 *2 (-2 (|:| -4215 (-776)) (|:| -2558 *8))) + (-5 *2 (-2 (|:| -4221 (-776)) (|:| -2564 *8))) (-5 *1 (-917 *4 *5 *6 *7 *8)))) ((*1 *2 *3) (|partial| -12 (-5 *3 (-337 (-412 (-551)) *4 *5 *6)) (-4 *4 (-1248 (-412 (-551)))) (-4 *5 (-1248 (-412 *4))) (-4 *6 (-346 (-412 (-551)) *4 *5)) - (-5 *2 (-2 (|:| -4215 (-776)) (|:| -2558 *6))) (-5 *1 (-918 *4 *5 *6))))) + (-5 *2 (-2 (|:| -4221 (-776)) (|:| -2564 *6))) (-5 *1 (-918 *4 *5 *6))))) (((*1 *2 *3) (-12 (-5 *3 (-337 *5 *6 *7 *8)) (-4 *5 (-426 *4)) (-4 *6 (-1248 *5)) (-4 *7 (-1248 (-412 *6))) (-4 *8 (-346 *5 *6 *7)) @@ -9155,7 +9155,7 @@ (((*1 *1 *2) (-12 (-5 *2 (-646 (-646 *3))) (-4 *3 (-1107)) (-4 *1 (-910 *3))))) (((*1 *2 *3) (-12 (-5 *3 (-1148 *4 *2)) (-14 *4 (-925)) - (-4 *2 (-13 (-1055) (-10 -7 (-6 (-4439 "*"))))) (-5 *1 (-909 *4 *2))))) + (-4 *2 (-13 (-1055) (-10 -7 (-6 (-4445 "*"))))) (-5 *1 (-909 *4 *2))))) (((*1 *2 *1) (-12 (-5 *2 (-2 (|:| |preimage| (-646 *3)) (|:| |image| (-646 *3)))) (-5 *1 (-908 *3)) (-4 *3 (-1107))))) @@ -9194,31 +9194,31 @@ (((*1 *2 *3) (-12 (-5 *3 (-774)) (-5 *2 - (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) + (-2 (|:| -3089 (-382)) (|:| -3991 (-1165)) (|:| |explanations| (-646 (-1165))) (|:| |extra| (-1041)))) (-5 *1 (-570)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-774)) (-5 *4 (-1069)) (-5 *2 - (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) + (-2 (|:| -3089 (-382)) (|:| -3991 (-1165)) (|:| |explanations| (-646 (-1165))) (|:| |extra| (-1041)))) (-5 *1 (-570)))) ((*1 *2 *3 *4) (-12 (-4 *1 (-792)) (-5 *3 (-1069)) (-5 *4 - (-2 (|:| |fn| (-317 (-226))) (|:| -1612 (-646 (-1095 (-847 (-226))))) + (-2 (|:| |fn| (-317 (-226))) (|:| -1613 (-646 (-1095 (-847 (-226))))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 - (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)) + (-2 (|:| -3089 (-382)) (|:| |explanations| (-1165)) (|:| |extra| (-1041)))))) ((*1 *2 *3 *4) (-12 (-4 *1 (-792)) (-5 *3 (-1069)) (-5 *4 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 - (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)) + (-2 (|:| -3089 (-382)) (|:| |explanations| (-1165)) (|:| |extra| (-1041)))))) ((*1 *2 *3 *4) (-12 (-4 *1 (-805)) (-5 *3 (-1069)) @@ -9227,40 +9227,40 @@ (|:| |fn| (-1272 (-317 (-226)))) (|:| |yinit| (-646 (-226))) (|:| |intvals| (-646 (-226))) (|:| |g| (-317 (-226))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) - (-5 *2 (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)))))) + (-5 *2 (-2 (|:| -3089 (-382)) (|:| |explanations| (-1165)))))) ((*1 *2 *3) (-12 (-5 *3 (-813)) (-5 *2 - (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) + (-2 (|:| -3089 (-382)) (|:| -3991 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-810)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-813)) (-5 *4 (-1069)) (-5 *2 - (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) + (-2 (|:| -3089 (-382)) (|:| -3991 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-810)))) ((*1 *2 *3 *4) (-12 (-4 *1 (-844)) (-5 *3 (-1069)) - (-5 *4 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))) - (-5 *2 (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)))))) + (-5 *4 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3887 (-646 (-226))))) + (-5 *2 (-2 (|:| -3089 (-382)) (|:| |explanations| (-1165)))))) ((*1 *2 *3 *4) (-12 (-4 *1 (-844)) (-5 *3 (-1069)) (-5 *4 - (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3887 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) - (-5 *2 (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)))))) + (-5 *2 (-2 (|:| -3089 (-382)) (|:| |explanations| (-1165)))))) ((*1 *2 *3) (-12 (-5 *3 (-846)) (-5 *2 - (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) + (-2 (|:| -3089 (-382)) (|:| -3991 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-845)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-846)) (-5 *4 (-1069)) (-5 *2 - (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) + (-2 (|:| -3089 (-382)) (|:| -3991 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-845)))) ((*1 *2 *3 *4) @@ -9274,17 +9274,17 @@ (|:| |dFinish| (-694 (-226)))))) (|:| |f| (-646 (-646 (-317 (-226))))) (|:| |st| (-1165)) (|:| |tol| (-226)))) - (-5 *2 (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)))))) + (-5 *2 (-2 (|:| -3089 (-382)) (|:| |explanations| (-1165)))))) ((*1 *2 *3) (-12 (-5 *3 (-904)) (-5 *2 - (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) + (-2 (|:| -3089 (-382)) (|:| -3991 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-903)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-904)) (-5 *4 (-1069)) (-5 *2 - (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) + (-2 (|:| -3089 (-382)) (|:| -3991 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-903))))) (((*1 *2 *2 *3) @@ -9342,7 +9342,7 @@ (-12 (-5 *3 (-646 *6)) (-5 *4 (-896 *5)) (-4 *5 (-1107)) (-4 *6 (-1222)) (-5 *2 (-112)) (-5 *1 (-897 *5 *6))))) (((*1 *2 *1) - (|partial| -12 (-5 *2 (-2 (|:| -2914 (-113)) (|:| |arg| (-646 (-896 *3))))) + (|partial| -12 (-5 *2 (-2 (|:| -2920 (-113)) (|:| |arg| (-646 (-896 *3))))) (-5 *1 (-896 *3)) (-4 *3 (-1107)))) ((*1 *2 *1 *3) (|partial| -12 (-5 *3 (-113)) (-5 *2 (-646 (-896 *4))) (-5 *1 (-896 *4)) @@ -9400,11 +9400,11 @@ (-4 *3 (-1044 (-1183))) (-4 *3 (-892 *5)) (-4 *4 (-619 (-896 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-5 *2 (-646 (-296 (-952 *3)))) (-5 *1 (-893 *5 *3 *4)) - (-4 *3 (-1055)) (-3758 (-4 *3 (-1044 (-1183)))) (-4 *3 (-892 *5)) + (-4 *3 (-1055)) (-3764 (-4 *3 (-1044 (-1183)))) (-4 *3 (-892 *5)) (-4 *4 (-619 (-896 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-5 *2 (-894 *5 *3)) (-5 *1 (-893 *5 *3 *4)) - (-3758 (-4 *3 (-1044 (-1183)))) (-3758 (-4 *3 (-1055))) (-4 *3 (-892 *5)) + (-3764 (-4 *3 (-1044 (-1183)))) (-3764 (-4 *3 (-1055))) (-4 *3 (-892 *5)) (-4 *4 (-619 (-896 *5)))))) (((*1 *2 *1 *3) (-12 (-4 *1 (-301)) (-5 *3 (-1183)) (-5 *2 (-112)))) ((*1 *2 *1 *3) (-12 (-4 *1 (-301)) (-5 *3 (-113)) (-5 *2 (-112)))) @@ -9468,7 +9468,7 @@ (-4 *4 (-875 *3))))) (((*1 *2 *2) (-12 (-5 *2 (-925)) (-5 *1 (-408 *3)) (-4 *3 (-409)))) ((*1 *2) (-12 (-5 *2 (-925)) (-5 *1 (-408 *3)) (-4 *3 (-409)))) - ((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4428)) (-4 *1 (-409)))) + ((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4434)) (-4 *1 (-409)))) ((*1 *2) (-12 (-4 *1 (-409)) (-5 *2 (-925)))) ((*1 *2 *1) (-12 (-4 *1 (-875 *3)) (-5 *2 (-1160 (-551)))))) (((*1 *2 *1) @@ -9505,7 +9505,7 @@ (|partial| -12 (-5 *3 (-776)) (-4 *5 (-367)) (-5 *2 (-175 *6)) (-5 *1 (-872 *5 *4 *6)) (-4 *4 (-1265 *5)) (-4 *6 (-1248 *5))))) (((*1 *2 *1) - (-12 (|has| *1 (-6 -4437)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) + (-12 (|has| *1 (-6 -4443)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-5 *2 (-646 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-646 *3)) (-5 *1 (-741 *3)) (-4 *3 (-1107)))) ((*1 *2 *1) (-12 (-5 *2 (-646 (-444))) (-5 *1 (-870))))) @@ -9656,34 +9656,34 @@ (((*1 *2 *3 *2) (-12 (-5 *3 (-776)) (-5 *1 (-861 *2)) (-4 *2 (-173))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-367)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-857 *3)))) + (-5 *2 (-2 (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-857 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-99 *5)) (-4 *5 (-367)) (-4 *5 (-1055)) - (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-858 *5 *3)) + (-5 *2 (-2 (|:| -2162 *3) (|:| -3321 *3))) (-5 *1 (-858 *5 *3)) (-4 *3 (-857 *5))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-367)) (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) + (-12 (-4 *4 (-367)) (-5 *2 (-2 (|:| -2162 *3) (|:| -3321 *3))) (-5 *1 (-771 *3 *4)) (-4 *3 (-713 *4)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-367)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-857 *3)))) + (-5 *2 (-2 (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-857 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-99 *5)) (-4 *5 (-367)) (-4 *5 (-1055)) - (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-858 *5 *3)) + (-5 *2 (-2 (|:| -2162 *3) (|:| -3321 *3))) (-5 *1 (-858 *5 *3)) (-4 *3 (-857 *5))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-857 *3)))) + (-5 *2 (-2 (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-857 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-99 *5)) (-4 *5 (-562)) (-4 *5 (-1055)) - (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-858 *5 *3)) + (-5 *2 (-2 (|:| -2162 *3) (|:| -3321 *3))) (-5 *1 (-858 *5 *3)) (-4 *3 (-857 *5))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-857 *3)))) + (-5 *2 (-2 (|:| -2162 *1) (|:| -3321 *1))) (-4 *1 (-857 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-99 *5)) (-4 *5 (-562)) (-4 *5 (-1055)) - (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-858 *5 *3)) + (-5 *2 (-2 (|:| -2162 *3) (|:| -3321 *3))) (-5 *1 (-858 *5 *3)) (-4 *3 (-857 *5))))) (((*1 *2 *3 *4 *2) (-12 (-5 *4 (-1 *2 *2)) (-4 *2 (-653 *5)) (-4 *5 (-1055)) @@ -9708,7 +9708,7 @@ ((*1 *1 *1 *1) (-12 (-4 *1 (-857 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-367)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2584 *1))) + (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2590 *1))) (-4 *1 (-857 *3))))) (((*1 *1 *1 *1) (-12 (-4 *1 (-857 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) (((*1 *1 *1 *1) (-12 (-4 *1 (-857 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) @@ -9718,13 +9718,13 @@ (((*1 *1 *1 *1) (-12 (-4 *1 (-857 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-367)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2584 *1))) + (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2590 *1))) (-4 *1 (-857 *3))))) (((*1 *2 *2 *2) (-12 (-4 *3 (-367)) (-5 *1 (-771 *2 *3)) (-4 *2 (-713 *3)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-857 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) (((*1 *1) - (-12 (-4 *1 (-409)) (-3758 (|has| *1 (-6 -4428))) - (-3758 (|has| *1 (-6 -4420))))) + (-12 (-4 *1 (-409)) (-3764 (|has| *1 (-6 -4434))) + (-3764 (|has| *1 (-6 -4426))))) ((*1 *2 *1) (-12 (-4 *1 (-431 *2)) (-4 *2 (-1107)) (-4 *2 (-855)))) ((*1 *2 *1) (-12 (-4 *1 (-835 *2)) (-4 *2 (-855)))) ((*1 *1) (-4 *1 (-849))) ((*1 *1 *1 *1) (-4 *1 (-855)))) @@ -9770,13 +9770,13 @@ (((*1 *2 *3) (-12 (-4 *1 (-844)) (-5 *3 - (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3887 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (-5 *2 (-1041)))) ((*1 *2 *3) (-12 (-4 *1 (-844)) - (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))) + (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3887 (-646 (-226))))) (-5 *2 (-1041))))) (((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-215 (-507))) (-5 *1 (-842))))) (((*1 *2 *1) (-12 (-4 *1 (-841 *3)) (-4 *3 (-1107)) (-5 *2 (-55))))) @@ -9866,7 +9866,7 @@ (((*1 *1) (-5 *1 (-829)))) (((*1 *2 *1) (-12 (-5 *2 (-1183)) (-5 *1 (-828))))) (((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| |cd| (-1165)) (|:| -3985 (-1165)))) (-5 *1 (-828))))) + (-12 (-5 *2 (-2 (|:| |cd| (-1165)) (|:| -3991 (-1165)))) (-5 *1 (-828))))) (((*1 *2 *1) (-12 (-5 *2 (-1165)) (-5 *1 (-828))))) (((*1 *2 *1) (-12 (-5 *2 (-1183)) (-5 *1 (-828))))) (((*1 *2 *1) (-12 (-5 *2 (-226)) (-5 *1 (-828))))) @@ -9936,11 +9936,11 @@ ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-694 *7)) (-5 *5 - (-1 (-2 (|:| |particular| (-3 *6 "failed")) (|:| -2199 (-646 *6))) *7 *6)) + (-1 (-2 (|:| |particular| (-3 *6 "failed")) (|:| -2200 (-646 *6))) *7 *6)) (-4 *6 (-367)) (-4 *7 (-663 *6)) (-5 *2 (-2 (|:| |particular| (-3 (-1272 *6) "failed")) - (|:| -2199 (-646 (-1272 *6))))) + (|:| -2200 (-646 (-1272 *6))))) (-5 *1 (-818 *6 *7)) (-5 *4 (-1272 *6))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-367)) @@ -9948,13 +9948,13 @@ (-2 (|:| A (-694 *5)) (|:| |eqs| (-646 - (-2 (|:| C (-694 *5)) (|:| |g| (-1272 *5)) (|:| -3699 *6) + (-2 (|:| C (-694 *5)) (|:| |g| (-1272 *5)) (|:| -3705 *6) (|:| |rh| *5)))))) (-5 *1 (-818 *5 *6)) (-5 *3 (-694 *5)) (-5 *4 (-1272 *5)) (-4 *6 (-663 *5)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-367)) (-4 *6 (-663 *5)) - (-5 *2 (-2 (|:| -1757 (-694 *6)) (|:| |vec| (-1272 *5)))) + (-5 *2 (-2 (|:| -1758 (-694 *6)) (|:| |vec| (-1272 *5)))) (-5 *1 (-818 *5 *6)) (-5 *3 (-694 *6)) (-5 *4 (-1272 *5))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-660 (-412 *6))) (-5 *4 (-1 (-646 *5) *6)) @@ -9995,27 +9995,27 @@ (((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-646 *5) *6)) (-4 *5 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *6 (-1248 *5)) - (-5 *2 (-646 (-2 (|:| |poly| *6) (|:| -3699 *3)))) + (-5 *2 (-646 (-2 (|:| |poly| *6) (|:| -3705 *3)))) (-5 *1 (-814 *5 *6 *3 *7)) (-4 *3 (-663 *6)) (-4 *7 (-663 (-412 *6))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-646 *5) *6)) (-4 *5 (-13 (-367) (-147) (-1044 (-551)) (-1044 (-412 (-551))))) (-4 *6 (-1248 *5)) - (-5 *2 (-646 (-2 (|:| |poly| *6) (|:| -3699 (-661 *6 (-412 *6)))))) + (-5 *2 (-646 (-2 (|:| |poly| *6) (|:| -3705 (-661 *6 (-412 *6)))))) (-5 *1 (-817 *5 *6)) (-5 *3 (-661 *6 (-412 *6)))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-1 (-646 *7) *7 (-1177 *7))) (-5 *5 (-1 (-410 *7) *7)) (-4 *7 (-1248 *6)) (-4 *6 (-13 (-367) (-147) (-1044 (-412 (-551))))) - (-5 *2 (-646 (-2 (|:| |frac| (-412 *7)) (|:| -3699 *3)))) + (-5 *2 (-646 (-2 (|:| |frac| (-412 *7)) (|:| -3705 *3)))) (-5 *1 (-814 *6 *7 *3 *8)) (-4 *3 (-663 *7)) (-4 *8 (-663 (-412 *7))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-410 *6) *6)) (-4 *6 (-1248 *5)) (-4 *5 (-13 (-367) (-147) (-1044 (-551)) (-1044 (-412 (-551))))) - (-5 *2 (-646 (-2 (|:| |frac| (-412 *6)) (|:| -3699 (-661 *6 (-412 *6)))))) + (-5 *2 (-646 (-2 (|:| |frac| (-412 *6)) (|:| -3705 (-661 *6 (-412 *6)))))) (-5 *1 (-817 *5 *6)) (-5 *3 (-661 *6 (-412 *6)))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-367)) (-4 *7 (-1248 *5)) (-4 *4 (-729 *5 *7)) - (-5 *2 (-2 (|:| -1757 (-694 *6)) (|:| |vec| (-1272 *5)))) + (-5 *2 (-2 (|:| -1758 (-694 *6)) (|:| |vec| (-1272 *5)))) (-5 *1 (-816 *5 *6 *7 *4 *3)) (-4 *6 (-663 *5)) (-4 *3 (-663 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-660 (-412 *2))) (-4 *2 (-1248 *4)) (-5 *1 (-815 *4 *2)) @@ -10026,22 +10026,22 @@ (((*1 *2 *3 *4) (-12 (-5 *3 (-660 (-412 *6))) (-5 *4 (-412 *6)) (-4 *6 (-1248 *5)) (-4 *5 (-13 (-367) (-147) (-1044 (-551)) (-1044 (-412 (-551))))) - (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2199 (-646 *4)))) + (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2200 (-646 *4)))) (-5 *1 (-815 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-660 (-412 *6))) (-4 *6 (-1248 *5)) (-4 *5 (-13 (-367) (-147) (-1044 (-551)) (-1044 (-412 (-551))))) - (-5 *2 (-2 (|:| -2199 (-646 (-412 *6))) (|:| -1757 (-694 *5)))) + (-5 *2 (-2 (|:| -2200 (-646 (-412 *6))) (|:| -1758 (-694 *5)))) (-5 *1 (-815 *5 *6)) (-5 *4 (-646 (-412 *6))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-661 *6 (-412 *6))) (-5 *4 (-412 *6)) (-4 *6 (-1248 *5)) (-4 *5 (-13 (-367) (-147) (-1044 (-551)) (-1044 (-412 (-551))))) - (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2199 (-646 *4)))) + (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2200 (-646 *4)))) (-5 *1 (-815 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-661 *6 (-412 *6))) (-4 *6 (-1248 *5)) (-4 *5 (-13 (-367) (-147) (-1044 (-551)) (-1044 (-412 (-551))))) - (-5 *2 (-2 (|:| -2199 (-646 (-412 *6))) (|:| -1757 (-694 *5)))) + (-5 *2 (-2 (|:| -2200 (-646 (-412 *6))) (|:| -1758 (-694 *5)))) (-5 *1 (-815 *5 *6)) (-5 *4 (-646 (-412 *6)))))) (((*1 *2 *2 *3) (-12 (-4 *4 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *3 (-1248 *4)) @@ -10053,11 +10053,11 @@ (((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-646 *5) *6)) (-4 *5 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *6 (-1248 *5)) - (-5 *2 (-646 (-2 (|:| -4396 *5) (|:| -3699 *3)))) (-5 *1 (-814 *5 *6 *3 *7)) + (-5 *2 (-646 (-2 (|:| -4402 *5) (|:| -3705 *3)))) (-5 *1 (-814 *5 *6 *3 *7)) (-4 *3 (-663 *6)) (-4 *7 (-663 (-412 *6)))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *5 (-1248 *4)) - (-5 *2 (-646 (-2 (|:| |deg| (-776)) (|:| -3699 *5)))) + (-5 *2 (-646 (-2 (|:| |deg| (-776)) (|:| -3705 *5)))) (-5 *1 (-814 *4 *5 *3 *6)) (-4 *3 (-663 *5)) (-4 *6 (-663 (-412 *5)))))) (((*1 *2 *3) (-12 (-4 *2 (-1248 *4)) (-5 *1 (-814 *4 *2 *3 *5)) @@ -10073,19 +10073,19 @@ (-4 *3 (-663 (-412 *2)))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *5 (-1248 *4)) - (-5 *2 (-646 (-2 (|:| -4216 *5) (|:| -3658 *5)))) (-5 *1 (-812 *4 *5 *3 *6)) + (-5 *2 (-646 (-2 (|:| -4222 *5) (|:| -3664 *5)))) (-5 *1 (-812 *4 *5 *3 *6)) (-4 *3 (-663 *5)) (-4 *6 (-663 (-412 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *4 (-1248 *5)) - (-5 *2 (-646 (-2 (|:| -4216 *4) (|:| -3658 *4)))) (-5 *1 (-812 *5 *4 *3 *6)) + (-5 *2 (-646 (-2 (|:| -4222 *4) (|:| -3664 *4)))) (-5 *1 (-812 *5 *4 *3 *6)) (-4 *3 (-663 *4)) (-4 *6 (-663 (-412 *4))))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *5 (-1248 *4)) - (-5 *2 (-646 (-2 (|:| -4216 *5) (|:| -3658 *5)))) (-5 *1 (-812 *4 *5 *6 *3)) + (-5 *2 (-646 (-2 (|:| -4222 *5) (|:| -3664 *5)))) (-5 *1 (-812 *4 *5 *6 *3)) (-4 *6 (-663 *5)) (-4 *3 (-663 (-412 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *4 (-1248 *5)) - (-5 *2 (-646 (-2 (|:| -4216 *4) (|:| -3658 *4)))) (-5 *1 (-812 *5 *4 *6 *3)) + (-5 *2 (-646 (-2 (|:| -4222 *4) (|:| -3664 *4)))) (-5 *1 (-812 *5 *4 *6 *3)) (-4 *6 (-663 *4)) (-4 *3 (-663 (-412 *4)))))) (((*1 *2 *3 *4) (|partial| -12 (-5 *4 (-412 *2)) (-4 *2 (-1248 *5)) @@ -10099,7 +10099,7 @@ (-12 (-5 *3 (-660 *4)) (-4 *4 (-346 *5 *6 *7)) (-4 *5 (-13 (-367) (-147) (-1044 (-551)) (-1044 (-412 (-551))))) (-4 *6 (-1248 *5)) (-4 *7 (-1248 (-412 *6))) - (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2199 (-646 *4)))) + (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2200 (-646 *4)))) (-5 *1 (-811 *5 *6 *7 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-1183)) (-4 *4 (-13 (-310) (-1044 (-551)) (-644 (-551)) (-147))) @@ -10125,12 +10125,12 @@ (-5 *2 (-646 (-2 - (|:| -4304 + (|:| -4310 (-2 (|:| |xinit| (-226)) (|:| |xend| (-226)) (|:| |fn| (-1272 (-317 (-226)))) (|:| |yinit| (-646 (-226))) (|:| |intvals| (-646 (-226))) (|:| |g| (-317 (-226))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) - (|:| -2263 + (|:| -2264 (-2 (|:| |stiffness| (-382)) (|:| |stability| (-382)) (|:| |expense| (-382)) (|:| |accuracy| (-382)) (|:| |intermediateResults| (-382))))))) @@ -10140,7 +10140,7 @@ (-5 *2 (-646 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226))))) (-5 *1 (-565)))) ((*1 *2 *1) @@ -10159,7 +10159,7 @@ (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-1183)) (-4 *6 (-13 (-310) (-1044 (-551)) (-644 (-551)) (-147))) (-4 *4 (-13 (-29 *6) (-1208) (-966))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -2199 (-646 *4)))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -2200 (-646 *4)))) (-5 *1 (-806 *6 *4 *3)) (-4 *3 (-663 *4))))) (((*1 *2 *3) (-12 (-4 *1 (-805)) @@ -10181,7 +10181,7 @@ (-4 *4 (-23)) (-14 *5 (-1 *3 *3 *4)) (-14 *6 (-1 (-3 *4 "failed") *4 *4)) (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4)))) ((*1 *1 *1) - (-3972 (-12 (-5 *1 (-296 *2)) (-4 *2 (-367)) (-4 *2 (-1222))) + (-3978 (-12 (-5 *1 (-296 *2)) (-4 *2 (-367)) (-4 *2 (-1222))) (-12 (-5 *1 (-296 *2)) (-4 *2 (-478)) (-4 *2 (-1222))))) ((*1 *1 *1) (-4 *1 (-478))) ((*1 *2 *2) (-12 (-5 *2 (-1272 *3)) (-4 *3 (-354)) (-5 *1 (-533 *3)))) @@ -10195,55 +10195,55 @@ (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3844 *4) (|:| -1714 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3844 *4) (|:| -1714 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3844 *4) (|:| -1714 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3844 *4) (|:| -1714 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3844 *4) (|:| -1714 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3844 *4) (|:| -1714 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3844 *4) (|:| -1714 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3844 *4) (|:| -1714 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3844 *4) (|:| -1714 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *5 *5 *4 *6) @@ -10251,12 +10251,12 @@ (-5 *3 (-1272 (-382))) (-5 *5 (-382)) (-5 *2 (-1278)) (-5 *1 (-793))))) (((*1 *2 *3 *4 *5 *6 *5 *3 *7) (-12 (-5 *4 (-551)) - (-5 *6 (-2 (|:| |try| (-382)) (|:| |did| (-382)) (|:| -1581 (-382)))) + (-5 *6 (-2 (|:| |try| (-382)) (|:| |did| (-382)) (|:| -1582 (-382)))) (-5 *7 (-1 (-1278) (-1272 *5) (-1272 *5) (-382))) (-5 *3 (-1272 (-382))) (-5 *5 (-382)) (-5 *2 (-1278)) (-5 *1 (-793)))) ((*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3) (-12 (-5 *4 (-551)) - (-5 *6 (-2 (|:| |try| (-382)) (|:| |did| (-382)) (|:| -1581 (-382)))) + (-5 *6 (-2 (|:| |try| (-382)) (|:| |did| (-382)) (|:| -1582 (-382)))) (-5 *7 (-1 (-1278) (-1272 *5) (-1272 *5) (-382))) (-5 *3 (-1272 (-382))) (-5 *5 (-382)) (-5 *2 (-1278)) (-5 *1 (-793))))) (((*1 *2 *3 *4 *5 *5 *5 *5 *4 *6) @@ -10271,13 +10271,13 @@ (((*1 *2 *3 *2) (-12 (-4 *1 (-792)) (-5 *2 (-1041)) (-5 *3 - (-2 (|:| |fn| (-317 (-226))) (|:| -1612 (-646 (-1095 (-847 (-226))))) + (-2 (|:| |fn| (-317 (-226))) (|:| -1613 (-646 (-1095 (-847 (-226))))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))))) ((*1 *2 *3 *2) (-12 (-4 *1 (-792)) (-5 *2 (-1041)) (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226))))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-1165)) (-5 *2 (-382)) (-5 *1 (-791))))) (((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-382)) (-5 *1 (-791))))) @@ -10421,13 +10421,13 @@ (-4 *3 (-1055))))) (((*1 *2 *1 *1) (-12 - (-5 *2 (-2 (|:| -4200 *3) (|:| |coef1| (-786 *3)) (|:| |coef2| (-786 *3)))) + (-5 *2 (-2 (|:| -4206 *3) (|:| |coef1| (-786 *3)) (|:| |coef2| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -4200 *3) (|:| |coef1| (-786 *3)))) (-5 *1 (-786 *3)) + (-12 (-5 *2 (-2 (|:| -4206 *3) (|:| |coef1| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -4200 *3) (|:| |coef2| (-786 *3)))) (-5 *1 (-786 *3)) + (-12 (-5 *2 (-2 (|:| -4206 *3) (|:| |coef2| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-694 (-412 (-551)))) @@ -10471,7 +10471,7 @@ (-4 *10 (-956 *9 *7 *8)) (-5 *2 (-2 (|:| |deter| (-646 (-1177 *10))) - (|:| |dterm| (-646 (-646 (-2 (|:| -3492 (-776)) (|:| |pcoef| *10))))) + (|:| |dterm| (-646 (-646 (-2 (|:| -3498 (-776)) (|:| |pcoef| *10))))) (|:| |nfacts| (-646 *6)) (|:| |nlead| (-646 *10)))) (-5 *1 (-783 *6 *7 *8 *9 *10)) (-5 *3 (-1177 *10)) (-5 *4 (-646 *6)) (-5 *5 (-646 *10))))) @@ -10480,7 +10480,7 @@ (-5 *1 (-782 *4 *5 *6 *3 *7)) (-4 *3 (-1248 *6)) (-14 *7 (-925))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| (-112)) (|:| -1718 *4)))) (-5 *1 (-781 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *3 *3 *4 *5) (-12 (-5 *3 (-1165)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) @@ -10495,7 +10495,7 @@ ((*1 *1 *1) (-5 *1 (-382))) ((*1 *2 *3 *4) (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1717 *4)))) + (-5 *2 (-646 (-2 (|:| |val| *3) (|:| -1718 *4)))) (-5 *1 (-781 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *2 *3) (-12 (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *2 (-1071 *4 *5 *6)) @@ -10925,19 +10925,19 @@ (-5 *1 (-753))))) (((*1 *2 *3 *4 *3 *3 *4 *4 *4 *5) (-12 (-5 *3 (-226)) (-5 *4 (-551)) - (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3508)))) (-5 *2 (-1041)) + (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3514)))) (-5 *2 (-1041)) (-5 *1 (-753))))) (((*1 *2 *3 *3 *4 *5 *3 *3 *4 *4 *4 *6) (-12 (-5 *4 (-551)) (-5 *5 (-694 (-226))) - (-5 *6 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3508)))) (-5 *3 (-226)) + (-5 *6 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3514)))) (-5 *3 (-226)) (-5 *2 (-1041)) (-5 *1 (-753))))) (((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) (-12 (-5 *3 (-226)) (-5 *4 (-551)) - (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3508)))) (-5 *2 (-1041)) + (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3514)))) (-5 *2 (-1041)) (-5 *1 (-753))))) (((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) (-12 (-5 *3 (-226)) (-5 *4 (-551)) - (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3508)))) (-5 *2 (-1041)) + (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3514)))) (-5 *2 (-1041)) (-5 *1 (-753))))) (((*1 *2 *3 *3 *4 *3) (-12 (-5 *3 (-551)) (-5 *4 (-694 (-226))) (-5 *2 (-1041)) (-5 *1 (-752))))) @@ -10977,7 +10977,7 @@ (-5 *1 (-751))))) (((*1 *2 *3 *3 *3 *3 *4 *5) (-12 (-5 *3 (-226)) (-5 *4 (-551)) - (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3508)))) (-5 *2 (-1041)) + (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3514)))) (-5 *2 (-1041)) (-5 *1 (-751))))) (((*1 *2 *3 *4 *5 *4) (-12 (-5 *3 (-694 (-226))) (-5 *4 (-551)) (-5 *5 (-112)) (-5 *2 (-1041)) @@ -11001,7 +11001,7 @@ (-4 *7 (-855)) (-4 *8 (-310)) (-4 *9 (-956 *8 *6 *7)) (-4 *6 (-798)) (-5 *2 (-2 (|:| |upol| (-1177 *8)) (|:| |Lval| (-646 *8)) - (|:| |Lfact| (-646 (-2 (|:| -4176 (-1177 *8)) (|:| -2576 (-551))))) + (|:| |Lfact| (-646 (-2 (|:| -4182 (-1177 *8)) (|:| -2582 (-551))))) (|:| |ctpol| *8))) (-5 *1 (-747 *6 *7 *8 *9))))) (((*1 *2 *3 *4 *5) @@ -11009,18 +11009,18 @@ (-4 *6 (-798)) (-4 *9 (-956 *8 *6 *7)) (-5 *2 (-2 (|:| |unitPart| *9) - (|:| |suPart| (-646 (-2 (|:| -4176 (-1177 *9)) (|:| -2576 (-551))))))) + (|:| |suPart| (-646 (-2 (|:| -4182 (-1177 *9)) (|:| -2582 (-551))))))) (-5 *1 (-747 *6 *7 *8 *9)) (-5 *3 (-1177 *9))))) (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-551)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *8 (-310)) (-4 *9 (-956 *8 *6 *7)) - (-5 *2 (-2 (|:| -2191 (-1177 *9)) (|:| |polval| (-1177 *8)))) + (-5 *2 (-2 (|:| -2192 (-1177 *9)) (|:| |polval| (-1177 *8)))) (-5 *1 (-747 *6 *7 *8 *9)) (-5 *3 (-1177 *9)) (-5 *4 (-1177 *8))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-798)) (-4 *4 (-855)) (-4 *6 (-310)) (-5 *2 (-410 *3)) (-5 *1 (-747 *5 *4 *6 *3)) (-4 *3 (-956 *6 *5 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -4176 (-1177 *6)) (|:| -2576 (-551))))) + (-12 (-5 *3 (-646 (-2 (|:| -4182 (-1177 *6)) (|:| -2582 (-551))))) (-4 *6 (-310)) (-4 *4 (-798)) (-4 *5 (-855)) (-5 *2 (-551)) (-5 *1 (-747 *4 *5 *6 *7)) (-4 *7 (-956 *6 *4 *5))))) (((*1 *2 *3) @@ -11040,18 +11040,18 @@ (((*1 *2 *3 *4) (-12 (-4 *6 (-562)) (-4 *2 (-956 *3 *5 *4)) (-5 *1 (-737 *5 *4 *6 *2)) (-5 *3 (-412 (-952 *6))) (-4 *5 (-798)) - (-4 *4 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $)))))))) + (-4 *4 (-13 (-855) (-10 -8 (-15 -4420 ((-1183) $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-1177 (-952 *6))) (-4 *6 (-562)) (-4 *2 (-956 (-412 (-952 *6)) *5 *4)) (-5 *1 (-737 *5 *4 *6 *2)) - (-4 *5 (-798)) (-4 *4 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $)))))))) + (-4 *5 (-798)) (-4 *4 (-13 (-855) (-10 -8 (-15 -4420 ((-1183) $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-1177 *2)) (-4 *2 (-956 (-412 (-952 *6)) *5 *4)) (-5 *1 (-737 *5 *4 *6 *2)) (-4 *5 (-798)) - (-4 *4 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $))))) (-4 *6 (-562))))) + (-4 *4 (-13 (-855) (-10 -8 (-15 -4420 ((-1183) $))))) (-4 *6 (-562))))) (((*1 *2 *3) - (-12 (-4 *4 (-798)) (-4 *5 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $))))) - (-4 *6 (-562)) (-5 *2 (-2 (|:| -2817 (-952 *6)) (|:| -2245 (-952 *6)))) + (-12 (-4 *4 (-798)) (-4 *5 (-13 (-855) (-10 -8 (-15 -4420 ((-1183) $))))) + (-4 *6 (-562)) (-5 *2 (-2 (|:| -2823 (-952 *6)) (|:| -2246 (-952 *6)))) (-5 *1 (-737 *4 *5 *6 *3)) (-4 *3 (-956 (-412 (-952 *6)) *4 *5))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-646 *8)) (-5 *4 (-135 *5 *6 *7)) (-14 *5 (-551)) @@ -11066,7 +11066,7 @@ (-5 *1 (-732 *5 *2)) (-4 *5 (-367))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1248 *5)) (-4 *5 (-367)) - (-5 *2 (-2 (|:| -3505 (-410 *3)) (|:| |special| (-410 *3)))) + (-5 *2 (-2 (|:| -3511 (-410 *3)) (|:| |special| (-410 *3)))) (-5 *1 (-732 *5 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-55)))) ((*1 *2 *1) @@ -11122,16 +11122,16 @@ ((*1 *2 *1) (-12 (-4 *2 (-1107)) (-5 *1 (-718 *3 *2 *4)) (-4 *3 (-855)) (-14 *4 - (-1 (-112) (-2 (|:| -2575 *3) (|:| -2576 *2)) - (-2 (|:| -2575 *3) (|:| -2576 *2))))))) + (-1 (-112) (-2 (|:| -2581 *3) (|:| -2582 *2)) + (-2 (|:| -2581 *3) (|:| -2582 *2))))))) (((*1 *1 *2) (-12 (-5 *2 (-925)) (-4 *1 (-372)))) ((*1 *2 *3 *3) (-12 (-5 *3 (-925)) (-5 *2 (-1272 *4)) (-5 *1 (-533 *4)) (-4 *4 (-354)))) ((*1 *2 *1) (-12 (-4 *2 (-855)) (-5 *1 (-718 *2 *3 *4)) (-4 *3 (-1107)) (-14 *4 - (-1 (-112) (-2 (|:| -2575 *2) (|:| -2576 *3)) - (-2 (|:| -2575 *2) (|:| -2576 *3))))))) + (-1 (-112) (-2 (|:| -2581 *2) (|:| -2582 *3)) + (-2 (|:| -2581 *2) (|:| -2582 *3))))))) (((*1 *2 *2) (-12 (-4 *3 (-1055)) (-5 *1 (-717 *3 *2)) (-4 *2 (-1248 *3))))) (((*1 *2 *1) (-12 (-4 *3 (-1055)) (-5 *2 (-1272 *3)) (-5 *1 (-717 *3 *4)) @@ -11156,7 +11156,7 @@ (((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10) (|partial| -12 (-5 *2 (-646 (-1177 *13))) (-5 *3 (-1177 *13)) (-5 *4 (-646 *12)) (-5 *5 (-646 *10)) (-5 *6 (-646 *13)) - (-5 *7 (-646 (-646 (-2 (|:| -3492 (-776)) (|:| |pcoef| *13))))) + (-5 *7 (-646 (-646 (-2 (|:| -3498 (-776)) (|:| |pcoef| *13))))) (-5 *8 (-646 (-776))) (-5 *9 (-1272 (-646 (-1177 *10)))) (-4 *12 (-855)) (-4 *10 (-310)) (-4 *13 (-956 *10 *11 *12)) (-4 *11 (-798)) (-5 *1 (-712 *11 *12 *10 *13))))) @@ -11204,17 +11204,17 @@ ((*1 *2 *2) (-12 (-5 *2 (-925)) (-5 *1 (-706))))) (((*1 *2 *3 *3) (-12 (-4 *3 (-310)) (-4 *3 (-173)) (-4 *4 (-376 *3)) (-4 *5 (-376 *3)) - (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-693 *3 *4 *5 *6)) + (-5 *2 (-2 (|:| -2162 *3) (|:| -3321 *3))) (-5 *1 (-693 *3 *4 *5 *6)) (-4 *6 (-691 *3 *4 *5)))) ((*1 *2 *3 *3) - (-12 (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-705 *3)) + (-12 (-5 *2 (-2 (|:| -2162 *3) (|:| -3321 *3))) (-5 *1 (-705 *3)) (-4 *3 (-310))))) (((*1 *2 *2 *3 *3) (-12 (-5 *2 (-694 *3)) (-4 *3 (-310)) (-5 *1 (-705 *3))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-694 *3)) (-4 *3 (-310)) (-5 *1 (-705 *3))))) (((*1 *2 *2) (-12 (-5 *2 (-694 *3)) (-4 *3 (-310)) (-5 *1 (-705 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-409)) (-5 *2 (-551)))) ((*1 *2 *1) (-12 (-5 *2 (-551)) (-5 *1 (-704))))) -(((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4428)) (-4 *1 (-409)))) +(((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4434)) (-4 *1 (-409)))) ((*1 *2) (-12 (-4 *1 (-409)) (-5 *2 (-925)))) ((*1 *2 *2) (-12 (-5 *2 (-925)) (-5 *1 (-704)))) ((*1 *2) (-12 (-5 *2 (-925)) (-5 *1 (-704))))) @@ -11250,49 +11250,49 @@ ((*1 *2 *2 *3 *2 *3) (-12 (-5 *3 (-551)) (-5 *1 (-701 *2)) (-4 *2 (-1248 *3))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| |deg| (-776)) (|:| -2987 *5)))) (-4 *5 (-1248 *4)) + (-12 (-5 *3 (-646 (-2 (|:| |deg| (-776)) (|:| -2993 *5)))) (-4 *5 (-1248 *4)) (-4 *4 (-354)) (-5 *2 (-646 *5)) (-5 *1 (-217 *4 *5)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-646 (-2 (|:| -4176 *5) (|:| -4392 (-551))))) (-5 *4 (-551)) + (-12 (-5 *3 (-646 (-2 (|:| -4182 *5) (|:| -4398 (-551))))) (-5 *4 (-551)) (-4 *5 (-1248 *4)) (-5 *2 (-646 *5)) (-5 *1 (-701 *5))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-551)) (-5 *2 (-646 (-2 (|:| -4176 *3) (|:| -4392 *4)))) + (-12 (-5 *4 (-551)) (-5 *2 (-646 (-2 (|:| -4182 *3) (|:| -4398 *4)))) (-5 *1 (-701 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-551)) (-5 *1 (-701 *2)) (-4 *2 (-1248 *3))))) (((*1 *1 *1) (-12 (-4 *1 (-285 *2)) (-4 *2 (-1222)) (-4 *2 (-1107)))) ((*1 *1 *1) (-12 (-4 *1 (-700 *2)) (-4 *2 (-1107))))) (((*1 *2 *1) (-12 (-4 *1 (-700 *3)) (-4 *3 (-1107)) - (-5 *2 (-646 (-2 (|:| -2263 *3) (|:| -2134 (-776)))))))) + (-5 *2 (-646 (-2 (|:| -2264 *3) (|:| -2135 (-776)))))))) (((*1 *2 *3 *4 *5 *5) (-12 (-5 *5 (-776)) (-4 *6 (-1107)) (-4 *7 (-906 *6)) (-5 *2 (-694 *7)) (-5 *1 (-697 *6 *7 *3 *4)) (-4 *3 (-376 *7)) - (-4 *4 (-13 (-376 *6) (-10 -7 (-6 -4437))))))) + (-4 *4 (-13 (-376 *6) (-10 -7 (-6 -4443))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-1272 (-317 (-226)))) (-5 *4 (-646 (-1183))) (-5 *2 (-694 (-317 (-226)))) (-5 *1 (-206)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-4 *6 (-906 *5)) (-5 *2 (-694 *6)) (-5 *1 (-697 *5 *6 *3 *4)) (-4 *3 (-376 *6)) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4437))))))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4443))))))) (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-776)) (-4 *6 (-1107)) (-4 *3 (-906 *6)) (-5 *2 (-694 *3)) (-5 *1 (-697 *6 *3 *7 *4)) (-4 *7 (-376 *3)) - (-4 *4 (-13 (-376 *6) (-10 -7 (-6 -4437))))))) + (-4 *4 (-13 (-376 *6) (-10 -7 (-6 -4443))))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-4 *3 (-906 *5)) (-5 *2 (-694 *3)) (-5 *1 (-697 *5 *3 *6 *4)) (-4 *6 (-376 *3)) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4437))))))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4443))))))) (((*1 *2 *2 *3) (-12 (-4 *4 (-1107)) (-4 *2 (-906 *4)) (-5 *1 (-697 *4 *2 *5 *3)) - (-4 *5 (-376 *2)) (-4 *3 (-13 (-376 *4) (-10 -7 (-6 -4437))))))) + (-4 *5 (-376 *2)) (-4 *3 (-13 (-376 *4) (-10 -7 (-6 -4443))))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-4 *2 (-906 *5)) (-5 *1 (-697 *5 *2 *3 *4)) - (-4 *3 (-376 *2)) (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4437))))))) + (-4 *3 (-376 *2)) (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4443))))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-4 *3 (-906 *5)) (-5 *2 (-1272 *3)) (-5 *1 (-697 *5 *3 *6 *4)) (-4 *6 (-376 *3)) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4437))))))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4443))))))) (((*1 *1 *2) (-12 (-5 *1 (-696 *2)) (-4 *2 (-618 (-868)))))) (((*1 *1) (-12 (-5 *1 (-696 *2)) (-4 *2 (-618 (-868)))))) (((*1 *2 *2 *2 *2 *2 *3) @@ -11423,11 +11423,11 @@ (-4 *8 (-956 *5 *6 *7)) (-4 *5 (-562)) (-4 *6 (-798)) (-5 *2 (-2 (|:| |particular| (-3 (-1272 (-412 *8)) "failed")) - (|:| -2199 (-646 (-1272 (-412 *8)))))) + (|:| -2200 (-646 (-1272 (-412 *8)))))) (-5 *1 (-674 *5 *6 *7 *8))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4438)))) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4438)))) (-5 *2 (-112)) + (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4444)))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4444)))) (-5 *2 (-112)) (-5 *1 (-672 *5 *6 *4 *3)) (-4 *3 (-691 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-694 *5)) (-5 *4 (-1272 *5)) (-4 *5 (-367)) (-5 *2 (-112)) @@ -11462,12 +11462,12 @@ (((*1 *1 *1 *1 *2) (-12 (-5 *2 (-551)) (-4 *1 (-656 *3)) (-4 *3 (-1222)))) ((*1 *1 *2 *1 *3) (-12 (-5 *3 (-551)) (-4 *1 (-656 *2)) (-4 *2 (-1222))))) (((*1 *2 *1) - (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4387 *4)))) + (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4393 *4)))) (-5 *1 (-654 *3 *4 *5)) (-4 *3 (-1107)) (-4 *4 (-23)) (-14 *5 *4)))) (((*1 *1 *2 *3) (-12 (-5 *1 (-654 *2 *3 *4)) (-4 *2 (-1107)) (-4 *3 (-23)) (-14 *4 *3)))) (((*1 *1 *2) - (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4387 *4)))) (-4 *3 (-1107)) + (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4393 *4)))) (-4 *3 (-1107)) (-4 *4 (-23)) (-14 *5 *4) (-5 *1 (-654 *3 *4 *5))))) (((*1 *2 *1 *2) (-12 (-5 *2 (-551)) (-5 *1 (-365 *3)) (-4 *3 (-1107)))) ((*1 *2 *1 *3) @@ -11488,7 +11488,7 @@ ((*1 *1 *1) (-12 (-5 *1 (-654 *2 *3 *4)) (-4 *2 (-1107)) (-4 *3 (-23)) (-14 *4 *3)))) (((*1 *1 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) - ((*1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-376 *2)) (-4 *2 (-1222)))) + ((*1 *1 *1) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-376 *2)) (-4 *2 (-1222)))) ((*1 *1 *1) (-12 (-5 *1 (-654 *2 *3 *4)) (-4 *2 (-1107)) (-4 *3 (-23)) (-14 *4 *3)))) (((*1 *1) @@ -11524,14 +11524,14 @@ (((*1 *1 *1 *1) (-12 (-5 *1 (-646 *2)) (-4 *2 (-1107)) (-4 *2 (-1222))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-694 *1)) (-5 *4 (-1272 *1)) (-4 *1 (-644 *5)) (-4 *5 (-1055)) - (-5 *2 (-2 (|:| -1757 (-694 *5)) (|:| |vec| (-1272 *5)))))) + (-5 *2 (-2 (|:| -1758 (-694 *5)) (|:| |vec| (-1272 *5)))))) ((*1 *2 *3) (-12 (-5 *3 (-694 *1)) (-4 *1 (-644 *4)) (-4 *4 (-1055)) (-5 *2 (-694 *4))))) (((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1272 *4)) (-4 *4 (-644 *5)) (-4 *5 (-367)) (-4 *5 (-562)) (-5 *2 (-1272 *5)) (-5 *1 (-643 *5 *4)))) ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1272 *4)) (-4 *4 (-644 *5)) (-3758 (-4 *5 (-367))) + (|partial| -12 (-5 *3 (-1272 *4)) (-4 *4 (-644 *5)) (-3764 (-4 *5 (-367))) (-4 *5 (-562)) (-5 *2 (-1272 (-412 *5))) (-5 *1 (-643 *5 *4))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-1272 *5)) (-4 *5 (-644 *4)) (-4 *4 (-562)) @@ -11723,7 +11723,7 @@ (|partial| -12 (-5 *5 (-2 (|:| |contp| *3) - (|:| -1963 (-646 (-2 (|:| |irr| *10) (|:| -2570 (-551))))))) + (|:| -1964 (-646 (-2 (|:| |irr| *10) (|:| -2576 (-551))))))) (-5 *6 (-646 *3)) (-5 *7 (-646 *8)) (-4 *8 (-855)) (-4 *3 (-310)) (-4 *10 (-956 *3 *9 *8)) (-4 *9 (-798)) (-5 *2 @@ -11778,11 +11778,11 @@ (-5 *2 (-646 (-2 - (|:| -4304 + (|:| -4310 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) - (|:| -2263 + (|:| -2264 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") @@ -11798,7 +11798,7 @@ (-3 (|:| |str| (-1160 (-226))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1612 + (|:| -1613 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -11813,7 +11813,7 @@ (((*1 *2 *1) (-12 (-4 *1 (-609 *3 *4)) (-4 *3 (-1107)) (-4 *4 (-1222)) (-5 *2 (-646 *3))))) (((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4437)) (-4 *1 (-609 *4 *3)) (-4 *4 (-1107)) + (-12 (|has| *1 (-6 -4443)) (-4 *1 (-609 *4 *3)) (-4 *4 (-1107)) (-4 *3 (-1222)) (-4 *3 (-1107)) (-5 *2 (-112))))) (((*1 *2 *1) (-12 (-4 *1 (-609 *2 *3)) (-4 *3 (-1222)) (-4 *2 (-1107)) (-4 *2 (-855))))) @@ -11823,10 +11823,10 @@ (-12 (-4 *1 (-57 *2 *3 *4)) (-4 *2 (-1222)) (-4 *3 (-376 *2)) (-4 *4 (-376 *2)))) ((*1 *1 *1 *2) - (-12 (|has| *1 (-6 -4438)) (-4 *1 (-609 *3 *2)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4444)) (-4 *1 (-609 *3 *2)) (-4 *3 (-1107)) (-4 *2 (-1222))))) (((*1 *2 *1 *3 *3) - (-12 (|has| *1 (-6 -4438)) (-4 *1 (-609 *3 *4)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4444)) (-4 *1 (-609 *3 *4)) (-4 *3 (-1107)) (-4 *4 (-1222)) (-5 *2 (-1278))))) (((*1 *2 *2 *3 *4) (-12 (-5 *3 (-646 (-616 *2))) (-5 *4 (-646 (-1183))) @@ -11848,6 +11848,8 @@ (((*1 *1) (-5 *1 (-602)))) (((*1 *1) (-5 *1 (-602)))) (((*1 *1) (-5 *1 (-602)))) +(((*1 *1) (-5 *1 (-602)))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-646 (-602))) (-5 *1 (-602))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-1032 (-847 (-551)))) (-5 *3 (-1160 (-2 (|:| |k| (-551)) (|:| |c| *4)))) (-4 *4 (-1055)) @@ -11958,10 +11960,13 @@ (((*1 *2 *2 *3) (|partial| -12 (-5 *3 (-776)) (-5 *1 (-592 *2)) (-4 *2 (-550)))) ((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -3109 *3) (|:| -2576 (-776)))) (-5 *1 (-592 *3)) + (-12 (-5 *2 (-2 (|:| -3115 *3) (|:| -2582 (-776)))) (-5 *1 (-592 *3)) (-4 *3 (-550))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-776)) (-5 *2 (-112)) (-5 *1 (-592 *3)) (-4 *3 (-550))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-511)) (-5 *3 (-602)) (-5 *1 (-591))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-511)) (-5 *3 (-602)) (-5 *1 (-591))))) +(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-511)) (-5 *3 (-602)) (-5 *1 (-591))))) (((*1 *1 *2 *3 *4) (-12 (-5 *3 @@ -12008,11 +12013,11 @@ (((*1 *2 *2 *3) (|partial| -12 (-5 *2 (-628 *4 *5)) (-5 *3 - (-1 (-2 (|:| |ans| *4) (|:| -3553 *4) (|:| |sol?| (-112))) (-551) *4)) + (-1 (-2 (|:| |ans| *4) (|:| -3559 *4) (|:| |sol?| (-112))) (-551) *4)) (-4 *4 (-367)) (-4 *5 (-1248 *4)) (-5 *1 (-579 *4 *5))))) (((*1 *2 *2 *3 *4) (|partial| -12 - (-5 *3 (-1 (-3 (-2 (|:| -2327 *4) (|:| |coeff| *4)) "failed") *4)) + (-5 *3 (-1 (-3 (-2 (|:| -2328 *4) (|:| |coeff| *4)) "failed") *4)) (-4 *4 (-367)) (-5 *1 (-579 *4 *2)) (-4 *2 (-1248 *4))))) (((*1 *2 *3 *4 *5) (|partial| -12 (-5 *4 (-1 *7 *7)) (-5 *5 (-646 (-412 *7))) (-4 *7 (-1248 *6)) @@ -12023,12 +12028,12 @@ (-5 *1 (-579 *6 *7))))) (((*1 *2 *3 *4 *3) (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1248 *5)) (-4 *5 (-367)) - (-5 *2 (-2 (|:| -2327 (-412 *6)) (|:| |coeff| (-412 *6)))) + (-5 *2 (-2 (|:| -2328 (-412 *6)) (|:| |coeff| (-412 *6)))) (-5 *1 (-579 *5 *6)) (-5 *3 (-412 *6))))) (((*1 *2 *3 *4 *5 *6) (|partial| -12 (-5 *4 (-1 *8 *8)) (-5 *5 - (-1 (-2 (|:| |ans| *7) (|:| -3553 *7) (|:| |sol?| (-112))) (-551) *7)) + (-1 (-2 (|:| |ans| *7) (|:| -3559 *7) (|:| |sol?| (-112))) (-551) *7)) (-5 *6 (-646 (-412 *8))) (-4 *7 (-367)) (-4 *8 (-1248 *7)) (-5 *3 (-412 *8)) (-5 *2 (-2 @@ -12039,7 +12044,7 @@ (-5 *1 (-579 *7 *8))))) (((*1 *2 *3 *4 *5 *6) (|partial| -12 (-5 *4 (-1 *8 *8)) - (-5 *5 (-1 (-3 (-2 (|:| -2327 *7) (|:| |coeff| *7)) "failed") *7)) + (-5 *5 (-1 (-3 (-2 (|:| -2328 *7) (|:| |coeff| *7)) "failed") *7)) (-5 *6 (-646 (-412 *8))) (-4 *7 (-367)) (-4 *8 (-1248 *7)) (-5 *3 (-412 *8)) (-5 *2 (-2 @@ -12051,19 +12056,19 @@ (((*1 *2 *3 *4 *5 *3) (-12 (-5 *4 (-1 *7 *7)) (-5 *5 - (-1 (-2 (|:| |ans| *6) (|:| -3553 *6) (|:| |sol?| (-112))) (-551) *6)) + (-1 (-2 (|:| |ans| *6) (|:| -3559 *6) (|:| |sol?| (-112))) (-551) *6)) (-4 *6 (-367)) (-4 *7 (-1248 *6)) (-5 *2 (-3 (-2 (|:| |answer| (-412 *7)) (|:| |a0| *6)) - (-2 (|:| -2327 (-412 *7)) (|:| |coeff| (-412 *7))) "failed")) + (-2 (|:| -2328 (-412 *7)) (|:| |coeff| (-412 *7))) "failed")) (-5 *1 (-579 *6 *7)) (-5 *3 (-412 *7))))) (((*1 *2 *3 *4 *5 *3) (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 (-1 (-3 (-2 (|:| -2327 *6) (|:| |coeff| *6)) "failed") *6)) + (-5 *5 (-1 (-3 (-2 (|:| -2328 *6) (|:| |coeff| *6)) "failed") *6)) (-4 *6 (-367)) (-4 *7 (-1248 *6)) (-5 *2 (-3 (-2 (|:| |answer| (-412 *7)) (|:| |a0| *6)) - (-2 (|:| -2327 (-412 *7)) (|:| |coeff| (-412 *7))) "failed")) + (-2 (|:| -2328 (-412 *7)) (|:| |coeff| (-412 *7))) "failed")) (-5 *1 (-579 *6 *7)) (-5 *3 (-412 *7))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-1 *7 *7)) (-5 *5 (-1 (-3 (-646 *6) "failed") (-551) *6 *6)) @@ -12073,13 +12078,13 @@ (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-1 *7 *7)) (-5 *5 - (-1 (-2 (|:| |ans| *6) (|:| -3553 *6) (|:| |sol?| (-112))) (-551) *6)) + (-1 (-2 (|:| |ans| *6) (|:| -3559 *6) (|:| |sol?