diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 1284 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1578 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1350 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8934 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 25839 |
5 files changed, 19492 insertions, 19493 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 69102a81..4f0796f1 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2300614 . 3499555790) +(2300680 . 3499558253) (-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."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . 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}."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4504 . T) (-4502 . T) (-4501 . T) ((-4509 "*") . T) (-4500 . T) (-4505 . T) (-4499 . T)) +((-4505 . T) (-4503 . T) (-4502 . T) ((-4510 "*") . T) (-4501 . T) (-4506 . T) (-4500 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -2173) +(-32 R -2174) ((|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 -1069) (QUOTE (-578))))) (-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 -4507))) +((|HasAttribute| |#1| (QUOTE -4508))) (-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}."))) -((-4507 . T) (-4508 . T)) +((-4508 . T) (-4509 . 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"))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . 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 -2173 UP UPUP -2217) +(-40 -2174 UP UPUP -1476) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4500 |has| (-421 |#2|) (-376)) (-4505 |has| (-421 |#2|) (-376)) (-4499 |has| (-421 |#2|) (-376)) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-362))) (-2225 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2225 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2225 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2225 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-362))))) (-2225 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -660) (QUOTE (-578)))) (-2225 (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -2173) +((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-362))) (-2226 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2226 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2226 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2226 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-362))))) (-2226 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -660) (QUOTE (-578)))) (-2226 (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +(-41 R -2174) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -444) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-319)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4504 |has| |#1| (-570)) (-4502 . T) (-4501 . T)) +((-4505 |has| |#1| (-570)) (-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-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."))) -((-4507 . T) (-4508 . T)) -((-2225 (-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2079) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2079) (|devaluate| |#2|))))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-871))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2079) (|devaluate| |#2|))))))) +((-4508 . T) (-4509 . T)) +((-2226 (-12 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2076) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2076) (|devaluate| |#2|))))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-871))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2076) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (LIST (QUOTE -1069) (QUOTE (-578))))) (-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}."))) -((-4504 . T)) +((-4505 . T)) NIL (-51 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2173) +(-54 |Base| R -2174) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -158,7 +158,7 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4507 . T) (-4508 . T)) +((-4508 . T) (-4509 . T)) NIL (-58 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) @@ -166,65 +166,65 @@ NIL NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -2179) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -2180) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -2179) +(-62 -2180) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -2179) +(-63 -2180) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2179) +(-64 -2180) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -2179) +(-65 -2180) ((|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 -2179) +(-66 -2180) ((|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 -2179) +(-67 -2180) ((|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 -2179) +(-68 -2180) ((|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 -2179) +(-69 -2180) ((|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 -2179) +(-70 -2180) ((|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 -2179) +(-71 -2180) ((|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 -2179) +(-72 -2180) ((|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 -2179) +(-73 -2180) ((|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 -2179) +(-74 -2180) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2179) +(-77 -2180) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2179) +(-78 -2180) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -2179) +(-79 -2180) ((|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 -2179) +(-80 -2180) ((|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 -2179) +(-81 -2180) ((|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 -2179) +(-82 -2180) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2179) +(-83 -2180) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2179) +(-84 -2180) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2179) +(-85 -2180) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2179) +(-86 -2180) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2179) +(-87 -2180) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -2179) +(-88 -2180) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -2179) +(-89 -2180) ((|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 (-376)))) (-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}."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -318,15 +318,15 @@ NIL NIL (-97) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4507 . T)) +((-4508 . 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."))) -((-4507 . T) ((-4509 "*") . T) (-4508 . T) (-4504 . T) (-4502 . T) (-4501 . T) (-4500 . T) (-4505 . T) (-4499 . T) (-4498 . T) (-4497 . T) (-4496 . T) (-4495 . T) (-4503 . T) (-4506 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4494 . T)) +((-4508 . T) ((-4510 "*") . T) (-4509 . T) (-4505 . T) (-4503 . T) (-4502 . T) (-4501 . T) (-4506 . T) (-4500 . T) (-4499 . T) (-4498 . T) (-4497 . T) (-4496 . T) (-4504 . T) (-4507 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4495 . 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}."))) -((-4504 . T)) +((-4505 . 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}."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4509 "*")))) +((|HasAttribute| |#1| (QUOTE (-4510 "*")))) (-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"))) -((-4507 . T)) +((-4508 . 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."))) -((-4508 . T)) +((-4509 . 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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2225 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147))))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2226 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147))))) (-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}"))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1131))) (|HasCategory| (-112) (LIST (QUOTE -321) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-112) (QUOTE (-871))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-112) (QUOTE (-1131))) (|HasCategory| (-112) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-112) (QUOTE (-102)))) (-111 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -396,22 +396,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-117 -2173 UP) +(-117 -2174 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 (-118 |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}."))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-119 |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}."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-938))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-118 |#1|) (QUOTE (-1053))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2225 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (QUOTE (-1183))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -118) (|devaluate| |#1|)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-938)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-118 |#1|) (QUOTE (-938))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-118 |#1|) (QUOTE (-1053))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2226 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (QUOTE (-1183))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -118) (|devaluate| |#1|)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-938)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) (-120 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4508))) +((|HasAttribute| |#1| (QUOTE -4509))) (-121 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 @@ -422,15 +422,15 @@ NIL NIL (-123 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"))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-124 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-125) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) NIL (-126 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -438,20 +438,20 @@ NIL NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4507 . T) (-4508 . T)) +((-4508 . T) (-4509 . T)) NIL (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129 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."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-130) ((|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."))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131)))))) (-2225 (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131))))) (|HasCategory| (-131) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-131) (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131)))) (|HasCategory| (-131) (QUOTE (-871))) (-2225 (|HasCategory| (-131) (QUOTE (-102))) (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-131) (QUOTE (-102))) (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131)))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131)))))) (-2226 (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131))))) (|HasCategory| (-131) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-131) (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131)))) (|HasCategory| (-131) (QUOTE (-871))) (-2226 (|HasCategory| (-131) (QUOTE (-102))) (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-131) (QUOTE (-102))) (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131)))))) (-131) ((|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 @@ -474,13 +474,13 @@ NIL NIL (-136) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4509 "*") . T)) +(((-4510 "*") . T)) NIL -(-137 |minix| -2590 S T$) +(-137 |minix| -2592 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-138 |minix| -2590 R) +(-138 |minix| -2592 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -502,8 +502,8 @@ NIL NIL (-143) ((|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}."))) -((-4507 . T) (-4497 . T) (-4508 . T)) -((-2225 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) +((-4508 . T) (-4498 . T) (-4509 . T)) +((-2226 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-144 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 @@ -513,12 +513,12 @@ NIL NIL NIL (-146) -((|constructor| (NIL "This domain provides the basic character data type.")) (|alphanumeric?| (((|Boolean|) $) "\\spad{alphanumeric?(c)} tests if \\spad{c} is either a letter or number,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{z} or A..\\spad{Z}.")) (|lowerCase?| (((|Boolean|) $) "\\spad{lowerCase?(c)} tests if \\spad{c} is an lower case letter,{} \\spadignore{i.e.} one of a..\\spad{z}.")) (|upperCase?| (((|Boolean|) $) "\\spad{upperCase?(c)} tests if \\spad{c} is an upper case letter,{} \\spadignore{i.e.} one of A..\\spad{Z}.")) (|alphabetic?| (((|Boolean|) $) "\\spad{alphabetic?(c)} tests if \\spad{c} is a letter,{} \\spadignore{i.e.} one of a..\\spad{z} or A..\\spad{Z}.")) (|hexDigit?| (((|Boolean|) $) "\\spad{hexDigit?(c)} tests if \\spad{c} is a hexadecimal numeral,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{f} or A..\\spad{F}.")) (|digit?| (((|Boolean|) $) "\\spad{digit?(c)} tests if \\spad{c} is a digit character,{} \\spadignore{i.e.} one of 0..9.")) (|lowerCase| (($ $) "\\spad{lowerCase(c)} converts an upper case letter to the corresponding lower case letter. If \\spad{c} is not an upper case letter,{} then it is returned unchanged.")) (|upperCase| (($ $) "\\spad{upperCase(c)} converts a lower case letter to the corresponding upper case letter. If \\spad{c} is not a lower case letter,{} then it is returned unchanged.")) (|verticalTab| (($) "\\spad{verticalTab} designates vertical tab.")) (|horizontalTab| (($) "\\spad{horizontalTab} designates horizontal tab.")) (|backspace| (($) "\\spad{backspace} designates the backspace character.")) (|formfeed| (($) "\\spad{formfeed} designates the form feed character.")) (|linefeed| (($) "\\spad{linefeed} designates the line feed character.")) (|carriageReturn| (($) "\\spad{carriageReturn} designates carriage return.")) (|newline| (($) "\\spad{newline} designates the new line character.")) (|underscore| (($) "\\spad{underscore} designates the underbar character.")) (|quote| (($) "\\spad{quote} provides the string quote character,{} \\spad{\"}.")) (|space| (($) "\\spad{space} provides the blank character.")) (|char| (($ (|String|)) "\\spad{char(s)} provides a character from a string \\spad{s} of length one.") (($ (|NonNegativeInteger|)) "\\spad{char(i)} provides a character corresponding to the integer code \\spad{i}. It is always \\spad{true} that \\spad{ord char i = i}.")) (|ord| (((|NonNegativeInteger|) $) "\\spad{ord(c)} provides an integral code corresponding to the character \\spad{c}. It is always \\spad{true} that \\spad{char ord c = c}."))) +((|constructor| (NIL "This domain provides the basic character data type.")) (|alphanumeric?| (((|Boolean|) $) "\\spad{alphanumeric?(c)} tests if \\spad{c} is either a letter or number,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{z} or A..\\spad{Z}.")) (|lowerCase?| (((|Boolean|) $) "\\spad{lowerCase?(c)} tests if \\spad{c} is an lower case letter,{} \\spadignore{i.e.} one of a..\\spad{z}.")) (|upperCase?| (((|Boolean|) $) "\\spad{upperCase?(c)} tests if \\spad{c} is an upper case letter,{} \\spadignore{i.e.} one of A..\\spad{Z}.")) (|alphabetic?| (((|Boolean|) $) "\\spad{alphabetic?(c)} tests if \\spad{c} is a letter,{} \\spadignore{i.e.} one of a..\\spad{z} or A..\\spad{Z}.")) (|hexDigit?| (((|Boolean|) $) "\\spad{hexDigit?(c)} tests if \\spad{c} is a hexadecimal numeral,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{f} or A..\\spad{F}.")) (|digit?| (((|Boolean|) $) "\\spad{digit?(c)} tests if \\spad{c} is a digit character,{} \\spadignore{i.e.} one of 0..9.")) (|lowerCase| (($ $) "\\spad{lowerCase(c)} converts an upper case letter to the corresponding lower case letter. If \\spad{c} is not an upper case letter,{} then it is returned unchanged.")) (|upperCase| (($ $) "\\spad{upperCase(c)} converts a lower case letter to the corresponding upper case letter. If \\spad{c} is not a lower case letter,{} then it is returned unchanged.")) (|escape| (($) "\\spad{escape} designate the escape character.")) (|verticalTab| (($) "\\spad{verticalTab} designates vertical tab.")) (|horizontalTab| (($) "\\spad{horizontalTab} designates horizontal tab.")) (|backspace| (($) "\\spad{backspace} designates the backspace character.")) (|formfeed| (($) "\\spad{formfeed} designates the form feed character.")) (|linefeed| (($) "\\spad{linefeed} designates the line feed character.")) (|carriageReturn| (($) "\\spad{carriageReturn} designates carriage return.")) (|newline| (($) "\\spad{newline} designates the new line character.")) (|underscore| (($) "\\spad{underscore} designates the underbar character.")) (|quote| (($) "\\spad{quote} provides the string quote character,{} \\spad{\"}.")) (|space| (($) "\\spad{space} provides the blank character.")) (|char| (($ (|String|)) "\\spad{char(s)} provides a character from a string \\spad{s} of length one.") (($ (|NonNegativeInteger|)) "\\spad{char(i)} provides a character corresponding to the integer code \\spad{i}. It is always \\spad{true} that \\spad{ord char i = i}.")) (|ord| (((|NonNegativeInteger|) $) "\\spad{ord(c)} provides an integral code corresponding to the character \\spad{c}. It is always \\spad{true} that \\spad{char ord c = c}."))) NIL NIL (-147) ((|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."))) -((-4504 . T)) +((-4505 . T)) NIL (-148 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}."))) @@ -526,9 +526,9 @@ NIL NIL (-149) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4504 . T)) +((-4505 . T)) NIL -(-150 -2173 UP UPUP) +(-150 -2174 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 @@ -539,14 +539,14 @@ NIL (-152 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 -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasAttribute| |#1| (QUOTE -4507))) +((|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasAttribute| |#1| (QUOTE -4508))) (-153 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 (-154 |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."))) -((-4502 . T) (-4501 . T) (-4504 . T)) +((-4503 . T) (-4502 . T) (-4505 . T)) NIL (-155) ((|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."))) @@ -568,7 +568,7 @@ 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 -(-160 R -2173) +(-160 R -2174) ((|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 @@ -599,10 +599,10 @@ NIL (-167 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 (-938))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4503)) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-570)))) +((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4504)) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-570)))) (-168 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})"))) -((-4500 -2225 (|has| |#1| (-570)) (-12 (|has| |#1| (-319)) (|has| |#1| (-938)))) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4503 |has| |#1| (-6 -4503)) (-4506 |has| |#1| (-6 -4506)) (-1924 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 -2226 (|has| |#1| (-570)) (-12 (|has| |#1| (-319)) (|has| |#1| (-938)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-1924 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-169 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."))) @@ -618,8 +618,8 @@ NIL NIL (-172 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}."))) -((-4500 -2225 (|has| |#1| (-570)) (-12 (|has| |#1| (-319)) (|has| |#1| (-938)))) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4503 |has| |#1| (-6 -4503)) (-4506 |has| |#1| (-6 -4506)) (-1924 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-362))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2225 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-362)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-938))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-938)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-938))))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-570)))) (-2225 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1091))) (-12 (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasAttribute| |#1| (QUOTE -4503)) (|HasAttribute| |#1| (QUOTE -4506)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-362))))) +((-4501 -2226 (|has| |#1| (-570)) (-12 (|has| |#1| (-319)) (|has| |#1| (-938)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-1924 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-362))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2226 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-362)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-938))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-938)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-938))))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-570)))) (-2226 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1091))) (-12 (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasAttribute| |#1| (QUOTE -4507)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-362))))) (-173 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -630,7 +630,7 @@ NIL NIL (-175) ((|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."))) -(((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-176) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -638,7 +638,7 @@ NIL NIL (-177 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4509 "*") . T) (-4500 . T) (-4505 . T) (-4499 . T) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") . T) (-4501 . T) (-4506 . T) (-4500 . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-178) ((|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}."))) @@ -692,7 +692,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-191 R -2173) +(-191 R -2174) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -804,23 +804,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -2173 UP UPUP R) +(-219 -2174 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 -(-220 -2173 FP) +(-220 -2174 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 (-221) ((|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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2225 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147))))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2226 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147))))) (-222) ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -2173) +(-223 R -2174) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -834,19 +834,19 @@ NIL NIL (-226 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-227 |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}."))) -((-4504 . T)) +((-4505 . T)) NIL -(-228 R -2173) +(-228 R -2174) ((|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 (-229) ((|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}."))) -((-1915 . T) (-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-1915 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-230) ((|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)}.}"))) @@ -854,19 +854,19 @@ NIL NIL (-231 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}"))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4509 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-232 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 (-233 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."))) -((-4508 . T)) +((-4509 . T)) NIL (-234 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((-4504 . T)) +((-4505 . T)) NIL (-235 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -878,7 +878,7 @@ NIL NIL (-237 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) NIL (-238 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) @@ -890,36 +890,36 @@ NIL NIL (-240) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-4504 . T)) +((-4505 . T)) NIL (-241 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 -4507))) +((|HasAttribute| |#1| (QUOTE -4508))) (-242 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}."))) -((-4508 . T)) +((-4509 . T)) NIL (-243) ((|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 -(-244 S -2590 R) +(-244 S -2592 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-871))) (|HasAttribute| |#3| (QUOTE -4504)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (QUOTE (-1131)))) -(-245 -2590 R) +((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-871))) (|HasAttribute| |#3| (QUOTE -4505)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (QUOTE (-1131)))) +(-245 -2592 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4501 |has| |#2| (-1080)) (-4502 |has| |#2| (-1080)) (-4504 |has| |#2| (-6 -4504)) (-4507 . T)) +((-4502 |has| |#2| (-1080)) (-4503 |has| |#2| (-1080)) (-4505 |has| |#2| (-6 -4505)) (-4508 . T)) NIL -(-246 -2590 A B) +(-246 -2592 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 -(-247 -2590 R) +(-247 -2592 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."))) -((-4501 |has| |#2| (-1080)) (-4502 |has| |#2| (-1080)) (-4504 |has| |#2| (-6 -4504)) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (LIST 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(|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2225 (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) 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(-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasAttribute| |#2| (QUOTE -4505)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))))) (-248) ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -930,7 +930,7 @@ NIL NIL (-250) ((|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}."))) -((-4500 . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-251 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."))) @@ -938,20 +938,20 @@ NIL NIL (-252 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}"))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-253 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 (-254 R) ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) NIL (-255 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4509 "*") |has| |#2| (-175)) (-4500 |has| |#2| (-570)) (-4505 |has| |#2| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#2| (QUOTE (-938))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4505)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) +(((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-570)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#2| (QUOTE (-938))) (-2226 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2226 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) (-256) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) NIL @@ -966,23 +966,23 @@ NIL NIL (-259 |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((-4504 -2225 (-3533 (|has| |#4| (-1080)) (|has| |#4| (-240))) (|has| |#4| (-6 -4504)) (-3533 (|has| |#4| (-1080)) (|has| |#4| (-927 (-1207))))) (-4501 |has| |#4| (-1080)) (-4502 |has| |#4| (-1080)) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-175))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-240))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-376))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-381))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-748))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-815))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-871))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1080))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (LIST 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(QUOTE (-578)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-1131)))) (-2226 (|HasAttribute| |#3| (QUOTE -4505)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -929) (QUOTE (-1207))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|))))) (-261 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-240)))) (-262 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."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) NIL (-263 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}."))) -((-4507 . T) (-4508 . T)) +((-4508 . T) (-4509 . T)) NIL (-264) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g),a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -1030,8 +1030,8 @@ NIL NIL (-275 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"))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#3| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#3| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-938))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#3| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#3| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) (-276 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1076,11 +1076,11 @@ 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 -(-287 R -2173) +(-287 R -2174) ((|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 -(-288 R -2173) +(-288 R -2174) ((|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 @@ -1106,7 +1106,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131)))) (-294 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}."))) -((-4508 . T)) +((-4509 . T)) NIL (-295 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}."))) @@ -1127,18 +1127,18 @@ NIL (-299 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 -4508))) +((|HasAttribute| |#1| (QUOTE -4509))) (-300 |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 -(-301 S R |Mod| -3749 -4168 |exactQuo|) +(-301 S R |Mod| -3305 -2157 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-302) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4500 . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-303) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1154,21 +1154,21 @@ NIL NIL (-306 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."))) -((-4504 -2225 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4501 |has| |#1| (-1080)) (-4502 |has| |#1| (-1080))) -((|HasCategory| |#1| (QUOTE (-376))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2225 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-314))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2225 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2225 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748)))) +((-4505 -2226 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-1080)) (-4503 |has| |#1| (-1080))) +((|HasCategory| |#1| (QUOTE (-376))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2226 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-314))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2226 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2226 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748)))) (-307 |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."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2079) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2076) (|devaluate| |#2|)))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102)))) (-308) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-309 -2173 S) +(-309 -2174 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 -(-310 E -2173) +(-310 E -2174) ((|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 @@ -1206,7 +1206,7 @@ NIL NIL (-319) ((|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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-320 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1216,7 +1216,7 @@ 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 -(-322 -2173) +(-322 -2174) ((|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 @@ -1230,8 +1230,8 @@ NIL NIL (-325 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))}."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-938))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-1053))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-871))) (-2225 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-871)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-1183))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-240))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -321) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -298) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-938))) (|HasCategory| $ (QUOTE (-147)))) (-2225 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-938))) (|HasCategory| $ (QUOTE (-147)))))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-938))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-1053))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-871))) (-2226 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-871)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-1183))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-240))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -321) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -298) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-938))) (|HasCategory| $ (QUOTE (-147)))) (-2226 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-938))) (|HasCategory| $ (QUOTE (-147)))))) (-326 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 @@ -1242,9 +1242,9 @@ NIL NIL (-328 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4504 -2225 (-12 (|has| |#1| (-570)) (-2225 (|has| |#1| (-1080)) (|has| |#1| (-487)))) (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) ((-4509 "*") |has| |#1| (-570)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-570)) (-4499 |has| |#1| (-570))) -((-2225 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))))) (|HasCategory| |#1| (QUOTE (-570))) (-2225 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-21))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-1080))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))))) (-2225 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (-2225 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2225 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-1080)))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570)))) (-2225 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (-2225 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))))) (-2225 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-1143)))) (-2225 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))))) (-2225 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (LIST (QUOTE -1069) (QUOTE (-578))))) -(-329 R -2173) +((-4505 -2226 (-12 (|has| |#1| (-570)) (-2226 (|has| |#1| (-1080)) (|has| |#1| (-487)))) (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-570)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-570)) (-4500 |has| |#1| (-570))) +((-2226 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))))) (|HasCategory| |#1| (QUOTE (-570))) (-2226 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-21))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-1080))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))))) (-2226 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (-2226 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2226 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2226 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-1080)))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570)))) (-2226 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (-2226 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))))) (-2226 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-1143)))) (-2226 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))))) (-2226 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2226 (-12 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (LIST (QUOTE -1069) (QUOTE (-578))))) +(-329 R -2174) ((|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 @@ -1254,8 +1254,8 @@ NIL NIL (-331 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."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1583) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|))))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2864) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2226 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1574) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1879) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-332 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 @@ -1266,7 +1266,7 @@ NIL NIL (-334 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."))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| (-578) (QUOTE (-814)))) (-335 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1282,19 +1282,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175)))) (-338 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-339 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."))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -2173) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -2174) ((|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 (-381)))) -(-341 -2173) +(-341 -2174) ((|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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-342) ((|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."))) @@ -1316,15 +1316,15 @@ 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 -(-347 S -2173 UP UPUP R) +(-347 S -2174 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 -(-348 -2173 UP UPUP R) +(-348 -2174 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 -(-349 -2173 UP UPUP R) +(-349 -2174 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 @@ -1338,32 +1338,32 @@ NIL NIL (-352 |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.}"))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-392)))) (|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (LIST (QUOTE -1069) (QUOTE (-578))))) (-353 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-354 S -2173 UP UPUP) +(-354 S -2174 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 (-381))) (|HasCategory| |#2| (QUOTE (-376)))) -(-355 -2173 UP UPUP) +(-355 -2174 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."))) -((-4500 |has| (-421 |#2|) (-376)) (-4505 |has| (-421 |#2|) (-376)) (-4499 |has| (-421 |#2|) (-376)) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-356 |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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((-2225 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147)))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2226 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147)))) (-357 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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2226 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-358 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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2226 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-359 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 @@ -1378,33 +1378,33 @@ NIL NIL (-362) ((|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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-363 R UP -2173) +(-363 R UP -2174) ((|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 (-364 |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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((-2225 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147)))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2226 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147)))) (-365 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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2226 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-366 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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2226 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-367 |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}."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((-2225 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147)))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2226 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147)))) (-368 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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) -(-369 -2173 GF) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2226 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +(-369 -2174 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 @@ -1412,21 +1412,21 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-371 -2173 FP FPP) +(-371 -2174 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 (-372 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}."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2226 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-373 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 (-374 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4504 . T)) +((-4505 . T)) NIL (-375 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1434,7 +1434,7 @@ NIL NIL (-376) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-377 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1450,7 +1450,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-570)))) (-380 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4504 |has| |#1| (-570)) (-4502 . T) (-4501 . T)) +((-4505 |has| |#1| (-570)) (-4503 . T) (-4502 . T)) NIL (-381) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1462,7 +1462,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-376)))) (-383 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) NIL (-384 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1471,14 +1471,14 @@ NIL (-385 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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131)))) +((|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131)))) (-386 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4507 . T)) +((-4508 . T)) NIL (-387 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4502 . T) (-4501 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4503 . T) (-4502 . T)) NIL (-388 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."))) @@ -1498,7 +1498,7 @@ NIL NIL (-392) ((|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}."))) -((-4490 . T) (-4498 . T) (-1915 . T) (-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4491 . T) (-4499 . T) (-1915 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-393 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1506,11 +1506,11 @@ NIL NIL (-394 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}"))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (QUOTE (-175)))) (-395 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}."))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) NIL (-396) ((|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}."))) @@ -1522,7 +1522,7 @@ NIL NIL (-398 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."))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131))))) (-399 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1534,7 +1534,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-871)))) (-401) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-402) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1546,13 +1546,13 @@ NIL NIL (-404 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) NIL (-405) ((|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 -(-406 -2173 UP UPUP R) +(-406 -2174 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 @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-412 -2179 |returnType| -3588 |symbols|) +(-412 -2180 |returnType| -3589 |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 -(-413 -2173 UP) +(-413 -2174 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1594,15 +1594,15 @@ NIL NIL (-416) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-417 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4490)) (|HasAttribute| |#1| (QUOTE -4498))) +((|HasAttribute| |#1| (QUOTE -4491)) (|HasAttribute| |#1| (QUOTE -4499))) (-418) ((|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\"."))) -((-1915 . T) (-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-1915 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-419 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."))) @@ -1614,15 +1614,15 @@ NIL NIL (-421 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."))) -((-4494 -12 (|has| |#1| (-6 -4505)) (|has| |#1| (-466)) (|has| |#1| (-6 -4494))) (-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850))))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4505)) (|HasAttribute| |#1| (QUOTE -4494)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +((-4495 -12 (|has| |#1| (-6 -4506)) (|has| |#1| (-466)) (|has| |#1| (-6 -4495))) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850))))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4495)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) (-422 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-423 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) NIL (-424 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1636,11 +1636,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-427 R -2173 UP A) +(-427 R -2174 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4504 . T)) +((-4505 . T)) NIL -(-428 R -2173 UP A |ibasis|) +(-428 R -2174 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1069) (|devaluate| |#2|)))) @@ -1654,12 +1654,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-376)))) (-431 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4504 |has| |#1| (-570)) (-4502 . T) (-4501 . T)) +((-4505 |has| |#1| (-570)) (-4503 . T) (-4502 . T)) NIL (-432 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2226 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) (-433 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1686,17 +1686,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-381)))) (-439 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4507 . T) (-4497 . T) (-4508 . T)) +((-4508 . T) (-4498 . T) (-4509 . T)) NIL -(-440 R -2173) +(-440 R -2174) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-441 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4494 -12 (|has| |#1| (-6 -4494)) (|has| |#2| (-6 -4494))) (-4501 . T) (-4502 . T) (-4504 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4494)) (|HasAttribute| |#2| (QUOTE -4494)))) -(-442 R -2173) +((-4495 -12 (|has| |#1| (-6 -4495)) (|has| |#2| (-6 -4495))) (-4502 . T) (-4503 . T) (-4505 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4495)) (|HasAttribute| |#2| (QUOTE -4495)))) +(-442 R -2174) ((|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 @@ -1706,17 +1706,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (-444 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}."))) -((-4504 -2225 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) ((-4509 "*") |has| |#1| (-570)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-570)) (-4499 |has| |#1| (-570))) +((-4505 -2226 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-570)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-570)) (-4500 |has| |#1| (-570))) NIL -(-445 R -2173) +(-445 R -2174) ((|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 -(-446 R -2173) +(-446 R -2174) ((|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)))) -(-447 R -2173) +(-447 R -2174) ((|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 @@ -1724,7 +1724,7 @@ 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 -(-449 R -2173 UP) +(-449 R -2174 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 -1069) (QUOTE (-48))))) @@ -1756,7 +1756,7 @@ 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 -(-457 R UP -2173) +(-457 R UP -2174) ((|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 @@ -1794,16 +1794,16 @@ NIL NIL (-466) ((|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}."))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-467 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"))) -((-4504 |has| (-421 (-981 |#1|)) (-570)) (-4502 . T) (-4501 . T)) +((-4505 |has| (-421 (-981 |#1|)) (-570)) (-4503 . T) (-4502 . T)) ((|HasCategory| (-421 (-981 |#1|)) (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| (-421 (-981 |#1|)) (QUOTE (-570)))) (-468 |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"))) -(((-4509 "*") |has| |#2| (-175)) (-4500 |has| |#2| (-570)) (-4505 |has| |#2| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#2| (QUOTE (-938))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4505)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) +(((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-570)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#2| (QUOTE (-938))) (-2226 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2226 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) (-469 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1830,7 +1830,7 @@ NIL NIL (-475 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) NIL (-476 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1838,7 +1838,7 @@ NIL NIL (-477 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102)))) (-478 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}."))) @@ -1868,7 +1868,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-485 |lv| -2173 R) +(-485 |lv| -2174 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1878,23 +1878,23 @@ NIL NIL (-487) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4504 . T)) +((-4505 . T)) NIL (-488 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1583) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|))))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2864) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2226 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1574) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1879) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-489 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4508 . T)) -((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2079) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131)))) +((-4509 . T)) +((-12 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2076) (|devaluate| |#2|)))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131)))) (-490 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)}"))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102)))) (-491) ((|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}."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-492) ((|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'."))) @@ -1902,29 +1902,29 @@ NIL NIL (-493 |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."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2079) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2076) (|devaluate| |#2|)))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102)))) (-494) ((|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. 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T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-499 -2174 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 @@ -1934,12 +1934,12 @@ NIL NIL (-501) ((|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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2225 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147))))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2226 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147))))) (-502 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 -4507)) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) +((|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-503 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1960,33 +1960,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-508 -2173 UP |AlExt| |AlPol|) +(-508 -2174 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-509) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (LIST (QUOTE -1069) (QUOTE (-578))))) (-510 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-511 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."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-512 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 -(-513 R UP -2173) +(-513 R UP -2174) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-514 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1131))) (|HasCategory| (-112) (LIST (QUOTE -321) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-112) (QUOTE (-871))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-112) (QUOTE (-1131))) (|HasCategory| (-112) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-112) (QUOTE (-102)))) (-515 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)}."))) @@ -2000,7 +2000,7 @@ 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 -(-518 -2173 |Expon| |VarSet| |DPoly|) +(-518 -2174 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-1207))))) @@ -2050,36 +2050,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-814)))) (-530 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-531) ((|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 (-532 |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}."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((-2225 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2226 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) (-533 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}."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-534 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."))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-535 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 -4508))) +((|HasAttribute| |#3| (QUOTE -4509))) (-536 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 -4508))) +((|HasAttribute| |#7| (QUOTE -4509))) (-537 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."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4509 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-538) ((|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 @@ -2112,7 +2112,7 @@ 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 ((-12 (|HasCategory| (-793) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-1131))))) -(-546 K -2173 |Par|) +(-546 K -2174 |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 @@ -2136,7 +2136,7 @@ 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 -(-552 K -2173 |Par|) +(-552 K -2174 |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 @@ -2166,7 +2166,7 @@ NIL NIL (-559) ((|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."))) -((-4505 . T) (-4506 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4506 . T) (-4507 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-560) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2186,13 +2186,13 @@ NIL NIL (-564 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2079) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102)))) -(-565 R -2173) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2076) (|devaluate| |#2|)))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102)))) +(-565 R -2174) ((|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 -(-566 R0 -2173 UP UPUP R) +(-566 R0 -2174 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 @@ -2202,7 +2202,7 @@ NIL NIL (-568 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This 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."))) -((-1915 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-1915 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-569 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."))) @@ -2210,9 +2210,9 @@ NIL NIL (-570) ((|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."))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-571 R -2173) +(-571 R -2174) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2224,7 +2224,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-574 R -2173 L) +(-574 R -2174 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -678) (|devaluate| |#2|)))) @@ -2232,31 +2232,31 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-576 -2173 UP UPUP R) +(-576 -2174 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 -(-577 -2173 UP) +(-577 -2174 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 (-578) ((|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."))) -((-4489 . T) (-4495 . T) (-4499 . T) (-4494 . T) (-4505 . T) (-4506 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4490 . T) (-4496 . T) (-4500 . T) (-4495 . T) (-4506 . T) (-4507 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-579) ((|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 -(-580 R -2173 L) +(-580 R -2174 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -678) (|devaluate| |#2|)))) -(-581 R -2173) +(-581 R -2174) ((|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 -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-1170)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-648))))) -(-582 -2173 UP) +(-582 -2174 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 @@ -2264,27 +2264,27 @@ 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 -(-584 -2173) +(-584 -2174) ((|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 (-585 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."))) -((-1915 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-1915 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-586) ((|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 -(-587 R -2173) +(-587 R -2174) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-648))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-570)))) -(-588 -2173 UP) +(-588 -2174 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-589 R -2173) +(-589 R -2174) ((|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 @@ -2306,21 +2306,21 @@ NIL NIL (-594 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-595 |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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381)))) (-596) ((|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 -(-597 R -2173) +(-597 R -2174) ((|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 -(-598 E -2173) +(-598 E -2174) ((|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 @@ -2328,9 +2328,9 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-600 -2173) +(-600 -2174) ((|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}."))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-1207))))) (-601 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) @@ -2358,19 +2358,19 @@ NIL NIL (-607 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2225 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-146) (QUOTE (-871))) (-2225 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2226 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-146) (QUOTE (-871))) (-2226 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-608 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 (-609 |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}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|)))) (|HasCategory| (-578) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-578)))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|)))) (|HasCategory| (-578) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -2864) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-578)))))) (-610 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4509 "*") |has| |#1| (-570)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-570)) (-4501 |has| |#1| (-570)) (-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-570)))) (-611) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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"))) @@ -2384,7 +2384,7 @@ 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 -(-614 R -2173 FG) +(-614 R -2174 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 @@ -2394,12 +2394,12 @@ NIL NIL (-616 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-617 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 -4508)) (|HasCategory| |#2| (QUOTE (-871))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#3| (QUOTE (-1131)))) +((|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-871))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#3| (QUOTE (-1131)))) (-618 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2410,8 +2410,8 @@ NIL NIL (-620 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4504 -2225 (-3533 (|has| |#2| (-380 |#1|)) (|has| |#1| (-570))) (-12 (|has| |#2| (-431 |#1|)) (|has| |#1| (-570)))) (-4502 . T) (-4501 . T)) -((-2225 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) +((-4505 -2226 (-3535 (|has| |#2| (-380 |#1|)) (|has| |#1| (-570))) (-12 (|has| |#2| (-431 |#1|)) (|has| |#1| (-570)))) (-4503 . T) (-4502 . T)) +((-2226 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-621) ((|constructor| (NIL "This is the datatype for the \\spad{JVM} bytecodes."))) NIL @@ -2438,15 +2438,15 @@ NIL NIL (-627 |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."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -2079) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -2076) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (QUOTE (-102)))) (-628 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 (-629 |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}."))) -((-4508 . T)) +((-4509 . T)) NIL (-630 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) @@ -2464,7 +2464,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -2173 UP) +(-634 -2174 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2486,19 +2486,19 @@ NIL NIL (-639 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."))) -((-4504 . T)) +((-4505 . T)) NIL (-640 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}."))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-870)))) -(-641 R -2173) +(-641 R -2174) ((|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 (-642 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"))) -((-4502 . T) (-4501 . T) ((-4509 "*") . T) (-4500 . T) (-4504 . T)) +((-4503 . T) (-4502 . T) ((-4510 "*") . T) (-4501 . T) (-4505 . T)) ((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (-643 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."))) @@ -2514,7 +2514,7 @@ NIL NIL (-646 |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}}."))) -((-4504 . T)) +((-4505 . T)) NIL (-647 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}}."))) @@ -2524,30 +2524,30 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-649 R -2173) +(-649 R -2174) ((|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 -(-650 |lv| -2173) +(-650 |lv| -2174) ((|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 (-651) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4508 . T)) -((-12 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -2079) (QUOTE (-52))))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (QUOTE (-1131)))) +((-4509 . T)) +((-12 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -2076) (QUOTE (-52))))))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (QUOTE (-1131)))) (-652 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-376)))) (-653 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4502 . T) (-4501 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4503 . T) (-4502 . T)) NIL (-654 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4504 -2225 (-3533 (|has| |#2| (-380 |#1|)) (|has| |#1| (-570))) (-12 (|has| |#2| (-431 |#1|)) (|has| |#1| (-570)))) (-4502 . T) (-4501 . T)) -((-2225 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) +((-4505 -2226 (-3535 (|has| |#2| (-380 |#1|)) (|has| |#1| (-570))) (-12 (|has| |#2| (-431 |#1|)) (|has| |#1| (-570)))) (-4503 . T) (-4502 . T)) +((-2226 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-655 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL @@ -2563,10 +2563,10 @@ NIL (-658 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 -((-3523 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) +((-3524 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) (-659 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) ((-12 (|HasCategory| (-657 |#2|) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-1131))))) (-660 R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) @@ -2574,7 +2574,7 @@ NIL NIL (-661 K B) ((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) NIL (-662 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2594,8 +2594,8 @@ NIL NIL (-666 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."))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-667 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2606,8 +2606,8 @@ NIL NIL (-669 S) ((|substitute| (($ |#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."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-670 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 @@ -2619,22 +2619,22 @@ NIL (-672 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4508))) +((|HasAttribute| |#1| (QUOTE -4509))) (-673 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-674 R -2173 L) +(-674 R -2174 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 (-675 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}}"))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) (-676 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) (-677 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2642,15 +2642,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-376)))) (-678 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}."))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-679 -2173 UP) +(-679 -2174 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)))) -(-680 A -2262) +(-680 A -3774) ((|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}}"))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) (-681 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) @@ -2666,7 +2666,7 @@ NIL NIL (-684 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}."))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (QUOTE (-813)))) (-685 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2674,7 +2674,7 @@ NIL NIL (-686 |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) (-4502 . T) (-4501 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4503 . T) (-4502 . T)) ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-175)))) (-687 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}."))) @@ -2682,13 +2682,13 @@ NIL NIL (-688 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}."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) NIL -(-689 -2173) +(-689 -2174) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-690 -2173 |Row| |Col| M) +(-690 -2174 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2698,8 +2698,8 @@ NIL NIL (-692 |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."))) -((-4504 . T) (-4507 . T) (-4501 . T) (-4502 . T)) -((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4509 "*"))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-570))) (-2225 (|HasAttribute| |#2| (QUOTE (-4509 "*"))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((-4505 . T) (-4508 . T) (-4502 . T) (-4503 . T)) +((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-570))) (-2226 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-693) ((|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 @@ -2719,7 +2719,7 @@ NIL (-697 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 -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-698) ((|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 @@ -2763,10 +2763,10 @@ NIL (-708 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4509 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-570)))) +((|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-570)))) (-709 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4507 . T) (-4508 . T)) +((-4508 . T) (-4509 . T)) NIL (-710 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) @@ -2774,8 +2774,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570)))) (-711 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."))) -((-4507 . T) (-4508 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4509 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4508 . T) (-4509 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-712 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 @@ -2784,7 +2784,7 @@ 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 -(-714 S -2173 FLAF FLAS) +(-714 S -2174 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 @@ -2794,11 +2794,11 @@ NIL NIL (-716) ((|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"))) -((-4500 . T) (-4505 |has| (-721) (-376)) (-4499 |has| (-721) (-376)) (-1924 . T) (-4506 |has| (-721) (-6 -4506)) (-4503 |has| (-721) (-6 -4503)) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| (-721) (QUOTE (-149))) (|HasCategory| (-721) (QUOTE (-147))) (|HasCategory| (-721) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-721) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-721) (QUOTE (-381))) (|HasCategory| (-721) (QUOTE (-376))) (-2225 (|HasCategory| (-721) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-239))) (-2225 (-12 (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207))))) (-2225 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-362)))) (|HasCategory| (-721) (QUOTE (-362))) (|HasCategory| (-721) (LIST (QUOTE -298) (QUOTE (-721)) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -321) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-721) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-721) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-721) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (-2225 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-362)))) (|HasCategory| (-721) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-721) (QUOTE (-1053))) (|HasCategory| (-721) (QUOTE (-1233))) (-12 (|HasCategory| (-721) (QUOTE (-1033))) (|HasCategory| (-721) (QUOTE (-1233)))) (-2225 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-376))) (-12 (|HasCategory| (-721) (QUOTE (-362))) (|HasCategory| (-721) (QUOTE (-938))))) (-2225 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-938)))) (-12 (|HasCategory| (-721) (QUOTE (-362))) (|HasCategory| (-721) (QUOTE (-938))))) (|HasCategory| (-721) (QUOTE (-559))) (-12 (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-1233)))) (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938))) (-2225 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-376)))) (-2225 (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (QUOTE (-239)))) (-2225 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-570)))) (-12 (|HasCategory| (-721) (QUOTE (-239))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-721) (QUOTE (-570))) (|HasAttribute| (-721) (QUOTE -4506)) (|HasAttribute| (-721) (QUOTE -4503)) (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-147)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-362))))) +((-4501 . T) (-4506 |has| (-721) (-376)) (-4500 |has| (-721) (-376)) (-1924 . T) (-4507 |has| (-721) (-6 -4507)) (-4504 |has| (-721) (-6 -4504)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-721) (QUOTE (-149))) (|HasCategory| (-721) (QUOTE (-147))) (|HasCategory| (-721) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-721) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-721) (QUOTE (-381))) (|HasCategory| (-721) (QUOTE (-376))) (-2226 (|HasCategory| (-721) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-239))) (-2226 (-12 (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207))))) (-2226 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-362)))) (|HasCategory| (-721) (QUOTE (-362))) (|HasCategory| (-721) (LIST (QUOTE -298) (QUOTE (-721)) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -321) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-721) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-721) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-721) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (-2226 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-362)))) (|HasCategory| (-721) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-721) (QUOTE (-1053))) (|HasCategory| (-721) (QUOTE (-1233))) (-12 (|HasCategory| (-721) (QUOTE (-1033))) (|HasCategory| (-721) (QUOTE (-1233)))) (-2226 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-376))) (-12 (|HasCategory| (-721) (QUOTE (-362))) (|HasCategory| (-721) (QUOTE (-938))))) (-2226 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-938)))) (-12 (|HasCategory| (-721) (QUOTE (-362))) (|HasCategory| (-721) (QUOTE (-938))))) (|HasCategory| (-721) (QUOTE (-559))) (-12 (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-1233)))) (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938))) (-2226 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-376)))) (-2226 (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (QUOTE (-239)))) (-2226 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-570)))) (-12 (|HasCategory| (-721) (QUOTE (-239))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-721) (QUOTE (-570))) (|HasAttribute| (-721) (QUOTE -4507)) (|HasAttribute| (-721) (QUOTE -4504)) (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-147)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-362))))) (-717 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4508 . T)) +((-4509 . T)) NIL (-718 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}."))) @@ -2808,13 +2808,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-720 OV E -2173 PG) +(-720 OV E -2174 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 (-721) ((|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}"))) -((-1915 . T) (-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-1915 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-722 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."))) @@ -2822,7 +2822,7 @@ NIL NIL (-723) ((|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}"))) -((-4506 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4507 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-724 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"))) @@ -2840,7 +2840,7 @@ 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 -(-728 S -4246 I) +(-728 S -4248 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 @@ -2850,7 +2850,7 @@ NIL NIL (-730 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)}.}"))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) NIL (-731 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}."))) @@ -2860,25 +2860,25 @@ 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 -(-733 R |Mod| -3749 -4168 |exactQuo|) +(-733 R |Mod| -3305 -2157 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-734 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4503 |has| |#1| (-376)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4504 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) (-735 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-736 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) (-4504 . T)) +((-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -3749 -4168 |exactQuo|) +(-737 R |Mod| -3305 -2157 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4504 . T)) +((-4505 . T)) NIL (-738 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2886,11 +2886,11 @@ NIL NIL (-739 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) NIL -(-740 -2173) +(-740 -2174) ((|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]]}."))) -((-4504 . T)) +((-4505 . T)) NIL (-741 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."))) @@ -2914,7 +2914,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-381)))) (-746 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."))) -((-4500 |has| |#1| (-376)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 |has| |#1| (-376)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-747 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."))) @@ -2924,7 +2924,7 @@ 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 -(-749 -2173 UP) +(-749 -2174 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 @@ -2942,8 +2942,8 @@ NIL NIL (-753 |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."))) -(((-4509 "*") |has| |#2| (-175)) (-4500 |has| |#2| (-570)) (-4505 |has| |#2| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#2| (QUOTE (-938))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4505)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) +(((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-570)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#2| (QUOTE (-938))) (-2226 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2226 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) (-754 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2958,15 +2958,15 @@ NIL NIL (-757 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) (-4504 . T)) +((-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) (-4505 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-871)))) (-758 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4497 . T) (-4508 . T)) +((-4498 . T) (-4509 . T)) NIL (-759 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}."))) -((-4507 . T) (-4497 . T) (-4508 . T)) +((-4508 . T) (-4498 . T) (-4509 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-760) ((|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."))) @@ -2978,7 +2978,7 @@ NIL NIL (-762 |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}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4502 . T) (-4501 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4503 . T) (-4502 . T) (-4505 . T)) NIL (-763 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"))) @@ -2994,7 +2994,7 @@ NIL NIL (-766 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}."))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) NIL (-767) ((|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}."))) @@ -3076,11 +3076,11 @@ 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 -(-787 -2173) +(-787 -2174) ((|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 -(-788 P -2173) +(-788 P -2174) ((|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 @@ -3088,7 +3088,7 @@ NIL NIL NIL NIL -(-790 UP -2173) +(-790 UP -2174) ((|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 @@ -3102,9 +3102,9 @@ NIL NIL (-793) ((|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."))) -(((-4509 "*") . T)) +(((-4510 "*") . T)) NIL -(-794 R -2173) +(-794 R -2174) ((|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 @@ -3124,7 +3124,7 @@ 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 -(-799 -2173 |ExtF| |SUEx| |ExtP| |n|) +(-799 -2174 |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 @@ -3138,23 +3138,23 @@ NIL NIL (-802 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."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207))))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (-3523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (-3523 (|HasCategory| |#1| (QUOTE (-559)))) (-3523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (-3523 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-578))))) (-3523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (-3523 (|HasCategory| |#1| (LIST (QUOTE -1023) (QUOTE (-578))))))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-938))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207))))) (-2226 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (-3524 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))))) (-2226 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (-3524 (|HasCategory| |#1| (QUOTE (-559)))) (-3524 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (-3524 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-578))))) (-3524 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (-3524 (|HasCategory| |#1| (LIST (QUOTE -1023) (QUOTE (-578))))))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) (-803 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL (-804 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4503 |has| |#1| (-376)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4504 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) (-805 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-806 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.}"))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) NIL (-807 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}."))) @@ -3206,25 +3206,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-381)))) (-819 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-820 -2225 R OS S) +(-820 -2226 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-821 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2225 (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2225 (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) +((-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2226 (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2226 (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (-822) ((|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 -(-823 R -2173 L) +(-823 R -2174 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 -(-824 R -2173) +(-824 R -2174) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3232,7 +3232,7 @@ 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 -(-826 R -2173) +(-826 R -2174) ((|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 @@ -3240,11 +3240,11 @@ 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 -(-828 -2173 UP UPUP R) +(-828 -2174 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 -(-829 -2173 UP L LQ) +(-829 -2174 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 @@ -3252,41 +3252,41 @@ 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 -(-831 -2173 UP L LQ) +(-831 -2174 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 -(-832 -2173 UP) +(-832 -2174 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-833 -2173 L UP A LO) +(-833 -2174 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 -(-834 -2173 UP) +(-834 -2174 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)))) -(-835 -2173 LO) +(-835 -2174 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 -(-836 -2173 LODO) +(-836 -2174 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 -(-837 -2590 S |f|) +(-837 -2592 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}."))) -((-4501 |has| |#2| (-1080)) (-4502 |has| |#2| (-1080)) (-4504 |has| |#2| (-6 -4504)) (-4507 . 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . 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T) (-4502 . T) (-4505 . 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T) (-4502 . T) (-4501 . T)) +(((-4510 "*") |has| |#2| (-376)) (-4501 |has| |#2| (-376)) (-4506 |has| |#2| (-376)) (-4500 |has| |#2| (-376)) (-4505 . T) (-4503 . T) (-4502 . T)) ((|HasCategory| |#2| (QUOTE (-376)))) (-840 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}))."))) @@ -3298,7 +3298,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-871)))) (-842) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-843) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) @@ -3326,7 +3326,7 @@ NIL NIL (-849 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}."))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-240)))) (-850) ((|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."))) @@ -3338,7 +3338,7 @@ NIL NIL (-852 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4507 . T) (-4497 . T) (-4508 . T)) +((-4508 . T) (-4498 . T) (-4509 . T)) NIL (-853) ((|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."))) @@ -3350,8 +3350,8 @@ NIL NIL (-855 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."))) -((-4504 |has| |#1| (-870))) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2225 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2225 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-559)))) +((-4505 |has| |#1| (-870))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2226 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2226 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-559)))) (-856 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3362,7 +3362,7 @@ NIL NIL (-858 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) (-4504 . T)) +((-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) (-859) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) @@ -3390,13 +3390,13 @@ NIL NIL (-865 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4504 |has| |#1| (-870))) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2225 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2225 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-559)))) +((-4505 |has| |#1| (-870))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2226 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2226 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-559)))) (-866) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-867 -2590 S) +(-867 -2592 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3410,7 +3410,7 @@ NIL NIL (-870) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4504 . T)) +((-4505 . T)) NIL (-871) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) @@ -3434,19 +3434,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175)))) (-876 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) NIL (-877 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 (-376))) (|HasCategory| |#1| (QUOTE (-570)))) -(-878 R |sigma| -4147) +(-878 R |sigma| -4148) ((|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."))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-879 |x| R |sigma| -4147) +(-879 |x| R |sigma| -4148) ((|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}."))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) (-880 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..)}."))) @@ -3490,7 +3490,7 @@ NIL NIL (-890 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) (-4504 . T)) +((-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (-891 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3502,24 +3502,24 @@ NIL NIL (-893 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-894 |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)."))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-895 |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)."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| (-894 |#1|) (QUOTE (-938))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-894 |#1|) (QUOTE (-1053))) (|HasCategory| (-894 |#1|) (QUOTE (-842))) (|HasCategory| (-894 |#1|) (QUOTE (-871))) (-2225 (|HasCategory| (-894 |#1|) (QUOTE (-842))) (|HasCategory| (-894 |#1|) (QUOTE (-871)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (QUOTE (-1183))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -894) (|devaluate| |#1|)) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-938)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-894 |#1|) (QUOTE (-938))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-894 |#1|) (QUOTE (-1053))) (|HasCategory| (-894 |#1|) (QUOTE (-842))) (|HasCategory| (-894 |#1|) (QUOTE (-871))) (-2226 (|HasCategory| (-894 |#1|) (QUOTE (-842))) (|HasCategory| (-894 |#1|) (QUOTE (-871)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (QUOTE (-1183))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -894) (|devaluate| |#1|)) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-938)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) (-896 |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)}."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2225 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2226 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) (-897 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 (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))))) (-898) ((|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 @@ -3579,7 +3579,7 @@ NIL (-912 |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 (-3523 (|HasCategory| |#2| (QUOTE (-1080)))) (-3523 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (-3523 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207))))) +((-12 (-3524 (|HasCategory| |#2| (QUOTE (-1080)))) (-3524 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (-3524 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207))))) (-913 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3588,7 +3588,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-915 R -4246) +(-915 R -4248) ((|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 @@ -3620,7 +3620,7 @@ 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 -(-923 UP -2173) +(-923 UP -2174) ((|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 @@ -3634,11 +3634,11 @@ NIL NIL (-926 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) NIL (-927 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4504 . T)) +((-4505 . T)) NIL (-928 A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) @@ -3651,14 +3651,14 @@ NIL (-930 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 (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-931 |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 (-932 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4504 . T)) +((-4505 . T)) NIL (-933 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3666,8 +3666,8 @@ NIL NIL (-934 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4504 . T)) -((-2225 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) +((-4505 . T)) +((-2226 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (-935 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3682,13 +3682,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-147)))) (-938) ((|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}."))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-939 |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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381)))) -(-940 R0 -2173 UP UPUP R) +(-940 R0 -2174 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 @@ -3702,7 +3702,7 @@ NIL NIL (-943 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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-944 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."))) @@ -3716,7 +3716,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-947 -2173) +(-947 -2174) ((|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 @@ -3726,17 +3726,17 @@ NIL NIL (-949) ((|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| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-950) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4509 "*") . T)) +(((-4510 "*") . T)) NIL -(-951 -2173 P) +(-951 -2174 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-952 |xx| -2173) +(-952 |xx| -2174) ((|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 @@ -3760,7 +3760,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-958 R -2173) +(-958 R -2174) ((|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 @@ -3772,7 +3772,7 @@ 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 -(-961 S R -2173) +(-961 S R -2174) ((|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 @@ -3792,11 +3792,11 @@ 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 -911) (|devaluate| |#1|)))) -(-966 R -2173 -4246) +(-966 R -2174 -4248) ((|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 -(-967 -4246) +(-967 -4248) ((|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 @@ -3818,8 +3818,8 @@ NIL NIL (-972 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-973 |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 @@ -3839,12 +3839,12 @@ NIL (-977 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 (-938))) (|HasAttribute| |#2| (QUOTE -4505)) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#4| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#4| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) +((|HasCategory| |#2| (QUOTE (-938))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#4| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#4| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (-978 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}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) NIL -(-979 E V R P -2173) +(-979 E V R P -2174) ((|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 @@ -3854,9 +3854,9 @@ NIL NIL (-981 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}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) -(-982 E V R P -2173) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-938))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +(-982 E V R P -2174) ((|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 (-466)))) @@ -3878,13 +3878,13 @@ NIL NIL (-987 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"))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-988) ((|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 -(-989 -2173) +(-989 -2174) ((|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 @@ -3898,12 +3898,12 @@ NIL NIL (-992 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}"))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4505))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-6 -4506)) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4506))) (-993 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"))) -((-4504 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) +((-4505 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-994) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3926,7 +3926,7 @@ NIL NIL (-999 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4507 . T) (-4508 . T)) +((-4508 . T) (-4509 . T)) NIL (-1000 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}}"))) @@ -3946,7 +3946,7 @@ NIL NIL (-1004 |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}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1005) ((|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}."))) @@ -3958,7 +3958,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-570)))) (-1007 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."))) -((-4507 . T)) +((-4508 . T)) NIL (-1008 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."))) @@ -3974,7 +3974,7 @@ NIL NIL (-1011 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}."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) NIL (-1012 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) @@ -3992,7 +3992,7 @@ 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 -(-1016 K R UP -2173) +(-1016 K R UP -2174) ((|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 @@ -4022,7 +4022,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-1183)))) (-1023 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}."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1024 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -4034,7 +4034,7 @@ NIL NIL (-1026 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."))) -((-4507 . T) (-4508 . T)) +((-4508 . T) (-4509 . T)) NIL (-1027 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}."))) @@ -4042,7 +4042,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-302)))) (-1028 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}."))) -((-4500 |has| |#1| (-302)) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 |has| |#1| (-302)) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1029 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}."))) @@ -4050,12 +4050,12 @@ NIL NIL (-1030 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.}"))) -((-4500 |has| |#1| (-302)) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) +((-4501 |has| |#1| (-302)) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-376))) (-2226 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) (-1031 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}."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1032 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4064,14 +4064,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1034 -2173 UP UPUP |radicnd| |n|) +(-1034 -2174 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4500 |has| (-421 |#2|) (-376)) (-4505 |has| (-421 |#2|) (-376)) (-4499 |has| (-421 |#2|) (-376)) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-362))) (-2225 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2225 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2225 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2225 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-362))))) (-2225 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -660) (QUOTE (-578)))) (-2225 (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-362))) (-2226 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2226 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2226 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2226 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-362))))) (-2226 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -660) (QUOTE (-578)))) (-2226 (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (-1035 |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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2225 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147))))) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2226 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147))))) (-1036) ((|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 @@ -4091,7 +4091,7 @@ NIL (-1040 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 -4508)) (|HasCategory| |#2| (QUOTE (-1131)))) +((|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-1131)))) (-1041 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 @@ -4102,21 +4102,21 @@ NIL NIL (-1043) ((|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}}"))) -((-4500 . T) (-4505 . T) (-4499 . T) (-4502 . T) (-4501 . T) ((-4509 "*") . T) (-4504 . T)) +((-4501 . T) (-4506 . T) (-4500 . T) (-4503 . T) (-4502 . T) ((-4510 "*") . T) (-4505 . T)) NIL -(-1044 R -2173) +(-1044 R -2174) ((|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 -(-1045 R -2173) +(-1045 R -2174) ((|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 -(-1046 -2173 UP) +(-1046 -2174 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 -(-1047 -2173 UP) +(-1047 -2174 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 @@ -4150,9 +4150,9 @@ NIL NIL (-1055 |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"))) -((-4500 . T) (-4505 . T) (-4499 . T) (-4502 . T) (-4501 . T) ((-4509 "*") . T) (-4504 . T)) -((-2225 (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (QUOTE (-578))))) -(-1056 -2173 L) +((-4501 . T) (-4506 . T) (-4500 . T) (-4503 . T) (-4502 . T) ((-4510 "*") . T) (-4505 . T)) +((-2226 (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (QUOTE (-578))))) +(-1056 -2174 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 @@ -4162,12 +4162,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1131)))) (-1058 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."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1059 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 (-4509 "*")))) +((|HasAttribute| |#1| (QUOTE (-4510 "*")))) (-1060 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 @@ -4188,14 +4188,14 @@ 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 -(-1065 -2173 |Expon| |VarSet| |FPol| |LFPol|) +(-1065 -2174 |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"))) -(((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1066) ((|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.