| (-112))) (-551) *6)) (-4 *6 (-367)) (-4 *7 (-1248 *6)) (-5 *2 (-2 (|:| |answer| (-588 (-412 *7))) (|:| |a0| *6))) (-5 *1 (-579 *6 *7)) (-5 *3 (-412 *7))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 (-1 (-3 (-2 (|:| -2327 *6) (|:| |coeff| *6)) "failed") *6)) + (-5 *5 (-1 (-3 (-2 (|:| -2328 *6) (|:| |coeff| *6)) "failed") *6)) (-4 *6 (-367)) (-4 *7 (-1248 *6)) (-5 *2 (-2 (|:| |answer| (-588 (-412 *7))) (|:| |a0| *6))) (-5 *1 (-579 *6 *7)) (-5 *3 (-412 *7))))) @@ -12111,7 +12116,7 @@ (-4 *4 (-1107)) (-5 *1 (-578 *4 *5))))) (((*1 *2 *3 *4 *3) (|partial| -12 (-5 *4 (-1183)) (-4 *5 (-13 (-562) (-1044 (-551)) (-147))) - (-5 *2 (-2 (|:| -2327 (-412 (-952 *5))) (|:| |coeff| (-412 (-952 *5))))) + (-5 *2 (-2 (|:| -2328 (-412 (-952 *5))) (|:| |coeff| (-412 (-952 *5))))) (-5 *1 (-575 *5)) (-5 *3 (-412 (-952 *5)))))) (((*1 *2 *3 *4 *5) (|partial| -12 (-5 *4 (-1183)) (-5 *5 (-646 (-412 (-952 *6)))) @@ -12140,7 +12145,7 @@ (-5 *1 (-573 *5 *6))))) (((*1 *2 *3 *3) (|partial| -12 (-4 *4 (-13 (-367) (-147) (-1044 (-551)))) (-4 *5 (-1248 *4)) - (-5 *2 (-2 (|:| -2327 (-412 *5)) (|:| |coeff| (-412 *5)))) + (-5 *2 (-2 (|:| -2328 (-412 *5)) (|:| |coeff| (-412 *5)))) (-5 *1 (-573 *4 *5)) (-5 *3 (-412 *5))))) (((*1 *2 *2) (|partial| -12 (-5 *2 (-412 *4)) (-4 *4 (-1248 *3)) @@ -12162,12 +12167,12 @@ (-4 *3 (-635)) (-4 *3 (-13 (-27) (-1208) (-426 *5)))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-1183)) (-4 *5 (-13 (-1044 (-551)) (-457) (-644 (-551)))) - (-5 *2 (-2 (|:| -2501 *3) (|:| |nconst| *3))) (-5 *1 (-572 *5 *3)) + (-5 *2 (-2 (|:| -2507 *3) (|:| |nconst| *3))) (-5 *1 (-572 *5 *3)) (-4 *3 (-13 (-27) (-1208) (-426 *5)))))) (((*1 *2 *3 *4 *5 *5 *6) (-12 (-5 *5 (-616 *4)) (-5 *6 (-1183)) (-4 *4 (-13 (-426 *7) (-27) (-1208))) (-4 *7 (-13 (-457) (-1044 (-551)) (-147) (-644 (-551)))) - (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2199 (-646 *4)))) + (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2200 (-646 *4)))) (-5 *1 (-571 *7 *4 *3)) (-4 *3 (-663 *4)) (-4 *3 (-1107))))) (((*1 *2 *2 *2 *2 *3 *3 *4) (|partial| -12 (-5 *3 (-616 *2)) (-5 *4 (-1 (-3 *2 "failed") *2 *2 (-1183))) @@ -12185,7 +12190,7 @@ (((*1 *2 *3 *4 *4 *3) (|partial| -12 (-5 *4 (-616 *3)) (-4 *3 (-13 (-426 *5) (-27) (-1208))) (-4 *5 (-13 (-457) (-1044 (-551)) (-147) (-644 (-551)))) - (-5 *2 (-2 (|:| -2327 *3) (|:| |coeff| *3))) (-5 *1 (-571 *5 *3 *6)) + (-5 *2 (-2 (|:| -2328 *3) (|:| |coeff| *3))) (-5 *1 (-571 *5 *3 *6)) (-4 *6 (-1107))))) (((*1 *2 *3 *4 *4) (-12 (-5 *4 (-616 *3)) (-4 *3 (-13 (-426 *5) (-27) (-1208))) @@ -12193,12 +12198,12 @@ (-5 *1 (-571 *5 *3 *6)) (-4 *6 (-1107))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1248 *5)) (-4 *5 (-367)) - (-4 *7 (-1248 (-412 *6))) (-5 *2 (-2 (|:| |answer| *3) (|:| -2326 *3))) + (-4 *7 (-1248 (-412 *6))) (-5 *2 (-2 (|:| |answer| *3) (|:| -2327 *3))) (-5 *1 (-568 *5 *6 *7 *3)) (-4 *3 (-346 *5 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1248 *5)) (-4 *5 (-367)) (-5 *2 - (-2 (|:| |answer| (-412 *6)) (|:| -2326 (-412 *6)) + (-2 (|:| |answer| (-412 *6)) (|:| -2327 (-412 *6)) (|:| |specpart| (-412 *6)) (|:| |polypart| *6))) (-5 *1 (-569 *5 *6)) (-5 *3 (-412 *6))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-551)) (-5 *3 (-776)) (-5 *1 (-567))))) @@ -12218,24 +12223,24 @@ (-12 (-5 *3 (-646 *8)) (-5 *4 (-646 - (-2 (|:| -2199 (-694 *7)) (|:| |basisDen| *7) + (-2 (|:| -2200 (-694 *7)) (|:| |basisDen| *7) (|:| |basisInv| (-694 *7))))) (-5 *5 (-776)) (-4 *8 (-1248 *7)) (-4 *7 (-1248 *6)) (-4 *6 (-354)) (-5 *2 - (-2 (|:| -2199 (-694 *7)) (|:| |basisDen| *7) (|:| |basisInv| (-694 *7)))) + (-2 (|:| -2200 (-694 *7)) (|:| |basisDen| *7) (|:| |basisInv| (-694 *7)))) (-5 *1 (-503 *6 *7 *8)))) ((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-551)) (-5 *1 (-567))))) (((*1 *2 *3 *4 *5 *5 *4 *6) (-12 (-5 *5 (-616 *4)) (-5 *6 (-1177 *4)) (-4 *4 (-13 (-426 *7) (-27) (-1208))) (-4 *7 (-13 (-457) (-1044 (-551)) (-147) (-644 (-551)))) - (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2199 (-646 *4)))) + (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2200 (-646 *4)))) (-5 *1 (-566 *7 *4 *3)) (-4 *3 (-663 *4)) (-4 *3 (-1107)))) ((*1 *2 *3 *4 *5 *5 *5 *4 *6) (-12 (-5 *5 (-616 *4)) (-5 *6 (-412 (-1177 *4))) (-4 *4 (-13 (-426 *7) (-27) (-1208))) (-4 *7 (-13 (-457) (-1044 (-551)) (-147) (-644 (-551)))) - (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2199 (-646 *4)))) + (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2200 (-646 *4)))) (-5 *1 (-566 *7 *4 *3)) (-4 *3 (-663 *4)) (-4 *3 (-1107))))) (((*1 *2 *2 *2 *3 *3 *4 *2 *5) (|partial| -12 (-5 *3 (-616 *2)) @@ -12268,13 +12273,13 @@ (|partial| -12 (-5 *4 (-616 *3)) (-5 *5 (-1177 *3)) (-4 *3 (-13 (-426 *6) (-27) (-1208))) (-4 *6 (-13 (-457) (-1044 (-551)) (-147) (-644 (-551)))) - (-5 *2 (-2 (|:| -2327 *3) (|:| |coeff| *3))) (-5 *1 (-566 *6 *3 *7)) + (-5 *2 (-2 (|:| -2328 *3) (|:| |coeff| *3))) (-5 *1 (-566 *6 *3 *7)) (-4 *7 (-1107)))) ((*1 *2 *3 *4 *4 *3 *4 *3 *5) (|partial| -12 (-5 *4 (-616 *3)) (-5 *5 (-412 (-1177 *3))) (-4 *3 (-13 (-426 *6) (-27) (-1208))) (-4 *6 (-13 (-457) (-1044 (-551)) (-147) (-644 (-551)))) - (-5 *2 (-2 (|:| -2327 *3) (|:| |coeff| *3))) (-5 *1 (-566 *6 *3 *7)) + (-5 *2 (-2 (|:| -2328 *3) (|:| |coeff| *3))) (-5 *1 (-566 *6 *3 *7)) (-4 *7 (-1107))))) (((*1 *2 *3 *4 *4 *3 *5) (-12 (-5 *4 (-616 *3)) (-5 *5 (-1177 *3)) @@ -12290,7 +12295,7 @@ (-12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-2 @@ -12305,7 +12310,7 @@ (|:| |singularitiesStream| (-3 (|:| |str| (-1160 (-226))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1612 + (|:| -1613 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -12316,7 +12321,7 @@ (|partial| -12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-2 @@ -12331,7 +12336,7 @@ (|:| |singularitiesStream| (-3 (|:| |str| (-1160 (-226))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1612 + (|:| -1613 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -12343,11 +12348,11 @@ (-5 *2 (-646 (-2 - (|:| -4304 + (|:| -4310 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) - (|:| -2263 + (|:| -2264 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") @@ -12363,7 +12368,7 @@ (-3 (|:| |str| (-1160 (-226))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1612 + (|:| -1613 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -12379,7 +12384,7 @@ (|partial| -12 (-5 *4 (-1183)) (-5 *6 (-646 (-616 *3))) (-5 *5 (-616 *3)) (-4 *3 (-13 (-27) (-1208) (-426 *7))) (-4 *7 (-13 (-457) (-147) (-1044 (-551)) (-644 (-551)))) - (-5 *2 (-2 (|:| -2327 *3) (|:| |coeff| *3))) (-5 *1 (-563 *7 *3))))) + (-5 *2 (-2 (|:| -2328 *3) (|:| |coeff| *3))) (-5 *1 (-563 *7 *3))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-1183)) (-4 *5 (-13 (-457) (-147) (-1044 (-551)) (-644 (-551)))) (-5 *2 (-588 *3)) (-5 *1 (-563 *5 *3)) @@ -12399,10 +12404,10 @@ (((*1 *2 *3 *4 *3) (|partial| -12 (-5 *4 (-1183)) (-4 *5 (-13 (-457) (-147) (-1044 (-551)) (-644 (-551)))) - (-5 *2 (-2 (|:| -2327 *3) (|:| |coeff| *3))) (-5 *1 (-563 *5 *3)) + (-5 *2 (-2 (|:| -2328 *3) (|:| |coeff| *3))) (-5 *1 (-563 *5 *3)) (-4 *3 (-13 (-27) (-1208) (-426 *5)))))) (((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -1956 *1) (|:| -4424 *1) (|:| |associate| *1))) + (-12 (-5 *2 (-2 (|:| -1957 *1) (|:| -4430 *1) (|:| |associate| *1))) (-4 *1 (-562))))) (((*1 *1 *1) (-4 *1 (-562)))) (((*1 *2 *1 *1) (-12 (-4 *1 (-562)) (-5 *2 (-112))))) @@ -12567,7 +12572,7 @@ (((*1 *2 *3) (-12 (-5 *3 (-1272 *4)) (-4 *4 (-354)) (-5 *2 (-1177 *4)) (-5 *1 (-533 *4))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126)))))) + (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3844 *4) (|:| -2581 (-1126)))))) (-4 *4 (-354)) (-5 *2 (-1278)) (-5 *1 (-533 *4))))) (((*1 *2 *1) (-12 (-4 *1 (-532)) (-5 *2 (-696 (-128)))))) (((*1 *2 *1) (-12 (-4 *1 (-532)) (-5 *2 (-696 (-555)))))) @@ -12710,14 +12715,14 @@ (-12 (-5 *3 (-925)) (-5 *2 (-1278)) (-5 *1 (-215 *4)) (-4 *4 (-13 (-855) - (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 (*2 $)) - (-15 -2152 (*2 $))))))) + (-10 -8 (-15 -4249 ((-1165) $ (-1183))) (-15 -4067 (*2 $)) + (-15 -2153 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-215 *3)) (-4 *3 (-13 (-855) - (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 (*2 $)) - (-15 -2152 (*2 $))))))) + (-10 -8 (-15 -4249 ((-1165) $ (-1183))) (-15 -4067 (*2 $)) + (-15 -2153 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-507))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-1055)) (-4 *7 (-1055)) (-4 *6 (-1248 *5)) @@ -12739,38 +12744,38 @@ (((*1 *2 *2 *2) (-12 (-5 *2 - (-2 (|:| -2199 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) - (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *4 (-1248 *3)) + (-2 (|:| -2200 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) + (-4 *3 (-13 (-310) (-10 -8 (-15 -4419 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *1 (-504 *3 *4 *5)) (-4 *5 (-415 *3 *4))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) + (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4419 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *1 (-504 *3 *4 *5)) (-4 *5 (-415 *3 *4))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) + (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4419 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *1 (-504 *3 *4 *5)) (-4 *5 (-415 *3 *4)))) ((*1 *2 *2 *2 *3) - (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) + (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4419 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *1 (-504 *3 *4 *5)) (-4 *5 (-415 *3 *4))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-776)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) + (-12 (-5 *2 (-776)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4419 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *1 (-504 *3 *4 *5)) (-4 *5 (-415 *3 *4))))) (((*1 *2 *3 *3 *2 *4) (-12 (-5 *3 (-694 *2)) (-5 *4 (-551)) - (-4 *2 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *5 (-1248 *2)) + (-4 *2 (-13 (-310) (-10 -8 (-15 -4419 ((-410 $) $))))) (-4 *5 (-1248 *2)) (-5 *1 (-504 *2 *5 *6)) (-4 *6 (-415 *2 *5))))) (((*1 *2 *3 *2 *4) (-12 (-5 *3 (-694 *2)) (-5 *4 (-776)) - (-4 *2 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *5 (-1248 *2)) + (-4 *2 (-13 (-310) (-10 -8 (-15 -4419 ((-410 $) $))))) (-4 *5 (-1248 *2)) (-5 *1 (-504 *2 *5 *6)) (-4 *6 (-415 *2 *5))))) (((*1 *2 *3 *4 *4) (-12 (-5 *4 (-776)) (-4 *5 (-354)) (-4 *6 (-1248 *5)) (-5 *2 (-646 - (-2 (|:| -2199 (-694 *6)) (|:| |basisDen| *6) + (-2 (|:| -2200 (-694 *6)) (|:| |basisDen| *6) (|:| |basisInv| (-694 *6))))) (-5 *1 (-503 *5 *6 *7)) (-5 *3 - (-2 (|:| -2199 (-694 *6)) (|:| |basisDen| *6) (|:| |basisInv| (-694 *6)))) + (-2 (|:| -2200 (-694 *6)) (|:| |basisDen| *6) (|:| |basisInv| (-694 *6)))) (-4 *7 (-1248 *6))))) (((*1 *2 *1) (-12 @@ -12788,25 +12793,25 @@ (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1222)) (-4 *4 (-376 *3)) (-4 *5 (-376 *3)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4438)) (-4 *1 (-494 *3)) + (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4444)) (-4 *1 (-494 *3)) (-4 *3 (-1222))))) (((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4437)) (-4 *1 (-494 *4)) + (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4443)) (-4 *1 (-494 *4)) (-4 *4 (-1222)) (-5 *2 (-112))))) (((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4437)) (-4 *1 (-494 *4)) + (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4443)) (-4 *1 (-494 *4)) (-4 *4 (-1222)) (-5 *2 (-112))))) (((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4437)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4443)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-4 *3 (-1107)) (-5 *2 (-776)))) ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4437)) (-4 *1 (-494 *4)) + (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4443)) (-4 *1 (-494 *4)) (-4 *4 (-1222)) (-5 *2 (-776))))) (((*1 *2 *1) (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1222)) (-4 *4 (-376 *3)) (-4 *5 (-376 *3)) (-5 *2 (-646 *3)))) ((*1 *2 *1) - (-12 (|has| *1 (-6 -4437)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) + (-12 (|has| *1 (-6 -4443)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-5 *2 (-646 *3))))) (((*1 *1 *2) (-12 (-5 *2 (-412 (-551))) (-5 *1 (-492))))) (((*1 *2 *3) @@ -12824,7 +12829,7 @@ (-4 *4 (-1055)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-646 (-551))) (-14 *3 (-646 (-1183))) (-5 *1 (-459 *3 *4 *5)) - (-4 *4 (-1055)) (-4 *5 (-239 (-4401 *3) (-776))))) + (-4 *4 (-1055)) (-4 *5 (-239 (-4407 *3) (-776))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-646 (-551))) (-5 *1 (-486 *3 *4)) (-14 *3 (-646 (-1183))) (-4 *4 (-1055))))) @@ -12888,33 +12893,33 @@ (-4 *7 (-956 *6 *5 *3)) (-5 *1 (-467 *5 *3 *6 *7 *2)) (-4 *2 (-13 (-1044 (-412 (-551))) (-367) - (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) + (-10 -8 (-15 -4396 ($ *7)) (-15 -3417 (*7 $)) (-15 -3416 (*7 $)))))))) (((*1 *2 *1) (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-14 *6 - (-1 (-112) (-2 (|:| -2575 *5) (|:| -2576 *2)) - (-2 (|:| -2575 *5) (|:| -2576 *2)))) - (-4 *2 (-239 (-4401 *3) (-776))) (-5 *1 (-466 *3 *4 *5 *2 *6 *7)) + (-1 (-112) (-2 (|:| -2581 *5) (|:| -2582 *2)) + (-2 (|:| -2581 *5) (|:| -2582 *2)))) + (-4 *2 (-239 (-4407 *3) (-776))) (-5 *1 (-466 *3 *4 *5 *2 *6 *7)) (-4 *5 (-855)) (-4 *7 (-956 *4 *2 (-869 *3)))))) (((*1 *2 *1) - (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *5 (-239 (-4401 *3) (-776))) + (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *5 (-239 (-4407 *3) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2575 *2) (|:| -2576 *5)) - (-2 (|:| -2575 *2) (|:| -2576 *5)))) + (-1 (-112) (-2 (|:| -2581 *2) (|:| -2582 *5)) + (-2 (|:| -2581 *2) (|:| -2582 *5)))) (-4 *2 (-855)) (-5 *1 (-466 *3 *4 *2 *5 *6 *7)) (-4 *7 (-956 *4 *5 (-869 *3)))))) (((*1 *1 *2 *3 *4) - (-12 (-14 *5 (-646 (-1183))) (-4 *2 (-173)) (-4 *4 (-239 (-4401 *5) (-776))) + (-12 (-14 *5 (-646 (-1183))) (-4 *2 (-173)) (-4 *4 (-239 (-4407 *5) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2575 *3) (|:| -2576 *4)) - (-2 (|:| -2575 *3) (|:| -2576 *4)))) + (-1 (-112) (-2 (|:| -2581 *3) (|:| -2582 *4)) + (-2 (|:| -2581 *3) (|:| -2582 *4)))) (-5 *1 (-466 *5 *2 *3 *4 *6 *7)) (-4 *3 (-855)) (-4 *7 (-956 *2 *4 (-869 *5)))))) (((*1 *1 *2 *3 *1) - (-12 (-14 *4 (-646 (-1183))) (-4 *2 (-173)) (-4 *3 (-239 (-4401 *4) (-776))) + (-12 (-14 *4 (-646 (-1183))) (-4 *2 (-173)) (-4 *3 (-239 (-4407 *4) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2575 *5) (|:| -2576 *3)) - (-2 (|:| -2575 *5) (|:| -2576 *3)))) + (-1 (-112) (-2 (|:| -2581 *5) (|:| -2582 *3)) + (-2 (|:| -2581 *5) (|:| -2582 *3)))) (-5 *1 (-466 *4 *2 *5 *3 *6 *7)) (-4 *5 (-855)) (-4 *7 (-956 *2 *3 (-869 *4)))))) (((*1 *2 *3 *2 *4 *5) @@ -12938,22 +12943,22 @@ (-5 *1 (-460 *5 *3))))) (((*1 *2) (|partial| -12 (-4 *3 (-562)) (-4 *3 (-173)) - (-5 *2 (-2 (|:| |particular| *1) (|:| -2199 (-646 *1)))) (-4 *1 (-371 *3)))) + (-5 *2 (-2 (|:| |particular| *1) (|:| -2200 (-646 *1)))) (-4 *1 (-371 *3)))) ((*1 *2) (|partial| -12 (-5 *2 (-2 (|:| |particular| (-458 *3 *4 *5 *6)) - (|:| -2199 (-646 (-458 *3 *4 *5 *6))))) + (|:| -2200 (-646 (-458 *3 *4 *5 *6))))) (-5 *1 (-458 *3 *4 *5 *6)) (-4 *3 (-173)) (-14 *4 (-925)) (-14 *5 (-646 (-1183))) (-14 *6 (-1272 (-694 *3)))))) (((*1 *2) (|partial| -12 (-4 *3 (-562)) (-4 *3 (-173)) - (-5 *2 (-2 (|:| |particular| *1) (|:| -2199 (-646 *1)))) (-4 *1 (-371 *3)))) + (-5 *2 (-2 (|:| |particular| *1) (|:| -2200 (-646 *1)))) (-4 *1 (-371 *3)))) ((*1 *2) (|partial| -12 (-5 *2 (-2 (|:| |particular| (-458 *3 *4 *5 *6)) - (|:| -2199 (-646 (-458 *3 *4 *5 *6))))) + (|:| -2200 (-646 (-458 *3 *4 *5 *6))))) (-5 *1 (-458 *3 *4 *5 *6)) (-4 *3 (-173)) (-14 *4 (-925)) (-14 *5 (-646 (-1183))) (-14 *6 (-1272 (-694 *3)))))) (((*1 *1 *2 *3) @@ -13058,7 +13063,7 @@ (-12 (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-5 *2 (-776)) (-5 *1 (-455 *4 *5 *6 *3)) (-4 *3 (-956 *4 *5 *6))))) (((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-2 (|:| |totdeg| (-776)) (|:| -2191 *4))) (-5 *5 (-776)) + (-12 (-5 *3 (-2 (|:| |totdeg| (-776)) (|:| -2192 *4))) (-5 *5 (-776)) (-4 *4 (-956 *6 *7 *8)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-5 *2 (-2 (|:| |lcmfij| *7) (|:| |totdeg| *5) (|:| |poli| *4) (|:| |polj| *4))) @@ -13115,7 +13120,7 @@ (-4 *5 (-798)) (-4 *2 (-956 *4 *5 *6)) (-5 *1 (-455 *4 *5 *6 *2)) (-4 *4 (-457)) (-4 *6 (-855))))) (((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-646 (-2 (|:| |totdeg| (-776)) (|:| -2191 *3)))) (-5 *4 (-776)) + (-12 (-5 *2 (-646 (-2 (|:| |totdeg| (-776)) (|:| -2192 *3)))) (-5 *4 (-776)) (-4 *3 (-956 *5 *6 *7)) (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) (-5 *1 (-455 *5 *6 *7 *3))))) (((*1 *2 *2) @@ -13243,7 +13248,7 @@ (-12 (-5 *3 (-925)) (-5 *4 (-410 *2)) (-4 *2 (-1248 *5)) (-5 *1 (-449 *5 *2)) (-4 *5 (-1055))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -4176 *4) (|:| -4392 (-551))))) + (-12 (-5 *3 (-646 (-2 (|:| -4182 *4) (|:| -4398 (-551))))) (-4 *4 (-1248 (-551))) (-5 *2 (-741 (-776))) (-5 *1 (-447 *4)))) ((*1 *2 *3) (-12 (-5 *3 (-410 *5)) (-4 *5 (-1248 *4)) (-4 *4 (-1055)) @@ -13279,7 +13284,7 @@ (-12 (-5 *4 (-112)) (-5 *5 (-1103 (-776))) (-5 *6 (-776)) (-5 *2 (-2 (|:| |contp| (-551)) - (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2570 (-551))))))) + (|:| -1964 (-646 (-2 (|:| |irr| *3) (|:| -2576 (-551))))))) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) @@ -13289,11 +13294,11 @@ (((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -2990 (-551)) (|:| -1963 (-646 *3)))) (-5 *1 (-447 *3)) + (-12 (-5 *2 (-2 (|:| -2996 (-551)) (|:| -1964 (-646 *3)))) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2 *1) (-12 (-5 *2 (-776)) (-5 *1 (-410 *3)) (-4 *3 (-562)))) ((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -4176 *4) (|:| -4392 (-551))))) + (-12 (-5 *3 (-646 (-2 (|:| -4182 *4) (|:| -4398 (-551))))) (-4 *4 (-1248 (-551))) (-5 *2 (-776)) (-5 *1 (-447 *4))))) (((*1 *2) (-12 (-5 *2 (-925)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *2) (-12 (-5 *2 (-925)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) @@ -13310,7 +13315,7 @@ (-12 (-5 *3 (-2 (|:| |contp| (-551)) - (|:| -1963 (-646 (-2 (|:| |irr| *4) (|:| -2570 (-551))))))) + (|:| -1964 (-646 (-2 (|:| |irr| *4) (|:| -2576 (-551))))))) (-4 *4 (-1248 (-551))) (-5 *2 (-410 *4)) (-5 *1 (-447 *4))))) (((*1 *2 *2) (-12 (-5 *2 (-393)) (-5 *1 (-442)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-393)) (-5 *1 (-442))))) @@ -13318,7 +13323,7 @@ (((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-1278)) (-5 *1 (-442))))) (((*1 *2) (-12 (-5 *2 (-1278)) (-5 *1 (-442))))) (((*1 *2 *1) - (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4354 "void"))) (-5 *1 (-441))))) + (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4360 "void"))) (-5 *1 (-441))))) (((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-441))))) (((*1 *1) (-5 *1 (-441)))) (((*1 *1) (-5 *1 (-441)))) @@ -13335,7 +13340,7 @@ (-12 (-4 *4 (-13 (-562) (-1044 (-551)))) (-4 *5 (-426 *4)) (-5 *2 (-3 (|:| |overq| (-1177 (-412 (-551)))) (|:| |overan| (-1177 (-48))) - (|:| -3053 (-112)))) + (|:| -3059 (-112)))) (-5 *1 (-440 *4 *5 *3)) (-4 *3 (-1248 *5))))) (((*1 *2 *3) (|partial| -12 (-4 *4 (-13 (-562) (-1044 (-551)))) (-4 *5 (-426 *4)) @@ -13378,19 +13383,19 @@ (-14 *4 (-1183)) (-14 *5 *2))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-457) (-1044 (-551)) (-644 (-551)))) - (-4 *2 (-13 (-27) (-1208) (-426 *3) (-10 -8 (-15 -4390 ($ *4))))) + (-4 *2 (-13 (-27) (-1208) (-426 *3) (-10 -8 (-15 -4396 ($ *4))))) (-4 *4 (-853)) (-4 *5 (-13 (-1251 *2 *4) (-367) (-1208) - (-10 -8 (-15 -4254 ($ $)) (-15 -4256 ($ $))))) + (-10 -8 (-15 -4260 ($ $)) (-15 -4262 ($ $))))) (-5 *1 (-429 *3 *2 *4 *5 *6 *7)) (-4 *6 (-989 *5)) (-14 *7 (-1183))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-112)) (-4 *6 (-13 (-457) (-1044 (-551)) (-644 (-551)))) - (-4 *3 (-13 (-27) (-1208) (-426 *6) (-10 -8 (-15 -4390 ($ *7))))) + (-4 *3 (-13 (-27) (-1208) (-426 *6) (-10 -8 (-15 -4396 ($ *7))))) (-4 *7 (-853)) (-4 *8 (-13 (-1251 *3 *7) (-367) (-1208) - (-10 -8 (-15 -4254 ($ $)) (-15 -4256 ($ $))))) + (-10 -8 (-15 -4260 ($ $)) (-15 -4262 ($ $))))) (-5 *2 (-3 (|:| |%series| *8) (|:| |%problem| (-2 (|:| |func| (-1165)) (|:| |prob| (-1165)))))) @@ -13398,11 +13403,11 @@ (-14 *10 (-1183))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-112)) (-4 *6 (-13 (-457) (-1044 (-551)) (-644 (-551)))) - (-4 *3 (-13 (-27) (-1208) (-426 *6) (-10 -8 (-15 -4390 ($ *7))))) + (-4 *3 (-13 (-27) (-1208) (-426 *6) (-10 -8 (-15 -4396 ($ *7))))) (-4 *7 (-853)) (-4 *8 (-13 (-1251 *3 *7) (-367) (-1208) - (-10 -8 (-15 -4254 ($ $)) (-15 -4256 ($ $))))) + (-10 -8 (-15 -4260 ($ $)) (-15 -4262 ($ $))))) (-5 *2 (-3 (|:| |%series| *8) (|:| |%problem| (-2 (|:| |func| (-1165)) (|:| |prob| (-1165)))))) @@ -13429,7 +13434,7 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1183)) (-4 *1 (-426 *3)) (-4 *3 (-1107))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1107)) - (-5 *2 (-2 (|:| -4398 (-551)) (|:| |var| (-616 *1)))) (-4 *1 (-426 *3))))) + (-5 *2 (-2 (|:| -4404 (-551)) (|:| |var| (-616 *1)))) (-4 *1 (-426 *3))))) (((*1 *2 *2 *2) (-12 (-5 *2 (-410 *3)) (-4 *3 (-562)) (-5 *1 (-424 *3))))) (((*1 *1 *2) (-12 (-5 *2 (-1272 *3)) (-4 *3 (-367)) (-4 *1 (-332 *3)))) ((*1 *1 *2 *3) @@ -13500,13 +13505,13 @@ (-5 *2 (-694 *3))))) (((*1 *1 *2 *3) (-12 (-5 *3 (-551)) (-5 *1 (-410 *2)) (-4 *2 (-562))))) (((*1 *2 *1) - (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4387 (-551))))) (-5 *1 (-365 *3)) + (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4393 (-551))))) (-5 *1 (-365 *3)) (-4 *3 (-1107)))) ((*1 *2 *1) (-12 (-4 *1 (-390 *3)) (-4 *3 (-1107)) - (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4387 (-776))))))) + (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4393 (-776))))))) ((*1 *2 *1) - (-12 (-5 *2 (-646 (-2 (|:| -4176 *3) (|:| -2576 (-551))))) (-5 *1 (-410 *3)) + (-12 (-5 *2 (-646 (-2 (|:| -4182 *3) (|:| -2582 (-551))))) (-5 *1 (-410 *3)) (-4 *3 (-562))))) (((*1 *1 *2 *3) (-12 (-5 *3 (-551)) (-5 *1 (-410 *2)) (-4 *2 (-562))))) (((*1 *2 *1 *2) (-12 (-5 *2 (-551)) (-5 *1 (-410 *3)) (-4 *3 (-562))))) @@ -13523,12 +13528,12 @@ ((*1 *2 *1) (-12 (-5 *1 (-410 *2)) (-4 *2 (-562))))) (((*1 *1 *1) (-12 (-5 *1 (-410 *2)) (-4 *2 (-562))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-776)) (-5 *3 (-112)) (-5 *1 (-110)))) - ((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4428)) (-4 *1 (-409)))) + ((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4434)) (-4 *1 (-409)))) ((*1 *2) (-12 (-4 *1 (-409)) (-5 *2 (-925))))) (((*1 *2 *3) - (-12 (-5 *3 (-551)) (|has| *1 (-6 -4428)) (-4 *1 (-409)) (-5 *2 (-925))))) + (-12 (-5 *3 (-551)) (|has| *1 (-6 -4434)) (-4 *1 (-409)) (-5 *2 (-925))))) (((*1 *2 *3) - (-12 (-5 *3 (-551)) (|has| *1 (-6 -4428)) (-4 *1 (-409)) (-5 *2 (-925))))) + (-12 (-5 *3 (-551)) (|has| *1 (-6 -4434)) (-4 *1 (-409)) (-5 *2 (-925))))) (((*1 *2 *1) (-12 (-4 *1 (-354)) (-5 *2 (-776)))) ((*1 *2 *1 *1) (|partial| -12 (-4 *1 (-407)) (-5 *2 (-776))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-407)) (-5 *2 (-776)))) @@ -13540,7 +13545,7 @@ (-12 (-4 *2 (-1248 *3)) (-5 *1 (-404 *3 *2)) (-4 *3 (-13 (-367) (-147)))))) (((*1 *2 *1) (-12 (-4 *3 (-13 (-367) (-147))) - (-5 *2 (-646 (-2 (|:| -2576 (-776)) (|:| -4216 *4) (|:| |num| *4)))) + (-5 *2 (-646 (-2 (|:| -2582 (-776)) (|:| -4222 *4) (|:| |num| *4)))) (-5 *1 (-404 *3 *4)) (-4 *4 (-1248 *3))))) (((*1 *2 *2) (-12 (-5 *2 (-646 (-1165))) (-5 *1 (-400))))) (((*1 *2 *3 *4 *5 *6) @@ -13633,13 +13638,13 @@ (((*1 *2 *3) (-12 (-5 *3 (-776)) (-5 *2 (-1278)) (-5 *1 (-382))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1222)) (-5 *1 (-379 *4 *2)) - (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4438))))))) + (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4444))))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1222)) (-5 *1 (-379 *4 *2)) - (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4438))))))) + (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4444))))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1222)) (-5 *1 (-379 *4 *2)) - (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4438))))))) + (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4444))))))) (((*1 *1 *2) (-12 (-5 *2 (-677 *3)) (-4 *3 (-855)) (-4 *1 (-378 *3 *4)) (-4 *4 (-173))))) (((*1 *2 *1) @@ -13648,11 +13653,11 @@ (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *1 (-376 *4)) (-4 *4 (-1222)) (-5 *2 (-112))))) (((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-551)) (|has| *1 (-6 -4438)) (-4 *1 (-376 *3)) (-4 *3 (-1222))))) + (-12 (-5 *2 (-551)) (|has| *1 (-6 -4444)) (-4 *1 (-376 *3)) (-4 *3 (-1222))))) (((*1 *1 *1) - (-12 (|has| *1 (-6 -4438)) (-4 *1 (-376 *2)) (-4 *2 (-1222)) (-4 *2 (-855)))) + (-12 (|has| *1 (-6 -4444)) (-4 *1 (-376 *2)) (-4 *2 (-1222)) (-4 *2 (-855)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3 *3)) (|has| *1 (-6 -4438)) (-4 *1 (-376 *3)) + (-12 (-5 *2 (-1 (-112) *3 *3)) (|has| *1 (-6 -4444)) (-4 *1 (-376 *3)) (-4 *3 (-1222))))) (((*1 *2) (-12 (-4 *3 (-173)) (-5 *2 (-1272 *1)) (-4 *1 (-371 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-371 *2)) (-4 *2 (-173))))) @@ -13731,8 +13736,8 @@ (-12 (-5 *3 (-1177 *4)) (-4 *4 (-354)) (-4 *2 (-13 (-407) - (-10 -7 (-15 -4390 (*2 *4)) (-15 -2197 ((-925) *2)) - (-15 -2199 ((-1272 *2) (-925))) (-15 -4372 (*2 *2))))) + (-10 -7 (-15 -4396 (*2 *4)) (-15 -2198 ((-925) *2)) + (-15 -2200 ((-1272 *2) (-925))) (-15 -4378 (*2 *2))))) (-5 *1 (-361 *2 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-354)) (-5 *2 (-964 (-1177 *4))) (-5 *1 (-360 *4)) @@ -13765,13 +13770,13 @@ ((*1 *2 *3) (-12 (-5 *3 (-1177 *4)) (-4 *4 (-354)) (-5 *2 (-112)) (-5 *1 (-360 *4))))) (((*1 *2) - (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3838 (-912 *3)) (|:| -2575 (-1126)))))) + (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3844 (-912 *3)) (|:| -2581 (-1126)))))) (-5 *1 (-356 *3 *4)) (-14 *3 (-925)) (-14 *4 (-925)))) ((*1 *2) - (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3838 *3) (|:| -2575 (-1126)))))) + (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3844 *3) (|:| -2581 (-1126)))))) (-5 *1 (-357 *3 *4)) (-4 *3 (-354)) (-14 *4 (-3 (-1177 *3) *2)))) ((*1 *2) - (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3838 *3) (|:| -2575 (-1126)))))) + (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3844 *3) (|:| -2581 (-1126)))))) (-5 *1 (-358 *3 *4)) (-4 *3 (-354)) (-14 *4 (-925))))) (((*1 *2) (-12 (-5 *2 (-694 (-912 *3))) (-5 *1 (-356 *3 *4)) (-14 *3 (-925)) @@ -13779,23 +13784,23 @@ ((*1 *2) (-12 (-5 *2 (-694 *3)) (-5 *1 (-357 *3 *4)) (-4 *3 (-354)) (-14 *4 - (-3 (-1177 *3) (-1272 (-646 (-2 (|:| -3838 *3) (|:| -2575 (-1126))))))))) + (-3 (-1177 *3) (-1272 (-646 (-2 (|:| -3844 *3) (|:| -2581 (-1126))))))))) ((*1 *2) (-12 (-5 *2 (-694 *3)) (-5 *1 (-358 *3 *4)) (-4 *3 (-354)) (-14 *4 (-925))))) (((*1 *2 *3) - (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126)))))) + (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3844 *4) (|:| -2581 (-1126)))))) (-4 *4 (-354)) (-5 *2 (-776)) (-5 *1 (-351 *4)))) ((*1 *2) (-12 (-5 *2 (-776)) (-5 *1 (-356 *3 *4)) (-14 *3 (-925)) (-14 *4 (-925)))) ((*1 *2) (-12 (-5 *2 (-776)) (-5 *1 (-357 *3 *4)) (-4 *3 (-354)) (-14 *4 - (-3 (-1177 *3) (-1272 (-646 (-2 (|:| -3838 *3) (|:| -2575 (-1126))))))))) + (-3 (-1177 *3) (-1272 (-646 (-2 (|:| -3844 *3) (|:| -2581 (-1126))))))))) ((*1 *2) (-12 (-5 *2 (-776)) (-5 *1 (-358 *3 *4)) (-4 *3 (-354)) (-14 *4 (-925))))) (((*1 *2) (-12 (-4 *1 (-354)) - (-5 *2 (-646 (-2 (|:| -4176 (-551)) (|:| -2576 (-551)))))))) + (-5 *2 (-646 (-2 (|:| -4182 (-551)) (|:| -2582 (-551)))))))) (((*1 *2 *3) (-12 (-4 *1 (-354)) (-5 *3 (-551)) (-5 *2 (-1195 (-925) (-776)))))) (((*1 *1) (-4 *1 (-354)))) (((*1 *2) @@ -13803,18 +13808,18 @@ (((*1 *2 *3) (-12 (-5 *3 (-925)) (-5 *2 - (-3 (-1177 *4) (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126))))))) + (-3 (-1177 *4) (-1272 (-646 (-2 (|:| -3844 *4) (|:| -2581 (-1126))))))) (-5 *1 (-351 *4)) (-4 *4 (-354))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-925)) - (-5 *2 (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126)))))) + (-5 *2 (-1272 (-646 (-2 (|:| -3844 *4) (|:| -2581 (-1126)))))) (-5 *1 (-351 *4)) (-4 *4 (-354))))) (((*1 *2 *3) - (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126)))))) + (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3844 *4) (|:| -2581 (-1126)))))) (-4 *4 (-354)) (-5 *2 (-694 *4)) (-5 *1 (-351 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-1177 *4)) (-4 *4 (-354)) - (-5 *2 (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126)))))) + (-5 *2 (-1272 (-646 (-2 (|:| -3844 *4) (|:| -2581 (-1126)))))) (-5 *1 (-351 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-1177 *4)) (-4 *4 (-354)) (-5 *2 (-964 (-1126))) @@ -14043,7 +14048,7 @@ (-3 (|:| |nullBranch| "null") (|:| |assignmentBranch| (-2 (|:| |var| (-1183)) (|:| |arrayIndex| (-646 (-952 (-551)))) - (|:| |rand| (-2 (|:| |ints2Floats?| (-112)) (|:| -3686 (-868)))))) + (|:| |rand| (-2 (|:| |ints2Floats?| (-112)) (|:| -3692 (-868)))))) (|:| |arrayAssignmentBranch| (-2 (|:| |var| (-1183)) (|:| |rand| (-868)) (|:| |ints2Floats?| (-112)))) @@ -14051,17 +14056,17 @@ (-2 (|:| |switch| (-1182)) (|:| |thenClause| (-333)) (|:| |elseClause| (-333)))) (|:| |returnBranch| - (-2 (|:| -3839 (-112)) - (|:| -3838 (-2 (|:| |ints2Floats?| (-112)) (|:| -3686 (-868)))))) + (-2 (|:| -3845 (-112)) + (|:| -3844 (-2 (|:| |ints2Floats?| (-112)) (|:| -3692 (-868)))))) (|:| |blockBranch| (-646 (-333))) (|:| |commentBranch| (-646 (-1165))) (|:| |callBranch| (-1165)) (|:| |forBranch| - (-2 (|:| -1612 (-1098 (-952 (-551)))) (|:| |span| (-952 (-551))) - (|:| -3665 (-333)))) + (-2 (|:| -1613 (-1098 (-952 (-551)))) (|:| |span| (-952 (-551))) + (|:| -3671 (-333)))) (|:| |labelBranch| (-1126)) - (|:| |loopBranch| (-2 (|:| |switch| (-1182)) (|:| -3665 (-333)))) + (|:| |loopBranch| (-2 (|:| |switch| (-1182)) (|:| -3671 (-333)))) (|:| |commonBranch| - (-2 (|:| -3985 (-1183)) (|:| |contents| (-646 (-1183))))) + (-2 (|:| -3991 (-1183)) (|:| |contents| (-646 (-1183))))) (|:| |printBranch| (-646 (-868))))) (-5 *1 (-333))))) (((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-333))))) @@ -14167,7 +14172,7 @@ (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1))) (-4 *1 (-310)))) ((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2584 *1))) + (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2590 *1))) (-4 *1 (-310))))) (((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-646 *1)) (-4 *1 (-310))))) (((*1 *2 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-853)) (-5 *1 (-307 *3))))) @@ -14200,7 +14205,7 @@ (|:| |singularitiesStream| (-3 (|:| |str| (-1160 (-226))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1612 + (|:| -1613 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -14210,13 +14215,13 @@ (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) + (-2 (|:| -3089 (-382)) (|:| -3991 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *2 (-1041)) (-5 *1 (-306)))) ((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) + (-2 (|:| -3089 (-382)) (|:| -3991 (-1165)) (|:| |explanations| (-646 (-1165))) (|:| |extra| (-1041)))) (-5 *2 (-1041)) (-5 *1 (-306))))) (((*1 *2 *3) (-12 (-5 *3 (-382)) (-5 *2 (-1165)) (-5 *1 (-306))))) @@ -14246,7 +14251,7 @@ (((*1 *2 *3) (-12 (-5 *3 (-646 (-226))) (-5 *2 (-1272 (-704))) (-5 *1 (-306))))) (((*1 *2 *3) (-12 (-5 *3 (-226)) (-5 *2 (-704)) (-5 *1 (-306))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) + (-12 (-5 *3 (-646 (-2 (|:| -3560 (-412 (-551))) (|:| -3559 (-412 (-551)))))) (-5 *2 (-646 (-226))) (-5 *1 (-306))))) (((*1 *2 *2) (-12 (-5 *2 (-1095 (-847 (-226)))) (-5 *1 (-306))))) (((*1 *2 *3) @@ -14258,7 +14263,7 @@ (|:| |exponentiations| (-551)) (|:| |functionCalls| (-551)))) (-5 *1 (-306))))) (((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))) + (-12 (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3887 (-646 (-226))))) (-5 *2 (-382)) (-5 *1 (-269)))) ((*1 *2 *3) (-12 (-5 *3 (-1272 (-317 (-226)))) (-5 *2 (-382)) (-5 *1 (-306))))) (((*1 *2 *3) (-12 (-5 *3 (-317 (-226))) (-5 *2 (-226)) (-5 *1 (-306))))) @@ -14277,7 +14282,7 @@ (-12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-1160 (-226))) (-5 *1 (-193)))) ((*1 *2 *3 *4 *5) @@ -14306,7 +14311,7 @@ (-12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-112)) (-5 *1 (-304))))) (((*1 *1 *1 *1) (-12 (-5 *1 (-296 *2)) (-4 *2 (-301)) (-4 *2 (-1222)))) @@ -14387,7 +14392,7 @@ (-12 (-5 *3 (-551)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1222)) (-4 *4 (-376 *2)) (-4 *5 (-376 *2)))) ((*1 *2 *1 *3 *2) - (-12 (|has| *1 (-6 -4438)) (-4 *1 (-291 *3 *2)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4444)) (-4 *1 (-291 *3 *2)) (-4 *3 (-1107)) (-4 *2 (-1222))))) (((*1 *2 *3 *4) (-12 (-4 *4 (-367)) (-5 *2 (-646 (-1160 *4))) (-5 *1 (-288 *4 *5)) @@ -14398,7 +14403,7 @@ (((*1 *1 *1 *2) (-12 (-5 *2 (-1239 (-551))) (-4 *1 (-285 *3)) (-4 *3 (-1222)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-551)) (-4 *1 (-285 *3)) (-4 *3 (-1222))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4437)) (-4 *1 (-236 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4443)) (-4 *1 (-236 *3)) (-4 *3 (-1107)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-285 *3)) (-4 *3 (-1222))))) (((*1 *1 *2 *3 *4) @@ -14501,11 +14506,11 @@ (-5 *3 (-3 (|:| |noa| - (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3887 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (|:| |lsa| - (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))))) + (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3887 (-646 (-226))))))) (-5 *2 (-646 (-1165))) (-5 *1 (-269))))) (((*1 *2 *3 *2) (-12 (-5 *2 (-1041)) (-5 *3 (-1183)) (-5 *1 (-269))))) (((*1 *2 *3) (-12 (-5 *3 (-317 (-226))) (-5 *2 (-112)) (-5 *1 (-269))))) @@ -14520,7 +14525,7 @@ (((*1 *2 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3887 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (-5 *1 (-269))))) @@ -14800,8 +14805,8 @@ (((*1 *1 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-855)) (-5 *1 (-246 *3))))) (((*1 *1 *1) (-12 (-4 *1 (-245 *2)) (-4 *2 (-1222))))) (((*1 *1 *1) (-12 (-4 *1 (-245 *2)) (-4 *2 (-1222))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-245 *2)) (-4 *2 (-1222))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-245 *2)) (-4 *2 (-1222))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-245 *2)) (-4 *2 (-1222))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-245 *2)) (-4 *2 (-1222))))) (((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-551)) (-5 *1 (-242)))) ((*1 *2 *3) (-12 (-5 *3 (-646 (-1165))) (-5 *2 (-551)) (-5 *1 (-242))))) (((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-1278)) (-5 *1 (-242)))) @@ -14873,13 +14878,13 @@ (((*1 *2 *2 *3 *2) (-12 (-5 *3 (-776)) (-4 *4 (-354)) (-5 *1 (-217 *4 *2)) (-4 *2 (-1248 *4))))) (((*1 *2 *3) - (-12 (-4 *4 (-354)) (-5 *2 (-646 (-2 (|:| |deg| (-776)) (|:| -2987 *3)))) + (-12 (-4 *4 (-354)) (-5 *2 (-646 (-2 (|:| |deg| (-776)) (|:| -2993 *3)))) (-5 *1 (-217 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-112)) (-4 *5 (-354)) (-5 *2 (-2 (|:| |cont| *5) - (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2570 (-551))))))) + (|:| -1964 (-646 (-2 (|:| |irr| *3) (|:| -2576 (-551))))))) (-5 *1 (-217 *5 *3)) (-4 *3 (-1248 *5))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-1 *2 *2)) (-4 *5 (-367)) (-4 *6 (-1248 (-412 *2))) @@ -14954,36 +14959,36 @@ (-12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-551)) (-5 *1 (-205))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-646 (-226))) (-5 *1 (-205))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) - (-5 *2 (-2 (|:| -2914 (-113)) (|:| |w| (-226)))) (-5 *1 (-205))))) + (-5 *2 (-2 (|:| -2920 (-113)) (|:| |w| (-226)))) (-5 *1 (-205))))) (((*1 *2 *3 *3 *2) (-12 (-5 *2 (-1041)) (-5 *3 (-1183)) (-5 *1 (-193))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-382)) (-5 *1 (-193))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-3 (|:| |continuous| "Continuous at the end points") @@ -14996,7 +15001,7 @@ (-12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) - (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) + (|:| -1613 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-3 (|:| |finite| "The range is finite") @@ -15039,7 +15044,7 @@ (|partial| -12 (-4 *3 (-1222)) (-5 *1 (-183 *3 *2)) (-4 *2 (-679 *3))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-367) (-853))) - (-5 *2 (-2 (|:| |start| *3) (|:| -1963 (-410 *3)))) (-5 *1 (-182 *4 *3)) + (-5 *2 (-2 (|:| |start| *3) (|:| -1964 (-410 *3)))) (-5 *1 (-182 *4 *3)) (-4 *3 (-1248 (-169 *4)))))) (((*1 *2 *2) (-12 (-4 *2 (-13 (-367) (-853))) (-5 *1 (-182 *2 *3)) @@ -15067,11 +15072,11 @@ (-4 *2 (-1248 (-169 *3)))))) (((*1 *2 *3 *3 *4) (-12 (-5 *4 (-112)) (-4 *5 (-13 (-367) (-853))) - (-5 *2 (-646 (-2 (|:| -1963 (-646 *3)) (|:| -1713 *5)))) + (-5 *2 (-646 (-2 (|:| -1964 (-646 *3)) (|:| -1714 *5)))) (-5 *1 (-182 *5 *3)) (-4 *3 (-1248 (-169 *5))))) ((*1 *2 *3 *3) (-12 (-4 *4 (-13 (-367) (-853))) - (-5 *2 (-646 (-2 (|:| -1963 (-646 *3)) (|:| -1713 *4)))) + (-5 *2 (-646 (-2 (|:| -1964 (-646 *3)) (|:| -1714 *4)))) (-5 *1 (-182 *4 *3)) (-4 *3 (-1248 (-169 *4)))))) (((*1 *2 *3 *4) (-12 (-5 *2 (-646 (-169 *4))) (-5 *1 (-155 *3 *4)) @@ -15141,6 +15146,7 @@ (((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-172))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-1141)) (-5 *3 (-294)) (-5 *1 (-168))))) (((*1 *2 *3) (-12 (-5 *3 (-1141)) (-5 *2 (-696 (-283))) (-5 *1 (-168))))) +(((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-646 (-696 (-283)))) (-5 *1 (-168))))) (((*1 *1) (-12 (-4 *1 (-166 *2)) (-4 *2 (-173))))) (((*1 *1 *2 *2) (-12 (-4 *1 (-166 *2)) (-4 *2 (-173))))) (((*1 *2 *1) @@ -15214,7 +15220,7 @@ (((*1 *2 *3 *1) (|partial| -12 (-5 *3 (-1 (-112) *2)) (-4 *1 (-151 *2)) (-4 *2 (-1222))))) (((*1 *1 *1) - (-12 (|has| *1 (-6 -4437)) (-4 *1 (-151 *2)) (-4 *2 (-1222)) + (-12 (|has| *1 (-6 -4443)) (-4 *1 (-151 *2)) (-4 *2 (-1222)) (-4 *2 (-1107))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-1227)) (-4 *5 (-1248 *4)) @@ -15227,7 +15233,7 @@ (-4 *3 (-1248 (-412 *4)))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-412 *6)) (-4 *5 (-1227)) (-4 *6 (-1248 *5)) - (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *3) (|:| |radicand| *6))) + (-5 *2 (-2 (|:| -2582 (-776)) (|:| -4404 *3) (|:| |radicand| *6))) (-5 *1 (-148 *5 *6 *7)) (-5 *4 (-776)) (-4 *7 (-1248 *3))))) (((*1 *2 *3) (|partial| -12 (-4 *4 (-1227)) (-4 *5 (-1248 *4)) @@ -15235,7 +15241,7 @@ (-5 *1 (-148 *4 *5 *3)) (-4 *3 (-1248 (-412 *5)))))) (((*1 *2 *3) (-12 (-4 *4 (-1227)) (-4 *5 (-1248 *4)) - (-5 *2 (-2 (|:| -4398 (-412 *5)) (|:| |poly| *3))) (-5 *1 (-148 *4 *5 *3)) + (-5 *2 (-2 (|:| -4404 (-412 *5)) (|:| |poly| *3))) (-5 *1 (-148 *4 *5 *3)) (-4 *3 (-1248 (-412 *5)))))) (((*1 *2 *1) (-12 (-5 *2 (-776)) (-5 *1 (-144))))) (((*1 *1 *2) (-12 (-5 *2 (-1165)) (-5 *1 (-144)))) @@ -15295,8 +15301,8 @@ ((*1 *2 *2) (-12 (-5 *2 (-776)) (-5 *1 (-120 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2 *3) (-12 (-5 *2 (-112)) (-5 *1 (-120 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *3 *2) (-12 (-5 *2 (-112)) (-5 *1 (-120 *3)) (-4 *3 (-1248 (-551)))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-119 *2)) (-4 *2 (-1222))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-119 *2)) (-4 *2 (-1222))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-119 *2)) (-4 *2 (-1222))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4444)) (-4 *1 (-119 *2)) (-4 *2 (-1222))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-367) (-1044 (-412 *2)))) (-5 *2 (-551)) (-5 *1 (-115 *4 *3)) (-4 *3 (-1248 *4))))) @@ -15336,11 +15342,11 @@ (|:| |singularities| (-1160 (-226))))) (-5 *1 (-105))))) (((*1 *2 *3) - (-12 (|has| *2 (-6 (-4439 "*"))) (-4 *5 (-376 *2)) (-4 *6 (-376 *2)) + (-12 (|has| *2 (-6 (-4445 "*"))) (-4 *5 (-376 *2)) (-4 *6 (-376 *2)) (-4 *2 (-1055)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1248 *2)) (-4 *4 (-691 *2 *5 *6))))) (((*1 *2 *3 *3) - (-12 (|has| *2 (-6 (-4439 "*"))) (-4 *5 (-376 *2)) (-4 *6 (-376 *2)) + (-12 (|has| *2 (-6 (-4445 "*"))) (-4 *5 (-376 *2)) (-4 *6 (-376 *2)) (-4 *2 (-1055)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1248 *2)) (-4 *4 (-691 *2 *5 *6))))) (((*1 *2 *3 *3) @@ -15380,7 +15386,7 @@ (((*1 *2 *3 *4) (-12 (-4 *5 (-367)) (-4 *5 (-562)) (-5 *2 - (-2 (|:| |minor| (-646 (-925))) (|:| -3699 *3) + (-2 (|:| |minor| (-646 (-925))) (|:| -3705 *3) (|:| |minors| (-646 (-646 (-925)))) (|:| |ops| (-646 *3)))) (-5 *1 (-90 *5 *3)) (-5 *4 (-925)) (-4 *3 (-663 *5))))) (((*1 *2 *3) @@ -15388,7 +15394,7 @@ (-5 *3 (-694 *4)) (-4 *5 (-663 *4))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-562)) - (-5 *2 (-2 (|:| -1757 (-694 *5)) (|:| |vec| (-1272 (-646 (-925)))))) + (-5 *2 (-2 (|:| -1758 (-694 *5)) (|:| |vec| (-1272 (-646 (-925)))))) (-5 *1 (-90 *5 *3)) (-5 *4 (-925)) (-4 *3 (-663 *5))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-776)) (-5 *1 (-58 *3)) (-4 *3 (-1222)))) ((*1 *1 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-1222)) (-5 *1 (-58 *3))))) @@ -15456,84 +15462,84 @@ (-4 *5 (-562)) (-5 *1 (-41 *5 *2)) (-4 *2 (-426 *5)) (-4 *2 (-13 (-367) (-301) - (-10 -8 (-15 -3411 ((-1131 *5 (-616 $)) $)) - (-15 -3410 ((-1131 *5 (-616 $)) $)) - (-15 -4390 ($ (-1131 *5 (-616 $)))))))))) + (-10 -8 (-15 -3417 ((-1131 *5 (-616 $)) $)) + (-15 -3416 ((-1131 *5 (-616 $)) $)) + (-15 -4396 ($ (-1131 *5 (-616 $)))))))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-457) (-1044 (-551)))) (-4 *3 (-562)) (-5 *1 (-41 *3 *2)) (-4 *2 (-426 *3)) (-4 *2 (-13 (-367) (-301) - (-10 -8 (-15 -3411 ((-1131 *3 (-616 $)) $)) - (-15 -3410 ((-1131 *3 (-616 $)) $)) - (-15 -4390 ($ (-1131 *3 (-616 $)))))))))) + (-10 -8 (-15 -3417 ((-1131 *3 (-616 $)) $)) + (-15 -3416 ((-1131 *3 (-616 $)) $)) + (-15 -4396 ($ (-1131 *3 (-616 $)))))))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-457) (-1044 (-551)))) (-4 *3 (-562)) (-5 *1 (-41 *3 *2)) (-4 *2 (-426 *3)) (-4 *2 (-13 (-367) (-301) - (-10 -8 (-15 -3411 ((-1131 *3 (-616 $)) $)) - (-15 -3410 ((-1131 *3 (-616 $)) $)) - (-15 -4390 ($ (-1131 *3 (-616 $)))))))))) + (-10 -8 (-15 -3417 ((-1131 *3 (-616 $)) $)) + (-15 -3416 ((-1131 *3 (-616 $)) $)) + (-15 -4396 ($ (-1131 *3 (-616 $)))))))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-457) (-1044 (-551)))) (-4 *3 (-562)) (-5 *1 (-41 *3 *2)) (-4 *2 (-426 *3)) (-4 *2 (-13 (-367) (-301) - 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(-10 -8 (-15 -3411 ((-1131 *3 (-616 $)) $)) - (-15 -3410 ((-1131 *3 (-616 $)) $)) - (-15 -4390 ($ (-1131 *3 (-616 $)))))))))) + (-10 -8 (-15 -3417 ((-1131 *3 (-616 $)) $)) + (-15 -3416 ((-1131 *3 (-616 $)) $)) + (-15 -4396 ($ (-1131 *3 (-616 $)))))))))) (((*1 *2 *3) (-12 (-5 *3 (-776)) (-4 *4 (-367)) (-4 *5 (-1248 *4)) (-5 *2 (-1278)) (-5 *1 (-40 *4 *5 *6 *7)) (-4 *6 (-1248 (-412 *5))) (-14 *7 *6)))) (((*1 *2 *3) (-12 (-5 *2 (-112)) (-5 *1 (-39 *3)) (-4 *3 (-1248 (-48)))))) (((*1 *2 *3 *1) (|partial| -12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1107)) (-4 *4 (-1107)) - (-5 *2 (-2 (|:| -4304 *3) (|:| -2263 *4)))))) + (-5 *2 (-2 (|:| -4310 *3) (|:| -2264 *4)))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-34)) (-5 *2 (-112))))) (((*1 *2 *1 *3) (-12 (-4 *1 (-34)) (-5 *3 (-776)) (-5 *2 (-112))))) (((*1 *2 *3 *4) @@ -15560,780 +15566,782 @@ ((*1 *1 *2) (-12 (-5 *2 (-952 *1)) (-4 *1 (-27)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1183)) (-4 *1 (-29 *3)) (-4 *3 (-562)))) ((*1 *1 *1) (-12 (-4 *1 (-29 *2)) (-4 *2 (-562))))) -((-1306 . 724159) (-1307 . 723763) (-1308 . 723642) (-1309 . 723540) - 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