}"))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -2079) (QUOTE (-52))))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-52) (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -2076) (QUOTE (-52))))))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-52) (QUOTE (-1131))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-102)))) (-1067) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4238,7 +4238,7 @@ NIL NIL (-1077 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}."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) ((-12 (|HasCategory| (-802 |#1| (-888 |#2|)) (QUOTE (-1131))) (|HasCategory| (-802 |#1| (-888 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -802) (|devaluate| |#1|) (LIST (QUOTE -888) (|devaluate| |#2|)))))) (|HasCategory| (-802 |#1| (-888 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-802 |#1| (-888 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| (-888 |#2|) (QUOTE (-381))) (|HasCategory| (-802 |#1| (-888 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-802 |#1| (-888 |#2|)) (QUOTE (-102)))) (-1078) ((|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"))) @@ -4250,9 +4250,9 @@ NIL NIL (-1080) ((|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."))) -((-4504 . T)) +((-4505 . T)) NIL -(-1081 |xx| -2173) +(-1081 |xx| -2174) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4266,12 +4266,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-376))) (|HasCategory| |#4| (QUOTE (-570))) (|HasCategory| |#4| (QUOTE (-175)))) (-1084 |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"))) -((-4507 . T) (-4502 . T) (-4501 . T)) +((-4508 . T) (-4503 . T) (-4502 . T)) NIL (-1085 |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}."))) -((-4507 . T) (-4502 . T) (-4501 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-2225 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-570))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-886))))) +((-4508 . T) (-4503 . T) (-4502 . T)) +((|HasCategory| |#3| (QUOTE (-175))) (-2226 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-570))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-886))))) (-1086 |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 @@ -4294,7 +4294,7 @@ NIL NIL (-1091) ((|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."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1092 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4302,19 +4302,19 @@ NIL NIL (-1093) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4495 . T) (-4499 . T) (-4494 . T) (-4505 . T) (-4506 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4496 . T) (-4500 . T) (-4495 . T) (-4506 . T) (-4507 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1094) ((|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}"))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -2079) (QUOTE (-52))))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-1131))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-52) (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -2076) (QUOTE (-52))))))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-1131))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-52) (QUOTE (-1131))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (QUOTE (-102)))) (-1095 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -1023) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-1207))))) (-1096 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) NIL (-1097) ((|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'."))) @@ -4338,7 +4338,7 @@ NIL NIL (-1102 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}."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) NIL (-1103 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."))) @@ -4356,11 +4356,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1107 |Base| R -2173) +(-1107 |Base| R -2174) ((|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 -(-1108 |Base| R -2173) +(-1108 |Base| R -2174) ((|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 @@ -4374,8 +4374,8 @@ NIL NIL (-1111 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."))) -((-4500 |has| |#1| (-376)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-362))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) +((-4501 |has| |#1| (-376)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-362))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-1112 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4402,8 +4402,8 @@ NIL NIL (-1118 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"))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-938))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1119 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 @@ -4446,7 +4446,7 @@ NIL NIL (-1129 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}."))) -((-4497 . T)) +((-4498 . T)) NIL (-1130 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4462,8 +4462,8 @@ NIL NIL (-1133 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)}}"))) -((-4507 . T) (-4497 . T) (-4508 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4508 . T) (-4498 . T) (-4509 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-1134 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL @@ -4490,7 +4490,7 @@ NIL NIL (-1140 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.}"))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) NIL (-1141) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4506,8 +4506,8 @@ NIL NIL (-1144 |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}."))) -((-4501 |has| |#3| (-1080)) (-4502 |has| |#3| (-1080)) (-4504 |has| |#3| (-6 -4504)) (-4507 . 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(((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4516,7 +4516,7 @@ 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 -(-1147 R -2173) +(-1147 R -2174) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4534,19 +4534,19 @@ NIL NIL (-1151) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4495 . T) (-4499 . T) (-4494 . T) (-4505 . T) (-4506 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4496 . T) (-4500 . T) (-4495 . T) (-4506 . T) (-4507 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1152 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4507 . T) (-4508 . T)) +((-4508 . T) (-4509 . T)) NIL (-1153 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-376))) (|HasAttribute| |#3| (QUOTE (-4509 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) +((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4510 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) (-1154 |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."))) -((-4507 . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4508 . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1155 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}."))) @@ -4554,17 +4554,17 @@ NIL NIL (-1156 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."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-938))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1157 |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}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-376)))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-376)))) (-1158 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}"))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) NIL -(-1159 UP -2173) +(-1159 UP -2174) ((|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 @@ -4618,19 +4618,19 @@ NIL NIL (-1172 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."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -321) (LIST (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131))) (-2225 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131)))) (-2225 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -632) (QUOTE (-886)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -321) (LIST (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131))))) (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -321) (LIST (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131))) (-2226 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131)))) (-2226 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -632) (QUOTE (-886)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -321) (LIST (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131))))) (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) (-1173 |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}."))) -((-4504 . T) (-4496 |has| |#2| (-6 (-4509 "*"))) (-4507 . T) (-4501 . T) (-4502 . T)) -((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4509 "*"))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-376))) (-2225 (|HasAttribute| |#2| (QUOTE (-4509 "*"))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((-4505 . T) (-4497 |has| |#2| (-6 (-4510 "*"))) (-4508 . T) (-4502 . T) (-4503 . T)) +((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-376))) (-2226 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-1174 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1175) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) NIL (-1176 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.}"))) @@ -4638,12 +4638,12 @@ NIL NIL (-1177 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."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1178 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}."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1179 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 @@ -4654,8 +4654,8 @@ NIL NIL (-1181 |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."))) -((-4508 . T)) -((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2079) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131)))) +((-4509 . T)) +((-12 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2076) (|devaluate| |#2|)))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131)))) (-1182) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4682,16 +4682,16 @@ NIL NIL (-1188 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) -((-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4509 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1189) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2225 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-146) (QUOTE (-871))) (-2225 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2226 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-146) (QUOTE (-871))) (-2226 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-1190 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4507 . T) (-4508 . T)) -((-12 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -2079) (|devaluate| |#1|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (QUOTE (-1131))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -2076) (|devaluate| |#1|)))))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (QUOTE (-1131))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (-2226 (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (QUOTE (-102)))) (-1191 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 @@ -4722,9 +4722,9 @@ NIL NIL (-1198 |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. 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We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1583) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|))))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (LIST (QUOTE -2864) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2226 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1574) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1879) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1206) ((|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 @@ -4766,8 +4766,8 @@ NIL NIL (-1209 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasAttribute| |#1| (QUOTE -4505))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-6 -4506)) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2226 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasAttribute| |#1| (QUOTE -4506))) (-1210) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) 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T)) -((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2079) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (QUOTE (-102)))) +((-4508 . T) (-4509 . T)) +((-12 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2076) (|devaluate| |#2|)))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2226 (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (QUOTE (-102)))) (-1221 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL @@ -4826,7 +4826,7 @@ NIL NIL (-1224 |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})}."))) -((-4508 . T)) +((-4509 . T)) NIL (-1225 |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."))) @@ -4866,8 +4866,8 @@ NIL NIL (-1234 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4508 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4509 . T) (-4508 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1235 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4876,7 +4876,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1237 R -2173) +(-1237 R -2174) ((|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 @@ -4884,7 +4884,7 @@ 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 -(-1239 R -2173) +(-1239 R -2174) ((|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 -633) (LIST (QUOTE -917) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -911) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -911) (|devaluate| |#1|))))) @@ -4894,12 +4894,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-381)))) (-1241 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) NIL (-1242 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-376)))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-376)))) (-1243 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4912,7 +4912,7 @@ 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 (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) -(-1246 -2173) +(-1246 -2174) ((|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 @@ -4938,7 +4938,7 @@ NIL NIL (-1252) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1253) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4962,7 +4962,7 @@ NIL NIL (-1258 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1259 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)}."))) @@ -4970,16 +4970,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-376)))) (-1260 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1261 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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|#3|) (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-175)))) (-12 (|HasCategory| (-1290 |#1| |#2| |#3|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1290 |#1| |#2| |#3|) (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1290 |#1| |#2| |#3|) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1290 |#1| |#2| |#3|) (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-376)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1290 |#1| |#2| |#3|) (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1290 |#1| |#2| |#3|) (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1263 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 @@ -5014,8 +5014,8 @@ NIL NIL (-1271 |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}"))) -(((-4509 "*") |has| |#2| (-175)) (-4500 |has| |#2| (-570)) (-4503 |has| |#2| (-376)) (-4505 |has| |#2| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4505)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) +(((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-570)) (-4504 |has| |#2| (-376)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2226 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2226 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2226 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2226 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) (-1272 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -5026,15 +5026,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-1183)))) (-1274 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}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4503 |has| |#1| (-376)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4504 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) NIL (-1275 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2863) (LIST (|devaluate| |#2|) (QUOTE (-1207)))))) +((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2864) (LIST (|devaluate| |#2|) (QUOTE (-1207)))))) (-1276 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1277 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -5046,7 +5046,7 @@ NIL NIL (-1279 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1280 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)}."))) @@ -5054,24 +5054,24 @@ NIL NIL (-1281 |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)}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1282 |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)}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1583) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2864) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2226 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1574) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1879) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-1283 |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."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1583) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|))))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2226 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2864) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2226 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1574) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1879) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1284 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))}."))) -(((-4509 "*") |has| (-1283 |#2| |#3| |#4|) (-175)) (-4500 |has| (-1283 |#2| |#3| |#4|) (-570)) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-175))) (-2225 (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-570)))) +(((-4510 "*") |has| (-1283 |#2| |#3| |#4|) (-175)) (-4501 |has| (-1283 |#2| |#3| |#4|) (-570)) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-175))) (-2226 (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-570)))) (-1285 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4508))) +((|HasAttribute| |#1| (QUOTE -4509))) (-1286 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5083,20 +5083,20 @@ NIL (-1288 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-578)))) (|HasCategory| |#2| (QUOTE (-988))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1583) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-988))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (LIST (QUOTE -1879) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1574) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376)))) (-1289 |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."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1290 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1583) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|))))))) +(((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-570)) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2226 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (LIST (QUOTE -2864) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2226 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1574) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1879) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1291 |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 -(-1292 -2173 UP L UTS) +(-1292 -2174 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 (-570)))) @@ -5114,7 +5114,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1296 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) NIL (-1297 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -5122,8 +5122,8 @@ NIL NIL (-1298 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4508 . T) (-4507 . T)) -((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-4509 . T) (-4508 . T)) +((-2226 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2226 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2226 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2226 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-1299) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5150,13 +5150,13 @@ NIL NIL (-1305 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4502 . T) (-4501 . T)) +((-4503 . T) (-4502 . T)) NIL (-1306 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 -(-1307 K R UP -2173) +(-1307 K R UP -2174) ((|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 @@ -5170,56 +5170,56 @@ NIL NIL (-1310 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)"))) -((-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) (-4504 . T)) +((-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (-1311 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}}."))) -((-4508 . T) (-4507 . T)) +((-4509 . T) (-4508 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1312 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})"))) -((-4501 . T) (-4502 . T) (-4504 . T)) +((-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1313 |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."))) -((-4504 . T) (-4500 |has| |#2| (-6 -4500)) (-4502 . T) (-4501 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4500))) +((-4505 . T) (-4501 |has| |#2| (-6 -4501)) (-4503 . T) (-4502 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4501))) (-1314 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 (-1315 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4500 |has| |#2| (-6 -4500)) (-4502 . T) (-4501 . T) (-4504 . T)) +((-4501 |has| |#2| (-6 -4501)) (-4503 . T) (-4502 . T) (-4505 . T)) NIL -(-1316 S -2173) +(-1316 S -2174) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1317 -2173) +(-1317 -2174) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1318 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4500 |has| |#2| (-6 -4500)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (LIST (QUOTE -739) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasAttribute| |#2| (QUOTE -4500))) +((-4501 |has| |#2| (-6 -4501)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (LIST (QUOTE -739) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasAttribute| |#2| (QUOTE -4501))) (-1319 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4500 |has| |#2| (-6 -4500)) (-4502 . T) (-4501 . T) (-4504 . T)) +((-4501 |has| |#2| (-6 -4501)) (-4503 . T) (-4502 . T) (-4505 . T)) NIL (-1320 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4500 |has| |#1| (-6 -4500)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4500))) +((-4501 |has| |#1| (-6 -4501)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4501))) (-1321 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4504 . T) (-4505 |has| |#1| (-6 -4505)) (-4500 |has| |#1| (-6 -4500)) (-4502 . T) (-4501 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasAttribute| |#1| (QUOTE -4505)) (|HasAttribute| |#1| (QUOTE -4500))) +((-4505 . T) (-4506 |has| |#1| (-6 -4506)) (-4501 |has| |#1| (-6 -4501)) (-4503 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4501))) (-1322 |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."))) -((-4500 |has| |#2| (-6 -4500)) (-4502 . T) (-4501 . T) (-4504 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4500))) +((-4501 |has| |#2| (-6 -4501)) (-4503 . T) (-4502 . T) (-4505 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4501))) (-1323) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL @@ -5238,7 +5238,7 @@ NIL NIL (-1327 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T)) +(((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL NIL NIL @@ -5256,4 +5256,4 @@ NIL NIL NIL NIL -((-3 NIL 2300594 2300599 2300604 2300609) (-2 NIL 2300574 2300579 2300584 2300589) (-1 NIL 2300554 2300559 2300564 2300569) (0 NIL 2300534 2300539 2300544 2300549) (-1327 "ZMOD.spad" 2300343 2300356 2300472 2300529) (-1326 "ZLINDEP.spad" 2299409 2299420 2300333 2300338) (-1325 "ZDSOLVE.spad" 2289353 2289375 2299399 2299404) (-1324 "YSTREAM.spad" 2288848 2288859 2289343 2289348) (-1323 "YDIAGRAM.spad" 2288482 2288491 2288838 2288843) (-1322 "XRPOLY.spad" 2287702 2287722 2288338 2288407) (-1321 "XPR.spad" 2285497 2285510 2287420 2287519) (-1320 "XPOLY.spad" 2285052 2285063 2285353 2285422) (-1319 "XPOLYC.spad" 2284371 2284387 2284978 2285047) (-1318 "XPBWPOLY.spad" 2282808 2282828 2284151 2284220) (-1317 "XF.spad" 2281271 2281286 2282710 2282803) (-1316 "XF.spad" 2279714 2279731 2281155 2281160) (-1315 "XFALG.spad" 2276762 2276778 2279640 2279709) (-1314 "XEXPPKG.spad" 2276013 2276039 2276752 2276757) (-1313 "XDPOLY.spad" 2275627 2275643 2275869 2275938) (-1312 "XALG.spad" 2275287 2275298 2275583 2275622) (-1311 "WUTSET.spad" 2271090 2271107 2274897 2274924) (-1310 "WP.spad" 2270289 2270333 2270948 2271015) (-1309 "WHILEAST.spad" 2270087 2270096 2270279 2270284) (-1308 "WHEREAST.spad" 2269758 2269767 2270077 2270082) (-1307 "WFFINTBS.spad" 2267421 2267443 2269748 2269753) (-1306 "WEIER.spad" 2265643 2265654 2267411 2267416) (-1305 "VSPACE.spad" 2265316 2265327 2265611 2265638) (-1304 "VSPACE.spad" 2265009 2265022 2265306 2265311) (-1303 "VOID.spad" 2264686 2264695 2264999 2265004) (-1302 "VIEW.spad" 2262366 2262375 2264676 2264681) (-1301 "VIEWDEF.spad" 2257567 2257576 2262356 2262361) (-1300 "VIEW3D.spad" 2241528 2241537 2257557 2257562) (-1299 "VIEW2D.spad" 2229419 2229428 2241518 2241523) (-1298 "VECTOR.spad" 2227940 2227951 2228191 2228218) (-1297 "VECTOR2.spad" 2226579 2226592 2227930 2227935) (-1296 "VECTCAT.spad" 2224483 2224494 2226547 2226574) (-1295 "VECTCAT.spad" 2222194 2222207 2224260 2224265) (-1294 "VARIABLE.spad" 2221974 2221989 2222184 2222189) (-1293 "UTYPE.spad" 2221618 2221627 2221964 2221969) (-1292 "UTSODETL.spad" 2220913 2220937 2221574 2221579) (-1291 "UTSODE.spad" 2219129 2219149 2220903 2220908) (-1290 "UTS.spad" 2214076 2214104 2217596 2217693) (-1289 "UTSCAT.spad" 2211555 2211571 2213974 2214071) (-1288 "UTSCAT.spad" 2208678 2208696 2211099 2211104) (-1287 "UTS2.spad" 2208273 2208308 2208668 2208673) (-1286 "URAGG.spad" 2202946 2202957 2208263 2208268) (-1285 "URAGG.spad" 2197583 2197596 2202902 2202907) (-1284 "UPXSSING.spad" 2195228 2195254 2196664 2196797) (-1283 "UPXS.spad" 2192524 2192552 2193360 2193509) (-1282 "UPXSCONS.spad" 2190283 2190303 2190656 2190805) (-1281 "UPXSCCA.spad" 2188854 2188874 2190129 2190278) (-1280 "UPXSCCA.spad" 2187567 2187589 2188844 2188849) (-1279 "UPXSCAT.spad" 2186156 2186172 2187413 2187562) (-1278 "UPXS2.spad" 2185699 2185752 2186146 2186151) (-1277 "UPSQFREE.spad" 2184113 2184127 2185689 2185694) (-1276 "UPSCAT.spad" 2181900 2181924 2184011 2184108) (-1275 "UPSCAT.spad" 2179393 2179419 2181506 2181511) (-1274 "UPOLYC.spad" 2174433 2174444 2179235 2179388) (-1273 "UPOLYC.spad" 2169365 2169378 2174169 2174174) (-1272 "UPOLYC2.spad" 2168836 2168855 2169355 2169360) (-1271 "UP.spad" 2165942 2165957 2166329 2166482) (-1270 "UPMP.spad" 2164842 2164855 2165932 2165937) (-1269 "UPDIVP.spad" 2164407 2164421 2164832 2164837) (-1268 "UPDECOMP.spad" 2162652 2162666 2164397 2164402) (-1267 "UPCDEN.spad" 2161861 2161877 2162642 2162647) (-1266 "UP2.spad" 2161225 2161246 2161851 2161856) (-1265 "UNISEG.spad" 2160578 2160589 2161144 2161149) (-1264 "UNISEG2.spad" 2160075 2160088 2160534 2160539) (-1263 "UNIFACT.spad" 2159178 2159190 2160065 2160070) (-1262 "ULS.spad" 2148962 2148990 2149907 2150336) (-1261 "ULSCONS.spad" 2140096 2140116 2140466 2140615) (-1260 "ULSCCAT.spad" 2137833 2137853 2139942 2140091) (-1259 "ULSCCAT.spad" 2135678 2135700 2137789 2137794) (-1258 "ULSCAT.spad" 2133910 2133926 2135524 2135673) (-1257 "ULS2.spad" 2133424 2133477 2133900 2133905) (-1256 "UINT8.spad" 2133301 2133310 2133414 2133419) (-1255 "UINT64.spad" 2133177 2133186 2133291 2133296) (-1254 "UINT32.spad" 2133053 2133062 2133167 2133172) (-1253 "UINT16.spad" 2132929 2132938 2133043 2133048) (-1252 "UFD.spad" 2131994 2132003 2132855 2132924) (-1251 "UFD.spad" 2131121 2131132 2131984 2131989) (-1250 "UDVO.spad" 2130002 2130011 2131111 2131116) (-1249 "UDPO.spad" 2127495 2127506 2129958 2129963) (-1248 "TYPE.spad" 2127427 2127436 2127485 2127490) (-1247 "TYPEAST.spad" 2127346 2127355 2127417 2127422) (-1246 "TWOFACT.spad" 2125998 2126013 2127336 2127341) (-1245 "TUPLE.spad" 2125484 2125495 2125897 2125902) (-1244 "TUBETOOL.spad" 2122351 2122360 2125474 2125479) (-1243 "TUBE.spad" 2120998 2121015 2122341 2122346) (-1242 "TS.spad" 2119597 2119613 2120563 2120660) (-1241 "TSETCAT.spad" 2106724 2106741 2119565 2119592) (-1240 "TSETCAT.spad" 2093837 2093856 2106680 2106685) (-1239 "TRMANIP.spad" 2088203 2088220 2093543 2093548) (-1238 "TRIMAT.spad" 2087166 2087191 2088193 2088198) (-1237 "TRIGMNIP.spad" 2085693 2085710 2087156 2087161) (-1236 "TRIGCAT.spad" 2085205 2085214 2085683 2085688) (-1235 "TRIGCAT.spad" 2084715 2084726 2085195 2085200) (-1234 "TREE.spad" 2083173 2083184 2084205 2084232) (-1233 "TRANFUN.spad" 2083012 2083021 2083163 2083168) (-1232 "TRANFUN.spad" 2082849 2082860 2083002 2083007) (-1231 "TOPSP.spad" 2082523 2082532 2082839 2082844) (-1230 "TOOLSIGN.spad" 2082186 2082197 2082513 2082518) (-1229 "TEXTFILE.spad" 2080747 2080756 2082176 2082181) (-1228 "TEX.spad" 2077893 2077902 2080737 2080742) (-1227 "TEX1.spad" 2077449 2077460 2077883 2077888) (-1226 "TEMUTL.spad" 2077004 2077013 2077439 2077444) (-1225 "TBCMPPK.spad" 2075097 2075120 2076994 2076999) (-1224 "TBAGG.spad" 2074147 2074170 2075077 2075092) (-1223 "TBAGG.spad" 2073205 2073230 2074137 2074142) (-1222 "TANEXP.spad" 2072613 2072624 2073195 2073200) (-1221 "TALGOP.spad" 2072337 2072348 2072603 2072608) (-1220 "TABLE.spad" 2070306 2070329 2070576 2070603) (-1219 "TABLEAU.spad" 2069787 2069798 2070296 2070301) (-1218 "TABLBUMP.spad" 2066590 2066601 2069777 2069782) (-1217 "SYSTEM.spad" 2065818 2065827 2066580 2066585) (-1216 "SYSSOLP.spad" 2063301 2063312 2065808 2065813) (-1215 "SYSPTR.spad" 2063200 2063209 2063291 2063296) (-1214 "SYSNNI.spad" 2062391 2062402 2063190 2063195) (-1213 "SYSINT.spad" 2061795 2061806 2062381 2062386) (-1212 "SYNTAX.spad" 2058001 2058010 2061785 2061790) (-1211 "SYMTAB.spad" 2056069 2056078 2057991 2057996) (-1210 "SYMS.spad" 2052092 2052101 2056059 2056064) (-1209 "SYMPOLY.spad" 2051098 2051109 2051180 2051307) (-1208 "SYMFUNC.spad" 2050599 2050610 2051088 2051093) (-1207 "SYMBOL.spad" 2048102 2048111 2050589 2050594) (-1206 "SWITCH.spad" 2044873 2044882 2048092 2048097) (-1205 "SUTS.spad" 2041921 2041949 2043340 2043437) (-1204 "SUPXS.spad" 2039204 2039232 2040053 2040202) (-1203 "SUP.spad" 2035924 2035935 2036697 2036850) (-1202 "SUPFRACF.spad" 2035029 2035047 2035914 2035919) (-1201 "SUP2.spad" 2034421 2034434 2035019 2035024) (-1200 "SUMRF.spad" 2033395 2033406 2034411 2034416) (-1199 "SUMFS.spad" 2033032 2033049 2033385 2033390) (-1198 "SULS.spad" 2022803 2022831 2023761 2024190) (-1197 "SUCHTAST.spad" 2022572 2022581 2022793 2022798) (-1196 "SUCH.spad" 2022254 2022269 2022562 2022567) (-1195 "SUBSPACE.spad" 2014369 2014384 2022244 2022249) (-1194 "SUBRESP.spad" 2013539 2013553 2014325 2014330) (-1193 "STTF.spad" 2009638 2009654 2013529 2013534) (-1192 "STTFNC.spad" 2006106 2006122 2009628 2009633) (-1191 "STTAYLOR.spad" 1998741 1998752 2005987 2005992) (-1190 "STRTBL.spad" 1996792 1996809 1996941 1996968) (-1189 "STRING.spad" 1995579 1995588 1995800 1995827) (-1188 "STREAM.spad" 1992380 1992391 1994987 1995002) (-1187 "STREAM3.spad" 1991953 1991968 1992370 1992375) (-1186 "STREAM2.spad" 1991081 1991094 1991943 1991948) (-1185 "STREAM1.spad" 1990787 1990798 1991071 1991076) (-1184 "STINPROD.spad" 1989723 1989739 1990777 1990782) (-1183 "STEP.spad" 1988924 1988933 1989713 1989718) (-1182 "STEPAST.spad" 1988158 1988167 1988914 1988919) (-1181 "STBL.spad" 1986242 1986270 1986409 1986424) (-1180 "STAGG.spad" 1985317 1985328 1986232 1986237) (-1179 "STAGG.spad" 1984390 1984403 1985307 1985312) (-1178 "STACK.spad" 1983630 1983641 1983880 1983907) (-1177 "SREGSET.spad" 1981298 1981315 1983240 1983267) (-1176 "SRDCMPK.spad" 1979859 1979879 1981288 1981293) (-1175 "SRAGG.spad" 1975002 1975011 1979827 1979854) (-1174 "SRAGG.spad" 1970165 1970176 1974992 1974997) (-1173 "SQMATRIX.spad" 1967708 1967726 1968624 1968711) (-1172 "SPLTREE.spad" 1962104 1962117 1966988 1967015) (-1171 "SPLNODE.spad" 1958692 1958705 1962094 1962099) (-1170 "SPFCAT.spad" 1957501 1957510 1958682 1958687) (-1169 "SPECOUT.spad" 1956053 1956062 1957491 1957496) (-1168 "SPADXPT.spad" 1947648 1947657 1956043 1956048) (-1167 "spad-parser.spad" 1947113 1947122 1947638 1947643) (-1166 "SPADAST.spad" 1946814 1946823 1947103 1947108) (-1165 "SPACEC.spad" 1931013 1931024 1946804 1946809) (-1164 "SPACE3.spad" 1930789 1930800 1931003 1931008) (-1163 "SORTPAK.spad" 1930338 1930351 1930745 1930750) (-1162 "SOLVETRA.spad" 1928101 1928112 1930328 1930333) (-1161 "SOLVESER.spad" 1926629 1926640 1928091 1928096) (-1160 "SOLVERAD.spad" 1922655 1922666 1926619 1926624) (-1159 "SOLVEFOR.spad" 1921117 1921135 1922645 1922650) (-1158 "SNTSCAT.spad" 1920717 1920734 1921085 1921112) (-1157 "SMTS.spad" 1918989 1919015 1920282 1920379) (-1156 "SMP.spad" 1916464 1916484 1916854 1916981) (-1155 "SMITH.spad" 1915309 1915334 1916454 1916459) (-1154 "SMATCAT.spad" 1913419 1913449 1915253 1915304) (-1153 "SMATCAT.spad" 1911461 1911493 1913297 1913302) (-1152 "SKAGG.spad" 1910424 1910435 1911429 1911456) (-1151 "SINT.spad" 1909364 1909373 1910290 1910419) (-1150 "SIMPAN.spad" 1909092 1909101 1909354 1909359) (-1149 "SIG.spad" 1908422 1908431 1909082 1909087) (-1148 "SIGNRF.spad" 1907540 1907551 1908412 1908417) (-1147 "SIGNEF.spad" 1906819 1906836 1907530 1907535) (-1146 "SIGAST.spad" 1906204 1906213 1906809 1906814) (-1145 "SHP.spad" 1904132 1904147 1906160 1906165) (-1144 "SHDP.spad" 1891810 1891837 1892319 1892418) (-1143 "SGROUP.spad" 1891418 1891427 1891800 1891805) (-1142 "SGROUP.spad" 1891024 1891035 1891408 1891413) (-1141 "SGCF.spad" 1884163 1884172 1891014 1891019) (-1140 "SFRTCAT.spad" 1883093 1883110 1884131 1884158) (-1139 "SFRGCD.spad" 1882156 1882176 1883083 1883088) (-1138 "SFQCMPK.spad" 1876793 1876813 1882146 1882151) (-1137 "SFORT.spad" 1876232 1876246 1876783 1876788) (-1136 "SEXOF.spad" 1876075 1876115 1876222 1876227) (-1135 "SEX.spad" 1875967 1875976 1876065 1876070) (-1134 "SEXCAT.spad" 1873739 1873779 1875957 1875962) (-1133 "SET.spad" 1872027 1872038 1873124 1873163) (-1132 "SETMN.spad" 1870477 1870494 1872017 1872022) (-1131 "SETCAT.spad" 1869962 1869971 1870467 1870472) (-1130 "SETCAT.spad" 1869445 1869456 1869952 1869957) (-1129 "SETAGG.spad" 1865994 1866005 1869425 1869440) (-1128 "SETAGG.spad" 1862551 1862564 1865984 1865989) (-1127 "SEQAST.spad" 1862254 1862263 1862541 1862546) (-1126 "SEGXCAT.spad" 1861410 1861423 1862244 1862249) (-1125 "SEG.spad" 1861223 1861234 1861329 1861334) (-1124 "SEGCAT.spad" 1860148 1860159 1861213 1861218) (-1123 "SEGBIND.spad" 1859906 1859917 1860095 1860100) (-1122 "SEGBIND2.spad" 1859604 1859617 1859896 1859901) (-1121 "SEGAST.spad" 1859318 1859327 1859594 1859599) (-1120 "SEG2.spad" 1858753 1858766 1859274 1859279) (-1119 "SDVAR.spad" 1858029 1858040 1858743 1858748) (-1118 "SDPOL.spad" 1855362 1855373 1855653 1855780) (-1117 "SCPKG.spad" 1853451 1853462 1855352 1855357) (-1116 "SCOPE.spad" 1852604 1852613 1853441 1853446) (-1115 "SCACHE.spad" 1851300 1851311 1852594 1852599) (-1114 "SASTCAT.spad" 1851209 1851218 1851290 1851295) (-1113 "SAOS.spad" 1851081 1851090 1851199 1851204) (-1112 "SAERFFC.spad" 1850794 1850814 1851071 1851076) (-1111 "SAE.spad" 1848264 1848280 1848875 1849010) (-1110 "SAEFACT.spad" 1847965 1847985 1848254 1848259) (-1109 "RURPK.spad" 1845624 1845640 1847955 1847960) (-1108 "RULESET.spad" 1845077 1845101 1845614 1845619) (-1107 "RULE.spad" 1843317 1843341 1845067 1845072) (-1106 "RULECOLD.spad" 1843169 1843182 1843307 1843312) (-1105 "RTVALUE.spad" 1842904 1842913 1843159 1843164) (-1104 "RSTRCAST.spad" 1842621 1842630 1842894 1842899) (-1103 "RSETGCD.spad" 1838999 1839019 1842611 1842616) (-1102 "RSETCAT.spad" 1828935 1828952 1838967 1838994) (-1101 "RSETCAT.spad" 1818891 1818910 1828925 1828930) (-1100 "RSDCMPK.spad" 1817343 1817363 1818881 1818886) (-1099 "RRCC.spad" 1815727 1815757 1817333 1817338) (-1098 "RRCC.spad" 1814109 1814141 1815717 1815722) (-1097 "RPTAST.spad" 1813811 1813820 1814099 1814104) (-1096 "RPOLCAT.spad" 1793171 1793186 1813679 1813806) (-1095 "RPOLCAT.spad" 1772244 1772261 1792754 1792759) (-1094 "ROUTINE.spad" 1767665 1767674 1770429 1770456) (-1093 "ROMAN.spad" 1766993 1767002 1767531 1767660) (-1092 "ROIRC.spad" 1766073 1766105 1766983 1766988) (-1091 "RNS.spad" 1764976 1764985 1765975 1766068) (-1090 "RNS.spad" 1763965 1763976 1764966 1764971) (-1089 "RNG.spad" 1763700 1763709 1763955 1763960) (-1088 "RNGBIND.spad" 1762860 1762874 1763655 1763660) (-1087 "RMODULE.spad" 1762625 1762636 1762850 1762855) (-1086 "RMCAT2.spad" 1762045 1762102 1762615 1762620) (-1085 "RMATRIX.spad" 1760833 1760852 1761176 1761215) (-1084 "RMATCAT.spad" 1756412 1756443 1760789 1760828) (-1083 "RMATCAT.spad" 1751881 1751914 1756260 1756265) (-1082 "RLINSET.spad" 1751585 1751596 1751871 1751876) (-1081 "RINTERP.spad" 1751473 1751493 1751575 1751580) (-1080 "RING.spad" 1750943 1750952 1751453 1751468) (-1079 "RING.spad" 1750421 1750432 1750933 1750938) (-1078 "RIDIST.spad" 1749813 1749822 1750411 1750416) (-1077 "RGCHAIN.spad" 1748341 1748357 1749243 1749270) (-1076 "RGBCSPC.spad" 1748122 1748134 1748331 1748336) (-1075 "RGBCMDL.spad" 1747652 1747664 1748112 1748117) (-1074 "RF.spad" 1745294 1745305 1747642 1747647) (-1073 "RFFACTOR.spad" 1744756 1744767 1745284 1745289) (-1072 "RFFACT.spad" 1744491 1744503 1744746 1744751) (-1071 "RFDIST.spad" 1743487 1743496 1744481 1744486) (-1070 "RETSOL.spad" 1742906 1742919 1743477 1743482) (-1069 "RETRACT.spad" 1742334 1742345 1742896 1742901) (-1068 "RETRACT.spad" 1741760 1741773 1742324 1742329) (-1067 "RETAST.spad" 1741572 1741581 1741750 1741755) (-1066 "RESULT.spad" 1739170 1739179 1739757 1739784) (-1065 "RESRING.spad" 1738517 1738564 1739108 1739165) (-1064 "RESLATC.spad" 1737841 1737852 1738507 1738512) (-1063 "REPSQ.spad" 1737572 1737583 1737831 1737836) (-1062 "REP.spad" 1735126 1735135 1737562 1737567) (-1061 "REPDB.spad" 1734833 1734844 1735116 1735121) (-1060 "REP2.spad" 1724491 1724502 1734675 1734680) (-1059 "REP1.spad" 1718687 1718698 1724441 1724446) (-1058 "REGSET.spad" 1716448 1716465 1718297 1718324) (-1057 "REF.spad" 1715783 1715794 1716403 1716408) (-1056 "REDORDER.spad" 1714989 1715006 1715773 1715778) (-1055 "RECLOS.spad" 1713772 1713792 1714476 1714569) (-1054 "REALSOLV.spad" 1712912 1712921 1713762 1713767) (-1053 "REAL.spad" 1712784 1712793 1712902 1712907) (-1052 "REAL0Q.spad" 1710082 1710097 1712774 1712779) (-1051 "REAL0.spad" 1706926 1706941 1710072 1710077) (-1050 "RDUCEAST.spad" 1706647 1706656 1706916 1706921) (-1049 "RDIV.spad" 1706302 1706327 1706637 1706642) (-1048 "RDIST.spad" 1705869 1705880 1706292 1706297) (-1047 "RDETRS.spad" 1704733 1704751 1705859 1705864) (-1046 "RDETR.spad" 1702872 1702890 1704723 1704728) (-1045 "RDEEFS.spad" 1701971 1701988 1702862 1702867) (-1044 "RDEEF.spad" 1700981 1700998 1701961 1701966) (-1043 "RCFIELD.spad" 1698167 1698176 1700883 1700976) (-1042 "RCFIELD.spad" 1695439 1695450 1698157 1698162) (-1041 "RCAGG.spad" 1693367 1693378 1695429 1695434) (-1040 "RCAGG.spad" 1691222 1691235 1693286 1693291) (-1039 "RATRET.spad" 1690582 1690593 1691212 1691217) (-1038 "RATFACT.spad" 1690274 1690286 1690572 1690577) (-1037 "RANDSRC.spad" 1689593 1689602 1690264 1690269) (-1036 "RADUTIL.spad" 1689349 1689358 1689583 1689588) (-1035 "RADIX.spad" 1686173 1686187 1687719 1687812) (-1034 "RADFF.spad" 1683912 1683949 1684031 1684187) (-1033 "RADCAT.spad" 1683507 1683516 1683902 1683907) (-1032 "RADCAT.spad" 1683100 1683111 1683497 1683502) (-1031 "QUEUE.spad" 1682331 1682342 1682590 1682617) (-1030 "QUAT.spad" 1680819 1680830 1681162 1681227) (-1029 "QUATCT2.spad" 1680439 1680458 1680809 1680814) (-1028 "QUATCAT.spad" 1678609 1678620 1680369 1680434) (-1027 "QUATCAT.spad" 1676530 1676543 1678292 1678297) (-1026 "QUAGG.spad" 1675357 1675368 1676498 1676525) (-1025 "QQUTAST.spad" 1675125 1675134 1675347 1675352) (-1024 "QFORM.spad" 1674743 1674758 1675115 1675120) (-1023 "QFCAT.spad" 1673445 1673456 1674645 1674738) (-1022 "QFCAT.spad" 1671738 1671751 1672940 1672945) (-1021 "QFCAT2.spad" 1671430 1671447 1671728 1671733) (-1020 "QEQUAT.spad" 1670988 1670997 1671420 1671425) (-1019 "QCMPACK.spad" 1665734 1665754 1670978 1670983) (-1018 "QALGSET.spad" 1661812 1661845 1665648 1665653) (-1017 "QALGSET2.spad" 1659807 1659826 1661802 1661807) (-1016 "PWFFINTB.spad" 1657222 1657244 1659797 1659802) (-1015 "PUSHVAR.spad" 1656560 1656580 1657212 1657217) (-1014 "PTRANFN.spad" 1652687 1652698 1656550 1656555) (-1013 "PTPACK.spad" 1649774 1649785 1652677 1652682) (-1012 "PTFUNC2.spad" 1649596 1649611 1649764 1649769) (-1011 "PTCAT.spad" 1648850 1648861 1649564 1649591) (-1010 "PSQFR.spad" 1648156 1648181 1648840 1648845) (-1009 "PSEUDLIN.spad" 1647041 1647052 1648146 1648151) (-1008 "PSETPK.spad" 1632473 1632490 1646919 1646924) (-1007 "PSETCAT.spad" 1626392 1626416 1632453 1632468) (-1006 "PSETCAT.spad" 1620285 1620311 1626348 1626353) (-1005 "PSCURVE.spad" 1619267 1619276 1620275 1620280) (-1004 "PSCAT.spad" 1618049 1618079 1619165 1619262) (-1003 "PSCAT.spad" 1616921 1616953 1618039 1618044) (-1002 "PRTITION.spad" 1615618 1615627 1616911 1616916) (-1001 "PRTDAST.spad" 1615336 1615345 1615608 1615613) (-1000 "PRS.spad" 1604897 1604915 1615292 1615297) (-999 "PRQAGG.spad" 1604332 1604342 1604865 1604892) (-998 "PROPLOG.spad" 1603904 1603912 1604322 1604327) (-997 "PROPFUN2.spad" 1603527 1603540 1603894 1603899) (-996 "PROPFUN1.spad" 1602925 1602936 1603517 1603522) (-995 "PROPFRML.spad" 1601493 1601504 1602915 1602920) (-994 "PROPERTY.spad" 1600981 1600989 1601483 1601488) (-993 "PRODUCT.spad" 1598663 1598675 1598947 1599002) (-992 "PR.spad" 1597055 1597067 1597754 1597881) (-991 "PRINT.spad" 1596807 1596815 1597045 1597050) (-990 "PRIMES.spad" 1595060 1595070 1596797 1596802) (-989 "PRIMELT.spad" 1593141 1593155 1595050 1595055) (-988 "PRIMCAT.spad" 1592768 1592776 1593131 1593136) (-987 "PRIMARR.spad" 1591620 1591630 1591798 1591825) (-986 "PRIMARR2.spad" 1590387 1590399 1591610 1591615) (-985 "PREASSOC.spad" 1589769 1589781 1590377 1590382) (-984 "PPCURVE.spad" 1588906 1588914 1589759 1589764) (-983 "PORTNUM.spad" 1588681 1588689 1588896 1588901) (-982 "POLYROOT.spad" 1587530 1587552 1588637 1588642) (-981 "POLY.spad" 1584865 1584875 1585380 1585507) (-980 "POLYLIFT.spad" 1584130 1584153 1584855 1584860) (-979 "POLYCATQ.spad" 1582248 1582270 1584120 1584125) (-978 "POLYCAT.spad" 1575718 1575739 1582116 1582243) (-977 "POLYCAT.spad" 1568526 1568549 1574926 1574931) (-976 "POLY2UP.spad" 1567978 1567992 1568516 1568521) (-975 "POLY2.spad" 1567575 1567587 1567968 1567973) (-974 "POLUTIL.spad" 1566516 1566545 1567531 1567536) (-973 "POLTOPOL.spad" 1565264 1565279 1566506 1566511) (-972 "POINT.spad" 1563949 1563959 1564036 1564063) (-971 "PNTHEORY.spad" 1560651 1560659 1563939 1563944) (-970 "PMTOOLS.spad" 1559426 1559440 1560641 1560646) (-969 "PMSYM.spad" 1558975 1558985 1559416 1559421) (-968 "PMQFCAT.spad" 1558566 1558580 1558965 1558970) (-967 "PMPRED.spad" 1558045 1558059 1558556 1558561) (-966 "PMPREDFS.spad" 1557499 1557521 1558035 1558040) (-965 "PMPLCAT.spad" 1556579 1556597 1557431 1557436) (-964 "PMLSAGG.spad" 1556164 1556178 1556569 1556574) (-963 "PMKERNEL.spad" 1555743 1555755 1556154 1556159) (-962 "PMINS.spad" 1555323 1555333 1555733 1555738) (-961 "PMFS.spad" 1554900 1554918 1555313 1555318) (-960 "PMDOWN.spad" 1554190 1554204 1554890 1554895) (-959 "PMASS.spad" 1553200 1553208 1554180 1554185) (-958 "PMASSFS.spad" 1552167 1552183 1553190 1553195) (-957 "PLOTTOOL.spad" 1551947 1551955 1552157 1552162) (-956 "PLOT.spad" 1546870 1546878 1551937 1551942) (-955 "PLOT3D.spad" 1543334 1543342 1546860 1546865) (-954 "PLOT1.spad" 1542491 1542501 1543324 1543329) (-953 "PLEQN.spad" 1529781 1529808 1542481 1542486) (-952 "PINTERP.spad" 1529403 1529422 1529771 1529776) (-951 "PINTERPA.spad" 1529187 1529203 1529393 1529398) (-950 "PI.spad" 1528796 1528804 1529161 1529182) (-949 "PID.spad" 1527766 1527774 1528722 1528791) (-948 "PICOERCE.spad" 1527423 1527433 1527756 1527761) (-947 "PGROEB.spad" 1526024 1526038 1527413 1527418) (-946 "PGE.spad" 1517641 1517649 1526014 1526019) (-945 "PGCD.spad" 1516531 1516548 1517631 1517636) (-944 "PFRPAC.spad" 1515680 1515690 1516521 1516526) (-943 "PFR.spad" 1512343 1512353 1515582 1515675) (-942 "PFOTOOLS.spad" 1511601 1511617 1512333 1512338) (-941 "PFOQ.spad" 1510971 1510989 1511591 1511596) (-940 "PFO.spad" 1510390 1510417 1510961 1510966) (-939 "PF.spad" 1509964 1509976 1510195 1510288) (-938 "PFECAT.spad" 1507646 1507654 1509890 1509959) (-937 "PFECAT.spad" 1505356 1505366 1507602 1507607) (-936 "PFBRU.spad" 1503244 1503256 1505346 1505351) (-935 "PFBR.spad" 1500804 1500827 1503234 1503239) (-934 "PERM.spad" 1496611 1496621 1500634 1500649) (-933 "PERMGRP.spad" 1491381 1491391 1496601 1496606) (-932 "PERMCAT.spad" 1490042 1490052 1491361 1491376) (-931 "PERMAN.spad" 1488574 1488588 1490032 1490037) (-930 "PENDTREE.spad" 1487798 1487808 1488086 1488091) (-929 "PDSPC.spad" 1486611 1486621 1487788 1487793) (-928 "PDSPC.spad" 1485422 1485434 1486601 1486606) (-927 "PDRING.spad" 1485264 1485274 1485402 1485417) (-926 "PDMOD.spad" 1485080 1485092 1485232 1485259) (-925 "PDEPROB.spad" 1484095 1484103 1485070 1485075) (-924 "PDEPACK.spad" 1478135 1478143 1484085 1484090) (-923 "PDECOMP.spad" 1477605 1477622 1478125 1478130) (-922 "PDECAT.spad" 1475961 1475969 1477595 1477600) (-921 "PDDOM.spad" 1475399 1475412 1475951 1475956) (-920 "PDDOM.spad" 1474835 1474850 1475389 1475394) (-919 "PCOMP.spad" 1474688 1474701 1474825 1474830) (-918 "PBWLB.spad" 1473276 1473293 1474678 1474683) (-917 "PATTERN.spad" 1467815 1467825 1473266 1473271) (-916 "PATTERN2.spad" 1467553 1467565 1467805 1467810) (-915 "PATTERN1.spad" 1465889 1465905 1467543 1467548) (-914 "PATRES.spad" 1463464 1463476 1465879 1465884) (-913 "PATRES2.spad" 1463136 1463150 1463454 1463459) (-912 "PATMATCH.spad" 1461333 1461364 1462844 1462849) (-911 "PATMAB.spad" 1460762 1460772 1461323 1461328) (-910 "PATLRES.spad" 1459848 1459862 1460752 1460757) (-909 "PATAB.spad" 1459612 1459622 1459838 1459843) (-908 "PARTPERM.spad" 1457620 1457628 1459602 1459607) (-907 "PARSURF.spad" 1457054 1457082 1457610 1457615) (-906 "PARSU2.spad" 1456851 1456867 1457044 1457049) (-905 "script-parser.spad" 1456371 1456379 1456841 1456846) (-904 "PARSCURV.spad" 1455805 1455833 1456361 1456366) (-903 "PARSC2.spad" 1455596 1455612 1455795 1455800) (-902 "PARPCURV.spad" 1455058 1455086 1455586 1455591) (-901 "PARPC2.spad" 1454849 1454865 1455048 1455053) (-900 "PARAMAST.spad" 1453977 1453985 1454839 1454844) (-899 "PAN2EXPR.spad" 1453389 1453397 1453967 1453972) (-898 "PALETTE.spad" 1452359 1452367 1453379 1453384) (-897 "PAIR.spad" 1451346 1451359 1451947 1451952) (-896 "PADICRC.spad" 1448587 1448605 1449758 1449851) (-895 "PADICRAT.spad" 1446495 1446507 1446716 1446809) (-894 "PADIC.spad" 1446190 1446202 1446421 1446490) (-893 "PADICCT.spad" 1444739 1444751 1446116 1446185) (-892 "PADEPAC.spad" 1443428 1443447 1444729 1444734) (-891 "PADE.spad" 1442180 1442196 1443418 1443423) (-890 "OWP.spad" 1441420 1441450 1442038 1442105) (-889 "OVERSET.spad" 1440993 1441001 1441410 1441415) (-888 "OVAR.spad" 1440774 1440797 1440983 1440988) (-887 "OUT.spad" 1439860 1439868 1440764 1440769) (-886 "OUTFORM.spad" 1429252 1429260 1439850 1439855) (-885 "OUTBFILE.spad" 1428670 1428678 1429242 1429247) (-884 "OUTBCON.spad" 1427676 1427684 1428660 1428665) (-883 "OUTBCON.spad" 1426680 1426690 1427666 1427671) (-882 "OSI.spad" 1426155 1426163 1426670 1426675) (-881 "OSGROUP.spad" 1426073 1426081 1426145 1426150) (-880 "ORTHPOL.spad" 1424558 1424568 1425990 1425995) (-879 "OREUP.spad" 1424011 1424039 1424238 1424277) (-878 "ORESUP.spad" 1423312 1423336 1423691 1423730) (-877 "OREPCTO.spad" 1421169 1421181 1423232 1423237) (-876 "OREPCAT.spad" 1415316 1415326 1421125 1421164) (-875 "OREPCAT.spad" 1409353 1409365 1415164 1415169) (-874 "ORDTYPE.spad" 1408590 1408598 1409343 1409348) (-873 "ORDTYPE.spad" 1407825 1407835 1408580 1408585) (-872 "ORDSTRCT.spad" 1407598 1407613 1407761 1407766) (-871 "ORDSET.spad" 1407298 1407306 1407588 1407593) (-870 "ORDRING.spad" 1406688 1406696 1407278 1407293) (-869 "ORDRING.spad" 1406086 1406096 1406678 1406683) (-868 "ORDMON.spad" 1405941 1405949 1406076 1406081) (-867 "ORDFUNS.spad" 1405073 1405089 1405931 1405936) (-866 "ORDFIN.spad" 1404893 1404901 1405063 1405068) (-865 "ORDCOMP.spad" 1403358 1403368 1404440 1404469) (-864 "ORDCOMP2.spad" 1402651 1402663 1403348 1403353) (-863 "OPTPROB.spad" 1401289 1401297 1402641 1402646) (-862 "OPTPACK.spad" 1393698 1393706 1401279 1401284) (-861 "OPTCAT.spad" 1391377 1391385 1393688 1393693) (-860 "OPSIG.spad" 1391031 1391039 1391367 1391372) (-859 "OPQUERY.spad" 1390580 1390588 1391021 1391026) (-858 "OP.spad" 1390322 1390332 1390402 1390469) (-857 "OPERCAT.spad" 1389788 1389798 1390312 1390317) (-856 "OPERCAT.spad" 1389252 1389264 1389778 1389783) (-855 "ONECOMP.spad" 1387997 1388007 1388799 1388828) (-854 "ONECOMP2.spad" 1387421 1387433 1387987 1387992) (-853 "OMSERVER.spad" 1386427 1386435 1387411 1387416) (-852 "OMSAGG.spad" 1386215 1386225 1386383 1386422) (-851 "OMPKG.spad" 1384831 1384839 1386205 1386210) (-850 "OM.spad" 1383804 1383812 1384821 1384826) (-849 "OMLO.spad" 1383229 1383241 1383690 1383729) (-848 "OMEXPR.spad" 1383063 1383073 1383219 1383224) (-847 "OMERR.spad" 1382608 1382616 1383053 1383058) (-846 "OMERRK.spad" 1381642 1381650 1382598 1382603) (-845 "OMENC.spad" 1380986 1380994 1381632 1381637) (-844 "OMDEV.spad" 1375295 1375303 1380976 1380981) (-843 "OMCONN.spad" 1374704 1374712 1375285 1375290) (-842 "OINTDOM.spad" 1374467 1374475 1374630 1374699) (-841 "OFMONOID.spad" 1372590 1372600 1374423 1374428) (-840 "ODVAR.spad" 1371851 1371861 1372580 1372585) (-839 "ODR.spad" 1371495 1371521 1371663 1371812) (-838 "ODPOL.spad" 1368784 1368794 1369124 1369251) (-837 "ODP.spad" 1356598 1356618 1356971 1357070) (-836 "ODETOOLS.spad" 1355247 1355266 1356588 1356593) (-835 "ODESYS.spad" 1352941 1352958 1355237 1355242) (-834 "ODERTRIC.spad" 1348950 1348967 1352898 1352903) (-833 "ODERED.spad" 1348349 1348373 1348940 1348945) (-832 "ODERAT.spad" 1345964 1345981 1348339 1348344) (-831 "ODEPRRIC.spad" 1343001 1343023 1345954 1345959) (-830 "ODEPROB.spad" 1342258 1342266 1342991 1342996) (-829 "ODEPRIM.spad" 1339592 1339614 1342248 1342253) (-828 "ODEPAL.spad" 1338978 1339002 1339582 1339587) (-827 "ODEPACK.spad" 1325644 1325652 1338968 1338973) (-826 "ODEINT.spad" 1325079 1325095 1325634 1325639) (-825 "ODEIFTBL.spad" 1322474 1322482 1325069 1325074) (-824 "ODEEF.spad" 1317965 1317981 1322464 1322469) (-823 "ODECONST.spad" 1317502 1317520 1317955 1317960) (-822 "ODECAT.spad" 1316100 1316108 1317492 1317497) (-821 "OCT.spad" 1314236 1314246 1314950 1314989) (-820 "OCTCT2.spad" 1313882 1313903 1314226 1314231) (-819 "OC.spad" 1311678 1311688 1313838 1313877) (-818 "OC.spad" 1309199 1309211 1311361 1311366) (-817 "OCAMON.spad" 1309047 1309055 1309189 1309194) (-816 "OASGP.spad" 1308862 1308870 1309037 1309042) (-815 "OAMONS.spad" 1308384 1308392 1308852 1308857) (-814 "OAMON.spad" 1308245 1308253 1308374 1308379) (-813 "OAGROUP.spad" 1308107 1308115 1308235 1308240) (-812 "NUMTUBE.spad" 1307698 1307714 1308097 1308102) (-811 "NUMQUAD.spad" 1295674 1295682 1307688 1307693) (-810 "NUMODE.spad" 1287028 1287036 1295664 1295669) (-809 "NUMINT.spad" 1284594 1284602 1287018 1287023) (-808 "NUMFMT.spad" 1283434 1283442 1284584 1284589) (-807 "NUMERIC.spad" 1275548 1275558 1283239 1283244) (-806 "NTSCAT.spad" 1274056 1274072 1275516 1275543) (-805 "NTPOLFN.spad" 1273607 1273617 1273973 1273978) (-804 "NSUP.spad" 1266560 1266570 1271100 1271253) (-803 "NSUP2.spad" 1265952 1265964 1266550 1266555) (-802 "NSMP.spad" 1262182 1262201 1262490 1262617) (-801 "NREP.spad" 1260560 1260574 1262172 1262177) (-800 "NPCOEF.spad" 1259806 1259826 1260550 1260555) (-799 "NORMRETR.spad" 1259404 1259443 1259796 1259801) (-798 "NORMPK.spad" 1257306 1257325 1259394 1259399) (-797 "NORMMA.spad" 1256994 1257020 1257296 1257301) (-796 "NONE.spad" 1256735 1256743 1256984 1256989) (-795 "NONE1.spad" 1256411 1256421 1256725 1256730) (-794 "NODE1.spad" 1255898 1255914 1256401 1256406) (-793 "NNI.spad" 1254793 1254801 1255872 1255893) (-792 "NLINSOL.spad" 1253419 1253429 1254783 1254788) (-791 "NIPROB.spad" 1251960 1251968 1253409 1253414) (-790 "NFINTBAS.spad" 1249520 1249537 1251950 1251955) (-789 "NETCLT.spad" 1249494 1249505 1249510 1249515) (-788 "NCODIV.spad" 1247710 1247726 1249484 1249489) (-787 "NCNTFRAC.spad" 1247352 1247366 1247700 1247705) (-786 "NCEP.spad" 1245518 1245532 1247342 1247347) (-785 "NASRING.spad" 1245114 1245122 1245508 1245513) (-784 "NASRING.spad" 1244708 1244718 1245104 1245109) (-783 "NARNG.spad" 1244060 1244068 1244698 1244703) (-782 "NARNG.spad" 1243410 1243420 1244050 1244055) (-781 "NAGSP.spad" 1242487 1242495 1243400 1243405) (-780 "NAGS.spad" 1232148 1232156 1242477 1242482) (-779 "NAGF07.spad" 1230579 1230587 1232138 1232143) (-778 "NAGF04.spad" 1224981 1224989 1230569 1230574) (-777 "NAGF02.spad" 1219050 1219058 1224971 1224976) (-776 "NAGF01.spad" 1214811 1214819 1219040 1219045) (-775 "NAGE04.spad" 1208511 1208519 1214801 1214806) (-774 "NAGE02.spad" 1199171 1199179 1208501 1208506) (-773 "NAGE01.spad" 1195173 1195181 1199161 1199166) (-772 "NAGD03.spad" 1193177 1193185 1195163 1195168) (-771 "NAGD02.spad" 1185924 1185932 1193167 1193172) (-770 "NAGD01.spad" 1180217 1180225 1185914 1185919) (-769 "NAGC06.spad" 1176092 1176100 1180207 1180212) (-768 "NAGC05.spad" 1174593 1174601 1176082 1176087) (-767 "NAGC02.spad" 1173860 1173868 1174583 1174588) (-766 "NAALG.spad" 1173401 1173411 1173828 1173855) (-765 "NAALG.spad" 1172962 1172974 1173391 1173396) (-764 "MULTSQFR.spad" 1169920 1169937 1172952 1172957) (-763 "MULTFACT.spad" 1169303 1169320 1169910 1169915) (-762 "MTSCAT.spad" 1167397 1167418 1169201 1169298) (-761 "MTHING.spad" 1167056 1167066 1167387 1167392) (-760 "MSYSCMD.spad" 1166490 1166498 1167046 1167051) (-759 "MSET.spad" 1164412 1164422 1166160 1166199) (-758 "MSETAGG.spad" 1164257 1164267 1164380 1164407) (-757 "MRING.spad" 1161234 1161246 1163965 1164032) (-756 "MRF2.spad" 1160804 1160818 1161224 1161229) (-755 "MRATFAC.spad" 1160350 1160367 1160794 1160799) (-754 "MPRFF.spad" 1158390 1158409 1160340 1160345) (-753 "MPOLY.spad" 1155861 1155876 1156220 1156347) (-752 "MPCPF.spad" 1155125 1155144 1155851 1155856) (-751 "MPC3.spad" 1154942 1154982 1155115 1155120) (-750 "MPC2.spad" 1154587 1154620 1154932 1154937) (-749 "MONOTOOL.spad" 1152938 1152955 1154577 1154582) (-748 "MONOID.spad" 1152257 1152265 1152928 1152933) (-747 "MONOID.spad" 1151574 1151584 1152247 1152252) (-746 "MONOGEN.spad" 1150322 1150335 1151434 1151569) (-745 "MONOGEN.spad" 1149092 1149107 1150206 1150211) (-744 "MONADWU.spad" 1147122 1147130 1149082 1149087) (-743 "MONADWU.spad" 1145150 1145160 1147112 1147117) (-742 "MONAD.spad" 1144310 1144318 1145140 1145145) (-741 "MONAD.spad" 1143468 1143478 1144300 1144305) (-740 "MOEBIUS.spad" 1142204 1142218 1143448 1143463) (-739 "MODULE.spad" 1142074 1142084 1142172 1142199) (-738 "MODULE.spad" 1141964 1141976 1142064 1142069) (-737 "MODRING.spad" 1141299 1141338 1141944 1141959) (-736 "MODOP.spad" 1139964 1139976 1141121 1141188) (-735 "MODMONOM.spad" 1139695 1139713 1139954 1139959) (-734 "MODMON.spad" 1136397 1136413 1137116 1137269) (-733 "MODFIELD.spad" 1135759 1135798 1136299 1136392) (-732 "MMLFORM.spad" 1134619 1134627 1135749 1135754) (-731 "MMAP.spad" 1134361 1134395 1134609 1134614) (-730 "MLO.spad" 1132820 1132830 1134317 1134356) (-729 "MLIFT.spad" 1131432 1131449 1132810 1132815) (-728 "MKUCFUNC.spad" 1130967 1130985 1131422 1131427) (-727 "MKRECORD.spad" 1130571 1130584 1130957 1130962) (-726 "MKFUNC.spad" 1129978 1129988 1130561 1130566) (-725 "MKFLCFN.spad" 1128946 1128956 1129968 1129973) (-724 "MKBCFUNC.spad" 1128441 1128459 1128936 1128941) (-723 "MINT.spad" 1127880 1127888 1128343 1128436) (-722 "MHROWRED.spad" 1126391 1126401 1127870 1127875) (-721 "MFLOAT.spad" 1124911 1124919 1126281 1126386) (-720 "MFINFACT.spad" 1124311 1124333 1124901 1124906) (-719 "MESH.spad" 1122093 1122101 1124301 1124306) (-718 "MDDFACT.spad" 1120304 1120314 1122083 1122088) (-717 "MDAGG.spad" 1119595 1119605 1120284 1120299) (-716 "MCMPLX.spad" 1115026 1115034 1115640 1115841) (-715 "MCDEN.spad" 1114236 1114248 1115016 1115021) (-714 "MCALCFN.spad" 1111358 1111384 1114226 1114231) (-713 "MAYBE.spad" 1110642 1110653 1111348 1111353) (-712 "MATSTOR.spad" 1107950 1107960 1110632 1110637) (-711 "MATRIX.spad" 1106537 1106547 1107021 1107048) (-710 "MATLIN.spad" 1103881 1103905 1106421 1106426) (-709 "MATCAT.spad" 1095403 1095425 1103849 1103876) (-708 "MATCAT.spad" 1086797 1086821 1095245 1095250) (-707 "MATCAT2.spad" 1086079 1086127 1086787 1086792) (-706 "MAPPKG3.spad" 1084994 1085008 1086069 1086074) (-705 "MAPPKG2.spad" 1084332 1084344 1084984 1084989) (-704 "MAPPKG1.spad" 1083160 1083170 1084322 1084327) (-703 "MAPPAST.spad" 1082475 1082483 1083150 1083155) (-702 "MAPHACK3.spad" 1082287 1082301 1082465 1082470) (-701 "MAPHACK2.spad" 1082056 1082068 1082277 1082282) (-700 "MAPHACK1.spad" 1081700 1081710 1082046 1082051) (-699 "MAGMA.spad" 1079490 1079507 1081690 1081695) (-698 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584396 585843 585848) (-376 "FIELD.spad" 583785 583793 584281 584374) (-375 "FIELD.spad" 583277 583287 583775 583780) (-374 "FGROUP.spad" 581924 581934 583257 583272) (-373 "FGLMICPK.spad" 580711 580726 581914 581919) (-372 "FFX.spad" 580086 580101 580427 580520) (-371 "FFSLPE.spad" 579589 579610 580076 580081) (-370 "FFPOLY.spad" 570851 570862 579579 579584) (-369 "FFPOLY2.spad" 569911 569928 570841 570846) (-368 "FFP.spad" 569308 569328 569627 569720) (-367 "FF.spad" 568756 568772 568989 569082) (-366 "FFNBX.spad" 567268 567288 568472 568565) (-365 "FFNBP.spad" 565781 565798 566984 567077) (-364 "FFNB.spad" 564246 564267 565462 565555) (-363 "FFINTBAS.spad" 561760 561779 564236 564241) (-362 "FFIELDC.spad" 559337 559345 561662 561755) (-361 "FFIELDC.spad" 557000 557010 559327 559332) (-360 "FFHOM.spad" 555748 555765 556990 556995) (-359 "FFF.spad" 553183 553194 555738 555743) (-358 "FFCGX.spad" 552030 552050 552899 552992) (-357 "FFCGP.spad" 550919 550939 551746 551839) (-356 "FFCG.spad" 549711 549732 550600 550693) (-355 "FFCAT.spad" 542884 542906 549550 549706) (-354 "FFCAT.spad" 536136 536160 542804 542809) (-353 "FFCAT2.spad" 535883 535923 536126 536131) (-352 "FEXPR.spad" 527600 527646 535639 535678) (-351 "FEVALAB.spad" 527308 527318 527590 527595) (-350 "FEVALAB.spad" 526801 526813 527085 527090) (-349 "FDIV.spad" 526243 526267 526791 526796) (-348 "FDIVCAT.spad" 524307 524331 526233 526238) (-347 "FDIVCAT.spad" 522369 522395 524297 524302) (-346 "FDIV2.spad" 522025 522065 522359 522364) (-345 "FCTRDATA.spad" 521033 521041 522015 522020) (-344 "FCPAK1.spad" 519600 519608 521023 521028) (-343 "FCOMP.spad" 518979 518989 519590 519595) (-342 "FC.spad" 508986 508994 518969 518974) (-341 "FAXF.spad" 501957 501971 508888 508981) (-340 "FAXF.spad" 494980 494996 501913 501918) (-339 "FARRAY.spad" 492977 492987 494010 494037) (-338 "FAMR.spad" 491113 491125 492875 492972) (-337 "FAMR.spad" 489233 489247 490997 491002) (-336 "FAMONOID.spad" 488901 488911 489187 489192) (-335 "FAMONC.spad" 487197 487209 488891 488896) (-334 "FAGROUP.spad" 486821 486831 487093 487120) (-333 "FACUTIL.spad" 485025 485042 486811 486816) (-332 "FACTFUNC.spad" 484219 484229 485015 485020) (-331 "EXPUPXS.spad" 481052 481075 482351 482500) (-330 "EXPRTUBE.spad" 478340 478348 481042 481047) (-329 "EXPRODE.spad" 475500 475516 478330 478335) (-328 "EXPR.spad" 470675 470685 471389 471684) (-327 "EXPR2UPS.spad" 466797 466810 470665 470670) (-326 "EXPR2.spad" 466502 466514 466787 466792) (-325 "EXPEXPAN.spad" 463303 463328 463935 464028) (-324 "EXIT.spad" 462974 462982 463293 463298) (-323 "EXITAST.spad" 462710 462718 462964 462969) (-322 "EVALCYC.spad" 462170 462184 462700 462705) (-321 "EVALAB.spad" 461742 461752 462160 462165) (-320 "EVALAB.spad" 461312 461324 461732 461737) (-319 "EUCDOM.spad" 458886 458894 461238 461307) (-318 "EUCDOM.spad" 456522 456532 458876 458881) (-317 "ESTOOLS.spad" 448368 448376 456512 456517) (-316 "ESTOOLS2.spad" 447971 447985 448358 448363) (-315 "ESTOOLS1.spad" 447656 447667 447961 447966) (-314 "ES.spad" 440471 440479 447646 447651) (-313 "ES.spad" 433192 433202 440369 440374) (-312 "ESCONT.spad" 429985 429993 433182 433187) (-311 "ESCONT1.spad" 429734 429746 429975 429980) (-310 "ES2.spad" 429239 429255 429724 429729) (-309 "ES1.spad" 428809 428825 429229 429234) (-308 "ERROR.spad" 426136 426144 428799 428804) (-307 "EQTBL.spad" 424166 424188 424375 424402) (-306 "EQ.spad" 418971 418981 421758 421870) (-305 "EQ2.spad" 418689 418701 418961 418966) (-304 "EP.spad" 415015 415025 418679 418684) (-303 "ENV.spad" 413693 413701 415005 415010) (-302 "ENTIRER.spad" 413361 413369 413637 413688) (-301 "EMR.spad" 412649 412690 413287 413356) (-300 "ELTAGG.spad" 410903 410922 412639 412644) (-299 "ELTAGG.spad" 409121 409142 410859 410864) (-298 "ELTAB.spad" 408596 408609 409111 409116) (-297 "ELFUTS.spad" 407983 408002 408586 408591) (-296 "ELEMFUN.spad" 407672 407680 407973 407978) (-295 "ELEMFUN.spad" 407359 407369 407662 407667) (-294 "ELAGG.spad" 405330 405340 407339 407354) (-293 "ELAGG.spad" 403238 403250 405249 405254) (-292 "ELABOR.spad" 402584 402592 403228 403233) (-291 "ELABEXPR.spad" 401516 401524 402574 402579) (-290 "EFUPXS.spad" 398292 398322 401472 401477) (-289 "EFULS.spad" 395128 395151 398248 398253) (-288 "EFSTRUC.spad" 393143 393159 395118 395123) (-287 "EF.spad" 387919 387935 393133 393138) (-286 "EAB.spad" 386195 386203 387909 387914) (-285 "E04UCFA.spad" 385731 385739 386185 386190) (-284 "E04NAFA.spad" 385308 385316 385721 385726) (-283 "E04MBFA.spad" 384888 384896 385298 385303) (-282 "E04JAFA.spad" 384424 384432 384878 384883) (-281 "E04GCFA.spad" 383960 383968 384414 384419) (-280 "E04FDFA.spad" 383496 383504 383950 383955) (-279 "E04DGFA.spad" 383032 383040 383486 383491) (-278 "E04AGNT.spad" 378882 378890 383022 383027) (-277 "DVARCAT.spad" 375772 375782 378872 378877) (-276 "DVARCAT.spad" 372660 372672 375762 375767) (-275 "DSMP.spad" 370034 370048 370339 370466) (-274 "DSEXT.spad" 369336 369346 370024 370029) (-273 "DSEXT.spad" 368545 368557 369235 369240) (-272 "DROPT.spad" 362504 362512 368535 368540) (-271 "DROPT1.spad" 362169 362179 362494 362499) (-270 "DROPT0.spad" 357026 357034 362159 362164) (-269 "DRAWPT.spad" 355199 355207 357016 357021) (-268 "DRAW.spad" 348075 348088 355189 355194) (-267 "DRAWHACK.spad" 347383 347393 348065 348070) (-266 "DRAWCX.spad" 344853 344861 347373 347378) (-265 "DRAWCURV.spad" 344400 344415 344843 344848) (-264 "DRAWCFUN.spad" 333932 333940 344390 344395) (-263 "DQAGG.spad" 332110 332120 333900 333927) (-262 "DPOLCAT.spad" 327459 327475 331978 332105) (-261 "DPOLCAT.spad" 322894 322912 327415 327420) (-260 "DPMO.spad" 314654 314670 314792 315005) (-259 "DPMM.spad" 306427 306445 306552 306765) (-258 "DOMTMPLT.spad" 306198 306206 306417 306422) (-257 "DOMCTOR.spad" 305953 305961 306188 306193) (-256 "DOMAIN.spad" 305040 305048 305943 305948) (-255 "DMP.spad" 302300 302315 302870 302997) (-254 "DMEXT.spad" 302167 302177 302268 302295) (-253 "DLP.spad" 301519 301529 302157 302162) (-252 "DLIST.spad" 299945 299955 300549 300576) (-251 "DLAGG.spad" 298362 298372 299935 299940) (-250 "DIVRING.spad" 297904 297912 298306 298357) (-249 "DIVRING.spad" 297490 297500 297894 297899) (-248 "DISPLAY.spad" 295680 295688 297480 297485) (-247 "DIRPROD.spad" 283227 283243 283867 283966) (-246 "DIRPROD2.spad" 282045 282063 283217 283222) (-245 "DIRPCAT.spad" 281238 281254 281941 282040) (-244 "DIRPCAT.spad" 280058 280076 280763 280768) (-243 "DIOSP.spad" 278883 278891 280048 280053) (-242 "DIOPS.spad" 277879 277889 278863 278878) (-241 "DIOPS.spad" 276849 276861 277835 277840) (-240 "DIFRING.spad" 276687 276695 276829 276844) (-239 "DIFFSPC.spad" 276266 276274 276677 276682) (-238 "DIFFSPC.spad" 275843 275853 276256 276261) (-237 "DIFFMOD.spad" 275332 275342 275811 275838) (-236 "DIFFDOM.spad" 274497 274508 275322 275327) (-235 "DIFFDOM.spad" 273660 273673 274487 274492) (-234 "DIFEXT.spad" 273479 273489 273640 273655) (-233 "DIAGG.spad" 273109 273119 273459 273474) (-232 "DIAGG.spad" 272747 272759 273099 273104) (-231 "DHMATRIX.spad" 270942 270952 272087 272114) (-230 "DFSFUN.spad" 264582 264590 270932 270937) (-229 "DFLOAT.spad" 261313 261321 264472 264577) (-228 "DFINTTLS.spad" 259544 259560 261303 261308) (-227 "DERHAM.spad" 257458 257490 259524 259539) (-226 "DEQUEUE.spad" 256665 256675 256948 256975) (-225 "DEGRED.spad" 256282 256296 256655 256660) (-224 "DEFINTRF.spad" 253819 253829 256272 256277) (-223 "DEFINTEF.spad" 252329 252345 253809 253814) (-222 "DEFAST.spad" 251697 251705 252319 252324) (-221 "DECIMAL.spad" 249706 249714 250067 250160) (-220 "DDFACT.spad" 247519 247536 249696 249701) (-219 "DBLRESP.spad" 247119 247143 247509 247514) (-218 "DBASIS.spad" 246745 246760 247109 247114) (-217 "DBASE.spad" 245409 245419 246735 246740) (-216 "DATAARY.spad" 244871 244884 245399 245404) (-215 "D03FAFA.spad" 244699 244707 244861 244866) (-214 "D03EEFA.spad" 244519 244527 244689 244694) (-213 "D03AGNT.spad" 243605 243613 244509 244514) (-212 "D02EJFA.spad" 243067 243075 243595 243600) (-211 "D02CJFA.spad" 242545 242553 243057 243062) (-210 "D02BHFA.spad" 242035 242043 242535 242540) (-209 "D02BBFA.spad" 241525 241533 242025 242030) (-208 "D02AGNT.spad" 236339 236347 241515 241520) (-207 "D01WGTS.spad" 234658 234666 236329 236334) (-206 "D01TRNS.spad" 234635 234643 234648 234653) (-205 "D01GBFA.spad" 234157 234165 234625 234630) (-204 "D01FCFA.spad" 233679 233687 234147 234152) (-203 "D01ASFA.spad" 233147 233155 233669 233674) (-202 "D01AQFA.spad" 232593 232601 233137 233142) (-201 "D01APFA.spad" 232017 232025 232583 232588) (-200 "D01ANFA.spad" 231511 231519 232007 232012) (-199 "D01AMFA.spad" 231021 231029 231501 231506) (-198 "D01ALFA.spad" 230561 230569 231011 231016) (-197 "D01AKFA.spad" 230087 230095 230551 230556) (-196 "D01AJFA.spad" 229610 229618 230077 230082) (-195 "D01AGNT.spad" 225677 225685 229600 229605) (-194 "CYCLOTOM.spad" 225183 225191 225667 225672) (-193 "CYCLES.spad" 221975 221983 225173 225178) (-192 "CVMP.spad" 221392 221402 221965 221970) (-191 "CTRIGMNP.spad" 219892 219908 221382 221387) (-190 "CTOR.spad" 219583 219591 219882 219887) (-189 "CTORKIND.spad" 219186 219194 219573 219578) (-188 "CTORCAT.spad" 218435 218443 219176 219181) (-187 "CTORCAT.spad" 217682 217692 218425 218430) (-186 "CTORCALL.spad" 217271 217281 217672 217677) (-185 "CSTTOOLS.spad" 216516 216529 217261 217266) (-184 "CRFP.spad" 210240 210253 216506 216511) (-183 "CRCEAST.spad" 209960 209968 210230 210235) (-182 "CRAPACK.spad" 209011 209021 209950 209955) (-181 "CPMATCH.spad" 208515 208530 208936 208941) (-180 "CPIMA.spad" 208220 208239 208505 208510) (-179 "COORDSYS.spad" 203229 203239 208210 208215) (-178 "CONTOUR.spad" 202640 202648 203219 203224) (-177 "CONTFRAC.spad" 198390 198400 202542 202635) (-176 "CONDUIT.spad" 198148 198156 198380 198385) (-175 "COMRING.spad" 197822 197830 198086 198143) (-174 "COMPPROP.spad" 197340 197348 197812 197817) (-173 "COMPLPAT.spad" 197107 197122 197330 197335) (-172 "COMPLEX.spad" 192484 192494 192728 192989) (-171 "COMPLEX2.spad" 192199 192211 192474 192479) (-170 "COMPILER.spad" 191748 191756 192189 192194) (-169 "COMPFACT.spad" 191350 191364 191738 191743) (-168 "COMPCAT.spad" 189422 189432 191084 191345) (-167 "COMPCAT.spad" 187222 187234 188886 188891) (-166 "COMMUPC.spad" 186970 186988 187212 187217) (-165 "COMMONOP.spad" 186503 186511 186960 186965) (-164 "COMM.spad" 186314 186322 186493 186498) (-163 "COMMAAST.spad" 186077 186085 186304 186309) (-162 "COMBOPC.spad" 184992 185000 186067 186072) (-161 "COMBINAT.spad" 183759 183769 184982 184987) (-160 "COMBF.spad" 181141 181157 183749 183754) (-159 "COLOR.spad" 179978 179986 181131 181136) (-158 "COLONAST.spad" 179644 179652 179968 179973) (-157 "CMPLXRT.spad" 179355 179372 179634 179639) (-156 "CLLCTAST.spad" 179017 179025 179345 179350) (-155 "CLIP.spad" 175125 175133 179007 179012) (-154 "CLIF.spad" 173780 173796 175081 175120) (-153 "CLAGG.spad" 170285 170295 173770 173775) (-152 "CLAGG.spad" 166661 166673 170148 170153) (-151 "CINTSLPE.spad" 165992 166005 166651 166656) (-150 "CHVAR.spad" 164130 164152 165982 165987) (-149 "CHARZ.spad" 164045 164053 164110 164125) (-148 "CHARPOL.spad" 163555 163565 164035 164040) (-147 "CHARNZ.spad" 163308 163316 163535 163550) (-146 "CHAR.spad" 160742 160750 163298 163303) (-145 "CFCAT.spad" 160070 160078 160732 160737) (-144 "CDEN.spad" 159266 159280 160060 160065) (-143 "CCLASS.spad" 157377 157385 158639 158678) (-142 "CATEGORY.spad" 156419 156427 157367 157372) (-141 "CATCTOR.spad" 156310 156318 156409 156414) (-140 "CATAST.spad" 155928 155936 156300 156305) (-139 "CASEAST.spad" 155642 155650 155918 155923) (-138 "CARTEN.spad" 151009 151033 155632 155637) (-137 "CARTEN2.spad" 150399 150426 150999 151004) (-136 "CARD.spad" 147694 147702 150373 150394) (-135 "CAPSLAST.spad" 147468 147476 147684 147689) (-134 "CACHSET.spad" 147092 147100 147458 147463) (-133 "CABMON.spad" 146647 146655 147082 147087) (-132 "BYTEORD.spad" 146322 146330 146637 146642) (-131 "BYTE.spad" 145749 145757 146312 146317) (-130 "BYTEBUF.spad" 143447 143455 144757 144784) (-129 "BTREE.spad" 142403 142413 142937 142964) (-128 "BTOURN.spad" 141291 141301 141893 141920) (-127 "BTCAT.spad" 140683 140693 141259 141286) (-126 "BTCAT.spad" 140095 140107 140673 140678) (-125 "BTAGG.spad" 139561 139569 140063 140090) (-124 "BTAGG.spad" 139047 139057 139551 139556) (-123 "BSTREE.spad" 137671 137681 138537 138564) (-122 "BRILL.spad" 135868 135879 137661 137666) (-121 "BRAGG.spad" 134808 134818 135858 135863) (-120 "BRAGG.spad" 133712 133724 134764 134769) (-119 "BPADICRT.spad" 131586 131598 131841 131934) (-118 "BPADIC.spad" 131250 131262 131512 131581) (-117 "BOUNDZRO.spad" 130906 130923 131240 131245) (-116 "BOP.spad" 126088 126096 130896 130901) (-115 "BOP1.spad" 123554 123564 126078 126083) (-114 "BOOLE.spad" 123204 123212 123544 123549) (-113 "BOOLE.spad" 122852 122862 123194 123199) (-112 "BOOLEAN.spad" 122290 122298 122842 122847) (-111 "BMODULE.spad" 122002 122014 122258 122285) (-110 "BITS.spad" 121385 121393 121600 121627) (-109 "BINDING.spad" 120798 120806 121375 121380) (-108 "BINARY.spad" 118812 118820 119168 119261) (-107 "BGAGG.spad" 118017 118027 118792 118807) (-106 "BGAGG.spad" 117230 117242 118007 118012) (-105 "BFUNCT.spad" 116794 116802 117210 117225) (-104 "BEZOUT.spad" 115934 115961 116744 116749) (-103 "BBTREE.spad" 112662 112672 115424 115451) (-102 "BASTYPE.spad" 112158 112166 112652 112657) (-101 "BASTYPE.spad" 111652 111662 112148 112153) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2300660 2300665 2300670 2300675) (-2 NIL 2300640 2300645 2300650 2300655) (-1 NIL 2300620 2300625 2300630 2300635) (0 NIL 2300600 2300605 2300610 2300615) (-1327 "ZMOD.spad" 2300409 2300422 2300538 2300595) (-1326 "ZLINDEP.spad" 2299475 2299486 2300399 2300404) (-1325 "ZDSOLVE.spad" 2289419 2289441 2299465 2299470) (-1324 "YSTREAM.spad" 2288914 2288925 2289409 2289414) (-1323 "YDIAGRAM.spad" 2288548 2288557 2288904 2288909) (-1322 "XRPOLY.spad" 2287768 2287788 2288404 2288473) (-1321 "XPR.spad" 2285563 2285576 2287486 2287585) (-1320 "XPOLY.spad" 2285118 2285129 2285419 2285488) (-1319 "XPOLYC.spad" 2284437 2284453 2285044 2285113) (-1318 "XPBWPOLY.spad" 2282874 2282894 2284217 2284286) (-1317 "XF.spad" 2281337 2281352 2282776 2282869) (-1316 "XF.spad" 2279780 2279797 2281221 2281226) (-1315 "XFALG.spad" 2276828 2276844 2279706 2279775) (-1314 "XEXPPKG.spad" 2276079 2276105 2276818 2276823) (-1313 "XDPOLY.spad" 2275693 2275709 2275935 2276004) (-1312 "XALG.spad" 2275353 2275364 2275649 2275688) (-1311 "WUTSET.spad" 2271156 2271173 2274963 2274990) (-1310 "WP.spad" 2270355 2270399 2271014 2271081) (-1309 "WHILEAST.spad" 2270153 2270162 2270345 2270350) (-1308 "WHEREAST.spad" 2269824 2269833 2270143 2270148) (-1307 "WFFINTBS.spad" 2267487 2267509 2269814 2269819) (-1306 "WEIER.spad" 2265709 2265720 2267477 2267482) (-1305 "VSPACE.spad" 2265382 2265393 2265677 2265704) (-1304 "VSPACE.spad" 2265075 2265088 2265372 2265377) (-1303 "VOID.spad" 2264752 2264761 2265065 2265070) (-1302 "VIEW.spad" 2262432 2262441 2264742 2264747) (-1301 "VIEWDEF.spad" 2257633 2257642 2262422 2262427) (-1300 "VIEW3D.spad" 2241594 2241603 2257623 2257628) (-1299 "VIEW2D.spad" 2229485 2229494 2241584 2241589) (-1298 "VECTOR.spad" 2228006 2228017 2228257 2228284) (-1297 "VECTOR2.spad" 2226645 2226658 2227996 2228001) (-1296 "VECTCAT.spad" 2224549 2224560 2226613 2226640) (-1295 "VECTCAT.spad" 2222260 2222273 2224326 2224331) (-1294 "VARIABLE.spad" 2222040 2222055 2222250 2222255) (-1293 "UTYPE.spad" 2221684 2221693 2222030 2222035) (-1292 "UTSODETL.spad" 2220979 2221003 2221640 2221645) (-1291 "UTSODE.spad" 2219195 2219215 2220969 2220974) (-1290 "UTS.spad" 2214142 2214170 2217662 2217759) (-1289 "UTSCAT.spad" 2211621 2211637 2214040 2214137) (-1288 "UTSCAT.spad" 2208744 2208762 2211165 2211170) (-1287 "UTS2.spad" 2208339 2208374 2208734 2208739) (-1286 "URAGG.spad" 2203012 2203023 2208329 2208334) (-1285 "URAGG.spad" 2197649 2197662 2202968 2202973) (-1284 "UPXSSING.spad" 2195294 2195320 2196730 2196863) (-1283 "UPXS.spad" 2192590 2192618 2193426 2193575) (-1282 "UPXSCONS.spad" 2190349 2190369 2190722 2190871) (-1281 "UPXSCCA.spad" 2188920 2188940 2190195 2190344) (-1280 "UPXSCCA.spad" 2187633 2187655 2188910 2188915) (-1279 "UPXSCAT.spad" 2186222 2186238 2187479 2187628) (-1278 "UPXS2.spad" 2185765 2185818 2186212 2186217) (-1277 "UPSQFREE.spad" 2184179 2184193 2185755 2185760) (-1276 "UPSCAT.spad" 2181966 2181990 2184077 2184174) (-1275 "UPSCAT.spad" 2179459 2179485 2181572 2181577) (-1274 "UPOLYC.spad" 2174499 2174510 2179301 2179454) (-1273 "UPOLYC.spad" 2169431 2169444 2174235 2174240) (-1272 "UPOLYC2.spad" 2168902 2168921 2169421 2169426) (-1271 "UP.spad" 2166008 2166023 2166395 2166548) (-1270 "UPMP.spad" 2164908 2164921 2165998 2166003) (-1269 "UPDIVP.spad" 2164473 2164487 2164898 2164903) (-1268 "UPDECOMP.spad" 2162718 2162732 2164463 2164468) (-1267 "UPCDEN.spad" 2161927 2161943 2162708 2162713) (-1266 "UP2.spad" 2161291 2161312 2161917 2161922) (-1265 "UNISEG.spad" 2160644 2160655 2161210 2161215) (-1264 "UNISEG2.spad" 2160141 2160154 2160600 2160605) (-1263 "UNIFACT.spad" 2159244 2159256 2160131 2160136) (-1262 "ULS.spad" 2149028 2149056 2149973 2150402) (-1261 "ULSCONS.spad" 2140162 2140182 2140532 2140681) (-1260 "ULSCCAT.spad" 2137899 2137919 2140008 2140157) (-1259 "ULSCCAT.spad" 2135744 2135766 2137855 2137860) (-1258 "ULSCAT.spad" 2133976 2133992 2135590 2135739) (-1257 "ULS2.spad" 2133490 2133543 2133966 2133971) (-1256 "UINT8.spad" 2133367 2133376 2133480 2133485) (-1255 "UINT64.spad" 2133243 2133252 2133357 2133362) (-1254 "UINT32.spad" 2133119 2133128 2133233 2133238) (-1253 "UINT16.spad" 2132995 2133004 2133109 2133114) (-1252 "UFD.spad" 2132060 2132069 2132921 2132990) (-1251 "UFD.spad" 2131187 2131198 2132050 2132055) (-1250 "UDVO.spad" 2130068 2130077 2131177 2131182) (-1249 "UDPO.spad" 2127561 2127572 2130024 2130029) (-1248 "TYPE.spad" 2127493 2127502 2127551 2127556) (-1247 "TYPEAST.spad" 2127412 2127421 2127483 2127488) (-1246 "TWOFACT.spad" 2126064 2126079 2127402 2127407) (-1245 "TUPLE.spad" 2125550 2125561 2125963 2125968) (-1244 "TUBETOOL.spad" 2122417 2122426 2125540 2125545) (-1243 "TUBE.spad" 2121064 2121081 2122407 2122412) (-1242 "TS.spad" 2119663 2119679 2120629 2120726) (-1241 "TSETCAT.spad" 2106790 2106807 2119631 2119658) (-1240 "TSETCAT.spad" 2093903 2093922 2106746 2106751) (-1239 "TRMANIP.spad" 2088269 2088286 2093609 2093614) (-1238 "TRIMAT.spad" 2087232 2087257 2088259 2088264) (-1237 "TRIGMNIP.spad" 2085759 2085776 2087222 2087227) (-1236 "TRIGCAT.spad" 2085271 2085280 2085749 2085754) (-1235 "TRIGCAT.spad" 2084781 2084792 2085261 2085266) (-1234 "TREE.spad" 2083239 2083250 2084271 2084298) (-1233 "TRANFUN.spad" 2083078 2083087 2083229 2083234) (-1232 "TRANFUN.spad" 2082915 2082926 2083068 2083073) (-1231 "TOPSP.spad" 2082589 2082598 2082905 2082910) (-1230 "TOOLSIGN.spad" 2082252 2082263 2082579 2082584) (-1229 "TEXTFILE.spad" 2080813 2080822 2082242 2082247) (-1228 "TEX.spad" 2077959 2077968 2080803 2080808) (-1227 "TEX1.spad" 2077515 2077526 2077949 2077954) (-1226 "TEMUTL.spad" 2077070 2077079 2077505 2077510) (-1225 "TBCMPPK.spad" 2075163 2075186 2077060 2077065) (-1224 "TBAGG.spad" 2074213 2074236 2075143 2075158) (-1223 "TBAGG.spad" 2073271 2073296 2074203 2074208) (-1222 "TANEXP.spad" 2072679 2072690 2073261 2073266) (-1221 "TALGOP.spad" 2072403 2072414 2072669 2072674) (-1220 "TABLE.spad" 2070372 2070395 2070642 2070669) (-1219 "TABLEAU.spad" 2069853 2069864 2070362 2070367) (-1218 "TABLBUMP.spad" 2066656 2066667 2069843 2069848) (-1217 "SYSTEM.spad" 2065884 2065893 2066646 2066651) (-1216 "SYSSOLP.spad" 2063367 2063378 2065874 2065879) (-1215 "SYSPTR.spad" 2063266 2063275 2063357 2063362) (-1214 "SYSNNI.spad" 2062457 2062468 2063256 2063261) (-1213 "SYSINT.spad" 2061861 2061872 2062447 2062452) (-1212 "SYNTAX.spad" 2058067 2058076 2061851 2061856) (-1211 "SYMTAB.spad" 2056135 2056144 2058057 2058062) (-1210 "SYMS.spad" 2052158 2052167 2056125 2056130) (-1209 "SYMPOLY.spad" 2051164 2051175 2051246 2051373) (-1208 "SYMFUNC.spad" 2050665 2050676 2051154 2051159) (-1207 "SYMBOL.spad" 2048168 2048177 2050655 2050660) (-1206 "SWITCH.spad" 2044939 2044948 2048158 2048163) (-1205 "SUTS.spad" 2041987 2042015 2043406 2043503) (-1204 "SUPXS.spad" 2039270 2039298 2040119 2040268) (-1203 "SUP.spad" 2035990 2036001 2036763 2036916) (-1202 "SUPFRACF.spad" 2035095 2035113 2035980 2035985) (-1201 "SUP2.spad" 2034487 2034500 2035085 2035090) (-1200 "SUMRF.spad" 2033461 2033472 2034477 2034482) (-1199 "SUMFS.spad" 2033098 2033115 2033451 2033456) (-1198 "SULS.spad" 2022869 2022897 2023827 2024256) (-1197 "SUCHTAST.spad" 2022638 2022647 2022859 2022864) (-1196 "SUCH.spad" 2022320 2022335 2022628 2022633) (-1195 "SUBSPACE.spad" 2014435 2014450 2022310 2022315) (-1194 "SUBRESP.spad" 2013605 2013619 2014391 2014396) (-1193 "STTF.spad" 2009704 2009720 2013595 2013600) (-1192 "STTFNC.spad" 2006172 2006188 2009694 2009699) (-1191 "STTAYLOR.spad" 1998807 1998818 2006053 2006058) (-1190 "STRTBL.spad" 1996858 1996875 1997007 1997034) (-1189 "STRING.spad" 1995645 1995654 1995866 1995893) (-1188 "STREAM.spad" 1992446 1992457 1995053 1995068) (-1187 "STREAM3.spad" 1992019 1992034 1992436 1992441) (-1186 "STREAM2.spad" 1991147 1991160 1992009 1992014) (-1185 "STREAM1.spad" 1990853 1990864 1991137 1991142) (-1184 "STINPROD.spad" 1989789 1989805 1990843 1990848) (-1183 "STEP.spad" 1988990 1988999 1989779 1989784) (-1182 "STEPAST.spad" 1988224 1988233 1988980 1988985) (-1181 "STBL.spad" 1986308 1986336 1986475 1986490) (-1180 "STAGG.spad" 1985383 1985394 1986298 1986303) (-1179 "STAGG.spad" 1984456 1984469 1985373 1985378) (-1178 "STACK.spad" 1983696 1983707 1983946 1983973) (-1177 "SREGSET.spad" 1981364 1981381 1983306 1983333) (-1176 "SRDCMPK.spad" 1979925 1979945 1981354 1981359) (-1175 "SRAGG.spad" 1975068 1975077 1979893 1979920) (-1174 "SRAGG.spad" 1970231 1970242 1975058 1975063) (-1173 "SQMATRIX.spad" 1967774 1967792 1968690 1968777) (-1172 "SPLTREE.spad" 1962170 1962183 1967054 1967081) (-1171 "SPLNODE.spad" 1958758 1958771 1962160 1962165) (-1170 "SPFCAT.spad" 1957567 1957576 1958748 1958753) (-1169 "SPECOUT.spad" 1956119 1956128 1957557 1957562) (-1168 "SPADXPT.spad" 1947714 1947723 1956109 1956114) (-1167 "spad-parser.spad" 1947179 1947188 1947704 1947709) (-1166 "SPADAST.spad" 1946880 1946889 1947169 1947174) (-1165 "SPACEC.spad" 1931079 1931090 1946870 1946875) (-1164 "SPACE3.spad" 1930855 1930866 1931069 1931074) (-1163 "SORTPAK.spad" 1930404 1930417 1930811 1930816) (-1162 "SOLVETRA.spad" 1928167 1928178 1930394 1930399) (-1161 "SOLVESER.spad" 1926695 1926706 1928157 1928162) (-1160 "SOLVERAD.spad" 1922721 1922732 1926685 1926690) (-1159 "SOLVEFOR.spad" 1921183 1921201 1922711 1922716) (-1158 "SNTSCAT.spad" 1920783 1920800 1921151 1921178) (-1157 "SMTS.spad" 1919055 1919081 1920348 1920445) (-1156 "SMP.spad" 1916530 1916550 1916920 1917047) (-1155 "SMITH.spad" 1915375 1915400 1916520 1916525) (-1154 "SMATCAT.spad" 1913485 1913515 1915319 1915370) (-1153 "SMATCAT.spad" 1911527 1911559 1913363 1913368) (-1152 "SKAGG.spad" 1910490 1910501 1911495 1911522) (-1151 "SINT.spad" 1909430 1909439 1910356 1910485) (-1150 "SIMPAN.spad" 1909158 1909167 1909420 1909425) (-1149 "SIG.spad" 1908488 1908497 1909148 1909153) (-1148 "SIGNRF.spad" 1907606 1907617 1908478 1908483) (-1147 "SIGNEF.spad" 1906885 1906902 1907596 1907601) (-1146 "SIGAST.spad" 1906270 1906279 1906875 1906880) (-1145 "SHP.spad" 1904198 1904213 1906226 1906231) (-1144 "SHDP.spad" 1891876 1891903 1892385 1892484) (-1143 "SGROUP.spad" 1891484 1891493 1891866 1891871) (-1142 "SGROUP.spad" 1891090 1891101 1891474 1891479) (-1141 "SGCF.spad" 1884229 1884238 1891080 1891085) (-1140 "SFRTCAT.spad" 1883159 1883176 1884197 1884224) (-1139 "SFRGCD.spad" 1882222 1882242 1883149 1883154) (-1138 "SFQCMPK.spad" 1876859 1876879 1882212 1882217) (-1137 "SFORT.spad" 1876298 1876312 1876849 1876854) (-1136 "SEXOF.spad" 1876141 1876181 1876288 1876293) (-1135 "SEX.spad" 1876033 1876042 1876131 1876136) (-1134 "SEXCAT.spad" 1873805 1873845 1876023 1876028) (-1133 "SET.spad" 1872093 1872104 1873190 1873229) (-1132 "SETMN.spad" 1870543 1870560 1872083 1872088) (-1131 "SETCAT.spad" 1870028 1870037 1870533 1870538) (-1130 "SETCAT.spad" 1869511 1869522 1870018 1870023) (-1129 "SETAGG.spad" 1866060 1866071 1869491 1869506) (-1128 "SETAGG.spad" 1862617 1862630 1866050 1866055) (-1127 "SEQAST.spad" 1862320 1862329 1862607 1862612) (-1126 "SEGXCAT.spad" 1861476 1861489 1862310 1862315) (-1125 "SEG.spad" 1861289 1861300 1861395 1861400) (-1124 "SEGCAT.spad" 1860214 1860225 1861279 1861284) (-1123 "SEGBIND.spad" 1859972 1859983 1860161 1860166) (-1122 "SEGBIND2.spad" 1859670 1859683 1859962 1859967) (-1121 "SEGAST.spad" 1859384 1859393 1859660 1859665) (-1120 "SEG2.spad" 1858819 1858832 1859340 1859345) (-1119 "SDVAR.spad" 1858095 1858106 1858809 1858814) (-1118 "SDPOL.spad" 1855428 1855439 1855719 1855846) (-1117 "SCPKG.spad" 1853517 1853528 1855418 1855423) (-1116 "SCOPE.spad" 1852670 1852679 1853507 1853512) (-1115 "SCACHE.spad" 1851366 1851377 1852660 1852665) (-1114 "SASTCAT.spad" 1851275 1851284 1851356 1851361) (-1113 "SAOS.spad" 1851147 1851156 1851265 1851270) (-1112 "SAERFFC.spad" 1850860 1850880 1851137 1851142) (-1111 "SAE.spad" 1848330 1848346 1848941 1849076) (-1110 "SAEFACT.spad" 1848031 1848051 1848320 1848325) (-1109 "RURPK.spad" 1845690 1845706 1848021 1848026) (-1108 "RULESET.spad" 1845143 1845167 1845680 1845685) (-1107 "RULE.spad" 1843383 1843407 1845133 1845138) (-1106 "RULECOLD.spad" 1843235 1843248 1843373 1843378) (-1105 "RTVALUE.spad" 1842970 1842979 1843225 1843230) (-1104 "RSTRCAST.spad" 1842687 1842696 1842960 1842965) (-1103 "RSETGCD.spad" 1839065 1839085 1842677 1842682) (-1102 "RSETCAT.spad" 1829001 1829018 1839033 1839060) (-1101 "RSETCAT.spad" 1818957 1818976 1828991 1828996) (-1100 "RSDCMPK.spad" 1817409 1817429 1818947 1818952) (-1099 "RRCC.spad" 1815793 1815823 1817399 1817404) (-1098 "RRCC.spad" 1814175 1814207 1815783 1815788) (-1097 "RPTAST.spad" 1813877 1813886 1814165 1814170) (-1096 "RPOLCAT.spad" 1793237 1793252 1813745 1813872) (-1095 "RPOLCAT.spad" 1772310 1772327 1792820 1792825) (-1094 "ROUTINE.spad" 1767731 1767740 1770495 1770522) (-1093 "ROMAN.spad" 1767059 1767068 1767597 1767726) (-1092 "ROIRC.spad" 1766139 1766171 1767049 1767054) (-1091 "RNS.spad" 1765042 1765051 1766041 1766134) (-1090 "RNS.spad" 1764031 1764042 1765032 1765037) (-1089 "RNG.spad" 1763766 1763775 1764021 1764026) (-1088 "RNGBIND.spad" 1762926 1762940 1763721 1763726) (-1087 "RMODULE.spad" 1762691 1762702 1762916 1762921) (-1086 "RMCAT2.spad" 1762111 1762168 1762681 1762686) (-1085 "RMATRIX.spad" 1760899 1760918 1761242 1761281) (-1084 "RMATCAT.spad" 1756478 1756509 1760855 1760894) (-1083 "RMATCAT.spad" 1751947 1751980 1756326 1756331) (-1082 "RLINSET.spad" 1751651 1751662 1751937 1751942) (-1081 "RINTERP.spad" 1751539 1751559 1751641 1751646) (-1080 "RING.spad" 1751009 1751018 1751519 1751534) (-1079 "RING.spad" 1750487 1750498 1750999 1751004) (-1078 "RIDIST.spad" 1749879 1749888 1750477 1750482) (-1077 "RGCHAIN.spad" 1748407 1748423 1749309 1749336) (-1076 "RGBCSPC.spad" 1748188 1748200 1748397 1748402) (-1075 "RGBCMDL.spad" 1747718 1747730 1748178 1748183) (-1074 "RF.spad" 1745360 1745371 1747708 1747713) (-1073 "RFFACTOR.spad" 1744822 1744833 1745350 1745355) (-1072 "RFFACT.spad" 1744557 1744569 1744812 1744817) (-1071 "RFDIST.spad" 1743553 1743562 1744547 1744552) (-1070 "RETSOL.spad" 1742972 1742985 1743543 1743548) (-1069 "RETRACT.spad" 1742400 1742411 1742962 1742967) (-1068 "RETRACT.spad" 1741826 1741839 1742390 1742395) (-1067 "RETAST.spad" 1741638 1741647 1741816 1741821) (-1066 "RESULT.spad" 1739236 1739245 1739823 1739850) (-1065 "RESRING.spad" 1738583 1738630 1739174 1739231) (-1064 "RESLATC.spad" 1737907 1737918 1738573 1738578) (-1063 "REPSQ.spad" 1737638 1737649 1737897 1737902) (-1062 "REP.spad" 1735192 1735201 1737628 1737633) (-1061 "REPDB.spad" 1734899 1734910 1735182 1735187) (-1060 "REP2.spad" 1724557 1724568 1734741 1734746) (-1059 "REP1.spad" 1718753 1718764 1724507 1724512) (-1058 "REGSET.spad" 1716514 1716531 1718363 1718390) (-1057 "REF.spad" 1715849 1715860 1716469 1716474) (-1056 "REDORDER.spad" 1715055 1715072 1715839 1715844) (-1055 "RECLOS.spad" 1713838 1713858 1714542 1714635) (-1054 "REALSOLV.spad" 1712978 1712987 1713828 1713833) (-1053 "REAL.spad" 1712850 1712859 1712968 1712973) (-1052 "REAL0Q.spad" 1710148 1710163 1712840 1712845) (-1051 "REAL0.spad" 1706992 1707007 1710138 1710143) (-1050 "RDUCEAST.spad" 1706713 1706722 1706982 1706987) (-1049 "RDIV.spad" 1706368 1706393 1706703 1706708) (-1048 "RDIST.spad" 1705935 1705946 1706358 1706363) (-1047 "RDETRS.spad" 1704799 1704817 1705925 1705930) (-1046 "RDETR.spad" 1702938 1702956 1704789 1704794) (-1045 "RDEEFS.spad" 1702037 1702054 1702928 1702933) (-1044 "RDEEF.spad" 1701047 1701064 1702027 1702032) (-1043 "RCFIELD.spad" 1698233 1698242 1700949 1701042) (-1042 "RCFIELD.spad" 1695505 1695516 1698223 1698228) (-1041 "RCAGG.spad" 1693433 1693444 1695495 1695500) (-1040 "RCAGG.spad" 1691288 1691301 1693352 1693357) (-1039 "RATRET.spad" 1690648 1690659 1691278 1691283) (-1038 "RATFACT.spad" 1690340 1690352 1690638 1690643) (-1037 "RANDSRC.spad" 1689659 1689668 1690330 1690335) (-1036 "RADUTIL.spad" 1689415 1689424 1689649 1689654) (-1035 "RADIX.spad" 1686239 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"FIELD.spad" 583343 583353 583841 583846) (-374 "FGROUP.spad" 581990 582000 583323 583338) (-373 "FGLMICPK.spad" 580777 580792 581980 581985) (-372 "FFX.spad" 580152 580167 580493 580586) (-371 "FFSLPE.spad" 579655 579676 580142 580147) (-370 "FFPOLY.spad" 570917 570928 579645 579650) (-369 "FFPOLY2.spad" 569977 569994 570907 570912) (-368 "FFP.spad" 569374 569394 569693 569786) (-367 "FF.spad" 568822 568838 569055 569148) (-366 "FFNBX.spad" 567334 567354 568538 568631) (-365 "FFNBP.spad" 565847 565864 567050 567143) (-364 "FFNB.spad" 564312 564333 565528 565621) (-363 "FFINTBAS.spad" 561826 561845 564302 564307) (-362 "FFIELDC.spad" 559403 559411 561728 561821) (-361 "FFIELDC.spad" 557066 557076 559393 559398) (-360 "FFHOM.spad" 555814 555831 557056 557061) (-359 "FFF.spad" 553249 553260 555804 555809) (-358 "FFCGX.spad" 552096 552116 552965 553058) (-357 "FFCGP.spad" 550985 551005 551812 551905) (-356 "FFCG.spad" 549777 549798 550666 550759) (-355 "FFCAT.spad" 542950 542972 549616 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"DLIST.spad" 300011 300021 300615 300642) (-251 "DLAGG.spad" 298428 298438 300001 300006) (-250 "DIVRING.spad" 297970 297978 298372 298423) (-249 "DIVRING.spad" 297556 297566 297960 297965) (-248 "DISPLAY.spad" 295746 295754 297546 297551) (-247 "DIRPROD.spad" 283293 283309 283933 284032) (-246 "DIRPROD2.spad" 282111 282129 283283 283288) (-245 "DIRPCAT.spad" 281304 281320 282007 282106) (-244 "DIRPCAT.spad" 280124 280142 280829 280834) (-243 "DIOSP.spad" 278949 278957 280114 280119) (-242 "DIOPS.spad" 277945 277955 278929 278944) (-241 "DIOPS.spad" 276915 276927 277901 277906) (-240 "DIFRING.spad" 276753 276761 276895 276910) (-239 "DIFFSPC.spad" 276332 276340 276743 276748) (-238 "DIFFSPC.spad" 275909 275919 276322 276327) (-237 "DIFFMOD.spad" 275398 275408 275877 275904) (-236 "DIFFDOM.spad" 274563 274574 275388 275393) (-235 "DIFFDOM.spad" 273726 273739 274553 274558) (-234 "DIFEXT.spad" 273545 273555 273706 273721) (-233 "DIAGG.spad" 273175 273185 273525 273540) (-232 "DIAGG.spad" 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"ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 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T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578))))) +((($) -2226 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) ((|#2|) . T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578))))) (|has| |#1| (-938)) ((((-886)) . T)) ((((-886)) . T)) @@ -23,23 +23,23 @@ ((((-550)) . T) (((-1189)) . T) (((-229)) . T) (((-392)) . T) (((-917 (-392))) . T)) (((|#1|) . T)) ((((-229)) . T) (((-886)) . T)) -(-2225 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2225 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) +(-2226 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2226 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) -(-2225 (|has| |#1| (-21)) (|has| |#1| (-870))) -((($ $) . T) ((#0=(-421 (-578)) #0#) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1| |#1|) . T)) -(-2225 (|has| |#1| (-842)) (|has| |#1| (-871))) +(-2226 (|has| |#1| (-21)) (|has| |#1| (-870))) +((($ $) . T) ((#0=(-421 (-578)) #0#) -2226 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1| |#1|) . T)) +(-2226 (|has| |#1| (-842)) (|has| |#1| (-871))) ((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) |has| |#1| (-1069 (-578))) ((|#1|) . T)) ((((-886)) . T)) ((((-886)) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) (|has| |#1| (-870)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) ((((-328 |#1|)) . T) (((-578)) . T) (($) . T)) (((|#1| |#2| |#3|) . T)) ((((-578)) . T) (((-894 |#1|)) . T) (($) . T) (((-421 (-578))) . T)) -((($) . T) (((-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T)) +((($) . T) (((-421 (-578))) -2226 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T)) ((((-421 (-578))) . T) (((-721)) . T) (($) . T)) ((((-886)) . T)) ((((-1212)) . T)) @@ -52,14 +52,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1212)) . T)) (((|#1|) . T) (((-578)) |has| |#1| (-1069 (-578))) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578))))) -(-2225 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) -(-2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) -(((|#2| (-496 (-4415 |#1|) (-793))) . T)) -((((-1207)) -2225 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +(-2226 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) +(-2226 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) +(((|#2| (-496 (-4416 |#1|) (-793))) . T)) +((((-1207)) -2226 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) (((|#1| (-545 (-1207))) . T)) ((((-1189)) . T) (((-987 (-131))) . T) (((-886)) . T)) ((((-886)) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (((#0=(-894 |#1|) #0#) . T) ((#1=(-421 (-578)) #1#) . T) (($ $) . T)) (|has| |#4| (-381)) (|has| |#3| (-381)) @@ -75,14 +75,14 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-570)) -((((-578)) . T) (((-421 (-578))) -2225 (|has| |#2| (-38 (-421 (-578)))) (|has| |#2| (-1069 (-421 (-578))))) ((|#2|) . T) (($) -2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) (((-888 |#1|)) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) -((((-2 (|:| -2480 |#1|) (|:| -2300 |#2|))) . T)) +((((-578)) . T) (((-421 (-578))) -2226 (|has| |#2| (-38 (-421 (-578)))) (|has| |#2| (-1069 (-421 (-578))))) ((|#2|) . T) (($) -2226 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) (((-888 |#1|)) . T)) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) +((((-2 (|:| -2481 |#1|) (|:| -4171 |#2|))) . T)) ((($) . T)) ((((-886)) |has| |#1| (-632 (-886))) ((|#1|) . T)) -((((-578)) . T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) ((|#1|) . T) (($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) (((-1207)) . T)) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) +((((-578)) . T) (((-421 (-578))) -2226 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) ((|#1|) . T) (($) -2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) (((-1207)) . T)) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) ((((-550)) |has| |#1| (-633 (-550)))) ((((-1207)) . T)) (((|#1|) . T)) @@ -103,12 +103,12 @@ ((((-886)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-421 (-578)) #0#) |has| |#2| (-38 (-421 (-578)))) ((|#2| |#2|) . T) (($ $) -2225 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))) +(((#0=(-421 (-578)) #0#) |has| |#2| (-38 (-421 (-578)))) ((|#2| |#2|) . 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T) (($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))) +((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (($) -2226 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))) +(((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578)))) ((|#1| |#1|) . T) (($ $) -2226 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))) ((($ $) . T)) ((($) . T)) ((((-578)) . T) (($) . T) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) @@ -132,30 +132,30 @@ (|has| |#1| (-381)) (((|#1|) . T)) ((((-886)) . T)) -((((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-421 (-578))) -2226 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) -(((|#1|) . 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T)) -(-2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) -(-2225 (|has| |#1| (-871)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-871)) (|has| |#1| (-1131))) (|has| |#1| (-1131)) -(-2225 (|has| |#1| (-871)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-871)) (|has| |#1| (-1131))) (|has| |#1| (-1131)) -(-2225 (|has| |#1| (-871)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-871)) (|has| |#1| (-1131))) (|has| |#1| (-870)) (((|#1| |#1|) . T)) ((($) . T) (((-421 (-578))) . T)) @@ -170,12 +170,12 @@ (|has| |#3| (-815)) (|has| |#3| (-815)) (((|#1| |#2|) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-362))) ((((-1212)) . T)) (((|#1| |#2|) . T)) (((|#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) (((-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|)))) -(-2225 (|has| |#1| (-102)) (|has| |#1| (-1131))) -(-2225 (|has| |#1| (-102)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-102)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-102)) (|has| |#1| (-1131))) ((((-578)) . T) (((-421 (-578))) . T)) (((|#1| (-1207) (-1119 (-1207)) (-545 (-1119 (-1207)))) . T)) ((((-578) |#1|) . T)) @@ -195,29 +195,29 @@ ((((-1189) |#1|) . T)) ((((-1265 (-578)) $) . T) (((-578) (-131)) . T)) (((|#1|) . T)) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) (((|#3| (-793)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) ((($) . T) (((-421 (-578))) . T)) ((($) . T)) ((($) . 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T)) ((((-421 (-578))) . T) (($) . T)) @@ -228,7 +228,7 @@ (((|#1|) . T)) (|has| |#2| (-376)) ((((-1265 (-578)) $) . T) (((-578) |#1|) . T)) -((($) -2225 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2226 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((($) . T) (((-578)) . T) (((-421 (-578))) . T)) (((|#1| |#2|) . T)) ((((-886)) . T)) @@ -241,13 +241,13 @@ ((((-886)) . T)) ((((-886)) . T)) (((|#1| |#1|) . T)) -(((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578)))) ((|#1| |#1|) . T) (($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))) -((($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1| |#1|) . T) ((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578))))) +(((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578)))) ((|#1| |#1|) . T) (($ $) -2226 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))) +((($ $) -2226 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1| |#1|) . T) ((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578))))) (((|#1|) . T)) (((|#1|) . T)) -((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (($) -2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))) -((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) -(((|#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) (($) |has| |#2| (-1080)) (((-578)) -12 (|has| |#2| (-660 (-578))) (|has| |#2| (-1080)))) +((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (($) -2226 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))) +((($) -2226 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +(((|#2|) -2226 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) (($) |has| |#2| (-1080)) (((-578)) -12 (|has| |#2| (-660 (-578))) (|has| |#2| (-1080)))) ((((-886)) . T)) ((((-886)) . T)) ((((-886)) . T)) @@ -258,10 +258,10 @@ ((((-172 (-229))) |has| |#1| (-1053)) (((-172 (-392))) |has| |#1| (-1053)) (((-550)) |has| |#1| (-633 (-550))) (((-1203 |#1|)) . T) (((-917 (-578))) |has| |#1| (-633 (-917 (-578)))) (((-917 (-392))) |has| |#1| (-633 (-917 (-392))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) (((|#1|) . T)) -(-2225 (|has| |#1| (-21)) (|has| |#1| (-870))) -(-2225 (|has| |#1| (-21)) (|has| |#1| (-870))) -((((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2225 (|has| |#1| (-376)) (|has| |#1| (-570))) ((|#2|) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) -(((|#1|) |has| |#1| (-175)) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2225 (|has| |#1| (-376)) (|has| |#1| (-570)))) +(-2226 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2226 (|has| |#1| (-21)) (|has| |#1| (-870))) +((((-421 (-578))) -2226 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2226 (|has| |#1| (-376)) (|has| |#1| (-570))) ((|#2|) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) +(((|#1|) |has| |#1| (-175)) (((-421 (-578))) -2226 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2226 (|has| |#1| (-376)) (|has| |#1| (-570)))) (|has| |#1| (-376)) ((((-886)) . T)) ((($) . T)) @@ -269,7 +269,7 @@ ((((-131)) . T)) (-12 (|has| |#4| (-240)) (|has| |#4| (-1080))) (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) -((($) -2225 (|has| |#2| (-240)) (|has| |#2| (-239)))) +((($) -2226 (|has| |#2| (-240)) (|has| |#2| (-239)))) (|has| |#4| (-1080)) (|has| |#3| (-1080)) ((((-886)) . T) (((-1212)) . T)) @@ -280,45 +280,45 @@ (((|#1|) . T)) ((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) |has| |#1| (-1069 (-578))) ((|#1|) . T)) (((|#1|) . T) (((-578)) |has| |#1| (-660 (-578)))) -(((|#2|) . T) (((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2338 (-1189)) (|:| -2079 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2339 (-1189)) (|:| -2076 |#1|))) . 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T)) -((((-2 (|:| -2480 |#1|) (|:| -2300 |#2|))) . T) (((-886)) . T)) +((((-2 (|:| -2481 |#1|) (|:| -4171 |#2|))) . T) (((-886)) . T)) ((((-550)) |has| |#1| (-633 (-550))) (((-917 (-392))) |has| |#1| (-633 (-917 (-392)))) (((-917 (-578))) |has| |#1| (-633 (-917 (-578))))) -(((|#4|) -2225 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080)))) -(((|#3|) -2225 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080)))) -((((-2 (|:| -2480 |#1|) (|:| -2300 |#2|))) . T)) +(((|#4|) -2226 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080)))) +(((|#3|) -2226 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080)))) +((((-2 (|:| -2481 |#1|) (|:| -4171 |#2|))) . T)) ((((-886)) . T)) ((((-886)) . T)) ((((-550)) . T) (((-578)) . T) (((-917 (-578))) . T) (((-392)) . T) (((-229)) . T)) @@ -326,15 +326,15 @@ (((|#1|) . T) (((-578)) |has| |#1| (-1069 (-578))) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578))))) ((($) . T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) . T) (((-578)) |has| |#2| (-660 (-578)))) ((((-421 $) (-421 $)) |has| |#2| (-570)) (($ $) . T) ((|#2| |#2|) . T)) -((($ (-1207)) -2225 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) -((((-2 (|:| -2338 (-1189)) (|:| -2079 (-52)))) . T)) +((($ (-1207)) -2226 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-2 (|:| -2339 (-1189)) (|:| -2076 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-938)) ((((-1189) (-52)) . T)) ((((-578)) |has| #0=(-421 |#2|) (-660 (-578))) ((#0#) . T)) ((((-550)) . T) (((-229)) . T) (((-392)) . T) (((-917 (-392))) . T)) ((((-886)) . T)) -(-2225 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +(-2226 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) (((|#1|) |has| |#1| (-175))) (((|#1| $) |has| |#1| (-298 |#1| |#1|))) ((((-886)) . T)) @@ -349,15 +349,15 @@ (|has| |#1| (-1131)) ((((-939 |#1|)) . T) (($) . T) (((-421 (-578))) . T)) (((|#1|) . T)) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) ((((-550)) |has| |#1| (-633 (-550)))) ((((-886)) . T) (((-1212)) . T)) -((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))) +((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2226 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))) ((((-1212)) . T)) -((($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) -((($) -2225 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +((($) -2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +((($) -2226 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) (|has| |#1| (-240)) -((($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +((($) -2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) (((|#1| (-545 (-840 (-1207)))) . T)) (((|#1| (-1002)) . T)) ((((-578)) . T) ((|#2|) . T)) @@ -369,7 +369,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1183)) -((((-2 (|:| -2338 (-1189)) (|:| -2079 |#1|))) . T)) +((((-2 (|:| -2339 (-1189)) (|:| -2076 |#1|))) . T)) (|has| (-1284 |#1| |#2| |#3| |#4|) (-147)) (|has| (-1284 |#1| |#2| |#3| |#4|) (-149)) (|has| |#1| (-147)) @@ -381,28 +381,28 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-578)) |has| |#2| (-660 (-578)))) -((((-1156 |#1| (-1207))) . T) (((-578)) . T) (((-840 (-1207))) . T) (($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) (((-1207)) . T)) +((((-1156 |#1| (-1207))) . T) (((-578)) . T) (((-840 (-1207))) . T) (($) -2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) -2226 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) (((-1207)) . 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T)) -((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +((($) -2226 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) ((((-886)) . T)) ((((-886)) . T)) (|has| (-1283 |#2| |#3| |#4|) (-149)) @@ -415,18 +415,18 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2225 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +(-2226 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) (((|#1|) . T)) ((($) . T)) ((((-578) |#1|) . T)) (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) -(-2225 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2226 (|has| |#1| (-21)) (|has| |#1| (-870))) ((((-886)) |has| |#1| (-1131))) -((($) -2225 (|has| |#1| (-240)) (|has| |#1| (-239)))) -(-2225 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143))) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-362))) +((($) -2226 (|has| |#1| (-240)) (|has| |#1| (-239)))) +(-2226 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-362))) ((((-939 |#1|)) . T)) ((((-421 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-578) |#1|))) @@ -437,7 +437,7 @@ ((((-886)) . T)) ((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-570))) (|has| |#1| (-376)) -(-2225 (-12 (|has| (-1290 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) +(-2226 (-12 (|has| (-1290 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-793) |#1|))) @@ -451,23 +451,23 @@ ((((-1265 (-578)) $) . T) (((-578) |#1|) . T)) ((((-886)) . T)) (((|#2|) . T)) -(-2225 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) +(-2226 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) ((((-578)) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-570))) ((($) |has| |#1| (-570)) (((-578)) . T)) (|has| |#2| (-815)) (|has| |#2| (-815)) -((((-1290 |#1| |#2| |#3|)) . 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T)) (((|#1|) . T)) @@ -1116,8 +1116,8 @@ (((|#1|) . T)) ((((-1207)) . T)) (|has| |#1| (-570)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) (|has| |#1| (-570)) (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) @@ -1129,7 +1129,7 @@ (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-149)) -(((|#2| (-247 (-4415 |#1|) (-793)) (-888 |#1|)) . T)) +(((|#2| (-247 (-4416 |#1|) (-793)) (-888 |#1|)) . T)) (((|#1| (-545 |#3|) |#3|) . T)) (|has| |#1| (-147)) (((#0=(-421 (-578)) #0#) |has| |#2| (-376)) (($ $) . T)) @@ -1143,12 +1143,12 @@ (|has| |#1| (-147)) ((((-421 (-578))) |has| |#2| (-376)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) -(-2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) -(-2225 (|has| |#1| (-362)) (|has| |#1| (-381))) +(-2226 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) +(-2226 (|has| |#1| (-362)) (|has| |#1| (-381))) ((((-1173 |#2| |#1|)) . T) ((|#1|) . T)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) -(((|#2|) . T) (((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (|has| |#3| (-815)) (|has| |#3| (-815)) ((((-886)) . T)) @@ -1176,18 +1176,18 @@ ((((-886)) . T)) ((((-886)) . T)) (((|#1| |#2|) . T)) -((((-1207)) -2225 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))) (((-1113)) . T)) +((((-1207)) -2226 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))) (((-1113)) . T)) (((|#1|) . T)) (((|#3|) . T) (((-631 $)) . T)) (((|#1| (-421 (-578))) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T) (($) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) ((($ (-1294 |#2|)) . T) (($ (-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207))))) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) -((((-578)) -2225 (-12 (|has| |#2| (-1069 (-578))) (|has| |#2| (-1131))) (|has| |#2| (-1080))) ((|#2|) |has| |#2| (-1131)) (((-421 (-578))) -12 (|has| |#2| (-1069 (-421 (-578)))) (|has| |#2| (-1131)))) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) +((((-578)) -2226 (-12 (|has| |#2| (-1069 (-578))) (|has| |#2| (-1131))) (|has| |#2| (-1080))) ((|#2|) |has| |#2| (-1131)) (((-421 (-578))) -12 (|has| |#2| (-1069 (-421 (-578)))) (|has| |#2| (-1131)))) (((|#1|) . T) (((-421 (-578))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-578)) . T) (($) . T) (((-421 (-578))) . T)) @@ -1195,15 +1195,15 @@ ((((-886)) . T)) ((((-886)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) (((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) |has| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (-321 (-2 (|:| -2338 |#1|) (|:| -2079 |#2|))))) -(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) (((-2 (|:| -2338 (-1189)) (|:| -2079 |#1|))) |has| (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|)) (-321 (-2 (|:| -2338 (-1189)) (|:| -2079 |#1|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) (((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) |has| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (-321 (-2 (|:| -2339 |#1|) (|:| -2076 |#2|))))) +(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) (((-2 (|:| -2339 (-1189)) (|:| -2076 |#1|))) |has| (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|)) (-321 (-2 (|:| -2339 (-1189)) (|:| -2076 |#1|))))) ((((-886)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) (((|#1|) . T)) ((($) . T) ((|#2|) . T) (((-578)) |has| |#2| (-660 (-578)))) ((((-1207) (-52)) . T)) -((((-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +((((-1207)) -2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-888 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-850)) @@ -1211,10 +1211,10 @@ ((($) . T) (((-578)) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T)) ((((-578)) . T) (($) . T) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) (|has| (-1125 |#1|) (-1131)) -(((|#2| |#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) -(((|#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)))) -((((-578) (-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2| |#2|) -2226 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2|) -2226 (|has| |#2| (-175)) (|has| |#2| (-376)))) +((((-578) (-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2226 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) ((((-578)) . T)) ((((-1212)) . T)) ((((-793)) . T)) @@ -1233,34 +1233,34 @@ (((|#1|) . T)) ((((-421 (-578))) . T) (($) . T)) ((($) . T) (((-421 (-578))) . T)) -(-2225 (|has| |#1| (-175)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-175)) (|has| |#1| (-570))) ((((-1212)) . T)) -(-2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) -(-2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((((-578)) . T)) -(-2225 (|has| |#1| (-175)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-175)) (|has| |#1| (-570))) (|has| |#1| (-147)) ((((-578)) . 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T)) (((|#1|) |has| |#1| (-321 |#1|))) @@ -1329,21 +1329,21 @@ (|has| |#1| (-381)) ((((-1207) $) |has| |#1| (-528 (-1207) $)) (($ $) |has| |#1| (-321 $)) ((|#1| |#1|) |has| |#1| (-321 |#1|)) (((-1207) |#1|) |has| |#1| (-528 (-1207) |#1|))) ((((-1207)) |has| |#1| (-927 (-1207)))) -(-2225 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-362))) +(-2226 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-362))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-402) |#1|) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-362))) -(-2225 (|has| |#1| (-102)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-102)) (|has| |#1| (-1131))) (((|#2|) . T) (((-886)) . T)) ((((-886)) . T)) (((|#2|) . T)) ((((-939 |#1|)) . T)) ((((-886)) . T) (((-1212)) . T)) ((((-1212)) . T)) -((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))) -((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))) +((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2226 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))) +((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) -2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-578)) . T) (($) . T) (((-421 (-578))) . T)) @@ -1352,7 +1352,7 @@ (((|#1|) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T)) (((|#1| |#1|) . T)) (((#0=(-894 |#1|)) |has| #0# (-321 #0#))) -((((-578)) . T) (($) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) (((-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-1069 (-421 (-578))))) ((|#1|) . T)) +((((-578)) . T) (($) -2226 (|has| |#1| (-376)) (|has| |#1| (-362))) (((-421 (-578))) -2226 (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-1069 (-421 (-578))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-815)) (|has| |#2| (-815)) @@ -1361,7 +1361,7 @@ (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (|has| |#2| (-1080)) ((($) . T) (((-578)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1233)) (((#0=(-578) #0#) . T) ((#1=(-421 (-578)) #1#) . T) (($ $) . T)) @@ -1375,7 +1375,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-578)) #0#) . T)) (|has| |#1| (-376)) ((((-578)) . T) (((-421 (-578))) . T) (($) . 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T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578))))) +((($) -2226 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) ((|#2|) . T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578))))) ((((-578)) |has| #0=(-421 |#2|) (-660 (-578))) ((#0#) . T)) ((($) . T) (((-578)) . T)) ((((-578) (-146)) . T)) -((((-578) (-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T) ((|#1| |#2|) . T)) +((((-578) (-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T) ((|#1| |#2|) . T)) ((((-421 (-578))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) ((((-886)) . T)) ((((-939 |#1|)) . T)) (|has| |#1| (-376)) @@ -1423,11 +1423,11 @@ (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-870)) -((($) -2225 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-570))) (((-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T)) +((($) -2226 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-570))) (((-421 (-578))) -2226 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T)) (|has| |#1| (-376)) (((|#1|) . T) (($) . T)) (|has| |#1| (-870)) -((($) . T) (((-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T)) +((($) . T) (((-421 (-578))) -2226 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T)) ((((-1207)) |has| |#1| (-927 (-1207)))) (|has| |#1| (-870)) ((((-520)) . T)) @@ -1443,7 +1443,7 @@ ((((-550)) . T)) ((((-886)) . T)) ((($) . T)) -((((-578) (-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T) (((-1265 (-578)) $) . T) ((|#1| |#2|) . T)) +((((-578) (-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T) (((-1265 (-578)) $) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-175))) @@ -1453,22 +1453,22 @@ (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) (((|#3|) . 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T)) -((((-1207)) -2225 (-12 (|has| |#4| (-927 (-1207))) (|has| |#4| (-1080))) (-12 (|has| |#4| (-929 (-1207))) (|has| |#4| (-1080))))) -((((-1207)) -2225 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) +((((-1207)) -2226 (-12 (|has| |#4| (-927 (-1207))) (|has| |#4| (-1080))) (-12 (|has| |#4| (-929 (-1207))) (|has| |#4| (-1080))))) +((((-1207)) -2226 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) (|has| |#1| (-570)) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) -(-2225 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-2226 (|has| |#1| (-240)) (|has| |#1| (-239))) ((((-894 |#1|)) . T) (((-421 (-578))) . T) (($) . T)) (|has| |#1| (-381)) (|has| |#1| (-381)) @@ -1477,7 +1477,7 @@ ((((-1189) |#1|) . T)) (|has| |#1| (-1183)) ((((-987 |#1|)) . T)) -(((#0=(-421 (-578)) #0#) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((|#1| |#1|) . T)) +(((#0=(-421 (-578)) #0#) -2226 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($ $) -2226 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((|#1| |#1|) . T)) ((((-421 (-578))) |has| |#1| (-1069 (-578))) (((-578)) |has| |#1| (-1069 (-578))) (((-1207)) |has| |#1| (-1069 (-1207))) ((|#1|) . T)) ((($) . T)) ((($) . T)) @@ -1485,7 +1485,7 @@ ((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) |has| |#1| (-1069 (-578))) ((|#1|) . T)) ((($) . T) (((-578)) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T)) ((((-578)) |has| |#1| (-911 (-578))) (((-392)) |has| |#1| (-911 (-392)))) -((((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((|#1|) . 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T)) -(((|#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2|) -2226 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) (|has| $ (-149)) ((((-421 |#2|)) . T)) ((((-421 (-578))) |has| #0=(-421 |#2|) (-1069 (-421 (-578)))) (((-578)) |has| #0# (-1069 (-578))) ((#0#) . T)) @@ -1570,11 +1570,11 @@ (|has| |#2| (-149)) (|has| |#1| (-149)) (|has| |#1| (-147)) -(-2225 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2226 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2225 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2226 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2225 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2226 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) (((|#1|) . T)) (|has| |#2| (-240)) @@ -1611,9 +1611,9 @@ ((((-886)) . T)) ((((-886)) . T)) ((((-1030 |#1|)) . T) ((|#1|) . T)) -((((-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-840 (-1207))) . 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T)) ((($) |has| |#1| (-570)) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) -((((-886)) -2225 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-886))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1131))) (((-1298 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2338 (-1189)) (|:| -2079 #0#))) . T)) +((((-886)) -2226 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-886))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1131))) (((-1298 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2339 (-1189)) (|:| -2076 #0#))) . T)) (((|#1|) . T)) ((((-886)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131)))) @@ -1758,7 +1758,7 @@ ((((-578)) . T)) (|has| |#2| (-149)) (|has| |#1| (-487)) -(-2225 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +(-2226 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) (|has| |#1| (-376)) ((((-886)) . T)) (|has| |#1| (-38 (-421 (-578)))) @@ -1769,8 +1769,8 @@ (|has| |#1| (-870)) ((((-886)) . T)) (((|#2|) . T)) -((((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2225 (|has| |#1| (-376)) (|has| |#1| (-570))) (((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) -(((|#1|) |has| |#1| (-175)) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2225 (|has| |#1| (-376)) (|has| |#1| (-570)))) +((((-421 (-578))) -2226 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2226 (|has| |#1| (-376)) (|has| |#1| (-570))) (((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) +(((|#1|) |has| |#1| (-175)) (((-421 (-578))) -2226 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2226 (|has| |#1| (-376)) (|has| |#1| (-570)))) ((($) |has| |#1| (-570)) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) (((|#2|) . T) (((-578)) . T) (((-841 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1779,8 +1779,8 @@ ((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T)) ((((-886)) . T)) ((((-886)) . T)) -(-2225 (|has| |#1| (-102)) (|has| |#1| (-1131))) -(((|#2| (-496 (-4415 |#1|) (-793)) (-888 |#1|)) . T)) +(-2226 (|has| |#1| (-102)) (|has| |#1| (-1131))) +(((|#2| (-496 (-4416 |#1|) (-793)) (-888 |#1|)) . T)) ((((-421 (-578))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1| (-545 (-1207)) (-1207)) . T)) (((|#1|) . T)) @@ -1801,19 +1801,19 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2338 (-1189)) (|:| -2079 |#1|))) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2339 (-1189)) (|:| -2076 |#1|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2338 (-1207)) (|:| -2079 (-52)))) . T)) +((((-2 (|:| -2339 (-1207)) (|:| -2076 (-52)))) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) ((((-1207) (-52)) . T)) ((((-421 (-578)) |#1|) . T) (($ $) . T)) (((|#1| (-578)) . T)) ((((-939 |#1|)) . T)) -(((|#1|) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) -((((-1207)) -2225 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) +(((|#1|) -2226 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) +((((-1207)) -2226 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) (((|#1|) . T) (((-578)) |has| |#1| (-1069 (-578))) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578))))) (|has| |#1| (-871)) (|has| |#1| (-871)) @@ -1834,15 +1834,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131)))) (((|#1|) |has| |#1| (-175))) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131)))) -(((|#3|) -2225 (|has| |#3| (-175)) (|has| |#3| (-376)))) -((($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) -(-2225 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-938))) -((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +(((|#3|) -2226 (|has| |#3| (-175)) (|has| |#3| (-376)))) +((($) -2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +(-2226 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-938))) +((($) -2226 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) ((($ |#2|) . T)) -((($ (-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) +((($ (-1207)) -2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) ((($ $) . T) ((#0=(-421 (-578)) #0#) . T)) ((((-578) |#2|) . T)) -(((|#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)))) +(((|#2|) -2226 (|has| |#2| (-175)) (|has| |#2| (-376)))) (|has| |#1| (-362)) (((|#3| |#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1131)))) (((|#2|) . T) (((-578)) . T)) @@ -1851,7 +1851,7 @@ (|has| |#1| (-842)) (|has| |#1| (-842)) (((|#1|) . T)) -(-2225 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362))) (|has| |#1| (-870)) (|has| |#1| (-870)) (|has| |#1| (-870)) @@ -1860,14 +1860,14 @@ ((((-578)) . T) (($) . T) (((-421 (-578))) . T)) (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-362))) (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) ((((-1207)) |has| |#1| (-927 (-1207))) (((-1113)) . T)) (((|#1|) . T)) (|has| |#1| (-870)) -(((#0=(-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) #0#) |has| (-2 (|:| -2338 (-1189)) (|:| -2079 (-52))) (-321 (-2 (|:| -2338 (-1189)) (|:| -2079 (-52)))))) +(((#0=(-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) #0#) |has| (-2 (|:| -2339 (-1189)) (|:| -2076 (-52))) (-321 (-2 (|:| -2339 (-1189)) (|:| -2076 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) (|has| |#1| (-1131)) ((((-886)) . T) (((-1212)) . T)) @@ -1891,14 +1891,14 @@ (((|#3|) . T)) (((|#1| (-793) (-1113)) . T)) ((((-146)) . T)) -((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) -2225 (|has| |#1| (-870)) (|has| |#1| (-1069 (-578)))) ((|#1|) . T)) +((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) -2226 (|has| |#1| (-870)) (|has| |#1| (-1069 (-578)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-146)) . 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T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1917,31 +1917,31 @@ ((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-570))) ((($) |has| |#1| (-570))) (((|#2|) . T)) -((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (($) -2225 (|has| |#1| (-175)) (|has| |#1| (-570)))) +((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (($) -2226 (|has| |#1| (-175)) (|has| |#1| (-570)))) ((($) |has| |#1| (-570)) ((|#1|) . T)) ((($) |has| |#1| (-870))) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) (|has| |#1| (-938)) ((((-1207)) . T)) ((((-886)) . T)) -((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) . 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T)) @@ -2159,8 +2159,8 @@ (|has| |#1| (-870)) (|has| |#1| (-870)) (((|#1| (-578) (-1113)) . T)) -(-2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +(-2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (((|#1| (-421 (-578)) (-1113)) . T)) (((|#1| (-793) (-1113)) . T)) (|has| |#1| (-871)) @@ -2174,41 +2174,41 @@ ((((-939 |#1|)) . T) (($) . T) (((-421 (-578))) . T)) (|has| |#1| (-1131)) ((((-421 (-578))) |has| |#2| (-376)) (($) . T) (((-578)) . T)) -((((-578)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) +((((-578)) -2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) (((|#1|) . 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T)) ((($) |has| |#1| (-240))) @@ -2243,12 +2243,12 @@ (|has| |#1| (-147)) ((($) |has| |#1| (-570)) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) (((|#1|) |has| |#1| (-175))) -((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-570))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +((($) -2226 (|has| |#1| (-175)) (|has| |#1| (-570))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) ((((-578)) . T) ((|#1|) . T) (($) . T) (((-421 (-578))) . T) (((-1207)) |has| |#1| (-1069 (-1207)))) (((|#1| |#2|) . T)) -((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) -2225 (|has| |#1| (-870)) (|has| |#1| (-1069 (-578)))) ((|#1|) . T)) -(-2225 (-12 (|has| |#4| (-240)) (|has| |#4| (-1080))) (-12 (|has| |#4| (-239)) (|has| |#4| (-1080)))) -(-2225 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) +((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) -2226 (|has| |#1| (-870)) (|has| |#1| (-1069 (-578)))) ((|#1|) . T)) +(-2226 (-12 (|has| |#4| (-240)) (|has| |#4| (-1080))) (-12 (|has| |#4| (-239)) (|has| |#4| (-1080)))) +(-2226 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) ((((-146)) . T)) (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) @@ -2259,13 +2259,13 @@ ((((-886)) . T)) (((|#1|) . T) (((-421 (-578))) . T) (($) . T)) ((($) . T) (((-578)) |has| |#1| (-660 (-578))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) (|has| |#1| (-376)) (|has| |#1| (-376)) ((($ |#2|) . T)) (|has| (-421 |#2|) (-240)) ((((-666 |#1|)) . T)) -((($ (-1294 |#2|)) . T) (($ (-1207)) -2225 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| (-1205 |#1| |#2| |#3|) (-929 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207)))))) +((($ (-1294 |#2|)) . T) (($ (-1207)) -2226 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| (-1205 |#1| |#2| |#3|) (-929 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207)))))) ((($ (-1294 |#2|)) . T) (($ (-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207))))) ((($ (-1294 |#2|)) . T) (($ (-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207))))) (|has| |#1| (-938)) @@ -2273,7 +2273,7 @@ (((|#2|) |has| |#2| (-1080))) (|has| |#1| (-376)) ((($) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) (((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) |has| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (-321 (-2 (|:| -2338 |#1|) (|:| -2079 |#2|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) (((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) |has| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (-321 (-2 (|:| -2339 |#1|) (|:| -2076 |#2|))))) (((|#1|) |has| |#1| (-175))) ((($ (-888 |#1|)) . T)) (((|#1| |#1|) . T)) @@ -2284,7 +2284,7 @@ (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T)) ((((-666 $)) . T) (((-1189)) . T) (((-1207)) . T) (((-578)) . T) (((-229)) . T) (((-886)) . T)) -((((-578)) -2225 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) ((|#3|) -2225 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080))) +((((-578)) -2226 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) ((|#3|) -2226 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080))) ((((-421 (-578))) . T) (((-578)) . T) (((-631 $)) . T)) (((|#1|) . T)) ((((-886)) . T)) @@ -2300,7 +2300,7 @@ (((|#1| (-793) (-1113)) . T)) ((((-886)) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-578)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-578)) -2225 (|has| (-421 (-578)) (-1069 (-578))) (|has| |#1| (-1069 (-578)))) (((-421 (-578))) . T)) +(((|#1|) . T) (((-578)) -2226 (|has| (-421 (-578)) (-1069 (-578))) (|has| |#1| (-1069 (-578)))) (((-421 (-578))) . T)) (((|#1| (-616 |#1| |#3|) (-616 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) @@ -2320,37 +2320,37 @@ ((((-721)) . T)) ((((-721)) . T)) (((|#2|) |has| |#2| (-175))) -(-2225 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-2226 (|has| |#1| (-240)) (|has| |#1| (-239))) ((((-578)) . T) ((|#2|) . T) (((-421 (-578))) |has| |#2| (-1069 (-421 (-578))))) -((((-112)) |has| |#1| (-1131)) (((-886)) -2225 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1131)))) +((((-112)) |has| |#1| (-1131)) (((-886)) -2226 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1131)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-578)) . T) (((-421 (-578))) . T)) ((((-578)) . T) (($) . T) (((-421 (-578))) . 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T) (((-421 (-578))) -2226 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T)) ((((-578) |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) (((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) |has| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (-321 (-2 (|:| -2338 |#1|) (|:| -2079 |#2|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) (((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) |has| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (-321 (-2 (|:| -2339 |#1|) (|:| -2076 |#2|))))) ((((-392)) . T)) ((((-721)) . T)) ((((-421 (-578))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1|) |has| |#1| (-175))) ((((-421 (-981 |#1|))) . T)) (((|#2| |#2|) . T)) -(-2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) -(-2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) +(-2226 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) +(-2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) (((|#1|) . T)) (((|#2|) . T)) (((|#3|) |has| |#3| (-1080))) @@ -2362,7 +2362,7 @@ ((((-1207)) |has| |#2| (-927 (-1207)))) (|has| |#1| (-871)) ((((-886)) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (|has| |#1| (-813)) ((((-421 (-578))) . T) (($) . T)) (|has| |#1| (-487)) @@ -2370,8 +2370,8 @@ (|has| |#1| (-381)) (|has| |#1| (-381)) (|has| |#1| (-376)) -(-2225 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-570)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) -((($) -2225 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-362)))) +(-2226 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-570)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) +((($) -2226 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-362)))) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-362)) @@ -2382,7 +2382,7 @@ (|has| |#1| (-38 (-421 (-578)))) (((|#2|) . T) (((-886)) . T)) (((|#2|) . T) (((-886)) . T)) -((($ (-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +((($ (-1207)) -2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) @@ -2393,18 +2393,18 @@ (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-871)) -((((-2 (|:| -2338 (-1189)) (|:| -2079 |#1|))) . T)) +((((-2 (|:| -2339 (-1189)) (|:| -2076 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-578)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) |has| (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)) (-321 (-2 (|:| -2338 |#1|) (|:| -2079 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131)))) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) |has| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (-321 (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131)))) (((|#2|) . T)) (|has| |#1| (-15 * (|#1| (-578) |#1|))) (((|#3|) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-381)) -(-2225 (-12 (|has| (-1290 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1290 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) +(-2226 (-12 (|has| (-1290 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1290 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-871)) (((|#2|) . T) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) |has| |#1| (-1069 (-578))) ((|#1|) . T)) @@ -2423,17 +2423,17 @@ (((|#1|) |has| |#1| (-376))) (((|#1|) |has| |#1| (-376))) ((((-886)) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) ((($ $) . T) (((-631 $) $) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) ((($) . 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T)) -((((-1207)) -2225 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) +((((-1207)) -2226 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) ((((-666 (-802 |#1| (-888 |#2|)))) . T) (((-886)) . T)) ((((-550)) |has| (-802 |#1| (-888 |#2|)) (-633 (-550)))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) @@ -2442,17 +2442,17 @@ (((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1131)))) (((|#1|) |has| |#1| (-175))) ((((-886)) . T)) -(-2225 (|has| |#2| (-466)) (|has| |#2| (-938))) +(-2226 (|has| |#2| (-466)) (|has| |#2| (-938))) (((|#1|) . T)) ((($) . T)) ((($) |has| |#1| (-570)) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) -((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-570))) ((|#1|) . 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T)) ((((-578)) -12 (|has| |#1| (-21)) (|has| |#2| (-21)))) @@ -2460,14 +2460,14 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) ((((-578)) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) (((#0=(-1283 |#2| |#3| |#4|)) . T) (((-421 (-578))) |has| #0# (-38 (-421 (-578)))) (($) . T)) ((((-578)) . T)) ((($) . T)) (|has| |#1| (-376)) -(-2225 (-12 (|has| (-1290 |#1| |#2| |#3|) (-149)) (|has| |#1| (-376))) (|has| |#1| (-149))) -(-2225 (-12 (|has| (-1290 |#1| |#2| |#3|) (-147)) (|has| |#1| (-376))) (|has| |#1| (-147))) +(-2226 (-12 (|has| (-1290 |#1| |#2| |#3|) (-149)) (|has| |#1| (-376))) (|has| |#1| (-149))) +(-2226 (-12 (|has| (-1290 |#1| |#2| |#3|) (-147)) (|has| |#1| (-376))) (|has| |#1| (-147))) (|has| |#1| (-376)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -2488,29 +2488,29 @@ ((((-421 (-578))) . #0=(|has| |#2| (-376))) (($) . #0#)) (|has| |#1| (-871)) ((((-421 (-578))) |has| |#2| (-376)) (($) . T)) -(-2225 (|has| |#1| (-102)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-102)) (|has| |#1| (-1131))) ((((-1173 |#2| |#1|)) . T) ((|#1|) . T) (((-578)) . T)) (((|#1| |#2|) . T)) -((((-578)) . T) ((|#1|) . 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T) (($ $) -2225 (|has| |#1| (-302)) (|has| |#1| (-376))) ((#0=(-421 (-578)) #0#) |has| |#1| (-376))) +(((|#1| |#1|) . T) (($ $) -2226 (|has| |#1| (-302)) (|has| |#1| (-376))) ((#0=(-421 (-578)) #0#) |has| |#1| (-376))) ((((-981 |#1|)) . T)) -((((-2 (|:| -2338 (-1207)) (|:| -2079 (-52)))) . T)) +((((-2 (|:| -2339 (-1207)) (|:| -2076 (-52)))) . T)) ((($) . T)) ((((-578) |#1|) . T)) ((((-1207)) |has| (-421 |#2|) (-927 (-1207)))) -(((|#1|) . T) (($) -2225 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-578))) |has| |#1| (-376))) +(((|#1|) . T) (($) -2226 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-578))) |has| |#1| (-376))) ((((-550)) |has| |#2| (-633 (-550)))) ((((-711 |#2|)) . T) (((-886)) . T)) (((|#1|) . T)) @@ -2518,24 +2518,24 @@ (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131)))) ((((-894 |#1|)) . 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T)) @@ -2642,13 +2642,13 @@ ((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) ((|#1|) . T) (((-578)) . T)) (|has| |#2| (-147)) (|has| |#2| (-149)) -(-2225 (|has| |#2| (-842)) (|has| |#2| (-871))) +(-2226 (|has| |#2| (-842)) (|has| |#2| (-871))) ((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T)) -(-2225 (|has| |#1| (-102)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-102)) (|has| |#1| (-1131))) ((((-578)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-578)) . T)) (((|#2|) . T)) -((((-1207)) -2225 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2226 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-376))) ((((-421 |#2|)) . T)) @@ -2657,10 +2657,10 @@ ((((-886)) . T)) ((((-886)) . T)) ((((-550)) |has| |#1| (-633 (-550)))) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) ((((-578)) . T) (($) . T) (((-421 (-578))) . 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T)) -(((|#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)))) -(((|#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080)))) -((($ (-1207)) -2225 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) +(((|#2|) -2226 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)))) +(((|#2|) -2226 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080)))) +((($ (-1207)) -2226 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) ((($ $) . T) ((#0=(-1283 |#2| |#3| |#4|) #0#) . T) ((#1=(-421 (-578)) #1#) |has| #0# (-38 (-421 (-578))))) ((((-939 |#1|)) . T)) (-12 (|has| |#1| (-376)) (|has| |#2| (-842))) @@ -2787,14 +2787,14 @@ ((((-886)) . T)) ((($) . T) (((-578)) . T)) ((($) . T)) -(-2225 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-570))) (|has| |#1| (-376)) (|has| |#1| (-376)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1283 |#2| |#3| |#4|)) . T) (((-421 (-578))) |has| #0# (-38 (-421 (-578))))) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -(-2225 (-12 (|has| |#1| (-319)) (|has| |#1| (-938))) (|has| |#1| (-376)) (|has| |#1| (-362))) -(-2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +(-2226 (-12 (|has| |#1| (-319)) (|has| |#1| (-938))) (|has| |#1| (-376)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) ((((-578)) |has| |#1| (-660 (-578))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-886)) . T)) @@ -2832,7 +2832,7 @@ ((($) . T)) (((|#4|) . T)) ((($) . T)) -((($ (-1207)) -2225 (-12 (|has| |#1| (-376)) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-929 (-1207)))))) +((($ (-1207)) -2226 (-12 (|has| |#1| (-376)) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-929 (-1207)))))) ((((-886)) . T)) (((|#1| (-545 (-1207))) . T)) ((($ $) . T)) @@ -2842,29 +2842,29 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131)))) (((|#2|) . T)) -(((|#2|) -2225 (|has| |#2| (-6 (-4509 "*"))) (|has| |#2| (-175)))) -(-2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) -(-2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) +(((|#2|) -2226 (|has| |#2| (-6 (-4510 "*"))) (|has| |#2| (-175)))) +(-2226 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) +(-2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) (|has| |#2| (-938)) (|has| |#1| (-938)) -((($) -2225 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) +((($) -2226 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) (((|#2|) |has| |#2| (-175))) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) ((((-1290 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-886)) . T)) ((((-886)) . T)) ((((-550)) . T) (((-578)) . T) (((-917 (-578))) . T) (((-392)) . T) (((-229)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-578)) . T)) -((((-2 (|:| -2338 (-1189)) (|:| -2079 (-52)))) . T)) +((((-2 (|:| -2339 (-1189)) (|:| -2076 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) ((((-886)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-578)) . T)) (((|#1| (-421 (-578))) . T)) (((|#1|) . T)) -(-2225 (|has| |#1| (-302)) (|has| |#1| (-376))) +(-2226 (|has| |#1| (-302)) (|has| |#1| (-376))) ((((-146)) . T)) ((((-578)) |has| #0=(-421 |#2|) (-660 (-578))) ((#0#) . T) (((-421 (-578))) . T) (($) . T)) (|has| |#1| (-870)) @@ -2880,7 +2880,7 @@ ((((-886)) . T)) ((((-886)) . T)) ((((-190)) . T) (((-886)) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-886)) . T)) ((((-886)) . T)) @@ -2897,8 +2897,8 @@ (|has| |#1| (-871)) ((((-886)) . T)) ((((-550)) |has| |#1| (-633 (-550)))) -((((-2 (|:| -2338 (-1189)) (|:| -2079 |#1|))) . T)) -((($) -2225 (-12 (|has| (-1205 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1205 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-578) |#1|))))) +((((-2 (|:| -2339 (-1189)) (|:| -2076 |#1|))) . T)) +((($) -2226 (-12 (|has| (-1205 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1205 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-578) |#1|))))) ((((-886)) . T)) (((|#2|) |has| |#2| (-376))) ((((-886)) . T)) @@ -2913,19 +2913,19 @@ (|has| |#3| (-1080)) (|has| |#1| (-1131)) ((((-1207) (-52)) . T)) -(-2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) +(-2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2225 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) -(-2225 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2226 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) +(-2226 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) (|has| |#1| (-938)) ((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T)) (|has| |#1| (-938)) (((|#1|) . T) (((-578)) . T) (((-421 (-578))) . T) (($) . T)) (((|#2|) . T)) -((($ (-1207)) -2225 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) +((($ (-1207)) -2226 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) (((#0=(-421 (-578)) #0#) . T) (($ $) . T)) ((((-578)) . T)) (((|#1|) . T)) @@ -2937,12 +2937,12 @@ (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) (|has| |#1| (-842)) (((#0=(-939 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-578)) #1#) . T)) ((((-421 |#2|)) . T)) (|has| |#1| (-870)) -((((-1234 |#1|)) . T) (((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) +((((-1234 |#1|)) . T) (((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) (((|#1| |#1|) . T) ((#0=(-421 (-578)) #0#) . T) ((#1=(-578) #1#) . T) (($ $) . T)) ((((-939 |#1|)) . T) (($) . T) (((-421 (-578))) . T)) (((|#2|) |has| |#2| (-1080)) (((-578)) -12 (|has| |#2| (-660 (-578))) (|has| |#2| (-1080)))) @@ -2961,36 +2961,36 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(-2225 (|has| |#1| (-147)) (|has| |#1| (-381))) -(-2225 (|has| |#1| (-147)) (|has| |#1| (-381))) -(-2225 (|has| |#1| (-147)) (|has| |#1| (-381))) -((((-2 (|:| -2338 (-1207)) (|:| -2079 (-52)))) . T)) +(-2226 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2226 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2226 (|has| |#1| (-147)) (|has| |#1| (-381))) +((((-2 (|:| -2339 (-1207)) (|:| -2076 (-52)))) . T)) ((((-578) |#3|) . T)) (((|#1|) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2338 (-1207)) (|:| -2079 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2339 (-1207)) (|:| -2076 #0#))) . T)) (|has| |#1| (-362)) ((((-578)) . T)) ((((-886)) . T)) (((|#1|) . T)) (((#0=(-1284 |#1| |#2| |#3| |#4|) $) |has| #0# (-298 #0# #0#))) (|has| |#1| (-376)) -(-2225 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) -(((|#1|) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) (((-578)) -2225 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) +(-2226 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) +(((|#1|) -2226 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) (((-578)) -2226 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) (((#0=(-1113) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-362))) (((#0=(-421 (-578)) #0#) . T) ((#1=(-721) #1#) . T) (($ $) . T)) ((((-328 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-421 (-578))) |has| |#1| (-376))) ((((-886)) . T)) (|has| |#1| (-1131)) (((|#1|) . T)) -(((|#1|) -2225 (|has| |#2| (-380 |#1|)) (|has| |#2| (-431 |#1|)))) -(((|#1|) -2225 (|has| |#2| (-380 |#1|)) (|has| |#2| (-431 |#1|)))) +(((|#1|) -2226 (|has| |#2| (-380 |#1|)) (|has| |#2| (-431 |#1|)))) +(((|#1|) -2226 (|has| |#2| (-380 |#1|)) (|has| |#2| (-431 |#1|)))) (((|#2|) . T)) ((((-421 (-578))) . T) (((-721)) . T) (($) . T)) ((((-593)) . T)) (((|#3| |#3|) . T)) -((($ (-1207)) -2225 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((($ (-1207)) -2226 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (|has| |#1| (-871)) (|has| |#2| (-240)) ((((-888 |#1|)) . T)) @@ -3011,10 +3011,10 @@ (|has| |#1| (-1131)) (((|#2|) . T)) (((|#1|) . T)) -((($) -2225 (|has| |#1| (-240)) (|has| |#1| (-239)))) +((($) -2226 (|has| |#1| (-240)) (|has| |#1| (-239)))) ((((-578)) . T)) (((|#2|) . T) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) ((|#1|) . T) (($) . T) (((-578)) . T)) -(-2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) +(-2226 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) (((|#2|) . T) (((-578)) |has| |#2| (-660 (-578)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3057,7 +3057,7 @@ (|has| |#2| (-1053)) ((($) . T)) (|has| |#1| (-938)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3067,32 +3067,32 @@ (|has| |#1| (-376)) ((((-939 |#1|)) . T)) ((($) . T) (((-578)) . T) ((|#1|) . T) (((-421 (-578))) . T)) -((($) -2225 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) -((($) |has| |#1| (-870)) (((-578)) -2225 (|has| |#1| (-21)) (|has| |#1| (-870)))) +((($) -2226 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +((($) |has| |#1| (-870)) (((-578)) -2226 (|has| |#1| (-21)) (|has| |#1| (-870)))) ((($ $) . T) ((#0=(-421 (-578)) #0#) . T)) -(-2225 (|has| |#1| (-381)) (|has| |#1| (-871))) +(-2226 (|has| |#1| (-381)) (|has| |#1| (-871))) (((|#1|) . T)) ((((-793)) . T)) ((((-886)) . T)) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207))))) ((((-421 |#2|) |#3|) . T)) -(-2225 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) +(-2226 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) ((($) . T) (((-421 (-578))) . T)) ((($) . T) (((-578)) . T) (((-421 (-578))) . T) (((-631 $)) . T)) ((((-578)) . T) (($) . T)) ((((-578)) . T) (($) . T)) ((((-793) |#1|) . T)) -(((|#2| (-247 (-4415 |#1|) (-793))) . T)) +(((|#2| (-247 (-4416 |#1|) (-793))) . T)) (((|#1| (-545 |#3|)) . T)) ((((-421 (-578))) . T)) -(-2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) +(-2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((((-1189)) . T) (((-886)) . T)) -(((#0=(-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) #0#) |has| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (-321 (-2 (|:| -2338 (-1207)) (|:| -2079 (-52)))))) +(((#0=(-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) #0#) |has| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (-321 (-2 (|:| -2339 (-1207)) (|:| -2076 (-52)))))) ((((-1189)) . T)) (|has| |#1| (-938)) (|has| |#2| (-376)) (((|#1|) . T) (($) . T) (((-578)) . T)) -(-2225 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2226 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) ((((-172 (-392))) . T) (((-229)) . T) (((-392)) . T)) ((((-886)) . T)) (((|#1|) . T)) @@ -3109,11 +3109,11 @@ (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) -(-2225 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362))) (|has| |#1| (-38 (-421 (-578)))) (-12 (|has| |#1| (-559)) (|has| |#1| (-850))) ((((-886)) . T)) -((((-1207)) -2225 (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))))) +((((-1207)) -2226 (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))))) (|has| |#1| (-376)) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207))))) (|has| |#1| (-376)) @@ -3126,13 +3126,13 @@ ((((-578) |#1|) . T)) ((((-1207)) |has| |#1| (-927 (-1207)))) (((|#1|) . T)) -(-2225 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-362))) +(-2226 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-362))) (((|#2|) |has| |#1| (-376))) (((|#2|) |has| |#1| (-376))) -(-2225 (|has| |#4| (-815)) (|has| |#4| (-871))) -(-2225 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2226 (|has| |#4| (-815)) (|has| |#4| (-871))) +(-2226 (|has| |#3| (-815)) (|has| |#3| (-871))) ((((-578)) . T) (($) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) @@ -3171,32 +3171,32 @@ ((((-392)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-392)))) (((-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-578))))) (((|#1|) . T)) ((($) . T) (((-578)) . T) ((|#2|) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) (((|#3|) . T)) ((((-1189)) . T) (((-520)) . T) (((-229)) . T) (((-578)) . T)) (((|#1|) . T)) (|has| |#1| (-376)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) (|has| |#1| (-376)) (|has| |#1| (-570)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131)))) ((((-421 |#2|)) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T)) -(-2225 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2226 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1080)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) -((((-2 (|:| -2338 (-1189)) (|:| -2079 |#1|))) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) +((((-2 (|:| -2339 (-1189)) (|:| -2076 |#1|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (|has| |#1| (-38 (-421 (-578)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-421 (-578)))) -(-2225 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2226 (|has| |#1| (-147)) (|has| |#1| (-381))) ((($) . T)) (|has| |#1| (-149)) -(-2225 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2226 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2225 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2226 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) ((($) . T)) ((((-595 |#1|)) . T)) @@ -3212,7 +3212,7 @@ ((((-421 (-578))) |has| |#2| (-1069 (-578))) (((-578)) |has| |#2| (-1069 (-578))) (((-1207)) |has| |#2| (-1069 (-1207))) ((|#2|) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-578)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2225 (|has| |#1| (-147)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-147)) (|has| |#1| (-362))) (|has| |#1| (-149)) ((((-886)) . T)) ((($) . T)) @@ -3232,15 +3232,15 @@ ((((-421 |#2|)) . T)) ((((-886)) . T)) (((|#1|) . T)) -((((-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) -(-2225 (|has| |#1| (-102)) (|has| |#1| (-1131))) +((((-1207)) -2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +(-2226 (|has| |#1| (-102)) (|has| |#1| (-1131))) (|has| |#1| (-813)) (|has| |#1| (-813)) ((((-886)) . T)) ((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T)) ((((-886)) . T)) ((((-550)) |has| |#1| (-633 (-550)))) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) ((((-116)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3250,7 +3250,7 @@ (((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-570)) (((-421 (-578))) |has| |#1| (-570))) ((((-886)) . T)) ((((-886)) . T)) -(-2225 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) +(-2226 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) (((#0=(-939 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-578)) #1#) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -3262,10 +3262,10 @@ ((((-886)) . T)) (((|#2|) . T)) ((((-578)) . T)) -((((-1207)) -2225 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +((((-1207)) -2226 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) ((((-886)) . T)) ((((-578)) . T)) -(-2225 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2226 (|has| |#2| (-815)) (|has| |#2| (-871))) ((((-172 (-392))) . T) (((-229)) . T) (((-392)) . T)) ((((-886)) . T)) ((((-886)) . T)) @@ -3277,11 +3277,11 @@ (((|#1|) . T) (($) . T) (((-421 (-578))) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) ((((-886)) . T)) ((((-578) $) . T) (((-666 (-578)) $) . T)) -(-2225 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1131))) (|has| |#1| (-1183)) ((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T)) ((($) . T)) @@ -3291,22 +3291,22 @@ (((#0=(-118 |#1|) $) |has| #0# (-298 #0# #0#))) (((|#1|) |has| |#1| (-175))) ((((-328 |#1|)) . T) (((-578)) . T)) -(-2225 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2226 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1| |#1|) . T)) ((((-886)) . T)) (((|#1|) . T)) ((((-116)) . T) ((|#1|) . T)) ((((-886)) . T)) -((((-1207)) -2225 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2226 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1|) |has| |#1| (-321 |#1|))) ((((-578) |#1|) . T) (((-1265 (-578)) $) . T)) (((|#1| |#2|) . T)) ((((-1207) |#1|) . T)) -(((|#1|) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)))) +(((|#1|) -2226 (|has| |#1| (-175)) (|has| |#1| (-376)))) (((|#1|) . T)) ((($ (-1207)) . T)) -(((|#1|) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080)))) +(((|#1|) -2226 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080)))) ((((-578)) . T) (((-421 (-578))) . T)) (((|#1|) . T)) (|has| |#1| (-570)) @@ -3315,15 +3315,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-578))) . T) (($) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) (|has| |#1| (-376)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) (|has| |#1| (-376)) (|has| |#1| (-570)) ((($) . T)) (|has| |#1| (-1131)) ((((-802 |#1| (-888 |#2|))) |has| (-802 |#1| (-888 |#2|)) (-321 (-802 |#1| (-888 |#2|))))) -(-2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) +(-2226 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3332,17 +3332,17 @@ (((|#1| (-793)) . T)) (|has| |#1| (-240)) (((|#1| (-545 (-1119 (-1207)))) . T)) -((($) -2225 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) +((($) -2226 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) ((((-595 |#1|)) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T)) ((((-578)) . T) (((-421 (-578))) . T) (($) . T)) -((((-2 (|:| -2338 (-1189)) (|:| -2079 (-52)))) . T)) +((((-2 (|:| -2339 (-1189)) (|:| -2076 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-578)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) (|has| |#2| (-376)) ((((-886)) . T)) ((((-886)) . T)) -(-2225 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2226 (|has| |#3| (-815)) (|has| |#3| (-871))) ((((-886)) . T)) ((((-1151)) . T) (((-886)) . T)) ((((-550)) . T) (((-886)) . T)) @@ -3353,14 +3353,14 @@ ((((-578)) . T)) (((|#3|) . T)) ((((-886)) . T)) -(-2225 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362))) -((((-578)) . 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T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) (((-1207)) . T)) +((((-1156 |#1| (-1207))) . T) (((-578)) . T) (((-1119 (-1207))) . T) (($) -2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) -2226 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) (((-1207)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1| (-1298 |#1|) (-1298 |#1|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-578))) . T)) @@ -3370,12 +3370,12 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-421 (-578))) . T)) -(((|#2|) |has| |#2| (-6 (-4509 "*")))) +(((|#2|) |has| |#2| (-6 (-4510 "*")))) (((|#1|) . T)) ((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) ((|#1|) . T) (((-578)) . T)) (((|#1|) . T)) ((((-886)) . T)) -(((#0=(-421 (-578)) #0#) |has| |#2| (-38 (-421 (-578)))) ((|#2| |#2|) . T) (($ $) -2225 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))) +(((#0=(-421 (-578)) #0#) |has| |#2| (-38 (-421 (-578)))) ((|#2| |#2|) . T) (($ $) -2226 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-306 |#3|)) . T)) (((|#1|) . T)) @@ -3384,30 +3384,30 @@ (((|#1|) . T) (((-421 (-578))) . T) (($) . T)) (((|#1|) . T) (((-421 (-578))) . T) (($) . T)) (((|#1|) . T) (((-421 (-578))) . T) (($) . T)) -((($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1| |#1|) . T) ((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578))))) -((($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1| |#1|) . T) ((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578))))) +((($ $) -2226 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1| |#1|) . 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T) (($) -2226 (|has| |#1| (-175)) (|has| |#1| (-570)))) (|has| |#1| (-570)) (((|#1|) |has| |#1| (-376))) ((((-578)) . T)) ((((-1207) #0=(-118 |#1|)) |has| #0# (-528 (-1207) #0#)) ((#0# #0#) |has| #0# (-321 #0#))) (|has| |#1| (-813)) (|has| |#1| (-813)) -((((-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +((((-1207)) -2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) (((|#2|) . T) (((-578)) |has| |#2| (-1069 (-578))) (((-421 (-578))) |has| |#2| (-1069 (-421 (-578))))) ((((-1113)) . T) ((|#2|) . T) (((-578)) |has| |#2| (-1069 (-578))) (((-421 (-578))) |has| |#2| (-1069 (-421 (-578))))) (((|#1|) . T)) @@ -3477,11 +3477,11 @@ ((($) |has| |#1| (-381))) (|has| |#2| (-842)) (|has| |#2| (-842)) -((((-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-578)))) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . 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T)) @@ -3496,7 +3496,7 @@ (|has| |#1| (-376)) (|has| |#1| (-376)) (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131)))) -(((|#2|) -2225 (|has| |#2| (-6 (-4509 "*"))) (|has| |#2| (-175)))) +(((|#2|) -2226 (|has| |#2| (-6 (-4510 "*"))) (|has| |#2| (-175)))) (((|#2|) . T)) (|has| |#1| (-376)) (((|#2|) . T)) @@ -3510,12 +3510,12 @@ (((|#2| (-793)) . T)) ((((-1207)) . T)) ((((-894 |#1|)) . T)) -(-2225 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) -(-2225 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-133)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-815)) (|has| |#3| (-1080))) +(-2226 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) +(-2226 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-133)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-815)) (|has| |#3| (-1080))) ((((-886)) . T)) (((|#1|) . T)) -(-2225 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2225 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) +(-2226 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2226 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) ((((-894 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-381)) @@ -3533,7 +3533,7 @@ (((|#1|) . T)) ((((-886)) . T)) ((($) . T) ((|#2|) . T) (((-421 (-578))) . T) (((-578)) |has| |#2| (-660 (-578)))) -(-2225 (|has| |#1| (-102)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-102)) (|has| |#1| (-1131))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) @@ -3542,7 +3542,7 @@ (((|#1|) . T)) ((((-886)) . T)) (|has| |#2| (-938)) -((((-2 (|:| -2338 (-1207)) (|:| -2079 (-52)))) . T)) +((((-2 (|:| -2339 (-1207)) (|:| -2076 (-52)))) . T)) ((((-550)) |has| |#2| (-633 (-550))) (((-917 (-392))) |has| |#2| (-633 (-917 (-392)))) (((-917 (-578))) |has| |#2| (-633 (-917 (-578))))) ((((-886)) . T)) ((((-886)) . T)) @@ -3553,7 +3553,7 @@ ((((-1203 |#1|)) . T) (((-886)) . T)) ((((-886)) . T)) ((((-421 (-578))) |has| |#2| (-1069 (-421 (-578)))) (((-578)) |has| |#2| (-1069 (-578))) ((|#2|) . T) (((-888 |#1|)) . T)) -((((-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-1113)) . T)) +((((-1207)) -2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-1113)) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-578))) . T)) ((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) |has| |#1| (-1069 (-578))) ((|#1|) . T) (((-1207)) . T)) ((((-886)) . T)) @@ -3573,10 +3573,10 @@ ((((-666 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-421 (-578)) |#1|)))) ((($) . T) (((-578)) . T) (((-1284 |#1| |#2| |#3| |#4|)) . T) (((-421 (-578))) . 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T) (((-578)) |has| |#1| (-660 (-578)))) @@ -3609,9 +3609,9 @@ ((($) . T) (((-421 (-578))) . T)) ((($) . T)) ((($) . T)) -(-2225 (|has| |#1| (-871)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-871)) (|has| |#1| (-1131))) (((|#1|) . T)) -((($) -2225 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +((($) -2226 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) ((((-886)) . T)) ((((-146)) . T)) (((|#1|) . T) (((-421 (-578))) . T)) @@ -3620,7 +3620,7 @@ ((((-886)) . T)) (((|#1|) . T)) (|has| |#1| (-1183)) -((($ (-1207)) -2225 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +((($ (-1207)) -2226 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) (((|#1|) . T)) (((|#1| (-545 (-888 |#2|)) (-888 |#2|) (-802 |#1| (-888 |#2|))) . 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T)) ((((-886)) . T) (((-1212)) . T)) -((((-666 |#1|)) . T) (((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) +((((-666 |#1|)) . T) (((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) ((((-1212)) . T)) ((((-1212)) . T)) ((((-1212)) . T)) @@ -3752,19 +3752,19 @@ ((((-1212)) . T)) ((((-886)) . T) (((-1212)) . T)) ((((-1212)) . T)) -((((-2 (|:| -2338 (-1207)) (|:| -2079 (-52)))) |has| (-2 (|:| -2338 (-1207)) (|:| -2079 (-52))) (-321 (-2 (|:| -2338 (-1207)) (|:| -2079 (-52)))))) -(-2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) +((((-2 (|:| -2339 (-1207)) (|:| -2076 (-52)))) |has| (-2 (|:| -2339 (-1207)) (|:| -2076 (-52))) (-321 (-2 (|:| -2339 (-1207)) (|:| -2076 (-52)))))) +(-2226 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) ((((-578) |#1|) . T)) ((((-578) |#1|) . T)) ((((-578) |#1|) . 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T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-362))) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-362))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) ((((-550)) |has| |#1| (-633 (-550)))) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) ((((-550)) |has| |#1| (-633 (-550)))) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) ((((-550)) |has| |#1| (-633 (-550)))) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-421 (-578)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-421 (-578))) . T) (($) . T)) @@ -3886,7 +3886,7 @@ ((((-886)) . T)) ((((-886)) . T)) ((((-886)) . T)) -(-2225 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-2226 (|has| |#1| (-240)) (|has| |#1| (-239))) (((|#1|) . T) (((-886)) . T) (((-1212)) . T)) ((((-1212)) . T)) ((((-886)) . T)) @@ -3895,21 +3895,21 @@ ((((-657 |#2|)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131)))) (((|#1| (-545 (-888 |#2|)) (-888 |#2|) (-802 |#1| (-888 |#2|))) . T)) -((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))) +((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2226 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) . T) (((-578)) |has| |#2| (-660 (-578)))) ((($) . T) (((-578)) . T)) -((($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +((($) -2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) ((((-1135)) . T)) ((((-886)) . T)) ((((-1212)) . T) (((-886)) . T)) ((((-1212)) . T) (((-886)) . T)) ((((-1212)) . T)) ((((-1212)) . T)) -((($) -2225 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +((($) -2226 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) ((($) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (((-578)) |has| |#1| (-660 (-578)))) ((($) . T) (((-578)) . T)) -((($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) +((($) -2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) (|has| |#2| (-938)) (((|#1| |#2| (-247 |#1| |#2|) (-247 |#1| |#2|)) . T)) ((((-886)) . T)) @@ -3925,9 +3925,9 @@ (((|#1| |#1|) |has| |#1| (-175))) ((((-721)) . T)) ((((-721)) . T)) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) ((((-1212)) . T)) -(-2225 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2226 (|has| |#2| (-815)) (|has| |#2| (-871))) (((|#1|) |has| |#1| (-175))) ((((-1212)) . T)) (((|#1| |#1|) . T)) @@ -3940,19 +3940,19 @@ (((|#1| (-578)) . T)) (((|#1|) . T)) ((((-421 (-578))) . T) (((-578)) . T) (($) . T)) -((($ (-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) +((($ (-1207)) -2226 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) (((|#1|) |has| |#1| (-175))) ((((-1212)) . T)) ((((-1212)) . T)) ((((-1212)) . T)) ((((-1212)) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-362))) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-362))) ((((-1212)) . T)) ((((-1212)) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -(-2225 (|has| |#1| (-175)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-175)) (|has| |#1| (-570))) (((|#1| (-578)) . T)) (((|#1| (-421 (-578))) . T)) (((|#1| (-793)) . T)) @@ -3960,24 +3960,24 @@ (((|#1| (-545 |#2|) |#2|) . T)) ((((-578) |#1|) . T)) ((((-578) |#1|) . T)) -(-2225 (|has| |#1| (-102)) (|has| |#1| (-1131))) -(-2225 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239))) +(-2226 (|has| |#1| (-102)) (|has| |#1| (-1131))) +(-2226 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239))) ((((-578) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-917 (-392))) . T) (((-917 (-578))) . T) (((-1207)) . T) (((-550)) . T)) -(-2225 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) -(-2225 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-133)) (|has| |#2| (-133))) (-12 (|has| |#1| (-815)) (|has| |#2| (-815)))) +(-2226 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2226 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-133)) (|has| |#2| (-133))) (-12 (|has| |#1| (-815)) (|has| |#2| (-815)))) ((((-886)) . T)) ((((-578)) . T)) ((((-578)) . T)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1207)) -12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) (|has| |#2| (-1080)) -(-2225 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) +(-2226 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-376)) @@ -4010,7 +4010,7 @@ (((|#1| |#2|) . T)) ((((-578)) . T) ((|#2|) |has| |#2| (-175))) ((((-116)) . T) ((|#1|) . T) (((-578)) . T)) -(-2225 (|has| |#1| (-362)) (|has| |#1| (-381))) +(-2226 (|has| |#1| (-362)) (|has| |#1| (-381))) (((|#1| |#2|) . T)) ((((-229)) . T)) ((((-421 (-578))) . T) (($) . T) (((-578)) . T)) @@ -4019,11 +4019,11 @@ ((($) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (((-578)) |has| |#1| (-660 (-578)))) ((($) . T) (((-578)) |has| |#1| (-660 (-578))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578))))) (((|#2|) |has| |#2| (-1131)) (((-578)) -12 (|has| |#2| (-1069 (-578))) (|has| |#2| (-1131))) (((-421 (-578))) -12 (|has| |#2| (-1069 (-421 (-578)))) (|has| |#2| (-1131)))) -(-2225 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2226 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1|) . T)) ((((-550)) |has| |#1| (-633 (-550)))) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131)))) ((((-578) $) . T) (((-666 (-578)) $) . T)) ((($) . T) (((-421 (-578))) . T)) (|has| |#1| (-938)) @@ -4035,14 +4035,14 @@ (((|#1| |#1|) |has| |#1| (-175))) (((|#1|) . T) (((-578)) . T)) ((((-1212)) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-570))) -(-2225 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-570))) +(-2226 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#2|) . T)) -(-2225 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2226 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) (((|#1|) . T)) -((((-886)) -2225 (-12 (|has| |#1| (-632 (-886))) (|has| |#2| (-632 (-886)))) (-12 (|has| |#1| (-1131)) (|has| |#2| (-1131))))) +((((-886)) -2226 (-12 (|has| |#1| (-632 (-886))) (|has| |#2| (-632 (-886)))) (-12 (|has| |#1| (-1131)) (|has| |#2| (-1131))))) ((((-421 |#2|) |#3|) . T)) ((((-421 (-578))) . T) (($) . T)) (|has| |#1| (-38 (-421 (-578)))) @@ -4051,7 +4051,7 @@ ((($) . T) (((-578)) . T)) (|has| (-421 |#2|) (-149)) (|has| (-421 |#2|) (-147)) -(-2225 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2226 (|has| |#3| (-815)) (|has| |#3| (-871))) ((($) . T)) ((((-721)) . T)) (((|#1|) . T) (((-421 (-578))) . T) (((-578)) . T) (($) . T)) @@ -4067,7 +4067,7 @@ ((((-1212)) . T)) ((((-578)) . T)) (((|#2|) . T)) -((((-1207)) -2225 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207)))))) +((((-1207)) -2226 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207)))))) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207))))) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4083,11 +4083,11 @@ ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1171 |#1| |#2|)) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2|) . T) (((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) -((((-2 (|:| -2338 (-1207)) (|:| -2079 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) +((((-2 (|:| -2339 (-1207)) (|:| -2076 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1053)) -(((|#2|) . T) (((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) ((($) . T)) ((((-886)) . T)) ((((-550)) |has| |#2| (-633 (-550))) (((-917 (-578))) |has| |#2| (-633 (-917 (-578)))) (((-917 (-392))) |has| |#2| (-633 (-917 (-392)))) (((-392)) . #0=(|has| |#2| (-1053))) (((-229)) . #0#)) @@ -4096,7 +4096,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578)))) -((((-1207)) -2225 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2226 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) ((((-886)) . T)) (((|#2|) . T)) ((((-886)) . T)) @@ -4106,15 +4106,15 @@ ((((-1205 |#1| |#2| |#3|)) . T)) ((((-1205 |#1| |#2| |#3|)) . T) (((-1198 |#1| |#2| |#3|)) . T)) ((((-886)) . T)) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) ((((-578) |#1|) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-376)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2225 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-578)) -12 (|has| |#4| (-660 (-578))) (|has| |#4| (-1080)))) -(((|#2|) . T) ((|#3|) -2225 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-578)) -12 (|has| |#3| (-660 (-578))) (|has| |#3| (-1080)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2226 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-578)) -12 (|has| |#4| (-660 (-578))) (|has| |#4| (-1080)))) +(((|#2|) . T) ((|#3|) -2226 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-578)) -12 (|has| |#3| (-660 (-578))) (|has| |#3| (-1080)))) (((|#1|) . T)) (((|#1|) . T)) ((((-118 |#1|)) . T)) @@ -4128,7 +4128,7 @@ ((((-190)) . T) (((-886)) . T)) ((((-886)) . T)) (((|#1|) . T)) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) ((((-578) |#1|) . T) (((-1265 (-578)) $) . T)) ((((-886)) . T)) (((|#1|) . T)) @@ -4136,14 +4136,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) (($ $) . T) (((-578) |#1|) . T)) ((($ $) . T) (((-421 (-578)) |#1|) . T)) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-938))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-938))) ((($ (-1207)) |has| |#1| (-1080))) -(-2225 (|has| |#1| (-871)) (|has| |#1| (-1131))) +(-2226 (|has| |#1| (-871)) (|has| |#1| (-1131))) ((((-886)) . T)) ((((-886)) . T)) ((((-886)) . T)) (((|#1| (-545 |#2|)) . T)) -((((-2 (|:| -2338 (-1207)) (|:| -2079 (-52)))) . T)) +((((-2 (|:| -2339 (-1207)) (|:| -2076 (-52)))) . T)) ((((-578) (-131)) . T)) (((|#1| (-578)) . T)) (((|#1| (-421 (-578))) . T)) @@ -4158,8 +4158,8 @@ ((((-1212)) . T)) ((((-886)) . T) (((-1212)) . T)) ((((-886)) . T) (((-1212)) . T)) -(-2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) -(-2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) +(-2226 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) +(-2226 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((($) . T)) (((|#2| (-545 (-888 |#1|))) . T)) ((((-1212)) . T)) @@ -4174,7 +4174,7 @@ ((((-1212)) . T)) ((((-886)) . T) (((-1212)) . T)) ((((-1212)) . T)) -((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) +((((-886)) -2226 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1189) |#1|) . T)) @@ -4182,7 +4182,7 @@ ((((-421 |#2|)) . T)) (|has| |#1| (-570)) (|has| |#1| (-570)) -((((-2 (|:| -2338 |#1|) (|:| -2079 |#2|))) . T)) +((((-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T)) (((|#2| (-793)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-421 (-578))) . T)) @@ -4192,14 +4192,14 @@ ((((-578)) . T) (($) . T)) (((|#2| $) |has| |#2| (-298 |#2| |#2|))) (((|#1| (-666 |#1|)) |has| |#1| (-870))) -(-2225 (|has| |#1| (-240)) (|has| |#1| (-362))) -(-2225 (|has| |#1| (-376)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-240)) (|has| |#1| (-362))) +(-2226 (|has| |#1| (-376)) (|has| |#1| (-362))) ((((-1294 |#1|)) . T) (((-578)) . T) ((|#2|) . T) (((-421 (-578))) |has| |#2| (-1069 (-421 (-578))))) (|has| |#1| (-1131)) (((|#1|) . T)) ((((-421 (-578))) . T) (($) . T)) -((((-1294 |#1|)) . T) (((-578)) . T) (($) -2225 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) (((-1113)) . T) ((|#2|) . T) (((-421 (-578))) -2225 (|has| |#2| (-38 (-421 (-578)))) (|has| |#2| (-1069 (-421 (-578)))))) -((((-1030 |#1|)) . T) ((|#1|) . T) (((-578)) -2225 (|has| (-1030 |#1|) (-1069 (-578))) (|has| |#1| (-1069 (-578)))) (((-421 (-578))) -2225 (|has| (-1030 |#1|) (-1069 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578)))))) +((((-1294 |#1|)) . T) (((-578)) . 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T) ((-492 . -93) T) ((-421 . -239) 191161) ((-368 . -632) 191143) ((-365 . -632) 191125) ((-357 . -632) 191107) ((-275 . -633) 190855) ((-275 . -632) 190837) ((-255 . -632) 190819) ((-255 . -633) 190680) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1172 . -632) 190662) ((-1151 . -662) 190649) ((-1151 . -1082) 190636) ((-841 . -748) T) ((-841 . -881) T) ((-616 . -300) 190613) ((-595 . -739) 190578) ((-493 . -633) NIL) ((-493 . -632) 190560) ((-532 . -739) 190505) ((-328 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-939 . -632) 190487) ((-939 . -633) 190469) ((-400 . -748) T) ((-896 . -1087) 190421) ((-896 . -111) 190359) ((-736 . -1080) T) ((-734 . -1274) 190343) ((-716 . -362) NIL) ((-116 . -102) T) ((-141 . -102) T) ((-138 . -102) T) ((-533 . -632) 190275) ((-392 . -817) T) ((-170 . -1248) T) ((-227 . -1131) T) ((-392 . -814) T) ((-59 . -633) 190236) ((-229 . -816) T) ((-229 . -813) T) ((-59 . -632) 190148) ((-229 . -748) T) ((-530 . -633) 190109) ((-530 . -632) 190021) ((-511 . -632) 189953) ((-510 . -633) 189914) ((-510 . -632) 189826) ((-1111 . -376) 189777) ((-40 . -425) 189754) ((-77 . -1248) T) ((-895 . -938) NIL) ((-372 . -341) 189738) ((-372 . -376) T) ((-366 . -341) 189722) ((-366 . -376) T) ((-358 . -341) 189706) ((-358 . -376) T) ((-328 . -296) 189685) ((-108 . -376) T) ((-70 . -1248) T) ((-661 . -1131) T) ((-1262 . -351) 189637) ((-895 . -670) 189582) ((-1262 . -390) 189534) ((-993 . -133) 189389) ((-837 . -133) 189260) ((-45 . -874) NIL) ((-987 . -673) 189244) ((-1256 . -683) T) ((-1118 . -175) 189155) ((-987 . -386) 189139) ((-1093 . -816) T) ((-1093 . -813) T) ((-896 . -635) 189037) ((-804 . -175) 188928) ((-802 . -175) 188839) ((-838 . -47) 188801) ((-1093 . -748) T) ((-339 . -503) 188785) ((-981 . -748) T) ((-1311 . -321) 188723) ((-1290 . -927) 188636) ((-468 . -175) 188547) ((-252 . -298) 188499) ((-1283 . -927) 188405) ((-1282 . -1087) 188240) ((-1262 . -927) 188073) ((-495 . -748) T) ((-1261 . -1087) 187881) ((-1242 . -302) 187860) ((-1217 . -1248) T) ((-1214 . -381) T) ((-1213 . -381) T) ((-1177 . -153) 187844) ((-1151 . -102) T) ((-1149 . -1131) T) ((-1111 . -23) T) ((-1111 . -1143) T) ((-1106 . -102) T) ((-1088 . -632) 187811) ((-1034 . -423) 187783) ((-956 . -984) T) ((-759 . -321) 187721) ((-75 . -1248) T) ((-686 . -395) 187693) ((-172 . -938) 187646) ((-30 . -984) T) ((-112 . -866) T) ((-1 . -632) 187628) ((-1030 . -921) 187549) ((-130 . -673) 187531) ((-50 . -639) 187515) ((-716 . -668) 187450) ((-609 . -927) 187363) ((-452 . -102) T) ((-130 . -386) 187345) ((-143 . -321) NIL) ((-896 . -1080) T) ((-855 . -871) 187324) ((-81 . -1248) T) ((-733 . -302) T) ((-40 . -1089) T) ((-595 . -175) T) ((-532 . -175) T) ((-525 . -632) 187306) ((-172 . -670) 187180) ((-521 . -632) 187162) ((-364 . -149) 187144) ((-364 . -147) T) ((-372 . -1143) T) ((-366 . -1143) T) ((-358 . -1143) T) ((-1035 . -319) T) ((-943 . -319) T) ((-896 . -250) T) ((-108 . -1143) T) ((-896 . -240) 187123) ((-1282 . -111) 186944) ((-1261 . -111) 186733) ((-252 . -1286) 186717) ((-578 . -870) T) ((-372 . -23) T) ((-367 . -362) T) ((-328 . -321) 186704) ((-325 . -321) 186645) ((-366 . -23) T) ((-331 . -133) T) ((-358 . -23) T) ((-1035 . -1053) T) ((-31 . -635) 186626) ((-108 . -23) T) ((-676 . -1082) 186610) ((-252 . -618) 186587) ((-661 . -739) 186571) ((-345 . -1131) T) ((-676 . -662) 186541) ((-1284 . -38) 186433) ((-1271 . -938) 186412) ((-112 . -1131) T) ((-838 . -1248) T) ((-427 . -1248) T) ((-1066 . -102) T) ((-1271 . -670) 186301) ((-895 . -816) NIL) ((-879 . -670) 186275) ((-895 . -813) NIL) ((-838 . -911) NIL) ((-895 . -748) T) ((-1118 . -528) 186148) ((-804 . -528) 186095) ((-802 . -528) 186047) ((-585 . -670) 186034) ((-838 . -1069) 185862) ((-468 . -528) 185805) ((-402 . -403) T) ((-1282 . -635) 185618) ((-1261 . -635) 185366) ((-60 . -1248) T) ((-640 . -871) 185345) ((-514 . -683) T) ((-1177 . -1007) 185314) ((-1055 . -668) 185251) ((-1034 . -466) T) ((-721 . -870) T) ((-524 . -814) T) ((-488 . -1087) 185086) ((-514 . -114) T) ((-356 . -1131) T) ((-325 . -1183) NIL) ((-301 . -133) T) ((-408 . -1131) T) ((-894 . -1089) T) ((-716 . -383) 185053) ((-367 . -668) 184983) ((-227 . -639) 184960) ((-339 . -298) 184912) ((-488 . -111) 184733) ((-1282 . -1080) T) ((-1261 . -1080) T) ((-838 . -390) 184717) ((-846 . -1248) T) ((-172 . -748) T) ((-1313 . -1248) T) ((-676 . -102) T) ((-1282 . -250) 184696) ((-1282 . -240) 184648) ((-1261 . -240) 184553) ((-1261 . -250) 184532) ((-1034 . -416) NIL) ((-692 . -660) 184480) ((-328 . -38) 184390) ((-325 . -38) 184319) ((-69 . -632) 184301) ((-331 . -507) 184267) ((-48 . -668) 184217) ((-1220 . -300) 184196) ((-1256 . -871) T) ((-1144 . -1143) 184174) ((-83 . -1248) T) ((-61 . -632) 184156) ((-888 . -874) T) ((-493 . -300) 184135) ((-1313 . -1069) 184112) ((-1195 . -1131) T) ((-1144 . -23) 183964) ((-838 . -927) 183900) ((-1271 . -748) T) ((-1133 . -1248) T) ((-488 . -635) 183726) ((-364 . -239) T) ((-1118 . -302) 183657) ((-995 . -1131) T) ((-918 . -102) T) ((-804 . -302) 183568) ((-339 . -19) 183552) ((-59 . -300) 183529) ((-802 . -302) 183460) ((-879 . -748) T) ((-119 . -870) NIL) ((-530 . -300) 183437) ((-339 . -618) 183414) ((-510 . -300) 183391) ((-468 . -302) 183322) ((-1066 . -321) 183173) ((-900 . -504) 183154) ((-900 . -632) 183120) ((-703 . -504) 183101) ((-585 . -748) T) ((-698 . -504) 183082) ((-703 . -632) 183032) ((-698 . -632) 182998) ((-684 . -632) 182980) ((-492 . -504) 182961) ((-492 . -632) 182927) ((-252 . -633) 182888) ((-252 . -504) 182865) ((-140 . -504) 182846) ((-139 . -504) 182827) ((-135 . -504) 182808) ((-252 . -632) 182700) ((-216 . -102) T) ((-140 . -632) 182666) ((-139 . -632) 182632) ((-135 . -632) 182598) ((-1178 . -34) T) ((-972 . -1248) T) ((-356 . -739) 182543) ((-692 . -25) T) ((-692 . -21) T) ((-1207 . -635) 182524) ((-343 . -1248) T) ((-488 . -1080) T) ((-654 . -431) 182489) ((-620 . -431) 182454) ((-1151 . -1183) T) ((-1283 . -319) 182433) ((-734 . -1082) 182256) ((-595 . -302) T) ((-532 . -302) T) ((-1262 . -319) 182235) ((-488 . -240) 182187) ((-488 . -250) 182166) ((-453 . -1248) T) ((-734 . -662) 181995) ((-1262 . -1053) NIL) ((-1111 . -133) T) ((-896 . -817) 181974) ((-146 . -102) T) ((-40 . -1131) T) ((-896 . -814) 181953) ((-666 . -1041) 181937) ((-594 . -1089) T) ((-578 . -1089) T) ((-509 . -1089) T) ((-421 . -466) T) ((-372 . -133) T) ((-328 . -414) 181921) ((-325 . -414) 181882) ((-366 . -133) T) ((-358 . -133) T) ((-1212 . -1131) T) ((-1151 . -38) 181869) ((-1125 . -632) 181836) ((-108 . -133) T) ((-983 . -1131) T) ((-950 . -1131) T) ((-793 . -1131) T) ((-694 . -1131) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1320 . -21) T) ((-1320 . -25) T) ((-1318 . -21) T) ((-1318 . -25) T) ((-686 . -1087) 181820) ((-545 . -871) T) ((-514 . -871) T) ((-378 . -1248) T) ((-368 . -1087) 181772) ((-365 . -1087) 181724) ((-357 . -1087) 181676) ((-260 . -1248) T) ((-259 . -1248) T) ((-275 . -1087) 181519) ((-255 . -1087) 181362) ((-686 . -111) 181341) ((-839 . -1252) 181320) ((-561 . -866) T) ((-328 . -929) 181286) ((-368 . -111) 181224) ((-365 . -111) 181162) ((-357 . -111) 181100) ((-275 . -111) 180929) ((-255 . -111) 180758) ((-325 . -929) NIL) ((-642 . -425) 180742) ((-44 . -21) T) ((-44 . -25) T) ((-934 . -874) 180693) ((-131 . -683) T) ((-837 . -660) 180599) ((-839 . -570) 180578) ((-501 . -874) T) ((-260 . -1069) 180405) ((-259 . -1069) 180232) ((-128 . -121) 180216) ((-221 . -874) T) ((-939 . -1087) 180181) ((-734 . -102) T) ((-721 . -1089) T) ((-611 . -635) 180162) ((-599 . -635) 180143) ((-550 . -637) 180046) ((-356 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-88 . -632) 180028) ((-939 . -111) 179984) ((-40 . -739) 179929) ((-894 . -1131) T) ((-686 . -635) 179906) ((-667 . -635) 179887) ((-368 . -635) 179824) ((-365 . -635) 179761) ((-357 . -635) 179698) ((-561 . -1131) T) ((-339 . -633) 179659) ((-339 . -632) 179571) ((-275 . -635) 179324) ((-255 . -635) 179109) ((-189 . -1248) T) ((-1261 . -814) 179062) ((-1261 . -817) 179015) ((-260 . -390) 178984) ((-259 . -390) 178953) ((-563 . -874) T) ((-676 . -38) 178923) ((-627 . -34) T) ((-496 . -1143) 178901) ((-489 . -34) T) ((-1144 . -133) 178772) ((-993 . -25) 178583) ((-939 . -635) 178533) ((-898 . -632) 178515) ((-218 . -866) T) ((-993 . -21) 178470) ((-837 . -25) 178303) ((-837 . -21) 178214) ((-1254 . -381) T) ((-642 . -1089) T) ((-1209 . -570) 178193) ((-1203 . -47) 178170) ((-368 . -1080) T) ((-365 . -1080) T) ((-496 . -23) 178022) ((-357 . -1080) T) ((-275 . -1080) T) ((-255 . -1080) T) ((-1156 . -47) 177994) ((-119 . -1089) T) ((-1065 . -670) 177968) ((-987 . -34) T) ((-368 . -240) 177947) ((-368 . -250) T) ((-365 . -240) 177926) ((-365 . -250) T) ((-357 . -240) 177905) ((-357 . -250) T) ((-275 . -338) 177877) ((-255 . -338) 177834) ((-275 . -240) 177813) ((-1188 . -153) 177797) ((-260 . -927) 177729) ((-259 . -927) 177661) ((-1173 . -921) 177582) ((-1113 . -871) T) ((-1265 . -1248) 177560) ((-428 . -1143) T) ((-1242 . -1033) 177526) ((-1085 . -23) T) ((-1055 . -870) T) ((-939 . -1080) T) ((-334 . -670) 177508) ((-723 . -239) T) ((-692 . -236) 177453) ((-1204 . -949) 177432) ((-1198 . -949) 177411) ((-1198 . -842) NIL) ((-1030 . -1082) 177307) ((-996 . -1248) T) ((-939 . -250) T) ((-839 . -376) 177286) ((-218 . -1131) T) ((-398 . -23) T) ((-129 . -1131) 177264) ((-123 . -1131) 177242) ((-939 . -240) T) ((-130 . -34) T) ((-392 . -670) 177207) ((-1030 . -662) 177155) ((-894 . -739) 177142) ((-1327 . -668) 177114) ((-1077 . -153) 177079) ((-1024 . -1248) T) ((-886 . -1248) T) ((-40 . -175) T) ((-716 . -425) 177061) ((-734 . -321) 177048) ((-858 . -670) 177008) ((-849 . -670) 176982) ((-331 . -25) T) ((-331 . -21) T) ((-680 . -298) 176961) ((-594 . -1131) T) ((-578 . -1131) T) ((-509 . -1131) T) ((-1203 . -1248) T) ((-252 . -300) 176938) ((-1156 . -1248) T) ((-878 . -1248) T) ((-325 . -274) 176899) ((-325 . -234) 176860) ((-1253 . -874) T) ((-1203 . -911) NIL) ((-55 . -1131) T) ((-1156 . -911) 176719) ((-131 . -871) T) ((-1203 . -1069) 176599) ((-1156 . -1069) 176482) ((-186 . -632) 176464) ((-878 . -1069) 176360) ((-804 . -298) 176287) ((-839 . -1143) T) ((-1065 . -748) T) ((-1077 . -1007) 176216) ((-616 . -673) 176200) ((-1034 . -921) 176107) ((-1030 . -102) T) ((-839 . -23) T) ((-734 . -1183) 176085) ((-716 . -1089) T) ((-616 . -386) 176069) ((-364 . -466) T) ((-356 . -302) T) ((-1299 . -1131) T) ((-256 . -1131) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1131) T) ((-721 . -1131) T) ((-374 . -487) T) ((-1242 . -632) 176051) ((-1203 . -390) 176035) ((-1156 . -390) 176019) ((-1055 . -425) 175981) ((-143 . -233) 175963) ((-392 . -816) T) ((-392 . -813) T) ((-894 . -175) T) ((-392 . -748) T) ((-733 . -632) 175945) ((-734 . -38) 175774) ((-1298 . -1296) 175758) ((-364 . -416) T) ((-1298 . -1131) 175708) ((-1221 . -1131) T) ((-594 . -739) 175695) ((-578 . -739) 175682) ((-509 . -739) 175647) ((-1284 . -668) 175537) ((-328 . -648) 175516) ((-858 . -748) T) ((-849 . -748) T) ((-1146 . -1248) T) ((-666 . -1248) T) ((-1111 . -660) 175464) ((-1203 . -927) 175407) ((-1156 . -927) 175391) ((-837 . -236) 175282) ((-684 . -1087) 175266) ((-108 . -660) 175248) ((-496 . -133) 175119) ((-1209 . -1143) T) ((-841 . -1248) T) ((-981 . -47) 175088) ((-642 . -1131) T) ((-684 . -111) 175067) ((-505 . -632) 175033) ((-339 . -300) 175010) ((-400 . -1248) T) ((-336 . -1248) T) ((-495 . -47) 174967) ((-1209 . -23) T) ((-119 . -1131) T) ((-103 . -102) 174917) ((-1310 . -1143) T) ((-562 . -871) T) ((-229 . -1248) T) ((-1085 . -133) T) ((-1055 . -1089) T) ((-1310 . -23) T) ((-1228 . -632) 174899) ((-841 . -1069) 174883) ((-1151 . -850) T) ((-1034 . -746) 174855) ((-1136 . -1131) T) ((-721 . -739) 174820) ((-600 . -632) 174802) ((-400 . -1069) 174786) ((-367 . -1089) T) ((-398 . -133) T) ((-336 . -1069) 174770) ((-1111 . -21) T) ((-1111 . -25) T) ((-1035 . -842) T) ((-229 . -911) 174752) ((-1035 . -949) T) ((-91 . -34) T) ((-1030 . -321) 174717) ((-943 . -949) T) ((-900 . -635) 174698) ((-736 . -670) 174658) ((-501 . -1252) T) ((-703 . -635) 174639) ((-698 . -635) 174620) ((-659 . -670) 174604) ((-221 . -1252) T) ((-421 . -921) 174525) ((-229 . -1069) 174485) ((-40 . -302) T) ((-501 . -570) T) ((-492 . -635) 174466) ((-372 . -25) T) ((-328 . -668) 174121) ((-325 . -668) 174035) ((-372 . -21) T) ((-366 . -25) T) ((-366 . -21) T) ((-221 . -570) T) ((-358 . -25) T) ((-358 . -21) T) ((-331 . -236) 173981) ((-252 . -635) 173958) ((-140 . -635) 173939) ((-139 . -635) 173920) ((-135 . -635) 173901) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1089) T) ((-594 . -175) T) ((-578 . -175) T) ((-509 . -175) T) ((-1093 . -1248) T) ((-981 . -1248) T) ((-735 . -1248) T) ((-661 . -298) 173868) ((-680 . -632) 173850) ((-495 . -1248) T) ((-759 . -758) 173834) ((-349 . -632) 173816) ((-68 . -396) T) ((-68 . -409) T) ((-1133 . -107) 173800) ((-1093 . -911) 173782) ((-981 . -911) 173707) ((-675 . -1143) T) ((-642 . -739) 173694) ((-495 . -911) NIL) ((-1177 . -102) T) ((-1125 . -637) 173678) ((-1093 . -1069) 173660) ((-97 . -632) 173642) ((-491 . -149) T) ((-981 . -1069) 173522) ((-119 . -739) 173467) ((-734 . -929) 173374) ((-675 . -23) T) ((-495 . -1069) 173250) ((-1118 . -633) NIL) ((-1118 . -632) 173232) ((-804 . -633) NIL) ((-804 . -632) 173193) ((-802 . -633) 172827) ((-802 . -632) 172741) ((-1144 . -660) 172647) ((-821 . -874) 172626) ((-475 . -632) 172608) ((-468 . -632) 172590) ((-468 . -633) 172451) ((-1066 . -233) 172397) ((-896 . -938) 172376) ((-128 . -34) T) ((-839 . -133) T) ((-671 . -632) 172358) ((-592 . -102) T) ((-368 . -1317) 172342) ((-365 . -1317) 172326) ((-357 . -1317) 172310) ((-123 . -528) 172243) ((-129 . -528) 172176) ((-525 . -814) T) ((-525 . -817) T) ((-524 . -816) T) ((-103 . -321) 172114) ((-226 . -102) 172064) ((-721 . -175) T) ((-716 . -1131) T) ((-896 . -670) 171980) ((-65 . -397) T) ((-286 . -632) 171962) ((-65 . -409) T) ((-981 . -390) 171946) ((-894 . -302) T) ((-50 . -632) 171928) ((-1151 . -668) 171900) ((-1030 . -38) 171848) ((-626 . -1131) T) ((-621 . -1131) T) ((-595 . -632) 171830) ((-495 . -390) 171814) ((-595 . -633) 171796) ((-532 . -632) 171778) ((-939 . -1317) 171765) ((-895 . -1248) T) ((-723 . -466) T) ((-509 . -528) 171731) ((-1309 . -1248) T) ((-1308 . -1248) T) ((-501 . -376) T) ((-368 . -381) 171710) ((-365 . -381) 171689) ((-357 . -381) 171668) ((-736 . -748) T) ((-221 . -376) T) ((-118 . -466) T) ((-1321 . -1312) 171652) ((-895 . -909) 171629) ((-895 . -911) NIL) ((-993 . -871) 171528) ((-837 . -871) 171479) ((-1255 . -102) T) ((-676 . -678) 171463) ((-1234 . -34) T) ((-174 . -632) 171445) ((-1144 . -25) 171278) ((-1144 . -21) 171189) ((-895 . -1069) 171166) ((-981 . -927) 171147) ((-1271 . -47) 171124) ((-939 . -381) T) ((-607 . -874) T) ((-59 . -673) 171108) ((-530 . -673) 171092) ((-495 . -927) 171069) ((-71 . -455) T) ((-71 . -409) T) ((-510 . -673) 171053) ((-59 . -386) 171037) ((-642 . -175) T) ((-530 . -386) 171021) ((-510 . -386) 171005) ((-560 . -1248) T) 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169722) ((-358 . -236) 169695) ((-177 . -466) T) ((-86 . -455) T) ((-226 . -321) 169633) ((-86 . -409) T) ((-227 . -632) 169615) ((-108 . -236) 169602) ((-221 . -23) T) ((-1322 . -1315) 169581) ((-699 . -1069) 169565) ((-594 . -302) T) ((-578 . -302) T) ((-509 . -302) T) ((-1271 . -1248) T) ((-138 . -484) 169520) ((-879 . -1248) T) ((-676 . -668) 169479) ((-48 . -1131) T) ((-734 . -274) 169463) ((-734 . -234) 169447) ((-895 . -927) NIL) ((-585 . -1248) T) ((-1271 . -911) NIL) ((-914 . -102) T) ((-910 . -102) T) ((-661 . -632) 169429) ((-402 . -1131) T) ((-172 . -390) 169413) ((-172 . -351) 169397) ((-1271 . -1069) 169277) ((-879 . -1069) 169173) ((-1173 . -102) T) ((-1030 . -929) 169096) ((-684 . -814) 169075) ((-675 . -133) T) ((-684 . -817) 169054) ((-119 . -528) 168962) ((-585 . -1069) 168944) ((-306 . -1305) 168914) ((-1198 . -874) NIL) ((-890 . -102) T) ((-992 . -570) 168893) ((-1242 . -1087) 168776) ((-1034 . -1082) 168721) ((-496 . -660) 168627) ((-933 . -1131) T) ((-1055 . -739) 168564) ((-733 . -1087) 168529) ((-1034 . -662) 168474) ((-636 . -102) T) ((-616 . -34) T) ((-1178 . -1248) T) ((-1242 . -111) 168343) ((-488 . -670) 168240) ((-367 . -739) 168185) ((-172 . -927) 168144) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168100) ((-1327 . -1089) T) ((-1271 . -390) 168084) ((-432 . -1252) 168062) ((-1149 . -632) 168044) ((-325 . -870) NIL) ((-432 . -570) T) ((-229 . -319) T) ((-1261 . -813) 167997) ((-1261 . -816) 167950) ((-1282 . -748) T) ((-1261 . -748) T) ((-48 . -739) 167915) ((-229 . -1053) T) ((-1284 . -425) 167881) ((-1271 . -927) 167824) ((-364 . -1305) 167801) ((-1242 . -635) 167683) ((-740 . -748) T) ((-345 . -632) 167665) ((-534 . -874) 167644) ((-1144 . -236) 167535) ((-112 . -632) 167517) ((-112 . -633) 167499) ((-740 . -487) T) ((-733 . -635) 167449) ((-1321 . -1082) 167433) ((-496 . -25) 167266) ((-129 . -503) 167250) ((-123 . -503) 167234) ((-496 . -21) 167145) ((-1321 . -662) 167115) ((-642 . -302) T) ((-600 . -1087) 167090) 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-1248) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1321 . -102) T) ((-1229 . -1248) T) ((-1228 . -635) 166423) ((-1119 . -1248) T) ((-1118 . -1087) 166266) ((-1107 . -1248) T) ((-275 . -938) 166245) ((-255 . -938) 166224) ((-804 . -1087) 166047) ((-802 . -1087) 165890) ((-627 . -1248) T) ((-1195 . -632) 165872) ((-1118 . -111) 165701) ((-1077 . -102) T) ((-489 . -1248) T) ((-475 . -1087) 165672) ((-468 . -1087) 165515) ((-686 . -670) 165499) ((-895 . -319) T) ((-804 . -111) 165308) ((-802 . -111) 165137) ((-368 . -670) 165089) ((-365 . -670) 165041) ((-357 . -670) 164993) ((-275 . -670) 164882) ((-255 . -670) 164771) ((-1189 . -871) T) ((-1119 . -1069) 164755) ((-1107 . -1069) 164732) ((-1035 . -874) T) ((-1031 . -34) T) ((-475 . -111) 164693) ((-468 . -111) 164522) ((-1002 . -874) T) ((-995 . -632) 164504) ((-992 . -1143) T) ((-987 . -1248) T) ((-128 . -1041) 164488) ((-872 . -1248) T) ((-895 . -1053) NIL) ((-757 . -1143) T) ((-737 . -1143) T) ((-680 . -635) 164406) 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-815) T) ((-525 . -816) T) ((-467 . -133) T) ((-421 . -1183) 160463) ((-227 . -1080) T) ((-306 . -102) 160245) ((-143 . -1131) T) ((-721 . -1033) T) ((-1136 . -298) 160201) ((-91 . -1248) T) ((-218 . -632) 160183) ((-129 . -632) 160115) ((-123 . -632) 160047) ((-1327 . -175) T) ((-1204 . -376) 160026) ((-1198 . -376) 160005) ((-328 . -1131) T) ((-432 . -133) T) ((-325 . -1131) T) ((-421 . -38) 159957) ((-1164 . -102) T) ((-1284 . -739) 159849) ((-1166 . -1293) T) ((-1127 . -1248) T) ((-1121 . -1248) T) ((-676 . -1089) T) ((-1104 . -1248) T) ((-1097 . -1248) T) ((-1067 . -1248) T) ((-1050 . -1248) T) ((-331 . -147) 159828) ((-331 . -149) 159807) ((-141 . -1131) T) ((-138 . -1131) T) ((-116 . -1131) T) ((-882 . -102) T) ((-645 . -1248) T) ((-497 . -1248) T) ((-594 . -632) 159789) ((-578 . -633) 159688) ((-578 . -632) 159670) ((-509 . -632) 159652) ((-509 . -633) 159597) ((-499 . -23) T) ((-222 . -1248) T) ((-496 . -871) 159548) ((-501 . -660) 159530) ((-994 . -632) 159512) ((-1034 . -929) 159421) ((-221 . -660) 159403) ((-229 . -418) T) ((-684 . -670) 159387) ((-55 . -632) 159369) ((-1203 . -949) 159348) ((-753 . -1143) T) ((-657 . -102) T) ((-529 . -1248) T) ((-524 . -1248) T) ((-522 . -1248) T) ((-364 . -102) T) ((-1247 . -1114) T) ((-1151 . -866) T) ((-840 . -871) T) ((-753 . -23) T) ((-356 . -1087) 159293) ((-1178 . -107) 159277) ((-1299 . -632) 159259) ((-1205 . -23) T) ((-1205 . -1143) T) ((-1204 . -1143) T) ((-659 . -1248) T) ((-1204 . -23) T) ((-1198 . -1143) T) ((-1198 . -23) T) ((-1173 . -274) 159243) ((-529 . -1069) 159227) ((-1173 . -234) 159211) ((-1157 . -1143) T) ((-356 . -111) 159140) ((-1035 . -1252) T) ((-128 . -1248) T) ((-943 . -1252) T) ((-1157 . -23) T) ((-1106 . -1131) T) ((-716 . -298) NIL) ((-736 . -1248) T) ((-1035 . -570) T) ((-943 . -570) T) ((-837 . -239) 159037) ((-625 . -683) T) ((-624 . -683) T) ((-257 . -1248) T) ((-190 . -1248) T) ((-164 . -1248) T) ((-159 . -1248) T) ((-256 . -632) 159019) ((-622 . -683) T) ((-821 . -133) T) 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156900) ((-392 . -1053) T) ((-108 . -149) T) ((-108 . -147) NIL) ((-45 . -242) 156850) ((-676 . -1131) T) ((-627 . -107) 156797) ((-499 . -133) T) ((-489 . -107) 156747) ((-247 . -1143) 156725) ((-31 . -1248) T) ((-896 . -390) 156709) ((-896 . -351) 156693) ((-247 . -23) 156545) ((-40 . -635) 156475) ((-1311 . -528) 156408) ((-1093 . -949) T) ((-1093 . -842) T) ((-595 . -381) T) ((-532 . -381) T) ((-1290 . -570) 156387) ((-1283 . -1252) 156366) ((-1283 . -570) 156317) ((-1282 . -1248) T) ((-1262 . -1252) 156296) ((-364 . -1183) T) ((-339 . -34) T) ((-44 . -431) 156280) ((-1212 . -635) 156216) ((-897 . -1248) T) ((-404 . -766) 156200) ((-1262 . -570) 156151) ((-1261 . -1248) T) ((-1173 . -668) 156110) ((-753 . -133) T) ((-694 . -635) 156094) ((-1261 . -911) 155967) ((-1261 . -909) 155937) ((-1205 . -133) T) ((-1204 . -133) T) ((-1198 . -133) T) ((-1157 . -133) T) ((-323 . -1114) T) ((-1055 . -1033) T) ((-759 . -528) 155870) ((-1035 . -23) T) ((-1035 . -1143) T) ((-918 . -1131) T) ((-146 . -866) T) ((-1034 . -362) NIL) ((-713 . -632) 155852) ((-972 . -874) 155831) ((-537 . -321) 155769) ((-1002 . -23) T) ((-143 . -528) NIL) ((-890 . -668) 155714) ((-943 . -1143) T) ((-943 . -23) T) ((-896 . -927) 155673) ((-364 . -38) 155638) ((-894 . -1087) 155625) ((-343 . -874) T) ((-82 . -632) 155607) ((-40 . -1080) T) ((-894 . -111) 155592) ((-740 . -1248) T) ((-723 . -102) T) ((-716 . -632) 155574) ((-616 . -1248) T) ((-610 . -570) 155553) ((-441 . -1143) T) ((-352 . -1082) 155537) ((-216 . -1131) T) ((-177 . -1082) 155469) ((-488 . -47) 155439) ((-40 . -240) 155411) ((-40 . -250) T) ((-136 . -102) T) ((-118 . -102) T) ((-609 . -570) 155390) ((-352 . -662) 155374) ((-716 . -633) 155282) ((-328 . -528) 155248) ((-177 . -662) 155180) ((-325 . -528) 155072) ((-501 . -236) 155059) ((-1282 . -1069) 155043) ((-1261 . -1069) 154829) ((-1030 . -425) 154813) ((-221 . -236) 154800) ((-441 . -23) T) ((-1151 . -175) T) ((-626 . -504) 154767) ((-621 . -504) 154749) ((-626 . -632) 154701) 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. -133) T) ((-1135 . -1131) T) ((-1034 . -1131) T) ((-62 . -632) 142043) ((-1111 . -921) 141912) ((-1055 . -814) T) ((-1055 . -817) T) ((-1290 . -25) T) ((-1290 . -21) T) ((-1283 . -21) T) ((-1283 . -25) T) ((-894 . -670) 141899) ((-1262 . -21) T) ((-1262 . -25) T) ((-1058 . -153) 141883) ((-1035 . -236) 141870) ((-896 . -842) 141849) ((-896 . -949) T) ((-734 . -298) 141776) ((-610 . -21) T) ((-352 . -668) 141735) ((-108 . -921) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141652) ((-40 . -748) T) ((-226 . -528) 141585) ((-609 . -25) T) ((-490 . -153) 141569) ((-477 . -153) 141553) ((-186 . -1248) T) ((-950 . -816) T) ((-950 . -748) T) ((-793 . -815) T) ((-793 . -816) T) ((-520 . -1131) T) ((-516 . -1131) T) ((-793 . -748) T) ((-229 . -376) T) ((-1320 . -1082) 141537) ((-1318 . -1082) 141521) ((-1320 . -662) 141491) ((-1188 . -1131) 141469) ((-895 . -1252) T) ((-1318 . -662) 141439) ((-1119 . -874) T) ((-676 . -632) 141421) ((-895 . -570) T) ((-716 . -381) NIL) ((-44 . -1082) 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137363) ((-1118 . -1248) T) ((-1066 . -300) 137338) ((-594 . -748) T) ((-578 . -816) T) ((-172 . -376) 137289) ((-578 . -813) T) ((-578 . -748) T) ((-509 . -748) T) ((-804 . -1248) T) ((-802 . -1248) T) ((-1177 . -503) 137273) ((-475 . -1248) T) ((-468 . -1248) T) ((-1320 . -1319) 137249) ((-1118 . -911) NIL) ((-895 . -1143) T) ((-119 . -938) NIL) ((-1318 . -1319) 137228) ((-671 . -1248) T) ((-804 . -911) NIL) ((-802 . -911) 137087) ((-1313 . -25) T) ((-1313 . -21) T) ((-1245 . -102) 137065) ((-1137 . -409) T) ((-642 . -670) 137052) ((-468 . -911) NIL) ((-697 . -102) 137002) ((-1118 . -1069) 136829) ((-895 . -23) T) ((-804 . -1069) 136688) ((-802 . -1069) 136545) ((-119 . -670) 136490) ((-468 . -1069) 136366) ((-286 . -1248) T) ((-328 . -635) 135930) ((-325 . -635) 135813) ((-50 . -1248) T) ((-404 . -668) 135782) ((-671 . -1069) 135766) ((-646 . -102) T) ((-595 . -1248) T) ((-532 . -1248) T) ((-226 . -503) 135750) ((-1298 . -34) T) ((-640 . -668) 135709) ((-301 . -1082) 135696) ((-138 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112390) ((-1198 . -1258) 112374) ((-529 . -25) T) ((-509 . -314) T) ((-525 . -23) T) ((-524 . -25) T) ((-522 . -25) T) ((-521 . -23) T) ((-432 . -1082) 112348) ((-421 . -1080) T) ((-331 . -1089) T) ((-716 . -319) T) ((-432 . -662) 112322) ((-108 . -870) T) ((-734 . -748) T) ((-421 . -250) T) ((-421 . -240) 112301) ((-392 . -236) 112288) ((-501 . -38) 112238) ((-221 . -38) 112188) ((-488 . -507) 112154) ((-659 . -21) T) ((-659 . -25) T) ((-1255 . -381) T) ((-1189 . -1175) T) ((-1132 . -102) T) ((-849 . -236) 112127) ((-723 . -632) 112109) ((-723 . -633) 112024) ((-736 . -21) T) ((-736 . -25) T) ((-1166 . -102) T) ((-496 . -668) 111803) ((-247 . -921) 111670) ((-136 . -632) 111652) ((-118 . -632) 111634) ((-159 . -25) T) ((-1320 . -1131) T) ((-896 . -660) 111582) ((-1318 . -1131) T) ((-889 . -1248) T) ((-992 . -102) T) ((-757 . -102) T) ((-737 . -102) T) ((-467 . -102) T) ((-838 . -466) 111533) ((-44 . -1131) T) ((-1119 . -871) T) ((-1094 . -321) 111384) ((-686 . -133) T) ((-1085 . -668) 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. |RecordCategory|) T) ((-1144 . -1089) 105417) ((-855 . -632) 105399) ((-1093 . -239) T) ((-594 . -949) T) ((-578 . -842) T) ((-578 . -949) T) ((-509 . -949) T) ((-138 . -1069) 105383) ((-229 . -95) T) ((-172 . -149) 105362) ((-75 . -455) T) ((0 . -632) 105344) ((-75 . -409) T) ((-172 . -147) 105295) ((-229 . -35) T) ((-49 . -632) 105277) ((-491 . -1089) T) ((-501 . -274) 105259) ((-501 . -234) 105241) ((-498 . -999) 105225) ((-221 . -274) 105207) ((-221 . -234) 105189) ((-81 . -455) T) ((-81 . -409) T) ((-1177 . -34) T) ((-753 . -102) T) ((-675 . -668) 105148) ((-1057 . -632) 105115) ((-514 . -298) 105065) ((-328 . -390) 105034) ((-325 . -390) 104995) ((-325 . -351) 104956) ((-1116 . -632) 104938) ((-838 . -978) 104885) ((-684 . -133) T) ((-1271 . -147) 104864) ((-1271 . -149) 104843) ((-1205 . -102) T) ((-1204 . -102) T) ((-1198 . -102) T) ((-1190 . -1131) T) ((-1157 . -102) T) ((-1106 . -1248) T) ((-226 . -34) T) ((-301 . -739) 104830) ((-1290 . -1289) 104814) ((-1190 . -629) 104790) ((-607 . -321) NIL) ((-1290 . -1276) 104767) ((-1181 . -233) 104717) ((-498 . -1131) 104695) ((-452 . -1248) T) ((-404 . -632) 104677) ((-524 . -871) T) ((-1151 . -1248) T) ((-1283 . -1281) 104638) ((-1283 . -1276) 104608) ((-1283 . -1279) 104592) ((-1262 . -1260) 104553) ((-1262 . -1276) 104530) ((-1262 . -1258) 104514) ((-1205 . -296) 104480) ((-640 . -632) 104462) ((-1204 . -296) 104428) ((-721 . -949) T) ((-1198 . -296) 104394) ((-1157 . -296) 104360) ((-1151 . -911) 104342) ((-1111 . -1131) T) ((-1092 . -1131) T) ((-48 . -314) T) ((-328 . -927) 104308) ((-325 . -927) NIL) ((-1092 . -1099) 104287) ((-821 . -38) 104271) ((-275 . -660) 104219) ((-112 . -874) T) ((-255 . -660) 104167) ((-723 . -1087) 104154) ((-609 . -1276) 104131) ((-1151 . -1069) 104113) ((-331 . -175) 104044) ((-372 . -1131) T) ((-366 . -1131) T) ((-358 . -1131) T) ((-514 . -19) 104026) ((-1133 . -153) 104010) ((-895 . -239) NIL) ((-108 . -1131) T) ((-118 . -1087) 103997) ((-733 . -376) T) ((-514 . -618) 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. -47) 98886) ((-372 . -175) T) ((-366 . -175) T) ((-533 . -57) 98860) ((-511 . -57) 98810) ((-364 . -1317) 98787) ((-229 . -466) T) ((-331 . -302) 98738) ((-358 . -175) T) ((-177 . -250) T) ((-1261 . -871) 98637) ((-108 . -175) T) ((-896 . -1023) 98621) ((-680 . -1143) T) ((-595 . -376) T) ((-595 . -341) 98608) ((-532 . -341) 98585) ((-532 . -376) T) ((-328 . -319) 98564) ((-325 . -319) T) ((-616 . -871) 98543) ((-1144 . -739) 98485) ((-623 . -1248) T) ((-534 . -294) 98469) ((-680 . -23) T) ((-432 . -234) 98453) ((-432 . -274) 98437) ((-325 . -1053) NIL) ((-349 . -23) T) ((-103 . -1041) 98421) ((-657 . -381) T) ((-45 . -36) 98400) ((-631 . -1131) T) ((-364 . -381) T) ((-538 . -102) T) ((-509 . -27) T) ((-247 . -321) 98338) ((-1118 . -1143) T) ((-1321 . -670) 98312) ((-804 . -1143) T) ((-802 . -1143) T) ((-1209 . -425) 98296) ((-468 . -1143) T) ((-1093 . -466) T) ((-1182 . -1131) T) ((-981 . -466) 98247) ((-1146 . -1114) T) ((-110 . -1131) T) ((-1118 . -23) T) ((-1190 . -528) 98030) 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90854) ((-1190 . -503) 90788) ((-1313 . -1082) 90772) ((-394 . -1087) 90756) ((-1313 . -662) 90726) ((-838 . -102) T) ((-491 . -250) T) ((-736 . -149) 90705) ((-736 . -147) 90684) ((-119 . -874) NIL) ((-498 . -503) 90668) ((-499 . -348) 90637) ((-526 . -1131) 90588) ((-1322 . -111) 90567) ((-1030 . -390) 90551) ((-427 . -102) T) ((-394 . -111) 90530) ((-1030 . -351) 90514) ((-290 . -1014) 90498) ((-289 . -1014) 90482) ((-1035 . -929) NIL) ((-1320 . -632) 90464) ((-1318 . -632) 90446) ((-110 . -528) NIL) ((-1203 . -1274) 90430) ((-878 . -876) 90414) ((-1209 . -1131) T) ((-103 . -1248) T) ((-981 . -978) 90375) ((-839 . -739) 90317) ((-1262 . -1183) NIL) ((-495 . -978) 90262) ((-1093 . -145) T) ((-60 . -102) 90212) ((-44 . -632) 90194) ((-78 . -632) 90176) ((-364 . -670) 90121) ((-625 . -1131) T) ((-624 . -1131) T) ((-622 . -1131) T) ((-1310 . -1131) T) ((-525 . -871) T) ((-301 . -298) 90100) ((-356 . -1143) T) ((-307 . -1131) T) ((-1030 . -927) 90059) ((-307 . -629) 90038) ((-1322 . 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-425) 85075) ((-721 . -1252) T) ((-651 . -298) 85028) ((-1118 . -660) 84976) ((-934 . -1131) T) ((-804 . -660) 84924) ((-802 . -660) 84872) ((-356 . -133) T) ((-301 . -632) 84854) ((-894 . -1143) T) ((-721 . -570) T) ((-131 . -635) 84836) ((-468 . -660) 84784) ((-172 . -921) 84705) ((-934 . -932) 84689) ((-392 . -466) T) ((-501 . -1131) T) ((-972 . -321) 84627) ((-723 . -670) 84599) ((-563 . -866) T) ((-221 . -1131) T) ((-328 . -949) 84578) ((-325 . -949) T) ((-325 . -842) NIL) ((-404 . -742) T) ((-894 . -23) T) ((-118 . -670) 84565) ((-488 . -147) 84544) ((-432 . -425) 84528) ((-488 . -149) 84507) ((-110 . -503) 84489) ((-323 . -635) 84470) ((-2 . -632) 84452) ((-189 . -102) T) ((-1189 . -19) 84434) ((-1189 . -618) 84409) ((-680 . -21) T) ((-680 . -25) T) ((-607 . -1175) T) ((-1144 . -298) 84386) ((-349 . -25) T) ((-349 . -21) T) ((-914 . -1248) T) ((-910 . -1248) T) ((-1320 . -1087) 84370) ((-247 . -668) 84149) ((-509 . -376) T) ((-1318 . -1087) 84133) ((-1313 . -38) 84103) ((-1282 . -1233) 84069) ((-1282 . -1236) 84035) ((-1271 . -921) 83938) ((-1203 . -1082) 83761) ((-1173 . -1248) T) ((-1156 . -1082) 83604) ((-878 . -1082) 83588) ((-651 . -618) 83563) ((-1282 . -95) 83529) ((-1282 . -239) 83481) ((-1265 . -102) 83459) ((-1203 . -662) 83288) ((-1156 . -662) 83137) ((-878 . -662) 83107) ((-1262 . -234) 83059) ((-1118 . -25) T) ((-563 . -1131) T) ((-1118 . -21) T) ((-992 . -1089) T) ((-545 . -814) T) ((-545 . -817) T) ((-119 . -1252) T) ((-890 . -1248) T) ((-642 . -570) T) ((-804 . -25) T) ((-804 . -21) T) ((-802 . -21) T) ((-802 . -25) T) ((-757 . -1089) T) ((-737 . -1089) T) ((-692 . -1087) 83043) ((-531 . -1114) T) ((-475 . -25) T) ((-119 . -570) T) ((-475 . -21) T) ((-468 . -25) T) ((-468 . -21) T) ((-1262 . -274) 82995) ((-1182 . -93) T) ((-1173 . -1069) 82891) ((-839 . -302) 82870) ((-1261 . -1233) 82836) ((-845 . -1131) T) ((-995 . -998) T) ((-692 . -111) 82815) ((-636 . -1248) T) ((-307 . -528) 82607) ((-1261 . -1236) 82573) ((-1261 . -239) 82432) ((-1256 . 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81418) ((-358 . -632) 81400) ((-66 . -410) T) ((-66 . -409) T) ((-108 . -633) 81330) ((-108 . -632) 81272) ((-214 . -922) T) ((-987 . -153) 81256) ((-793 . -133) T) ((-692 . -635) 81174) ((-136 . -748) T) ((-118 . -748) T) ((-1282 . -35) 81140) ((-1085 . -503) 81124) ((-594 . -23) T) ((-578 . -23) T) ((-509 . -23) T) ((-1261 . -95) 81090) ((-1261 . -35) 81056) ((-1203 . -102) T) ((-1156 . -102) T) ((-878 . -102) T) ((-231 . -503) 81040) ((-1320 . -111) 81019) ((-1318 . -111) 80998) ((-44 . -1087) 80982) ((-1321 . -1248) T) ((-1320 . -635) 80928) ((-1320 . -1080) T) ((-1318 . -635) 80857) ((-1318 . -1080) T) ((-1271 . -1274) 80841) ((-879 . -876) 80825) ((-1209 . -302) 80804) ((-1135 . -1248) T) ((-110 . -298) 80754) ((-1034 . -1248) T) ((-130 . -153) 80736) ((-1173 . -927) 80695) ((-44 . -111) 80674) ((-1253 . -1131) T) ((-1212 . -1293) T) ((-1198 . -870) NIL) ((-1197 . -504) 80655) ((-692 . -1080) T) ((-1197 . -632) 80621) ((-1189 . -632) 80603) ((-488 . -239) 80555) ((-1094 . -629) 80530) ((-1025 . -504) 80511) ((-74 . -455) T) ((-74 . -409) T) ((-1094 . -1131) T) ((-154 . -1087) 80495) ((-1025 . -632) 80461) ((-692 . -240) 80440) ((-585 . -568) 80424) ((-368 . -149) 80403) ((-368 . -147) 80354) ((-365 . -149) 80333) ((-365 . -147) 80284) ((-357 . -149) 80263) ((-357 . -147) 80214) ((-275 . -147) 80193) ((-275 . -149) 80172) ((-255 . -149) 80151) ((-119 . -376) T) ((-255 . -147) 80130) ((-1189 . -633) NIL) ((-154 . -111) 80109) ((-1034 . -1069) 79997) ((-1188 . -1248) T) ((-716 . -1252) T) ((-821 . -1089) T) ((-721 . -1143) T) ((-1034 . -390) 79974) ((-520 . -1248) T) ((-516 . -1248) T) ((-939 . -147) T) ((-939 . -149) 79956) ((-894 . -133) T) ((-837 . -1087) 79877) ((-721 . -23) T) ((-716 . -570) T) ((-229 . -1082) 79842) ((-669 . -632) 79774) ((-669 . -633) 79735) ((-651 . -633) NIL) ((-651 . -632) 79717) ((-501 . -175) T) ((-229 . -662) 79682) ((-221 . -175) T) ((-227 . -21) T) ((-227 . -25) T) ((-488 . -1236) 79648) ((-488 . -1233) 79614) ((-285 . -632) 79596) ((-284 . -632) 79578) ((-283 . -632) 79560) ((-282 . -632) 79542) ((-281 . -632) 79524) ((-514 . -673) 79506) ((-280 . -632) 79488) ((-352 . -748) T) ((-279 . -632) 79470) ((-110 . -19) 79452) ((-177 . -748) T) ((-514 . -386) 79434) ((-215 . -632) 79416) ((-534 . -1180) 79400) ((-514 . -125) T) ((-110 . -618) 79375) ((-214 . -632) 79357) ((-488 . -35) 79323) ((-488 . -95) 79289) ((-212 . -632) 79271) ((-211 . -632) 79253) ((-210 . -632) 79235) ((-209 . -632) 79217) ((-206 . -632) 79199) ((-205 . -632) 79181) ((-204 . -632) 79163) ((-203 . -632) 79145) ((-202 . -632) 79127) ((-201 . -632) 79109) ((-200 . -632) 79091) ((-550 . -1134) 79043) ((-199 . -632) 79025) ((-198 . -632) 79007) ((-45 . -503) 78944) ((-197 . -632) 78926) ((-196 . -632) 78908) ((-154 . -635) 78877) ((-1146 . -102) T) ((-837 . -111) 78793) ((-666 . -102) 78723) ((-661 . -21) T) ((-661 . -25) T) ((-496 . -298) 78700) ((-1321 . -1069) 78684) ((-1144 . -632) 78377) ((-1132 . -1131) T) ((-1077 . -1248) T) ((-1203 . 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. -949) T) ((-723 . -842) T) ((-441 . -632) 39859) ((-1151 . -21) T) ((-1151 . -25) T) ((-692 . -390) 39843) ((-118 . -949) T) ((-896 . -274) 39827) ((-896 . -234) 39811) ((-44 . -1248) T) ((-78 . -1248) T) ((-128 . -127) 39795) ((-1085 . -34) T) ((-1320 . -1069) 39769) ((-1318 . -1069) 39726) ((-1271 . -1089) T) ((-879 . -1089) T) ((-368 . -1183) 39705) ((-365 . -1183) 39684) ((-357 . -1183) 39663) ((-496 . -816) 39642) ((-496 . -815) 39621) ((-231 . -34) T) ((-496 . -748) 39599) ((-821 . -635) 39445) ((-684 . -1082) 39429) ((-60 . -503) 39413) ((-585 . -1089) T) ((-1203 . -175) 39304) ((-684 . -662) 39288) ((-488 . -929) 39194) ((-154 . -1248) T) ((-1156 . -175) 39105) ((-1093 . -1131) T) ((-1118 . -978) 39050) ((-981 . -1131) T) ((-839 . -670) 39001) ((-804 . -978) 38970) ((-735 . -1131) T) ((-802 . -978) 38937) ((-530 . -294) 38921) ((-692 . -927) 38880) ((-495 . -1131) T) ((-468 . -978) 38847) ((-79 . -1248) T) ((-368 . -38) 38812) ((-365 . -38) 38777) ((-357 . -38) 38742) ((-275 . -38) 38591) ((-255 . -38) 38440) ((-939 . -1183) T) ((-538 . -504) 38421) ((-642 . -149) 38400) ((-642 . -147) 38379) ((-538 . -632) 38345) ((-119 . -149) T) ((-119 . -147) NIL) ((-428 . -748) T) ((-821 . -1080) T) ((-578 . -239) T) ((-509 . -239) T) ((-356 . -466) T) ((-1290 . -1033) 38311) ((-1283 . -1033) 38277) ((-1262 . -1033) 38243) ((-939 . -38) 38208) ((-229 . -739) 38173) ((-1030 . -133) T) ((-659 . -668) 38142) ((-331 . -47) 38112) ((-40 . -423) 38084) ((-142 . -632) 38066) ((-993 . -1248) T) ((-837 . -1248) T) ((-177 . -949) T) ((-563 . -381) T) ((-736 . -668) 38011) ((-619 . -635) 37992) ((-356 . -416) T) ((-693 . -635) 37973) ((-325 . -236) NIL) ((-183 . -635) 37954) ((-163 . -635) 37935) ((-158 . -635) 37916) ((-156 . -635) 37897) ((-534 . -300) 37874) ((-1261 . -234) 37844) ((-1261 . -274) 37814) ((-1245 . -1248) 37792) ((-1209 . -670) 37717) ((-900 . -102) T) ((-837 . -1069) 37544) ((-45 . -34) T) ((-703 . -102) T) ((-698 . -102) T) ((-684 . -102) T) ((-676 . -21) T) 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. -1131) T) ((-981 . -175) 33211) ((-804 . -1274) 33195) ((-666 . -528) 33128) ((-77 . -632) 33110) ((-753 . -338) 33075) ((-1209 . -748) T) ((-585 . -1131) T) ((-495 . -175) 32986) ((-252 . -321) 32924) ((-1173 . -1143) T) ((-70 . -632) 32906) ((-1310 . -748) T) ((-1205 . -1080) T) ((-1204 . -1080) T) ((-1198 . -1080) T) ((-339 . -102) 32836) ((-1173 . -23) T) ((-2 . -1248) T) ((-1157 . -1080) T) ((-91 . -1152) 32820) ((-890 . -1143) T) ((-1205 . -240) 32779) ((-1204 . -250) 32758) ((-1204 . -240) 32710) ((-1198 . -240) 32597) ((-1198 . -250) 32576) ((-331 . -927) 32482) ((-890 . -23) T) ((-172 . -739) 32310) ((-421 . -1252) T) ((-1132 . -381) T) ((-1034 . -376) T) ((-894 . -466) T) ((-1055 . -149) T) ((-972 . -298) 32262) ((-325 . -871) NIL) ((-1282 . -668) 32144) ((-898 . -102) T) ((-1261 . -668) 31999) ((-734 . -25) T) ((-421 . -570) T) ((-734 . -21) T) ((-539 . -635) 31980) ((-367 . -149) 31962) ((-367 . -147) T) ((-1178 . -1131) 31940) ((-467 . -742) T) ((-75 . -632) 31922) 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. -632) 15850) ((-1311 . -1241) 15819) ((-495 . -632) 15801) ((-495 . -633) 15662) ((-275 . -425) 15646) ((-255 . -425) 15630) ((-325 . -239) NIL) ((-260 . -111) 15546) ((-259 . -111) 15462) ((-1255 . -683) T) ((-1205 . -670) 15387) ((-1204 . -670) 15284) ((-1198 . -670) 15136) ((-1157 . -670) 15061) ((-364 . -133) T) ((-82 . -455) T) ((-82 . -409) T) ((-1034 . -25) T) ((-1034 . -21) T) ((-897 . -1131) 15012) ((-40 . -1082) 14957) ((-896 . -739) 14909) ((-40 . -662) 14854) ((-392 . -302) T) ((-172 . -1033) 14805) ((-1118 . -929) 14704) ((-716 . -401) T) ((-1030 . -1028) 14688) ((-723 . -1143) T) ((-716 . -168) 14670) ((-804 . -929) 14577) ((-802 . -929) 14561) ((-1282 . -1131) T) ((-1261 . -1131) T) ((-1195 . -102) T) ((-328 . -1233) 14540) ((-328 . -1236) 14519) ((-468 . -929) 14496) ((-328 . -988) 14475) ((-136 . -1143) T) ((-118 . -1143) T) ((-1001 . -1248) T) ((-888 . -1248) T) ((-723 . -23) T) ((-675 . -1248) T) ((-616 . -1296) 14459) ((-616 . -1131) 14409) ((-545 . -874) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 2a23591e..68715178 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3499555788) -(4510 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3499558251) +(4511 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -490,677 +490,675 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |associates?| |s17dgf| |cAsech| |convert| |s17adf| - |changeMeasure| |cache| |exprToUPS| |kmax| |character?| |deepestTail| - |Ci| |nil?| |bringDown| |matrixConcat3D| |hue| |asechIfCan| - |clearFortranOutputStack| |OMconnOutDevice| |elementary| - |sumOfSquares| |mindegTerm| |unexpand| |rightDiscriminant| |exptMod| - |odd?| |karatsubaOnce| |checkRur| |s13aaf| |euclideanSize| - |getDatabase| |sqfrFactor| |jvmDoubleConstantTag| |assign| - |setTopPredicate| |float| |tab1| |setScreenResolution3D| |nonQsign| - |subresultantSequence| |var1StepsDefault| |zeroVector| - |initiallyReduce| |expPot| |makeTerm| |latex| |d01gbf| |karatsuba| - |partialNumerators| |copy!| |d02ejf| |OMbindTCP| |push| |algebraicOf| - |bandedHessian| |variationOfParameters| |startTableGcd!| |cschIfCan| - |findCycle| |qinterval| |factorPolynomial| |padecf| |radicalSimplify| - |genericRightTrace| |jvmUTF8ConstantTag| |putProperties| |po| - |inputBinaryFile| |principalIdeal| |cycleElt| |graphImage| |rootSimp| - |changeName| |showTheIFTable| |semiResultantReduitEuclidean| F2FG - |mapExpon| |s17dlf| |mix| |collectUpper| |incr| |shift| |macroExpand| - |badNum| |palgextint0| |isConnected?| |separateDegrees| |scopes| - |trapezoidalo| |OMputEndObject| |contract| |upperBound| |dn| |hi| - |transform| |direction| |failed?| |bright| |f04asf| |OMputEndError| - |boundOfCauchy| |quasiComponent| |inR?| |completeHermite| |minus!| - |bumptab1| |number?| |selectPolynomials| |iicsch| |closed| - |fullPartialFraction| |s14aaf| |PollardSmallFactor| |lex| |qroot| - |signAround| |adjoint| |mappingAst| |eval| |integralRepresents| - |toseInvertible?| |solveLinearPolynomialEquationByFractions| GE - |iFTable| |insertMatch| |tan2trig| |gbasis| |diag| |palgLODE0| |Is| - |nativeModuleExtension| |unitCanonical| |choosemon| - |basisOfLeftNucleus| |expr| |numer| |lift| GT |insert!| |mathieu12| - |setrest!| |jvmStringConstantTag| |d01alf| |jvmLongConstantTag| - |charClass| |OMgetEndBVar| |const| |pole?| |s15adf| |eq| |denom| - |reduce| |expandTrigProducts| |setlast!| LE - |zeroSetSplitIntoTriangularSystems| |permutationRepresentation| - |currentScope| |rubiksGroup| |rewriteIdealWithRemainder| |power!| - |mainMonomial| |iter| |generalizedContinuumHypothesisAssumed?| - |c06gcf| LT |aQuartic| |coefficients| |makeMulti| |scalarTypeOf| - |e02akf| |SturmHabichtCoefficients| |LyndonBasis| |c06fuf| |pi| - |modularFactor| |nextsubResultant2| |verticalTab| |moebiusMu| - |addMatch| EQ |f01mcf| |ocf2ocdf| |iprint| |jacobi| |setchildren!| - |variable| |infinity| |makeUnit| |idealSimplify| |mkAnswer| |Lazard2| - |say| |selectAndPolynomials| |zeroMatrix| |integralAtInfinity?| - |OMputInteger| |initials| |rightFactorIfCan| |iterators| - |linkToFortran| |insertionSort!| |conjugate| |sec2cos| |RittWuCompare| - |insert| |csubst| |algintegrate| |factorSquareFreePolynomial| - |computeCycleLength| |bivariateSLPEBR| |strongGenerators| - |selectFiniteRoutines| |sizeMultiplication| |c06fqf| |Si| - |primextintfrac| |doubleComplex?| |printInfo!| |tanNa| - |createThreeSpace| |kernel| |intermediateResultsIF| |infRittWu?| - |clip| |closeComponent| |e01bff| |prinb| |ratpart| |e04dgf| |height| - |mkcomm| |cycleSplit!| |exp| |binomThmExpt| |list| |s18aff| |queue| - |typeList| |maxrow| |size| |generate| |lazyPquo| - |nextPrimitiveNormalPoly| |squareFreePrim| |style| |mapGen| |draw| - |basisOfLeftNucloid| |mapDown!| |linears| |integrate| |s17aff| - |currentEnv| |signature| |dominantTerm| |associatorDependence| - |numericalIntegration| |noncommutativeJordanAlgebra?| |cCot| - |quasiAlgebraicSet| |tan2cot| |iiGamma| |nextSubsetGray| - |semiResultantEuclidean1| |physicalLength| |palglimint0| |e02ddf| - |wholeRagits| |preprocess| |exprHasWeightCosWXorSinWX| - |sortConstraints| |one?| |c06frf| |squareFreePart| |support| |redmat| - |acotIfCan| |solveLinearPolynomialEquationByRecursion| - |removeIrreducibleRedundantFactors| |byte| |rightRankPolynomial| - |jvmPrivate| |accuracyIF| |completeEval| - |rightCharacteristicPolynomial| |infinityNorm| |inverseLaplace| - |supDimElseRittWu?| |isEquiv| |primitivePart| |makeObject| |f01qcf| - |multiplyExponents| |bfEntry| |monicModulo| |tanintegrate| |jvmStrict| - |pop!| |polygon?| |imagK| |cyclicSubmodule| |cycleLength| |coef| - |digit| |swap| |build| |irDef| |stoseSquareFreePart| |tubePlot| - |makeFloatFunction| |evenInfiniteProduct| |enqueue!| - |transcendentalDecompose| |incrementBy| |multisect| |rightUnit| - |hessian| |argument| |cyclotomic| |randomLC| UP2UTS |denominators| - |indices| |pseudoRemainder| |SturmHabichtSequence| |makeViewport3D| - |d01fcf| |expand| |pair?| |monomial?| |element?| |linSolve| - |numberOfFactors| |explicitEntries?| |balancedFactorisation| - |rightUnits| |algint| |OMUnknownCD?| |filterWhile| |printingInfo?| - |binomial| |getVariableOrder| |errorInfo| |normalized?| |leftOne| - |viewWriteDefault| |quadraticNorm| |pol| |OMgetEndApp| |light| - |filterUntil| |diagonal?| |oblateSpheroidal| |prologue| |jvmPublic| - |algebraicSort| |kernels| |removeSinhSq| |OMgetAtp| |outputAsTex| - |cosIfCan| |randnum| |split| |select| |int| |clipBoolean| - |parametersOf| |supersub| |semiLastSubResultantEuclidean| - |irreducible?| |operator| |halfExtendedSubResultantGcd2| |iifact| - |ldf2lst| |weight| |complexEigenvalues| |linearAssociatedExp| - |scaleRoots| |contractSolve| |rectangularMatrix| |cRationalPower| - |permutation| |simpsono| |getBadValues| |integralMatrix| |clikeUniv| - |diagonalProduct| |drawStyle| |increase| |f07adf| |upperCase?| - |univariate| |cond| |numberOfMonomials| |mesh?| |quoByVar| |equality| - |extractTop!| |center| |extractBottom!| |internalIntegrate| - |negative?| |gcdPrimitive| |tail| |differentialVariables| |d02gbf| - |getCode| |ideal| |distFact| |s18dcf| |tubePoints| |laguerre| |e02zaf| - |showTheRoutinesTable| |gethi| |radicalEigenvalues| |ran| |setUnion| - |multiset| |symFunc| |generateIrredPoly| |true| - |removeRedundantFactorsInContents| |resetAttributeButtons| - |functionIsContinuousAtEndPoints| |ksec| |factor| - |associatedEquations| |writeByte!| |coordinate| |iiatanh| |makeRecord| - |initial| |typeLists| |squareFree| |iiasech| |sequences| |exprex| - |sqrt| |delete!| |discreteLog| |isAtom| |GospersMethod| |tree| - |exportedOperators| |leftTraceMatrix| |yCoord| |sech2cosh| - |fortranLinkerArgs| |real| |iisin| |setOfMinN| |f02bjf| |chebyshevT| - |makeEq| |definingInequation| |f02abf| |aCubic| |imag| |addPoint2| - |capacity| |firstNumer| |has?| |rightRemainder| |central?| - |rationalFunction| |directProduct| |OMread| |outputSpacing| - |readUInt16!| |generalizedContinuumHypothesisAssumed| |hex| - |exprHasAlgebraicWeight| |subscript| |unmakeSUP| |e01sff| |exponents| - |substitute| |iicos| |chiSquare| |numberOfIrreduciblePoly| - |factorsOfDegree| |s17ajf| |brace| |adaptive3D?| |trigs| |cycleEntry| - |froot| |rationalIfCan| |roughBase?| |solveid| |numericIfCan| - |destruct| |selectMultiDimensionalRoutines| |returns| |coth2tanh| - |rational| |principal?| |reopen!| |f04mbf| |OMclose| |makingStats?| - |rootPower| |possiblyNewVariety?| |simpleBounds?| |in?| |empty?| - |asecIfCan| |lowerCase?| |encodingDirectory| |minrank| |epilogue| - |perfectSqrt| |jvmFieldrefConstantTag| |fullDisplay| |hdmpToP| - |balancedBinaryTree| |generalizedInverse| |commutator| - |basisOfLeftAnnihilator| |spherical| |failed| |invmultisect| - |toseInvertibleSet| |lhs| |halfExtendedResultant2| |monomial| - |setButtonValue| |subHeight| |measure2Result| |measure| |options| - |edf2fi| |laplace| |rhs| |divisorCascade| |flexible?| |multivariate| - |se2rfi| |minset| |lowerBound| |aromberg| |getOperator| |imagE| - |gcdprim| |mainContent| |SFunction| |variables| - |rightMinimalPolynomial| |radicalEigenvector| |printInfo| |d01amf| - |OMreceive| |nil| |f2df| |width| |symmetricRemainder| |superHeight| - |quickSort| |expintegrate| |LagrangeInterpolation| |string| - |swapRows!| |iteratedInitials| |basisOfMiddleNucleus| |whitePoint| - |s21bbf| |bezoutDiscriminant| |variable?| |approximants| |red| - |lexico| |alphabetic| |log| |lazy?| |rk4f| |ffactor| |pomopo!| - |listexp| |unravel| |rename| |createPrimitivePoly| |approximate| - |normalize| |interval| |rk4qc| |solid| |iicosh| |quotientByP| - |figureUnits| |semicolonSeparate| |complex| |monicRightDivide| - |reflect| |unit?| |taylor| |rightZero| |position!| - |nextIrreduciblePoly| |isImplies| |size?| |palginfieldint| - |chineseRemainder| |mathieu11| |constructor| |toseSquareFreePart| - |inc| |laurent| |cCos| |rightTrim| |e02bbf| |resultantEuclidean| - |jacobian| |resetBadValues| |iicot| |createNormalPrimitivePoly| - |explimitedint| |indicialEquation| |firstSubsetGray| |s19adf| - |puiseux| |reset| |li| |leftTrim| |coerceS| |outputArgs| |merge!| - |startStats!| |expextendedint| |optional| |hexDigit?| |shrinkable| - |power| |keys| |edf2ef| |normalElement| |normalizedAssociate| - |rewriteSetByReducingWithParticularGenerators| |perfectNthRoot| - |setVariableOrder| |c06ebf| |dictionary| |removeZero| |separant| |inv| - |write| |stack| |iiasinh| |invertibleSet| |socf2socdf| |multiple?| - |factor1| |addBadValue| |derivative| |partialFraction| - |findConstructor| |save| |ground?| |e02bcf| |optpair| |Aleph| - |palgRDE0| |dimensionOfIrreducibleRepresentation| |acscIfCan| - |localAbs| |extend| |insertTop!| |ground| |cSin| |rowEchelonLocal| - |leastAffineMultiple| |over| |OMgetApp| |permutations| |weakBiRank| - |var1Steps| |pureLex| |legendreP| |leadingMonomial| |constantOpIfCan| - |adaptive?| |readInt32!| |contains?| |jvmFloatConstantTag| - |bivariatePolynomials| |numberOfFractionalTerms| |LyndonWordsList1| - |d03faf| |octon| |leadingCoefficient| |notelem| |lyndon?| - |constantToUnaryFunction| |deref| |imagk| |viewport2D| |mainMonomials| - |dihedral| |definingPolynomial| |unvectorise| |primitiveMonomials| - |rightTrace| |setMinPoints3D| |screenResolution3D| |degree| - |writeUInt8!| |left| |curry| |fprindINFO| |headAst| |maxIndex| - |reductum| |horizConcat| |d02cjf| |dequeue| |userOrdered?| |right| - |mapSolve| |KrullNumber| |createZechTable| |positiveSolve| - |stoseInternalLastSubResultant| |stop| |atrapezoidal| |argumentList!| - |bfKeys| |pseudoQuotient| |redPo| |mr| |fortranCarriageReturn| - |clipParametric| |att2Result| |outputList| |rename!| |twist| - |leftExactQuotient| |sechIfCan| |lighting| |swapColumns!| |enumerate| - |innerSolve1| |cAcosh| |cycleTail| |decimal| |zeroDimPrime?| - |initializeGroupForWordProblem| |entry| |irreducibleFactors| |e01sef| - |positiveRemainder| |makeSketch| |palgextint| |musserTrials| |s17acf| - |factorSquareFreeByRecursion| |bitCoef| |explogs2trigs| |endOfFile?| - |unary?| |weights| |mappingMode| |f02axf| |fixedPoint| |ridHack1| - |alternative?| |groebner| |selectPDERoutines| |graphCurves| - |symmetricSquare| |makeop| |plenaryPower| |prefix| |coord| - |graphStates| |leadingTerm| |changeBase| |retractable?| |zero?| - |OMcloseConn| |relativeApprox| |uncouplingMatrices| - |fillPascalTriangle| |gradient| |e04naf| |squareFreeLexTriangular| - |generic?| |minPol| |constantIfCan| |lfintegrate| |cCsc| |linefeed| - |genericRightDiscriminant| |trigs2explogs| |OMputEndBind| - |explicitlyEmpty?| |infiniteProduct| |f02fjf| |OMgetEndAtp| |rule| - |expt| |scripted?| |monicLeftDivide| |sumOfKthPowerDivisors| - |noLinearFactor?| |leftRecip| |overlabel| |setLength!| BY |ipow| - |qelt| |showRegion| |decrease| |sumSquares| |numberOfCycles| |plus!| - |rquo| |coerceL| |rdHack1| |predicates| |qsetelt| |pdct| |rdregime| - |nthRootIfCan| |generalInfiniteProduct| |setAdaptive3D| |setColumn!| - |characteristicSet| |iiacot| |numerator| |identity| |symbol| |xRange| - |idealiserMatrix| |Lazard| |extractSplittingLeaf| |reduced?| - |halfExtendedSubResultantGcd1| |createLowComplexityNormalBasis| - |increment| |lyndonIfCan| F |repeating| |expression| |find| |yRange| - |graeffe| |name| |vconcat| |status| |mainPrimitivePart| |monic?| - |lprop| |increasePrecision| |saturate| |integer| |zRange| - |genericLeftTraceForm| |body| |elem?| |internal?| |stopMusserTrials| - |numFunEvals| |bat| |OMgetError| |besselK| |map!| |writeBytes!| - |conditionsForIdempotents| |rightDivide| |e01sbf| |cons| |datalist| - |void| |logIfCan| |LazardQuotient2| |fortranDoubleComplex| - |currentCategoryFrame| |qsetelt!| |totalGroebner| |splitSquarefree| - |polyRDE| |computeCycleEntry| NOT |basisOfRightNucleus| |modulus| - |outputForm| |reduceByQuasiMonic| |super| |mainVariable| |modularGcd| - |returnTypeOf| |e02dcf| OR |uniform| |listOfLists| - |rootOfIrreduciblePoly| |key?| |cAcos| |rowEchLocal| |OMReadError?| - |semiResultantEuclideannaif| |semiDegreeSubResultantEuclidean| AND - |iidsum| |makeprod| |constant?| |internalSubPolSet?| |depth| - |asinhIfCan| |fractRagits| |selectODEIVPRoutines| |rootPoly| - |integralDerivationMatrix| |expressIdealMember| |getZechTable| - |f01brf| |specialTrigs| |cot2trig| |e02adf| |minPoints| - |linearDependenceOverZ| |source| |summation| |mantissa| |associator| - |OMParseError?| |readLineIfCan!| |acsch| |trapezoidal| |diff| - |isPower| |weierstrass| |pToDmp| |jvmSuper| |sturmSequence| - |reverseLex| |unprotectedRemoveRedundantFactors| |outputFixed| - |c06fpf| |port| |computeBasis| |d02raf| |part?| |create3Space| - |separate| |clearTheIFTable| |complexNormalize| |e02bef| |subMatrix| - |internalDecompose| |readByte!| |repSq| |coshIfCan| |mathieu24| - |removeRoughlyRedundantFactorsInPol| |expIfCan| |t| - |selectOrPolynomials| |copies| |binary| |subCase?| |corrPoly| - |interpolate| |newSubProgram| |pmComplexintegrate| |singRicDE| - |bindings| |exponent| |exactQuotient!| |llprop| |fintegrate| - |multinomial| |upperCase| |permutationGroup| - |purelyAlgebraicLeadingMonomial?| |factorial| |rightRecip| |updatF| - |basis| |perfectSquare?| |surface| |irreducibleFactor| |c06gbf| - |roughUnitIdeal?| |sin2csc| |common| |rootKerSimp| |rational?| |prem| - |radicalRoots| |iiexp| * |genericLeftMinimalPolynomial| |paren| - |wreath| |diophantineSystem| |shellSort| |s14baf| |f02agf| - |argumentListOf| |inHallBasis?| |removeRedundantFactorsInPols| - |compound?| |mkPrim| |lazyPseudoQuotient| |key| |numberOfVariables| - |internalZeroSetSplit| |noValueMode| |oddInfiniteProduct| |f02akf| - |lazyPremWithDefault| |monicRightFactorIfCan| |cap| - |semiIndiceSubResultantEuclidean| |elColumn2!| |redpps| |ReduceOrder| - |previous| |OMlistSymbols| = |fortranLiteral| |index?| |critB| - |shiftLeft| |filename| |numberOfComputedEntries| |bipolar| - |inconsistent?| |enterInCache| |hash| |triangular?| |phiCoord| - |printStatement| |coerceImages| |withPredicates| |iisech| - |rewriteIdealWithHeadRemainder| |complexForm| |count| < |category| - |antiCommutative?| |double| |polyRicDE| |eigenMatrix| |extractPoint| - |parse| |jokerMode| |acoshIfCan| |diagonals| > |domain| |c05pbf| - |buildSyntax| |tableForDiscreteLogarithm| |perspective| - |maximumExponent| |cycles| |initTable!| |fractionPart| <= |package| - |poisson| |complexElementary| |splitLinear| |roughEqualIdeals?| - |univariate?| |showAllElements| |cyclicEntries| - |stiffnessAndStabilityFactor| |mapdiv| >= |complexRoots| - |intPatternMatch| |sparsityIF| |leftMult| |sumOfDivisors| |eulerPhi| - |isAbsolutelyIrreducible?| |maxrank| |curve| |powerSum| - |realEigenvectors| |imagJ| |selectIntegrationRoutines| |abs| - |eigenvector| |triangularSystems| |setRealSteps| - |squareFreePolynomial| |solveRetract| |column| |cExp| - |quotedOperators| |setClosed| |putGraph| + |s18def| |rotate!| - |doublyTransitive?| |rationalPower| |argscript| |iilog| |hitherPlane| - |continuedFraction| - |virtualDegree| |dAndcExp| |shiftRoots| - |declare!| |integralBasis| |more?| |member?| / |vedf2vef| |jvmNative| - |certainlySubVariety?| |pquo| |leadingIdeal| |sinhcosh| - |skewSFunction| |stronglyReduce| |groebnerFactorize| |biRank| - |radicalOfLeftTraceForm| |dec| |iiacos| |companionBlocks| |ptree| - |singleFactorBound| |lookup| |s21baf| |cyclicGroup| |isTimes| - |lSpaceBasis| |mergeFactors| |cAcsc| |meshPar2Var| |space| |open| - |minimumExponent| |doubleDisc| |subresultantVector| |applyRules| - |lookupFunction| |OMsupportsCD?| |index| |rspace| |subNode?| - |antiAssociative?| |semiResultantEuclidean2| |changeWeightLevel| - |exponentialOrder| |headReduced?| |square?| |transcendenceDegree| - |kind| |goto| |doubleFloatFormat| |cAcoth| |factorset| |dfRange| - |relationsIdeal| |fmecg| |functionIsFracPolynomial?| |cycle| |bag| - |f04faf| |extractClosed| |gcdcofactprim| |op| |largest| - |colorFunction| |createLowComplexityTable| |whatInfinity| |setPoly| - |quote| |segment| |operations| |pair| |dmp2rfi| |getCurve| |rk4a| - |augment| |entry?| |f02wef| |SturmHabichtMultiple| |lquo| - |leftMinimalPolynomial| |OMputSymbol| |endSubProgram| |cyclic?| - |imagI| |constantOperator| |comment| |d01anf| |green| |byteBuffer| - |logpart| |minRowIndex| |push!| |jacobiIdentity?| |smith| |laurentRep| - |getGoodPrime| |step| |d02kef| |mirror| |vertConcat| - |pointSizeDefault| |useSingleFactorBound| |leftUnits| - |binarySearchTree| |duplicates?| |solve1| |iisqrt2| |minPoly| - |getSyntaxFormsFromFile| |mvar| |identityMatrix| |ScanRoman| - |scanOneDimSubspaces| |printHeader| |jvmTransient| |polyred| - |dimension| |varselect| |complexEigenvectors| |realSolve| |f02ajf| - |vspace| |fill!| |palgintegrate| |seed| |evaluate| |clipSurface| - |OMsend| |singularAtInfinity?| |OMgetEndBind| |float?| - |quasiMonicPolynomials| |zero| |zeroDimensional?| |f04adf| - |listYoungTableaus| |getExplanations| |splitNodeOf!| |union| - |symbolTable| |pleskenSplit| |linearPart| |totalDegree| |moduleSum| - |removeRoughlyRedundantFactorsInPols| |rk4| |retract| |dim| - |purelyTranscendental?| |c06eaf| |maxdeg| |elements| |product| - |euclideanNormalForm| |nilFactor| |rightPower| - |resultantReduitEuclidean| |invertibleElseSplit?| |And| - |curveColorPalette| |numberOfChildren| |regularRepresentation| - |result| |lfunc| |exponential1| |pushFortranOutputStack| |nthExponent| - |mapUnivariateIfCan| |zeroOf| |lexTriangular| |oddlambert| |s19acf| - |Or| |mainKernel| |popFortranOutputStack| |tanIfCan| |setFormula!| - |OMgetObject| |pointPlot| |minColIndex| |quartic| |commutative?| - |safeFloor| |unitVector| |OMputEndAttr| |Not| |less?| |insertRoot!| - |FormatRoman| |monomials| |df2fi| |outputAsFortran| |complexIntegrate| - |ratPoly| |tubePointsDefault| |realElementary| |c06gqf| - |ScanFloatIgnoreSpaces| |iitanh| |generalPosition| |OMputString| - |messagePrint| |jvmAbstract| |sequence| |child?| |doubleRank| |graphs| - |f02aff| |splitConstant| |An| |setleft!| |exQuo| |arrayStack| |nary?| - |createIrreduciblePoly| |rangeIsFinite| |limitedIntegrate| - |squareMatrix| |expenseOfEvaluation| |makeSeries| |iisinh| |e02gaf| - |removeSuperfluousQuasiComponents| |cAsin| |setMaxPoints| |f07fef| - |sinh2csch| |monicDivide| |mulmod| |firstUncouplingMatrix| - |discriminant| |setelt!| |composites| |submod| |leader| - |algSplitSimple| |reducedSystem| |content| |closedCurve| |rootProduct| - |nsqfree| |relerror| |probablyZeroDim?| |squareFreeFactors| - |viewport3D| |primlimintfrac| |search| |e04fdf| |extractIndex| - |prevPrime| |slex| |inverseIntegralMatrixAtInfinity| - |decreasePrecision| |readInt8!| |OMconnInDevice| |paraboloidal| - |cSinh| |unit| |mapUp!| |stoseInvertible?| |hostPlatform| |isQuotient| - |expint| |normalizeAtInfinity| |hclf| |clearTheSymbolTable| - |extension| |BasicMethod| |simpson| |optAttributes| - |inverseIntegralMatrix| |elRow2!| |mathieu23| |inGroundField?| - |rotatey| |f04qaf| |orthonormalBasis| |pascalTriangle| |f04mcf| - |approxNthRoot| |retractIfCan| |finiteBound| |log2| |readIfCan!| - |solveInField| |viewThetaDefault| |OMgetEndError| |cPower| |id| - |errorKind| |integralMatrixAtInfinity| |OMputBind| |basicSet| - |lowerPolynomial| |composite| |algebraicDecompose| |divide| - |normalForm| |subst| |prod| |binding| |intcompBasis| |lo| |nextPrime| - |removeSinSq| |dflist| |hexDigit| |tracePowMod| |prefixRagits| - |repeating?| |unitNormal| |error| |leadingCoefficientRicDE| - |semiDiscriminantEuclidean| |bothWays| |stFuncN| |prepareDecompose| - |curveColor| |irVar| |nextPrimitivePoly| |leftDivide| |powmod| - |wholePart| |second| |lp| |setValue!| |eq?| |s01eaf| |listOfMonoms| - |pushNewContour| |expandPower| |map| |callForm?| |f01qef| - |removeRoughlyRedundantFactorsInContents| |complexZeros| |third| - |host| |s19abf| |wordInGenerators| |cos2sec| |removeCosSq| |e01bef| - |string?| |drawComplex| |symbolIfCan| |listRepresentation| |objects| - |formula| |leftDiscriminant| |imports| |characteristicPolynomial| - |moebius| |dmpToP| |getlo| |close| |tower| |mapBivariate| |csch2sinh| - |ddFact| |stoseInvertibleSet| |incrementKthElement| |base| - |palglimint| |semiSubResultantGcdEuclidean2| |simplifyLog| |fi2df| - |sylvesterSequence| |bivariate?| |packageCall| |regime| |reducedForm| - |fortranLogical| |parents| |factors| |e01daf| |normal01| |normal?| - |lazyResidueClass| |symmetricProduct| |display| |problemPoints| - |pr2dmp| |vector| |parametric?| |thetaCoord| |tablePow| |e02ahf| - |satisfy?| |extendedSubResultantGcd| |resultant| |testDim| - |OMputError| |maxPoints3D| |differentiate| |changeNameToObjf| - |normDeriv2| |any?| |nrows| |atoms| |aLinear| |unknownEndian| - |toroidal| |postfix| |jordanAlgebra?| |listLoops| |OMgetBVar| - |quasiRegular?| |e04jaf| |ncols| |numberOfComponents| - |rightTraceMatrix| |permanent| GF2FG |makeCrit| |divergence| |moduloP| - |torsionIfCan| |reindex| |sayLength| |coerce| |iisec| |replace| |next| - |head| |dot| |complexNumeric| |getProperty| |f04maf| |checkForZero| - |multMonom| |torsion?| |categories| |construct| |coerceListOfPairs| - |write!| |lazyGintegrate| |gcdcofact| |input| |randomR| |sts2stst| - |xn| |OMputEndAtp| |leadingSupport| |axes| |subscriptedVariables| - |generalizedEigenvectors| |library| |fixPredicate| |leftRank| - |directory| |decompose| |basisOfCentroid| |toseLastSubResultant| - |UpTriBddDenomInv| |scalarMatrix| |removeConstantTerm| |OMputAttr| - |systemSizeIF| |powerAssociative?| |fortranReal| |nand| |contours| - |rightExtendedGcd| |integerBound| |makeYoungTableau| |setprevious!| - |integers| |realEigenvalues| |init| |iiacoth| |sn| |rationalPoints| - |leftScalarTimes!| |s17agf| |matrix| |setPredicates| - |viewDeltaYDefault| |algebraicCoefficients?| |subResultantsChain| - |node?| |cAsec| |s17dcf| |lfextlimint| |leftTrace| |component| |pow| - |d01ajf| |unparse| |bumptab| |leftAlternative?| |partition| - |nullSpace| |curve?| |zoom| |set| |superscript| |horizontalTab| |qPot| - |gcdPolynomial| |list?| |beauzamyBound| |quasiMonic?| |setTex!| - |delete| |stoseInvertibleSetreg| |listConjugateBases| - |univariateSolve| |debug3D| |primintfldpoly| |cAsinh| |lfinfieldint| - |empty| |divisors| |selectNonFiniteRoutines| |squareTop| |wholeRadix| - |Nul| |forLoop| |recur| |derivationCoordinates| |rCoord| - |subResultantGcdEuclidean| |children| |conjugates| |selectfirst| - |useNagFunctions| |fracPart| |omError| |associatedSystem| |hermite| - |systemCommand| |difference| |associative?| |padicFraction| |mainForm| - |leaves| |changeVar| |padicallyExpand| |partitions| |psolve| - |aQuadratic| |characteristic| |standardBasisOfCyclicSubmodule| - |processTemplate| |nthExpon| |particularSolution| |nextNormalPoly| - |double?| |bezoutMatrix| |subResultantChain| |splitDenominator| - |linearPolynomials| |pushucoef| |ScanFloatIgnoreSpacesIfCan| - |viewpoint| |absolutelyIrreducible?| |primitive?| |e02baf| |assert| - |f02aef| |car| |ord| |normal| |constantLeft| |coleman| - |initiallyReduced?| |cosSinInfo| |categoryFrame| |showTheSymbolTable| - |startPolynomial| |hasTopPredicate?| |distance| |npcoef| - |carriageReturn| |zeroSetSplit| |legendre| |pointColorPalette| - |oneDimensionalArray| |safetyMargin| |generators| |wronskianMatrix| - |SturmHabicht| |range| |deleteRoutine!| |OMunhandledSymbol| |closed?| - |parent| |setvalue!| |makeVariable| |generalizedEigenvector| - |numberOfNormalPoly| |nextPartition| |expintfldpoly| |stopTable!| - |rarrow| |weighted| |rules| |critMTonD1| |iCompose| |lazyPseudoDivide| - |checkPrecision| |show| |primeFrobenius| |monomialIntegrate| - |rischDEsys| |completeHensel| |refine| |root| |besselI| |linearForm| - |setErrorBound| |edf2efi| |hconcat| |partialDenominators| |plot| - |bounds| |viewSizeDefault| |cAcsch| |rank| - |degreeSubResultantEuclidean| |high| |trace| |components| - |doubleResultant| |iomode| |uniform01| |sub| |symbol?| - |linearlyDependentOverZ?| |setDifference| |raisePolynomial| |isOpen?| - |sin?| |compBound| |rightMult| |hermiteH| |goodPoint| |low| - |loopPoints| |d01akf| |log10| |identification| |unknown| - |stiffnessAndStabilityOfODEIF| |putColorInfo| |recolor| |Hausdorff| - |divideIfCan| |genericPosition| |s21bcf| |jvmStatic| |bitand| |sup| - |OMencodingBinary| |nthRoot| |alphabetic?| |newLine| |tubeRadius| - |f02xef| |setCondition!| |fortran| |trivialIdeal?| |bitior| - |extractIfCan| SEGMENT |setLabelValue| |univariatePolynomials| - |rightOne| |matrixDimensions| |pointColorDefault| |leftRankPolynomial| - |useSingleFactorBound?| |exactQuotient| |viewPosDefault| - |cyclotomicFactorization| |credPol| |s20acf| |arity| |setPosition| - |stripCommentsAndBlanks| |makeResult| |combineFeatureCompatibility| - |signatureAst| |numberOfPrimitivePoly| |bitTruth| |repeatUntilLoop| - |rischNormalize| |putProperty| |setMaxPoints3D| |lists| - |resultantEuclideannaif| |f02aaf| |pile| |compiledFunction| - |quadratic| |makeSin| |table| |cotIfCan| |irreducibleRepresentation| - |mergeDifference| |radix| |indicialEquationAtInfinity| |readLine!| - |binaryTournament| |createPrimitiveElement| |exists?| |new| |df2mf| - |environment| |pack!| |lintgcd| |bsolve| |mapMatrixIfCan| - |rightQuotient| |showSummary| |logGamma| |ravel| |showClipRegion| - |rightNorm| |universe| |symmetric?| |interReduce| |lagrange| - |getMultiplicationTable| |rroot| |factorsOfCyclicGroupSize| |block| - |reshape| |normFactors| |romberg| |bottom!| |zeroDimPrimary?| - |loadNativeModule| |iterationVar| |outlineRender| |modifyPointData| - |showAttributes| |parabolic| |cn| |univcase| |headRemainder| - |stopTableGcd!| |unitsColorDefault| |OMencodingXML| |divideExponents| - |edf2df| |dequeue!| |conditionP| |morphism| |tanSum| |cup| - |leadingIndex| |readUInt32!| |B1solve| |innerEigenvectors| |output| - |nonSingularModel| |sum| |gderiv| |factorAndSplit| |rightGcd| - |wordInStrongGenerators| |erf| |leftUnit| |externalList| |crushedSet| - |realZeros| |dimensionsOf| |degreeSubResultant| |zeroSquareMatrix| - |leftFactorIfCan| |removeRedundantFactors| |jordanAdmissible?| - |roughBasicSet| |cSech| |simplify| |triangSolve| |ldf2vmf| |update| - |script| |representationType| FG2F |lowerCase| |rootOf| - |RemainderList| |aspFilename| |clearDenominator| |intChoose| - |totalLex| |taylorQuoByVar| |OMgetSymbol| |infinite?| |dilog| - |elaborate| |rightRegularRepresentation| |OMsupportsSymbol?| - |lazyIntegrate| |univariatePolynomialsGcds| - |internalSubQuasiComponent?| |purelyAlgebraic?| |internalAugment| - |ode| |sin| |complexLimit| |acothIfCan| |createNormalPoly| - |setMinPoints| |symmetricDifference| |resetVariableOrder| |tex| - |iiabs| |karatsubaDivide| |adaptive| |cos| |condition| |conical| - |drawComplexVectorField| |pade| RF2UTS |iiperm| |bitLength| - |rootBound| |OMopenFile| |complexExpand| |tan| |exp1| |curryRight| - |overlap| |redPol| |numberOfComposites| |factorList| |position| - |leftFactor| |stoseIntegralLastSubResultant| |branchPoint?| |cot| - |alternating| |pToHdmp| |factorFraction| |headReduce| |rootRadius| - |removeCoshSq| |setAdaptive| |isExpt| |perfectNthPower?| |sec| - |OMmakeConn| |getMatch| |backOldPos| |ratDsolve| |makeSUP| |varList| - |members| |stoseInvertibleSetsqfreg| |hasHi| |LazardQuotient| |csc| - |replaceKthElement| |decomposeFunc| |reify| |fixedPointExquo| - |factorGroebnerBasis| |units| |axesColorDefault| |lllp| |htrigs| |sh| - |asin| |showArrayValues| |chiSquare1| |Vectorise| |e04mbf| - |thenBranch| |listBranches| |e01bhf| |medialSet| - |univariatePolynomial| |acos| |fortranDouble| |bit?| |shuffle| - |prinshINFO| |reverse| |distribute| |cAtanh| |OMwrite| |invmod| - |topPredicate| |bytes| |atan| |subtractIfCan| |resultantnaif| |pdf2ef| - |trailingCoefficient| |showScalarValues| |showIntensityFunctions| - |OMreadFile| |quoted?| |supRittWu?| |opeval| |acot| |mkIntegral| - |bat1| |normalizedDivide| |UnVectorise| |inputOutputBinaryFile| - |rootNormalize| |f2st| |d02bhf| |substring?| - |unrankImproperPartitions0| |sign| |countRealRootsMultiple| |asec| - |eigenvectors| |leftReducedSystem| |zerosOf| |polCase| |code| |s15aef| - |ref| |rewriteIdealWithQuasiMonicGenerators| |mainVariables| - |symbolTableOf| |generic| |acsc| |wrregime| |roughSubIdeal?| - |jvmNameAndTypeConstantTag| |s13adf| |null?| |quadratic?| |suffix?| - |sylvesterMatrix| |subSet| |iisqrt3| |integral| |sinh| |cscIfCan| - |lazyPrem| |rationalApproximation| |writable?| |dimensions| |powers| - |rotatex| |pmintegrate| |polarCoordinates| |mpsode| |cosh| - |functionIsOscillatory| |sort!| |irCtor| |charthRoot| |groebSolve| - |elseBranch| |arbitrary| |prefix?| |primitiveElement| - |var2StepsDefault| |bernoulli| |mainCharacterization| |tanh| - |basisOfNucleus| |irForm| |modularGcdPrimitive| |c06gsf| |totolex| - |cosh2sech| |yCoordinates| |viewZoomDefault| |Frobenius| - |seriesToOutputForm| |floor| |coth| |calcRanges| |baseRDE| - |wordsForStrongGenerators| |leaf?| |leftRegularRepresentation| - |unaryFunction| |localReal?| |numberOfDivisors| |equiv| |e04ucf| - |compile| |sech| |intersect| |explicitlyFinite?| |f04atf| - |alternatingGroup| |OMgetType| |plus| |FormatArabic| - |mainSquareFreePart| |diagonalMatrix| |f01ref| |csch| |isMult| - |cyclicParents| |categoryMode| |monomRDE| |outputMeasure| |singular?| - |integral?| |mainDefiningPolynomial| |mainCoefficients| |asinh| - |mapUnivariate| |limitPlus| |blankSeparate| |commonDenominator| - |stopTableInvSet!| |binaryTree| |leadingExponent| |normalDenom| |top| - |scan| |acosh| |eof?| |LiePolyIfCan| |OMUnknownSymbol?| |shufflein| - |primitivePart!| |continue| |times| |infix?| |midpoint| |d03edf| - |deriv| |ignore?| |atanh| |yellow| |janko2| |currentSubProgram| - |genericLeftNorm| |sort| |newTypeLists| |mask| |resize| |pointLists| - |e01bgf| |fglmIfCan| |acoth| |leadingBasisTerm| - |tryFunctionalDecomposition| |infieldint| |collectUnder| - 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|factorGroebnerBasis| |e02dcf| |complexNumericIfCan| + |numberOfComponents| |kernel| |basisOfMiddleNucleus| |double?| + |euclideanGroebner| |vertConcat| |discriminantEuclidean| |linears| + |uniform| |axesColorDefault| |height| |rightTraceMatrix| |isAnd| |exp| + |bezoutMatrix| |list| |neglist| |whitePoint| |midpoints| + |pointSizeDefault| |size| |generate| |integrate| |lllp| |listOfLists| + |zag| |permanent| |draw| |s21bbf| |subResultantChain| + |linearAssociatedLog| |useSingleFactorBound| |writeInt8!| |currentEnv| + |s17aff| |signature| |rootOfIrreduciblePoly| |htrigs| GF2FG + |updateStatus!| |bezoutDiscriminant| |splitDenominator| |leftUnits| + |removeSquaresIfCan| |rotate| |dominantTerm| |key?| |sh| |makeCrit| + |d01asf| |variable?| |linearPolynomials| |binarySearchTree| + |idealiser| UTS2UP |associatorDependence| |cAcos| |showArrayValues| + |divergence| |digits| |byte| |approximants| |pushucoef| |duplicates?| + |OMgetInteger| |quasiRegular| |numericalIntegration| |rowEchLocal| + 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+ |nextSubsetGray| |medialSet| |constant?| |head| |prime?| |select| + |int| |pomopo!| |car| |ScanRoman| |deepCopy| |operator| |returnType!| + |semiResultantEuclidean1| |internalSubPolSet?| |univariatePolynomial| + |henselFact| |dot| |ord| |listexp| |addmod| |scanOneDimSubspaces| + |rootsOf| |physicalLength| |fortranDouble| |asinhIfCan| |getProperty| + |bernoulliB| |unravel| |constantLeft| |reseed| |printHeader| + |univariate| |besselY| |cond| |palglimint0| |bit?| |fractRagits| + |f04maf| |recoverAfterFail| |center| |jvmIntegerConstantTag| |rename| + |coleman| |jvmTransient| |tail| |outputFloating| |e02ddf| |shuffle| + |selectODEIVPRoutines| |checkForZero| |setnext!| |createPrimitivePoly| + |initiallyReduced?| |frobenius| |polyred| |hasPredicate?| + |wholeRagits| |rootPoly| |prinshINFO| |multMonom| |OMserve| + |normalize| |true| |cosSinInfo| |restorePrecision| |dimension| + |exprHasLogarithmicWeights| |factor| |distribute| + |integralDerivationMatrix| |makeRecord| + |solveLinearPolynomialEquation| |torsion?| |initial| |categoryFrame| + |interval| |palgint| |varselect| |degreePartition| |sqrt| + |identitySquareMatrix| |cAtanh| |expressIdealMember| + |coerceListOfPairs| |tree| |rk4qc| |showTheSymbolTable| |updatD| + |complexEigenvectors| |real| |diagonal| |getZechTable| |OMwrite| + |write!| |times!| |solid| |startPolynomial| |every?| |realSolve| + |imag| |coth2trigh| |invmod| |f01brf| |f02awf| |lazyGintegrate| + |f02ajf| |cfirst| |directProduct| |solveLinearlyOverQ| |specialTrigs| + |topPredicate| |gcdcofact| |patternMatchTimes| |addPoint2| + |factorials| |vspace| |extensionDegree| |bytes| |cot2trig| |randomR| + |lambert| |capacity| |fill!| |screenResolution| |validExponential| + |brace| |subtractIfCan| |e02adf| |matrixGcd| |sts2stst| |firstNumer| + |basisOfCenter| |palgintegrate| |UP2ifCan| |destruct| |xn| |setEmpty!| + |has?| |lastSubResultantEuclidean| |seed| |usingTable?| + |squareFreeLexTriangular| |rightGcd| |primextendedint| |OMputEndAtp| + |rightRemainder| |evaluate| |asinIfCan| |approxSqrt| |generic?| + |wordInStrongGenerators| |leadingSupport| |f01rdf| |genericRightTrace| + |central?| |inverse| |clipSurface| |monicDecomposeIfCan| |leftUnit| + |minPol| |failed| |split!| |axes| |jvmUTF8ConstantTag| |lhs| + |rationalFunction| |d02bbf| |monomial| |constantIfCan| |externalList| + |subscriptedVariables| |computeInt| |options| |putProperties| |OMread| + |rhs| |member?| |tab| |multivariate| |selectsecond| |lfintegrate| + |crushedSet| |generalizedEigenvectors| |highCommonTerms| + |outputSpacing| |vedf2vef| |exprToXXP| |variables| |setOrder| |cCsc| + |realZeros| |printInfo| |fixPredicate| |primes| |nil| |readUInt16!| + |width| |jvmNative| |findBinding| |color| |linefeed| |dimensionsOf| + |string| |subresultantSequence| + |generalizedContinuumHypothesisAssumed| |plotPolar| + |certainlySubVariety?| |vectorise| |genericRightDiscriminant| + |degreeSubResultant| |newReduc| |stFuncN| |var1StepsDefault| |hex| + |log| |reduceLODE| |pquo| |tanhIfCan| |zeroSquareMatrix| + |trigs2explogs| |LiePoly| |prepareDecompose| |zeroVector| + |approximate| |exprHasAlgebraicWeight| |leadingIdeal| |ceiling| + |tryFunctionalDecomposition?| |OMputEndBind| |leftFactorIfCan| + |curveColor| |hasSolution?| |complex| |subscript| |df2ef| |sinhcosh| + |taylor| |explicitlyEmpty?| |removeRedundantFactors| + |totalDifferential| |irVar| |skewSFunction| |unmakeSUP| |constructor| + |monomialIntPoly| |iicsch| |numericalOptimization| |nextPrimitivePoly| + |laurent| |jordanAdmissible?| |rightTrim| |inc| |infiniteProduct| + |solveLinearPolynomialEquationByFractions| |makeViewport2D| |quotient| + |e01sff| |lexGroebner| |stronglyReduce| |closed| |prepareSubResAlgo| + |puiseux| |reset| |li| |leftTrim| |f02fjf| |roughBasicSet| |iFTable| + |leftDivide| |exponents| |optional| |groebnerFactorize| |printStats!| + |reorder| |keys| |fullPartialFraction| |powmod| |cSech| |OMgetEndAtp| + |palgint0| |insertMatch| |substitute| |biRank| |hcrf| |lifting1| |inv| + |write| |stack| |expt| |simplify| |lfextendedint| |wholePart| |d01apf| + |iicos| |radicalOfLeftTraceForm| |deepExpand| |cTan| |save| |ground?| + |scripted?| |triangSolve| |shanksDiscLogAlgorithm| |setValue!| |slash| + |chiSquare| |iiacos| |shallowCopy| |setAttributeButtonStep| |ground| + |ldf2vmf| |monicLeftDivide| |eq?| |sdf2lst| |iicoth| |OMgetEndBVar| + |numberOfIrreduciblePoly| |companionBlocks| |acschIfCan| |distdfact| + |leadingMonomial| |representationType| |sumOfKthPowerDivisors| + |LyndonWordsList| |s01eaf| |whileLoop| |const| |factorsOfDegree| + |singleFactorBound| |viewPhiDefault| |mapExponents| + |leadingCoefficient| |noLinearFactor?| FG2F |multiEuclidean| + |listOfMonoms| |pole?| |collect| |s17ajf| |lookup| |OMopenString| + |removeSuperfluousCases| |primitiveMonomials| |leftRecip| |lowerCase| + |readBytes!| |pushNewContour| |left| |create| |adaptive3D?| |s21baf| + |removeZeroes| |completeSmith| |reductum| |overlabel| |rootOf| |roman| + |expandPower| |monomRDEsys| |right| |trigs| |elliptic?| |cyclicGroup| + |remove!| |stop| |setLength!| |RemainderList| |callForm?| + |generalTwoFactor| |subNodeOf?| |mr| |cycleEntry| |s13acf| |isTimes| + |outputList| |shiftRight| |ipow| |aspFilename| |d01bbf| |f01qef| + |pointColor| |froot| |lSpaceBasis| |entries| |csc2sin| |entry| + |clearDenominator| |showRegion| + |removeRoughlyRedundantFactorsInContents| |airyAi| |nextColeman| + |rationalIfCan| |mergeFactors| |mainValue| |ode1| |decrease| + |intChoose| |complexZeros| |twoFactor| |halfExtendedResultant1| + |roughBase?| |cAcsc| LODO2FUN |minGbasis| |sumSquares| |totalLex| + |host| |generalSqFr| |rowEchelon| |solveid| |iiacsc| |meshPar2Var| + |leftGcd| |prefix| |taylorQuoByVar| |numberOfCycles| |limitedint| + |s19abf| |jvmClassConstantTag| |numericIfCan| |space| |hyperelliptic| + |realRoots| |mappingAst| |plus!| |OMgetSymbol| |kovacic| + |wordInGenerators| |pushuconst| |selectMultiDimensionalRoutines| + |appendPoint| |minimumExponent| |iicsc| |integralRepresents| + |infinite?| |rquo| |HenselLift| |cos2sec| |readable?| |returns| |rule| + |elaboration| |doubleDisc| |eigenvalues| |toseInvertible?| |elaborate| + |coerceL| |moreAlgebraic?| |removeCosSq| BY |qfactor| |qelt| + |coth2tanh| |subresultantVector| |bumprow| |clearTheFTable| + |rightRegularRepresentation| |rdHack1| |alphanumeric| |e01bef| + |iiasec| |qsetelt| |applyRules| |rational| |flagFactor| |mathieu12| + |merge| |OMsupportsSymbol?| |predicates| |string?| |cross| |rowEch| + |symbol| |xRange| |lookupFunction| |principal?| |tanAn| |setrest!| + |e01baf| |drawComplex| |pdct| |lazyIntegrate| |setImagSteps| F + |linearMatrix| |expression| |reopen!| |yRange| |jvmInterface| |name| + |jvmStringConstantTag| |OMsupportsCD?| |bubbleSort!| |rdregime| + |univariatePolynomialsGcds| |symbolIfCan| |nextsousResultant2| + |integer| |zRange| |f04mbf| |body| |rspace| |coefficient| |points| + |nthRootIfCan| |internalSubQuasiComponent?| |showFortranOutputStack| + |listRepresentation| |map!| |OMclose| |antisymmetricTensors| + |subNode?| |digit?| |cons| |datalist| |void| |purelyAlgebraic?| + |generalInfiniteProduct| |iibinom| |leftDiscriminant| |qsetelt!| + |makingStats?| |alphanumeric?| |antiAssociative?| |cubic| NOT + |setAdaptive3D| |internalAugment| |imports| |ODESolve| |super| + |rootPower| |integralCoordinates| |semiResultantEuclidean2| + |elaborateFile| OR |setColumn!| |ode| |characteristicPolynomial| + |polygon| |c06fuf| |possiblyNewVariety?| |extendIfCan| + |changeWeightLevel| AND |tableau| |complexLimit| |moebius| + |characteristicSet| |depth| |solve| |simpleBounds?| |exponentialOrder| + |OMconnectTCP| |rewriteSetWithReduction| |iiacot| |acothIfCan| + |presuper| |dmpToP| |modularFactor| |in?| |headReduced?| |intensity| + |createMultiplicationTable| |source| |createNormalPoly| |mantissa| + |numerator| |getlo| |call| |acsch| |polynomialZeros| |empty?| + |square?| |nextsubResultant2| |expandLog| |identity| |setMinPoints| + |genericLeftTrace| |mapBivariate| |verticalTab| |port| |asecIfCan| + |testModulus| |transcendenceDegree| |overset?| |idealiserMatrix| + |symmetricDifference| |lifting| |csch2sinh| |lowerCase?| |goto| + |nullary| |subPolSet?| |latex| |Lazard| |resetVariableOrder| |ddFact| + |BumInSepFFE| |encodingDirectory| |t| |doubleFloatFormat| |polygamma| + |OMencodingSGML| |iiabs| |d01gbf| |extractSplittingLeaf| |invertIfCan| + |stoseInvertibleSet| |brillhartTrials| |bindings| |minrank| + |moebiusMu| |cAcoth| |componentUpperBound| |karatsuba| |reduced?| + |karatsubaDivide| |incrementKthElement| |nextLatticePermutation| + |epilogue| |sorted?| |factorset| |newline| |adaptive| + |halfExtendedSubResultantGcd1| |palglimint| |indiceSubResultant| + |common| |perfectSqrt| |qroot| |dfRange| |indiceSubResultantEuclidean| + |scale| * |conical| |createLowComplexityNormalBasis| + |semiSubResultantGcdEuclidean2| |radicalEigenvectors| |signAround| + |jvmFieldrefConstantTag| |relationsIdeal| |rur| |dihedralGroup| + |drawComplexVectorField| |increment| |e02def| |simplifyLog| |key| + |fullDisplay| |adjoint| |bandedJacobian| |fmecg| |cdr| |lyndonIfCan| + |pade| |fi2df| |ScanArabic| |hdmpToP| |functionIsFracPolynomial?| + |semiSubResultantGcdEuclidean1| |previous| |fractRadix| = |repeating| + RF2UTS |c02aff| |sylvesterSequence| |filename| |balancedBinaryTree| + |charpol| |cycle| |useEisensteinCriterion| |hash| |find| |iiperm| + |normInvertible?| |bivariate?| |generalizedInverse| |bag| + |internalIntegrate0| |digamma| |count| < |graeffe| |category| + |packageCall| |bitLength| |double| |exponential| |parse| |f04faf| + |OMputFloat| |createGenericMatrix| > |domain| |rootBound| |vconcat| + |regime| |resetNew| |numberOfMonomials| |critM| |extractClosed| + |countRealRoots| <= |numerators| |OMopenFile| |status| |reducedForm| + |package| |mesh?| |gcdcofactprim| |constantRight| |mainExpression| + |mix| >= |complexExpand| |mainPrimitivePart| |ellipticCylindrical| + |fortranLogical| |quoByVar| |jvmVolatile| |largest| |interactiveEnv| + |collectUpper| |factors| |subQuasiComponent?| |equality| + |colorFunction| |consnewpol| |implies| |badNum| |quadratic| + |argumentList!| |getProperties| |e01daf| |extractTop!| + |createLowComplexityTable| |leftLcm| |rightFactorCandidate| + |bfKeys| + |makeSin| |palgRDE| |normal01| |extractBottom!| |whatInfinity| |max| + |stosePrepareSubResAlgo| - |cotIfCan| |pseudoQuotient| |normal?| + |declare!| |real?| |internalIntegrate| |crest| / |redPo| + |irreducibleRepresentation| |lazyResidueClass| |getOrder| + |associates?| |negative?| |shufflein| |acoshIfCan| |mesh| + |fortranCarriageReturn| |mergeDifference| |dec| |symmetricProduct| + |acosIfCan| |ptree| |s17dgf| |gcdPrimitive| |primitivePart!| + |diagonals| |integralBasisAtInfinity| |clipParametric| |radix| + |problemPoints| |setfirst!| |differentialVariables| |open| |cAsech| + |c05pbf| |midpoint| |d02gaf| |att2Result| |indicialEquationAtInfinity| + |index| |d02gbf| |s17adf| |d03edf| |buildSyntax| |countable?| + |rename!| |readLine!| |readInt8!| |s18adf| |kind| |getCode| + |changeMeasure| |tableForDiscreteLogarithm| |deriv| |tRange| + |binaryTournament| |twist| |OMconnInDevice| |oddintegers| |ignore?| + |exprToUPS| |ideal| |perspective| |op| |f02adf| + |createPrimitiveElement| |leftExactQuotient| |addMatch| |before?| + |paraboloidal| |segment| |yellow| |pair| |kmax| |distFact| + |operations| |maximumExponent| |exists?| |sechIfCan| |cCosh| |cSinh| + |character?| |s18dcf| |cycles| |janko2| |antisymmetric?| + |partialNumerators| |comment| |df2mf| |lighting| |unit| |lazyEvaluate| + |tubePoints| |deepestTail| |currentSubProgram| |initTable!| |df2st| + |copy!| |step| |environment| |swapColumns!| |mapUp!| |flexibleArray| + |Ci| |laguerre| |genericLeftNorm| |fractionPart| + |primPartElseUnitCanonical| |pack!| |d02ejf| |f01mcf| |enumerate| + |separateFactors| |stoseInvertible?| |e02zaf| |nil?| |poisson| + |newTypeLists| |nor| |ocf2ocdf| |lintgcd| |innerSolve1| |trim| + |hostPlatform| |enterPointData| |bringDown| |showTheRoutinesTable| + |complexElementary| |resize| |topFortranOutputStack| |cAcosh| |expint| + |bsolve| |getGraph| |zero| |hasoln| |splitLinear| |gethi| |pointLists| + |matrixConcat3D| |union| |symbolTable| |even?| |mapMatrixIfCan| + |cycleTail| |normalizeAtInfinity| |minimalPolynomial| |retract| + |startTableInvSet!| |changeName| |dim| |hue| |radicalEigenvalues| + |e01bgf| |roughEqualIdeals?| |option?| |decimal| |hclf| + |rightQuotient| |firstDenom| |And| |ran| |critBonD| |showTheIFTable| + |result| |pushFortranOutputStack| |asechIfCan| |fglmIfCan| + |univariate?| |compose| |logGamma| |zeroDimPrime?| |norm| + |clearTheSymbolTable| |Or| |order| |leadingBasisTerm| + |semiResultantReduitEuclidean| |clearFortranOutputStack| |setUnion| + |popFortranOutputStack| |showAllElements| |toScale| |getConstant| + |initializeGroupForWordProblem| |showClipRegion| |extension| |Not| + |polyPart| |tryFunctionalDecomposition| |multiset| |OMconnOutDevice| + |cyclicEntries| |outputAsFortran| |deepestInitial| |rightNorm| + |irreducibleFactors| |BasicMethod| |s19aaf| |bits| |elementary| + |symFunc| |stiffnessAndStabilityFactor| |infieldint| |sPol| |universe| + |e01sef| |simpson| |inverseColeman| |cylindrical| |sumOfSquares| + |generateIrredPoly| |collectUnder| |mapdiv| |stoseLastSubResultant| + |positiveRemainder| |symmetric?| |optAttributes| |pseudoDivide| |Beta| + |removeRedundantFactorsInContents| |mindegTerm| |complexRoots| + |factorOfDegree| |safeCeiling| |makeSketch| |interReduce| + |inverseIntegralMatrix| |definingEquations| |fTable| F2FG + |resetAttributeButtons| |unexpand| |intPatternMatch| |printTypes| + |front| |leader| |palgextint| |lagrange| |elRow2!| |pointData| + |factorSFBRlcUnit| |mapExpon| |functionIsContinuousAtEndPoints| + |rightDiscriminant| |sparsityIF| |trueEqual| |c05adf| |search| + |getMultiplicationTable| |musserTrials| |mathieu23| |routines| + |lastSubResultantElseSplit| |s17dlf| |ksec| |exptMod| |leftMult| + |maxPoints| |simplifyExp| |s17acf| |isQuotient| |rroot| |eyeDistance| + |inGroundField?| |ricDsolve| |associatedEquations| |odd?| + |sumOfDivisors| |row| |insertBottom!| |rotatey| + |factorsOfCyclicGroupSize| |factorSquareFreeByRecursion| |prindINFO| + |s14aaf| |rischDE| |writeByte!| |karatsubaOnce| |heapSort| |eulerPhi| + |d01aqf| |retractIfCan| |block| |bitCoef| |PollardSmallFactor| + |f04qaf| |viewDefaults| |cSec| |checkRur| |id| |coordinate| + |genericRightMinimalPolynomial| |isAbsolutelyIrreducible?| + |genericLeftDiscriminant| |explogs2trigs| |normFactors| |lex| + |badValues| |orthonormalBasis| |subst| |is?| |iiatanh| |s13aaf| |lo| + |primaryDecomp| |maxrank| |rightExactQuotient| |romberg| |endOfFile?| + |pascalTriangle| |setStatus!| |controlPanel| |error| |euclideanSize| + |typeLists| |e02aef| |curve| |operators| |unary?| |bottom!| |f04mcf| + |upperCase!| |clipPointsDefault| |getDatabase| |second| |lp| + |squareFree| |powerSum| |overbar| |denominator| |weights| + |zeroDimPrimary?| |map| |makeCos| |approxNthRoot| |divisor| |iiasech| + |third| |sqfrFactor| |cschIfCan| |createMultiplicationMatrix| + |realEigenvectors| |mapmult| |mappingMode| |iterationVar| + |finiteBound| |cCsch| |s20adf| |objects| |formula| + |jvmDoubleConstantTag| |findCycle| |sequences| |stirling2| |imagJ| + |complete| |close| |tower| |f02axf| |outlineRender| |printCode| |log2| + |LowTriBddDenomInv| |base| |qinterval| |exprex| |assign| + |reducedQPowers| |selectIntegrationRoutines| |hMonic| |fixedPoint| + |modifyPointData| |OMputEndBVar| |readIfCan!| |parents| |sample| + |delete!| |setTopPredicate| |branchIfCan| |abs| |f04jgf| |display| + |parabolic| |ridHack1| |vector| |solveInField| |remainder| + |fortranLiteralLine| |discreteLog| |e02akf| |eigenvector| |OMreadStr| + |invertible?| |alternative?| |univcase| |differentiate| |pushdown| + |viewThetaDefault| |conjug| |nrows| |isAtom| + |SturmHabichtCoefficients| |lazyIrreducibleFactors| + |triangularSystems| |makeGraphImage| |groebner| |headRemainder| + |divideIfCan!| |OMgetEndError| |isPlus| |ncols| |GospersMethod| + |extract!| |setRealSteps| |maxColIndex| |selectPDERoutines| + |stopTableGcd!| |cPower| |writeLine!| |quadraticForm| + |exportedOperators| |coerce| |next| |LyndonBasis| + |squareFreePolynomial| |terms| |leftQuotient| |complexNumeric| + |unitsColorDefault| |graphCurves| |errorKind| |nlde| + |brillhartIrreducible?| |categories| |construct| |leftTraceMatrix| + |getStream| |solveRetract| |input| |multiplyCoefficients| + |symmetricSquare| |OMencodingXML| |inspect| |integralMatrixAtInfinity| + |mdeg| |yCoord| |extendedint| |column| |library| |geometric| + |directory| |makeop| |divideExponents| |genus| |OMputBind| + |drawToScale| |sech2cosh| |exteriorDifferential| |cExp| |birth| + |edf2df| |plenaryPower| |duplicates| |basicSet| |tube| + |fortranLinkerArgs| |tab1| |someBasis| |quotedOperators| |init| + |radicalSolve| |sn| |lowerPolynomial| |iprint| |coord| |dequeue!| + |matrix| |e02ajf| |tan2trig| |hspace| |iisin| |setScreenResolution3D| + |isOr| |setClosed| |airyBi| |gbasis| |jacobi| |conditionP| + |graphStates| |critMonD1| |composite| |cot2tan| |setOfMinN| |nonQsign| + |normalDeriv| |putGraph| |parabolicCylindrical| |set| |morphism| + |leadingTerm| |limit| |setchildren!| |diag| |algebraicDecompose| + |createPrimitiveNormalPoly| |delete| |f02bjf| |s18def| |mathieu22| + |infLex?| |changeBase| |tanSum| |polar| |divide| |lepol| |chebyshevT| + |cartesian| |rotate!| |lineColorDefault| |cup| |retractable?| + |branchPointAtInfinity?| |normalForm| |elRow1!| |makeEq| + |doublyTransitive?| |critT| |expenseOfEvaluationIF| |leadingIndex| + |zero?| |prod| |PDESolve| |maxint| |systemCommand| |computePowers| + |definingInequation| |rationalPower| |leaves| |minimize| |readUInt32!| + |OMcloseConn| |binding| |point?| |laplacian| |f02abf| |argscript| + |subspace| |physicalLength!| |B1solve| |relativeApprox| |intcompBasis| + |s17akf| |OMgetVariable| |aCubic| |iilog| |meshFun2Var| + |extendedResultant| |uncouplingMatrices| |innerEigenvectors| + |upperBound| |assert| |rotatez| |nextPrime| |setProperty| |normal| + |OMputApp| |hitherPlane| |OMputEndError| |sturmVariationsOf| + |nonSingularModel| |fillPascalTriangle| |finite?| |removeSinSq| + |linearAssociatedOrder| |monomial?| |continuedFraction| |coHeight| + |boundOfCauchy| |tanh2trigh| |dn| |gradient| |gderiv| |localUnquote| + |dflist| |chebyshevU| |element?| |virtualDegree| |zCoord| + |quasiComponent| |prolateSpheroidal| |hexDigit| |factorAndSplit| + |transform| |e04naf| |palgLODE0| |upDateBranches| |OMgetEndAttr| + |linSolve| |rules| |dAndcExp| |s17aef| |integralLastSubResultant| + |checkPrecision| |show| |formfeed| |tracePowMod| |Is| |conjunction| + |numberOfFactors| |bezoutResultant| |shiftRoots| |makeFR| |Aleph| + |cycleElt| |isOpen?| |antiCommutator| |prefixRagits| + |nativeModuleExtension| |e02daf| |explicitEntries?| |rank| |sinhIfCan| + |integralBasis| |leastPower| |trace| |sin?| |graphImage| |palgRDE0| + |basisOfRightNucloid| |repeating?| |e04ycf| |balancedFactorisation| + |fortranTypeOf| |more?| |anticoord| |rootSimp| |compBound| + |dimensionOfIrreducibleRepresentation| |unitNormal| |linearDependence| + |presub| |rightUnits| |log10| |critpOrder| |unknown| |rightMult| + |acscIfCan| |leadingCoefficientRicDE| |subResultantGcd| |ParCondList| + |arbitrary| |algint| |irreducibleFactor| |bitand| |inf| |localAbs| + |hermiteH| |semiDiscriminantEuclidean| |outputAsScript| |c06gbf| + |f02bbf| |OMUnknownCD?| |fortran| |primitiveElement| |bitior| |revert| + SEGMENT |goodPoint| |extend| |underscore| |bothWays| + |genericRightTraceForm| |printingInfo?| |roughUnitIdeal?| + |var2StepsDefault| |triangulate| |insertTop!| |low| + |completeEchelonBasis| |binomial| |bernoulli| |sin2csc| |evenlambert| + |cSin| |loopPoints| |realElementary| |middle| |ParCond| |rootKerSimp| + |getVariableOrder| |mainCharacterization| |lists| |addMatchRestricted| + |rowEchelonLocal| |d01akf| |seriesSolve| |c06gqf| |exprToGenUPS| + |table| |errorInfo| |basisOfNucleus| |rational?| |sinIfCan| + |leastAffineMultiple| |identification| |ScanFloatIgnoreSpaces| + |graphState| |minordet| |new| |normalized?| |irForm| |prem| + |stiffnessAndStabilityOfODEIF| |over| |ratDenom| |iitanh| + |showSummary| |just| |ravel| |leftOne| |modularGcdPrimitive| + |radicalRoots| |startTable!| |putColorInfo| |OMgetApp| + |generalPosition| |compactFraction| |rightAlternative?| |reshape| + |viewWriteDefault| |iiexp| |c06gsf| |subTriSet?| |recolor| |curryLeft| + |permutations| |loadNativeModule| |OMputString| |showAttributes| |cn| + |parseString| |quadraticNorm| |genericLeftMinimalPolynomial| |totolex| + |iroot| |weakBiRank| |Hausdorff| |c06ecf| |messagePrint| |pol| |paren| + |cosh2sech| |tValues| |droot| |var1Steps| |divideIfCan| |jvmAbstract| + |output| |constantKernel| |sum| |OMgetEndApp| |wreath| |yCoordinates| + |functorData| |erf| |genericPosition| |pureLex| |sequence| + |LyndonCoordinates| |anfactor| |light| |diophantineSystem| + |viewZoomDefault| |totalfract| |s21bcf| |legendreP| |child?| + |nextItem| |jvmFinal| |diagonal?| |update| |script| |shellSort| + |Frobenius| |dual| |constantOpIfCan| |jvmStatic| |doubleRank| |move| + |optional?| |oblateSpheroidal| |seriesToOutputForm| |s14baf| + |tensorProduct| |dilog| |sup| |adaptive?| |back| |graphs| |allRootsOf| + |prologue| |f02agf| |floor| |s17ahf| |sin| |readInt32!| + |OMencodingBinary| |f02aff| |cycleRagits| |patternVariable| + |jvmPublic| |tex| |calcRanges| |argumentListOf| |getPickedPoints| + |cos| |condition| |contains?| |nthRoot| |splitConstant| |vark| + |coordinates| |algebraicSort| |inHallBasis?| |baseRDE| + |mightHaveRoots| |tan| |alphabetic?| |jvmFloatConstantTag| |An| + |outputBinaryFile| |setProperties| |position| |removeSinhSq| + |wordsForStrongGenerators| |removeRedundantFactorsInPols| + |laurentIfCan| |cot| |newLine| |bivariatePolynomials| |setleft!| + |groebner?| |minPoints3D| |OMgetAtp| |leaf?| |compound?| |harmonic| + |sec| |tubeRadius| |numberOfFractionalTerms| |exQuo| |besselJ| + |normalise| |varList| |outputAsTex| |leftRegularRepresentation| + |mkPrim| |structuralConstants| |csc| |LyndonWordsList1| |f02xef| + |arrayStack| |reduction| |modifyPoint| |units| |cosIfCan| + |unaryFunction| |lazyPseudoQuotient| |imagi| |asin| |d03faf| + |setCondition!| |nary?| |taylorIfCan| |palgLODE| |randnum| + |localReal?| |numberOfVariables| |stFunc1| |acos| + |createIrreduciblePoly| |octon| |trivialIdeal?| |reverse| |c05nbf| + |binaryFunction| |integralAtInfinity?| |split| |numberOfDivisors| + |internalZeroSetSplit| |cothIfCan| |atan| |notelem| |extractIfCan| + |rangeIsFinite| |meatAxe| |sizeLess?| |OMputInteger| |clipBoolean| + |noValueMode| |equiv| |root?| |acot| |setLabelValue| |lyndon?| + |limitedIntegrate| |primlimitedint| |solid?| |contract| |initials| + |substring?| |parametersOf| |e04ucf| |oddInfiniteProduct| |ranges| + |asec| |constantToUnaryFunction| |univariatePolynomials| |belong?| + |squareMatrix| |code| |primeFactor| |rightFactorIfCan| |supersub| + |f02akf| |intersect| |lowerCase!| |acsc| |rightOne| |deref| + |expenseOfEvaluation| |factorSquareFree| |region| |suffix?| + |semiLastSubResultantEuclidean| |lazyPremWithDefault| + |explicitlyFinite?| |freeOf?| |linkToFortran| |sinh| + |matrixDimensions| |imagk| |makeSeries| |algebraicVariables| |f01maf| + |irreducible?| |f04atf| |monicRightFactorIfCan| |createNormalElement| + |insertionSort!| |cosh| |viewport2D| |pointColorDefault| |iisinh| + |bombieriNorm| |s15adf| |tubeRadiusDefault| + |halfExtendedSubResultantGcd2| |prefix?| |cap| |alternatingGroup| + |abelianGroup| |conjugate| |tanh| |leftRankPolynomial| |mainMonomials| + |e02gaf| |ListOfTerms| |comparison| |expandTrigProducts| |iifact| + |OMgetType| |semiIndiceSubResultantEuclidean| |isNot| |sec2cos| |coth| + |dihedral| |useSingleFactorBound?| |pushdterm| + |removeSuperfluousQuasiComponents| |setFieldInfo| |setlast!| |ldf2lst| + |elColumn2!| |FormatArabic| |f01rcf| |compile| |sech| |exactQuotient| + |definingPolynomial| |cAsin| |e02bdf| |domainTemplate| |plus| |weight| + |redpps| |mainSquareFreePart| |eulerE| |csch| |unvectorise| + |viewPosDefault| |eisensteinIrreducible?| |setMaxPoints| + |chainSubResultants| |complexEigenvalues| |ReduceOrder| + |diagonalMatrix| |powern| |asinh| |cyclotomicFactorization| + |rightTrace| |f07fef| |setPrologue!| |numFunEvals3D| + |linearAssociatedExp| |f01ref| |top| |OMlistSymbols| + |extendedIntegrate| |acosh| |credPol| |setMinPoints3D| |cAtan| + |sinh2csch| |numberOfOperations| |continue| |times| |scaleRoots| + |infix?| |isMult| |fortranLiteral| |leftPower| |atanh| |s20acf| + |symmetricGroup| |screenResolution3D| |sort| |monicDivide| |rst| + |mask| |contractSolve| |index?| |cyclicParents| |removeDuplicates| + |acoth| |arity| |degree| |partialQuotients| |mulmod| + |characteristicSerie| |rectangularMatrix| |critB| |categoryMode| + |coerceP| |asech| |setPosition| |algDsolve| |writeUInt8!| + |firstUncouplingMatrix| |random| |outputGeneral| |cRationalPower| + |monomRDE| |shiftLeft| |extendedEuclidean| |curry| + |stripCommentsAndBlanks| |jvmProtected| |discriminant| |null| |pushup| + |monom| |permutation| |outputMeasure| |numberOfComputedEntries| + |closedCurve?| |fprindINFO| |makeResult| |setelt!| |baseRDEsys| + |homogeneous?| |not| |simpsono| |bipolar| |singular?| |xCoord| |value| + |combineFeatureCompatibility| |headAst| |deleteProperty!| |composites| + |lyndon| |and| |getBadValues| |integral?| |inconsistent?| |positive?| + |maxIndex| |signatureAst| |lieAdmissible?| |submod| |or| |isOp| + |integralMatrix| |mainDefiningPolynomial| |enterInCache| |e02agf| + |node| |numberOfPrimitivePoly| |horizConcat| |algSplitSimple| + |fortranCompilerName| |cardinality| |xor| |clikeUniv| |triangular?| + |mainCoefficients| |arg1| |euler| |bitTruth| |reducedSystem| + |function| |d02cjf| |point| |nothing| |resultantReduit| |OMgetFloat| + |case| |mapUnivariate| |diagonalProduct| |arg2| |phiCoord| + |initiallyReduce| |interpretString| |dequeue| |repeatUntilLoop| + |unitCanonical| |OMencodingUnknown| |content| |Zero| |schema| + |drawStyle| |printStatement| |limitPlus| |expPot| |OMputAtp| + |arguments| |rischNormalize| |userOrdered?| |evaluateInverse| + |closedCurve| |OMputBVar| |One| |increase| |kroneckerDelta| + |blankSeparate| |coerceImages| |makeTerm| |conditions| |putProperty| + |mapSolve| |series| |rootProduct| |schwerpunkt| |orbits| |f07adf| + |withPredicates| |commonDenominator| |match| |viewWriteAvailable| + |setMaxPoints3D| |KrullNumber| |isobaric?| |nsqfree| |sncndn| + |upperCase?| |iisech| |typeForm| |stopTableInvSet!| |rightLcm| + |createZechTable| |resultantEuclideannaif| |relerror| |qualifier| + |property| |flatten| |binaryTree| |rewriteIdealWithHeadRemainder| + |stoseInvertible?sqfreg| |f02aaf| |positiveSolve| |probablyZeroDim?| + |shape| |iiasin| |preprocess| |leadingExponent| |complexForm| |nthr| + |min| |pile| |stoseInternalLastSubResultant| |squareFreeFactors| + |trunc| |clearTable!| |elt| |exprHasWeightCosWXorSinWX| + |antiCommutative?| |normalDenom| |defineProperty| |compiledFunction| + |atrapezoidal| |asimpson| |viewport3D| |chvar| |sortConstraints| + |polyRicDE| |scan| |youngGroup| |constant| |simplifyPower| + |primlimintfrac| |zeroDim?| |one?| |eof?| |eigenMatrix| |child| + |iicosh| |hasTopPredicate?| |e04fdf| |selectOptimizationRoutines| + |getButtonValue| |c06frf| |extractPoint| |LiePolyIfCan| + |clipWithRanges| |quotientByP| |distance| |lcm| |minIndex| + |extractIndex| |f04axf| |squareFreePart| |jokerMode| |clearCache| + |OMUnknownSymbol?| |iExquo| |figureUnits| |npcoef| |rightScalarTimes!| + |prevPrime| |equation| |unitNormalize| |support| |OMsetEncoding| + |carriageReturn| |semicolonSeparate| |append| |e02dff| |slex| + |hdmpToDmp| |redmat| |minPoints| |resultantnaif| |var2Steps| + |monicRightDivide| |zeroSetSplit| |gcd| + |inverseIntegralMatrixAtInfinity| |addPoint| |ode2| |pdf2ef| + |acotIfCan| |linearDependenceOverZ| |outerProduct| |sqfree| |dom| + |reflect| |legendre| |false| |decreasePrecision| |genericRightNorm| + |showTheFTable| |solveLinearPolynomialEquationByRecursion| |summation| + |trailingCoefficient| |attributeData| |label| |pointColorPalette| + |unit?| |s17def| |removeIrreducibleRedundantFactors| |associator| + |showScalarValues| |bandedHessian| |fortranComplex| + |oneDimensionalArray| |rightZero| |OMsend| |monicCompleteDecompose| + |multiEuclideanTree| |rightRankPolynomial| |showIntensityFunctions| + |OMParseError?| |variationOfParameters| |extractProperty| + |safetyMargin| |position!| |singularAtInfinity?| + |jvmMethodrefConstantTag| |complementaryBasis| |jvmPrivate| + |OMreadFile| |readLineIfCan!| |startTableGcd!| |disjunction| + |nextIrreduciblePoly| |generators| |d01gaf| |OMgetEndBind| |rightRank| + |accuracyIF| |trapezoidal| |quoted?| |properties| |title| + |wronskianMatrix| |isImplies| |directSum| |float?| |fixedPoints| + |completeEval| |diff| |supRittWu?| |leftRank| |addiag| |translate| + |size?| |SturmHabicht| |s17dhf| |quasiMonicPolynomials| |infix| + |rightCharacteristicPolynomial| |opeval| |isPower| |decompose| |untab| + |range| |palginfieldint| |zeroDimensional?| |denomLODE| + |primPartElseUnitCanonical!| |infinityNorm| |mkIntegral| |weierstrass| + |basisOfCentroid| |primintegrate| |e| |chineseRemainder| + |deleteRoutine!| |f04adf| |algebraic?| |inverseLaplace| |pToDmp| + |bat1| |groebnerIdeal| |toseLastSubResultant| |option| Y + |OMunhandledSymbol| |mathieu11| |lflimitedint| |listYoungTableaus| + |groebgen| |zeroSetSplitIntoTriangularSystems| |supDimElseRittWu?| + |jvmSuper| |normalizedDivide| |shade| |UpTriBddDenomInv| + |toseSquareFreePart| |closed?| |coefChoose| |getExplanations| + |rombergo| |permutationRepresentation| |isEquiv| |UnVectorise| + |sturmSequence| |mainVariable?| |scalarMatrix| |cCos| |parent| + |splitNodeOf!| |stFunc2| |factorByRecursion| |currentScope| + |primitivePart| |inputOutputBinaryFile| |reverseLex| + |removeConstantTerm| |secIfCan| |e02bbf| |setvalue!| |pleskenSplit| + |trace2PowMod| |commaSeparate| |f01qcf| |rootNormalize| + |unprotectedRemoveRedundantFactors| |removeDuplicates!| |OMputAttr| + |makeVariable| |resultantEuclidean| |linearPart| |dark| + |minimumDegree| |multiplyExponents| |f2st| |outputFixed| |cyclic| + |systemSizeIF| |generalizedEigenvector| |jacobian| |laguerreL| + |totalDegree| |frst| |bfEntry| |c06fpf| |d02bhf| |powerAssociative?| + |setref| |numberOfNormalPoly| |resetBadValues| |moduleSum| + |gramschmidt| |apply| |showAll?| |test| |nonLinearPart| |monicModulo| + |computeBasis| |unrankImproperPartitions0| |operation| |fortranReal| + |iicot| |nextPartition| |f07fdf| |removeRoughlyRedundantFactorsInPols| + |numberOfHues| |first| |tanintegrate| |d02raf| |sign| |nand| |f04arf| + |createNormalPrimitivePoly| |expintfldpoly| |rk4| |drawCurves| |rest| + |localIntegralBasis| |parts| |jvmStrict| |Ei| |part?| + |countRealRootsMultiple| |mainMonomial| |contours| |explimitedint| + |stopTable!| |quatern| |purelyTranscendental?| |radPoly| |pop!| + |eigenvectors| |create3Space| |rightExtendedGcd| |taylorRep| + |indicialEquation| |rarrow| |c06eaf| |colorDef| |pdf2df| |polygon?| + |leftReducedSystem| |separate| |integerBound| |OMgetBind| + |firstSubsetGray| |weighted| |innerint| |maxdeg| |setleaves!| |imagK| + |zerosOf| |clearTheIFTable| |makeYoungTableau| + |unrankImproperPartitions1| |critMTonD1| |s19adf| |rationalPoint?| + |elements| |imagj| |cyclicSubmodule| |polCase| |complexNormalize| + |setprevious!| |nthFlag| |pattern| |iCompose| |coerceS| |maxRowIndex| + |product| |Gamma| |cycleLength| |e02bef| |s15aef| |nodeOf?| |integers| + |remove| |outputArgs| |lazyPseudoDivide| |euclideanNormalForm| + |lazyPseudoRemainder| |fixedDivisor| + |generalizedContinuumHypothesisAssumed?| |digit| |subMatrix| + |realEigenvalues| |ref| |internalInfRittWu?| ** |primeFrobenius| + |merge!| |nilFactor| |round| |atanhIfCan| |iiacoth| |swap| + |rewriteIdealWithQuasiMonicGenerators| |internalDecompose| |c06gcf| + |s18aef| |last| |monomialIntegrate| |startStats!| |linGenPos| + |rightPower| |iiacsch| |rationalPoints| |build| |readByte!| + |mainVariables| |aQuartic| |transcendent?| |message| |assoc| + |factorPolynomial| |expextendedint| |rischDEsys| |modTree| + |resultantReduitEuclidean| |integerIfCan| |irDef| |repSq| + |symbolTableOf| |leftScalarTimes!| |s21bdf| |hexDigit?| |padecf| + |completeHensel| |comp| |knownInfBasis| |invertibleElseSplit?| + |leftRemainder| |stoseSquareFreePart| |generic| |coshIfCan| |s17agf| + |noKaratsuba| |radicalSimplify| |shrinkable| |refine| + |curveColorPalette| |getRef| |dualSignature| |tubePlot| |mathieu24| + |wrregime| |setPredicates| |atanIfCan| |root| |power| + |numberOfChildren| |magnitude| |determinant| |makeFloatFunction| + |roughSubIdeal?| |removeRoughlyRedundantFactorsInPol| + |reducedDiscriminant| |viewDeltaYDefault| |edf2ef| |besselI| + |lieAlgebra?| |regularRepresentation| |logical?| |evenInfiniteProduct| + |jvmNameAndTypeConstantTag| |expIfCan| |algebraicCoefficients?| + |internalLastSubResultant| |normalElement| |linearForm| |lfunc| + |setStatus| |setScreenResolution| |OMbindTCP| |concat| |enqueue!| + |s13adf| |selectOrPolynomials| |inrootof| |subResultantsChain| + |setErrorBound| |normalizedAssociate| |f07aef| |exponential1| |module| + |push| |copies| |transcendentalDecompose| |iitan| |null?| |node?| + |coefficients| |edf2efi| |precision| + |rewriteSetByReducingWithParticularGenerators| |nthExponent| + |leftExtendedGcd| |createRandomElement| |quadratic?| |algebraicOf| + |select!| |multisect| |binary| |interpret| |cAsec| |makeMulti| + |perfectNthRoot| |hconcat| |leftCharacteristicPolynomial| + |mapUnivariateIfCan| |littleEndian| |sylvesterMatrix| |rightUnit| + |scalarTypeOf| |subCase?| |s17dcf| |indicialEquations| + |partialDenominators| |setVariableOrder| |zeroOf| |blue| |open?| + |hessian| |corrPoly| |subSet| |lfextlimint| |connect| |c06ebf| |plot| + |lexTriangular| |isList| |mat| |nullary?| |argument| |iisqrt3| + |interpolate| |leftTrace| |po| |dictionary| |bounds| |f01qdf| + |oddlambert| |setIntersection| |component| |inputBinaryFile| + |cyclotomic| |integral| |newSubProgram| |voidMode| |optimize| + |removeZero| |viewSizeDefault| |s19acf| |OMputEndApp| + |collectQuasiMonic| |randomLC| |palgextint0| |pmComplexintegrate| + |pow| |cscIfCan| |principalIdeal| |tanh2coth| |delta| |separant| + |cAcsch| |setClipValue| |mainKernel| |iipow| |d01alf| |isConnected?| + UP2UTS |singRicDE| |lazyPrem| |d01ajf| |nodes| |iiasinh| + |degreeSubResultantEuclidean| |nthCoef| |tanIfCan| |backspace| + |denominators| |separateDegrees| |rationalApproximation| |unparse| + |jvmLongConstantTag| |exponent| |linear| |setEpilogue!| + |invertibleSet| |high| |tanQ| |setFormula!| |sizePascalTriangle| + |charClass| |indices| |level| |writable?| |exactQuotient!| |leftZero| + |bumptab| |socf2socdf| |components| |leviCivitaSymbol| |OMgetObject| + |e01saf| |ef2edf| |pseudoRemainder| |llprop| |dimensions| + |leftAlternative?| |polynomial| |doubleResultant| |multiple?| + |fortranInteger| |pointPlot| |jvmSynchronized| |target| + |SturmHabichtSequence| |powers| |fintegrate| |d03eef| |partition| + |iomode| |factor1| |minColIndex| |youngDiagram| |bracket| + |makeViewport3D| |multinomial| |rotatex| |leftNorm| |nullSpace| + |addBadValue| |uniform01| |setLegalFortranSourceExtensions| |quartic| + |bipolarCylindrical| |d01fcf| |pmintegrate| |upperCase| + |jvmInterfaceMethodConstantTag| |curve?| |multiple| |any| |lambda| + |derivative| |sub| |top!| |commutative?| |debug| |transpose| |pair?| + |polarCoordinates| |permutationGroup| |OMputVariable| |zoom| + |applyQuote| |partialFraction| |symbol?| |safeFloor| |sincos| + |rangePascalTriangle| D |purelyAlgebraicLeadingMonomial?| |mpsode| + |c02agf| |superscript| |findConstructor| |linearlyDependentOverZ?| + |cyclotomicDecomposition| |unitVector| |dmpToHdmp| |RittWuCompare| + |factorial| |functionIsOscillatory| |scopes| |horizontalTab| + |external?| |setDifference| |e02bcf| |Lazard2| |OMputEndAttr| |lllip| + |qqq| |csubst| |sort!| |plusInfinity| |rightRecip| |trapezoidalo| + |qPot| |constantCoefficientRicDE| |ruleset| |predicate| + |raisePolynomial| |optpair| |numberOfImproperPartitions| |less?| + |reciprocalPolynomial| |algintegrate| |updatF| |minusInfinity| + |irCtor| |OMputEndObject| |complex?| |gcdPolynomial| |insertRoot!| + |convergents| |selectAndPolynomials| |fibonacci| + |factorSquareFreePolynomial| |basis| |charthRoot| |symmetricTensors| + |list?| |lfinfieldint| |commutator| |setright!| |zeroMatrix| + |FormatRoman| |meshPar1Var| |computeCycleLength| |groebSolve| + |perfectSquare?| |beauzamyBound| |normalizeIfCan| |suchThat| + |basisOfLeftAnnihilator| |empty| |monomials| |autoReduced?| + |nextSublist| |bivariateSLPEBR| |elseBranch| |surface| |gensym| + |quasiMonic?| |spherical| |divisors| |df2fi| |prime| + |lastSubResultant| |strongGenerators| |mkAnswer| |OMgetEndObject| + |setTex!| |setelt| |selectNonFiniteRoutines| |invmultisect| + |basisOfCommutingElements| |complexIntegrate| |getIdentifier| |type| + |selectFiniteRoutines| |exp1| |monic?| |nthFractionalTerm| + |stoseInvertibleSetreg| |rem| |squareTop| |toseInvertibleSet| + |ratPoly| |compdegd| |print| |concat!| |sizeMultiplication| + |curryRight| |lprop| |listConjugateBases| |atom?| |copy| |quo| + |halfExtendedResultant2| |wholeRadix| |ip4Address| |tubePointsDefault| + |close!| |resolve| |c06fqf| |overlap| |increasePrecision| |declare| + |lazyVariations| |univariateSolve| |setButtonValue| |Nul| |readUInt8!| + |Si| |redPol| |saturate| |numeric| |OMputObject| |debug3D| + |parameters| |div| |forLoop| |subHeight| |setPoly| |addPointLast| + |complexSolve| |primextintfrac| |genericLeftTraceForm| + |numberOfComposites| |imaginary| |inR?| |radical| |primintfldpoly| + |exquo| |measure2Result| |recur| |basisOfRightAnnihilator| |quote| + |bigEndian| |match?| |doubleComplex?| |factorList| |elem?| + |completeHermite| |cAsinh| |leastMonomial| ~= |derivationCoordinates| + |measure| |rootSplit| |dmp2rfi| |fortranCharacter| |printInfo!| + |leftFactor| |internal?| |minus!| |autoCoerce| |#| |edf2fi| |rCoord| + |reduceBasisAtInfinity| |getCurve| |s18acf| |tanNa| |stopMusserTrials| + |stoseIntegralLastSubResultant| |hypergeometric0F1| |pr2dmp| ~ + |laplace| |subResultantGcdEuclidean| |swap!| |rk4a| |generalLambert| + |createThreeSpace| |branchPoint?| |numFunEvals| |parametric?| + |getOperands| |divisorCascade| |direction| |read!| |children| + |augment| |length| |iiatan| |intermediateResultsIF| |alternating| + |bat| |coercePreimagesImages| |thetaCoord| |char| |elliptic| |failed?| + |flexible?| |conjugates| |entry?| |scripts| |box| |infRittWu?| + |OMgetError| |pToHdmp| |tablePow| |rootDirectory| |/\\| |f04asf| + |se2rfi| |selectfirst| |f02wef| |selectSumOfSquaresRoutines| + |generator| |stronglyReduced?| |clip| |factorFraction| |besselK| + |heap| |e02ahf| |\\/| |useNagFunctions| |minset| |innerSolve| + |SturmHabichtMultiple| |complement| |obj| |closeComponent| + |writeBytes!| |headReduce| |ptFunc| |satisfy?| |fracPart| |nil| + |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
\ No newline at end of file diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index f33eaa64..9e33c0d7 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,1047 +1,1047 @@ -(3472629 . 3499555805) -((-3587 (((-112) (-1 (-112) |#2| |#2|) $) 86 T ELT) (((-112) $) NIL T ELT)) (-3394 (($ (-1 (-112) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-4330 ((|#2| $ (-578) |#2|) NIL T ELT) ((|#2| $ (-1265 (-578)) |#2|) 44 T ELT)) (-3927 (($ $) 80 T ELT)) (-1483 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3275 (((-578) (-1 (-112) |#2|) $) 27 T ELT) (((-578) |#2| $) NIL T ELT) (((-578) |#2| $ (-578)) 96 T ELT)) (-3903 (((-666 |#2|) $) 13 T ELT)) (-4168 (($ (-1 (-112) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2198 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-2774 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-1537 (($ |#2| $ 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T) ((-107 #0=(-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T) ((-102) -2226 (|has| |#2| (-1131)) (|has| |#2| (-102)) (|has| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (-1131)) (|has| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (-871)) (|has| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (-102))) ((-632 (-886)) -2226 (|has| |#2| (-1131)) (|has| |#2| (-632 (-886))) (|has| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (-1131)) (|has| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (-871)) (|has| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (-632 (-886)))) ((-153 #1=(-2 (|:| -2339 |#1|) (|:| -2076 |#2|))) . T) ((-633 (-550)) |has| (-2 (|:| -2339 |#1|) (|:| -2076 |#2|)) (-633 (-550))) ((-233 #0#) . T) ((-242 #0#) . T) ((-298 #2=(-578) #1#) . T) ((-298 (-1265 (-578)) $) . T) ((-298 |#1| |#2|) . T) ((-300 #2# #1#) . T) ((-300 |#1| |#2|) . 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T) ((-236 $) -2225 (|has| |#1| (-362)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) -2225 (|has| |#1| (-362)) (|has| |#1| (-240))) ((-239) -2225 (|has| |#1| (-362)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-296) |has| |#1| (-1233)) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) -2225 (|has| |#1| (-570)) (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-319) -2225 (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-416) |has| |#1| (-362)) ((-381) -2225 (|has| |#1| (-381)) (|has| |#1| (-362))) ((-362) |has| |#1| (-362)) ((-383 |#1| #1#) . T) ((-423 |#1| #1#) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-414 |#1|) . T) ((-425 |#1|) . T) ((-466) -2225 (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-507) |has| |#1| (-1233)) ((-528 (-1207) |#1|) |has| |#1| (-528 (-1207) |#1|)) ((-528 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-570) -2225 (|has| |#1| (-570)) (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-668 #0#) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-670 #2=(-578)) |has| |#1| (-660 (-578))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-662 |#1|) . T) ((-662 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-660 #2#) |has| |#1| (-660 (-578))) ((-660 |#1|) . T) ((-739 #0#) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-739 |#1|) . T) ((-739 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-746 |#1| #1#) . T) ((-748) . T) ((-921 $ #3=(-1207)) -2225 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #3#) -2225 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-392)) |has| |#1| (-911 (-392))) ((-911 (-578)) |has| |#1| (-911 (-578))) ((-909 |#1|) . T) ((-938) -12 (|has| |#1| (-319)) (|has| |#1| (-938))) ((-949) -2225 (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1033) -12 (|has| |#1| (-1033)) (|has| |#1| (-1233))) ((-1069 (-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) ((-1069 (-578)) |has| |#1| (-1069 (-578))) ((-1069 |#1|) . T) ((-1082 #0#) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-1082 |#1|) . T) ((-1082 $) . T) ((-1087 #0#) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-1087 |#1|) . T) ((-1087 $) . T) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1183) |has| |#1| (-362)) ((-1233) |has| |#1| (-1233)) ((-1236) |has| |#1| (-1233)) ((-1248) . T) ((-1252) -2225 (|has| |#1| (-362)) (|has| |#1| (-376)) (-12 (|has| |#1| (-319)) (|has| |#1| (-938))))) +((-2614 (*1 *2 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) (-4388 (*1 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) (-3405 (*1 *1 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) (-1924 (*1 *1 *2 *2) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) (-1791 (*1 *2 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) (-1781 (*1 *2 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) (-4392 (*1 *1 *1 *2) (|partial| -12 (-4 *1 (-168 *2)) (-4 *2 (-175)) (-4 *2 (-570)))) (-2822 (*1 *1 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)) (-4 *2 (-1091)))) (-4119 (*1 *2 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)) (-4 *2 (-1233)))) (-4238 (*1 *2 *1) (-12 (-4 *1 (-168 *3)) (-4 *3 (-175)) (-4 *3 (-1091)) (-4 *3 (-1233)) (-5 *2 (-2 (|:| |r| *3) (|:| |phi| *3))))) (-3144 (*1 *2 *1) (-12 (-4 *1 (-168 *3)) (-4 *3 (-175)) (-4 *3 (-559)) (-5 *2 (-112)))) (-2154 (*1 *2 *1) (-12 (-4 *1 (-168 *3)) (-4 *3 (-175)) (-4 *3 (-559)) (-5 *2 (-421 (-578))))) (-2082 (*1 *2 *1) (|partial| -12 (-4 *1 (-168 *3)) (-4 *3 (-175)) (-4 *3 (-559)) (-5 *2 (-421 (-578)))))) +(-13 (-746 |t#1| (-1203 |t#1|)) (-425 |t#1|) (-234 |t#1|) (-351 |t#1|) (-414 |t#1|) (-909 |t#1|) (-390 |t#1|) (-175) (-10 -8 (-6 -1924) (-15 -4388 ($)) (-15 -3405 ($ $)) (-15 -1924 ($ |t#1| |t#1|)) (-15 -1791 (|t#1| $)) (-15 -1781 (|t#1| $)) (-15 -2614 (|t#1| $)) (IF (|has| |t#1| (-570)) (PROGN (-6 (-570)) (-15 -4392 ((-3 $ "failed") $ |t#1|))) |%noBranch|) (IF (|has| |t#1| (-319)) (-6 (-319)) |%noBranch|) (IF (|has| |t#1| (-6 -4507)) (-6 -4507) |%noBranch|) (IF (|has| |t#1| (-6 -4504)) (-6 -4504) |%noBranch|) (IF (|has| |t#1| (-376)) (-6 (-376)) |%noBranch|) (IF (|has| |t#1| (-633 (-550))) (-6 (-633 (-550))) |%noBranch|) (IF (|has| |t#1| (-149)) (-6 (-149)) |%noBranch|) (IF (|has| |t#1| (-147)) (-6 (-147)) |%noBranch|) (IF (|has| |t#1| (-1053)) (PROGN (-6 (-633 (-172 (-229)))) (-6 (-633 (-172 (-392))))) |%noBranch|) (IF (|has| |t#1| (-1091)) (-15 -2822 ($ $)) |%noBranch|) (IF (|has| |t#1| (-1233)) (PROGN (-6 (-1233)) (-15 -4119 (|t#1| $)) (IF (|has| |t#1| (-1033)) (-6 (-1033)) |%noBranch|) (IF (|has| |t#1| (-1091)) (-15 -4238 ((-2 (|:| |r| |t#1|) (|:| |phi| |t#1|)) $)) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (-559)) (PROGN (-15 -3144 ((-112) $)) (-15 -2154 ((-421 (-578)) $)) (-15 -2082 ((-3 (-421 (-578)) "failed") $))) |%noBranch|) (IF (|has| |t#1| (-938)) (IF (|has| |t#1| (-319)) (-6 (-938)) |%noBranch|) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-578))) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1233)) ((-95) |has| |#1| (-1233)) ((-102) . T) ((-111 #0# #0#) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -2226 (|has| |#1| (-362)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -2226 (|has| |#1| (-1069 (-421 (-578)))) (|has| |#1| (-362)) (|has| |#1| (-376))) ((-635 (-578)) . T) ((-635 |#1|) . T) ((-635 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-886)) . T) ((-175) . T) ((-633 (-172 (-229))) |has| |#1| (-1053)) ((-633 (-172 (-392))) |has| |#1| (-1053)) ((-633 (-550)) |has| |#1| (-633 (-550))) ((-633 (-917 (-392))) |has| |#1| (-633 (-917 (-392)))) ((-633 (-917 (-578))) |has| |#1| (-633 (-917 (-578)))) ((-633 #1=(-1203 |#1|)) . T) ((-236 $) -2226 (|has| |#1| (-362)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) -2226 (|has| |#1| (-362)) (|has| |#1| (-240))) ((-239) -2226 (|has| |#1| (-362)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-296) |has| |#1| (-1233)) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) -2226 (|has| |#1| (-570)) (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-319) -2226 (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-416) |has| |#1| (-362)) ((-381) -2226 (|has| |#1| (-381)) (|has| |#1| (-362))) ((-362) |has| |#1| (-362)) ((-383 |#1| #1#) . T) ((-423 |#1| #1#) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-414 |#1|) . T) ((-425 |#1|) . T) ((-466) -2226 (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-507) |has| |#1| (-1233)) ((-528 (-1207) |#1|) |has| |#1| (-528 (-1207) |#1|)) ((-528 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-570) -2226 (|has| |#1| (-570)) (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-668 #0#) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-670 #2=(-578)) |has| |#1| (-660 (-578))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-662 |#1|) . T) ((-662 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-660 #2#) |has| |#1| (-660 (-578))) ((-660 |#1|) . T) ((-739 #0#) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-739 |#1|) . T) ((-739 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-746 |#1| #1#) . T) ((-748) . T) ((-921 $ #3=(-1207)) -2226 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #3#) -2226 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-392)) |has| |#1| (-911 (-392))) ((-911 (-578)) |has| |#1| (-911 (-578))) ((-909 |#1|) . T) ((-938) -12 (|has| |#1| (-319)) (|has| |#1| (-938))) ((-949) -2226 (|has| |#1| (-362)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1033) -12 (|has| |#1| (-1033)) (|has| |#1| (-1233))) ((-1069 (-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) ((-1069 (-578)) |has| |#1| (-1069 (-578))) ((-1069 |#1|) . T) ((-1082 #0#) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-1082 |#1|) . T) ((-1082 $) . T) ((-1087 #0#) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-1087 |#1|) . T) ((-1087 $) . T) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1183) |has| |#1| (-362)) ((-1233) |has| |#1| (-1233)) ((-1236) |has| |#1| (-1233)) ((-1248) . 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(|has| $ (-6 -4508)) ELT))) (((-245 |#1| |#2|) (-142) (-793) (-1248)) (T -245)) -((-1799 (*1 *1 *2) (-12 (-5 *2 (-1298 *4)) (-4 *4 (-1248)) (-4 *1 (-245 *3 *4)))) (-2626 (*1 *1 *2) (-12 (-5 *2 (-950)) (-4 *1 (-245 *3 *4)) (-4 *4 (-1080)) (-4 *4 (-1248)))) (-2868 (*1 *2 *1 *1) (-12 (-4 *1 (-245 *3 *2)) (-4 *2 (-1248)) (-4 *2 (-1080))))) -(-13 (-618 (-578) |t#2|) (-632 (-1298 |t#2|)) (-10 -8 (-6 -4507) (-15 -1799 ($ (-1298 |t#2|))) (IF (|has| |t#2| (-1131)) (-6 (-425 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1080)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-234 |t#2|)) (-6 (-390 |t#2|)) (-15 -2626 ($ (-950))) (-15 -2868 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-133)) (-6 (-133)) |%noBranch|) (IF (|has| |t#2| (-23)) (-6 (-23)) |%noBranch|) (IF (|has| |t#2| (-21)) (-6 (-21)) |%noBranch|) (IF (|has| |t#2| (-748)) (-6 (-662 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-381)) (-6 (-381)) |%noBranch|) (IF (|has| |t#2| (-175)) (-6 (-739 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-6 -4504)) (-6 -4504) |%noBranch|) (IF (|has| |t#2| (-871)) (-6 (-871)) |%noBranch|) (IF (|has| |t#2| (-815)) (-6 (-815)) |%noBranch|) (IF (|has| |t#2| (-376)) (-6 (-1305 |t#2|)) |%noBranch|))) -(((-21) -2225 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-23) -2225 (|has| |#2| (-1080)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -2225 (|has| |#2| (-1080)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -2225 (|has| |#2| (-1131)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2225 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -2225 (|has| |#2| (-1080)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-578))) -12 (|has| |#2| (-1069 (-421 (-578)))) (|has| |#2| (-1131))) ((-635 (-578)) -2225 (|has| |#2| (-1080)) (-12 (|has| |#2| (-1069 (-578))) (|has| |#2| (-1131)))) ((-635 |#2|) |has| |#2| (-1131)) ((-632 (-886)) -2225 (|has| |#2| (-1131)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-886))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1298 |#2|)) . T) ((-236 $) -2225 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-234 |#2|) |has| |#2| (-1080)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1080))) ((-239) -2225 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-274 |#2|) |has| |#2| (-1080)) ((-298 #1=(-578) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1080)) ((-425 |#2|) |has| |#2| (-1131)) ((-503 |#2|) . T) ((-618 #1# |#2|) . T) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((-668 (-578)) -2225 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -2225 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1080)) ((-670 #2=(-578)) -12 (|has| |#2| (-660 (-578))) (|has| |#2| (-1080))) ((-670 |#2|) -2225 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1080)) ((-662 |#2|) -2225 (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-660 #2#) -12 (|has| |#2| (-660 (-578))) (|has| |#2| (-1080))) ((-660 |#2|) |has| |#2| (-1080)) ((-739 |#2|) -2225 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-748) |has| |#2| (-1080)) ((-814) |has| |#2| (-815)) ((-815) |has| |#2| (-815)) ((-816) |has| |#2| (-815)) ((-817) |has| |#2| (-815)) ((-871) -2225 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-874) -2225 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-921 $ #3=(-1207)) -2225 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-927 (-1207)) -12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) ((-929 #3#) -2225 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-1069 #0#) -12 (|has| |#2| (-1069 (-421 (-578)))) (|has| |#2| (-1131))) ((-1069 (-578)) -12 (|has| |#2| (-1069 (-578))) (|has| |#2| (-1131))) ((-1069 |#2|) |has| |#2| (-1131)) ((-1082 |#2|) -2225 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1087 |#2|) -2225 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1080) |has| |#2| (-1080)) ((-1089) |has| |#2| (-1080)) ((-1143) |has| |#2| (-1080)) ((-1131) -2225 (|has| |#2| (-1131)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1248) . T) ((-1305 |#2|) |has| |#2| (-376))) -((-3460 (((-247 |#1| |#3|) (-1 |#3| |#2| |#3|) (-247 |#1| |#2|) |#3|) 21 T ELT)) (-1483 ((|#3| (-1 |#3| |#2| |#3|) (-247 |#1| |#2|) |#3|) 23 T ELT)) (-2774 (((-247 |#1| |#3|) (-1 |#3| |#2|) (-247 |#1| |#2|)) 18 T ELT))) -(((-246 |#1| |#2| |#3|) (-10 -7 (-15 -3460 ((-247 |#1| |#3|) (-1 |#3| |#2| |#3|) (-247 |#1| |#2|) |#3|)) (-15 -1483 (|#3| (-1 |#3| |#2| |#3|) (-247 |#1| |#2|) |#3|)) (-15 -2774 ((-247 |#1| |#3|) (-1 |#3| |#2|) (-247 |#1| |#2|)))) (-793) (-1248) (-1248)) (T -246)) -((-2774 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-247 *5 *6)) (-14 *5 (-793)) (-4 *6 (-1248)) (-4 *7 (-1248)) (-5 *2 (-247 *5 *7)) (-5 *1 (-246 *5 *6 *7)))) (-1483 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-247 *5 *6)) (-14 *5 (-793)) (-4 *6 (-1248)) (-4 *2 (-1248)) (-5 *1 (-246 *5 *6 *2)))) (-3460 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-247 *6 *7)) (-14 *6 (-793)) (-4 *7 (-1248)) (-4 *5 (-1248)) (-5 *2 (-247 *6 *5)) (-5 *1 (-246 *6 *7 *5))))) 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|#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -2226 (|has| |#2| (-1080)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -2226 (|has| |#2| (-1131)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2226 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -2226 (|has| |#2| (-1080)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-578))) -12 (|has| |#2| (-1069 (-421 (-578)))) (|has| |#2| (-1131))) ((-635 (-578)) -2226 (|has| |#2| (-1080)) (-12 (|has| |#2| (-1069 (-578))) (|has| |#2| (-1131)))) ((-635 |#2|) |has| |#2| (-1131)) ((-632 (-886)) -2226 (|has| |#2| (-1131)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-886))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1298 |#2|)) . T) ((-236 $) -2226 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-234 |#2|) |has| |#2| (-1080)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1080))) ((-239) -2226 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-274 |#2|) |has| |#2| (-1080)) ((-298 #1=(-578) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1080)) ((-425 |#2|) |has| |#2| (-1131)) ((-503 |#2|) . T) ((-618 #1# |#2|) . T) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((-668 (-578)) -2226 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -2226 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1080)) ((-670 #2=(-578)) -12 (|has| |#2| (-660 (-578))) (|has| |#2| (-1080))) ((-670 |#2|) -2226 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1080)) ((-662 |#2|) -2226 (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-660 #2#) -12 (|has| |#2| (-660 (-578))) (|has| |#2| (-1080))) ((-660 |#2|) |has| |#2| (-1080)) ((-739 |#2|) -2226 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-748) |has| |#2| (-1080)) ((-814) |has| |#2| (-815)) ((-815) |has| |#2| (-815)) ((-816) |has| |#2| (-815)) ((-817) |has| |#2| (-815)) ((-871) -2226 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-874) -2226 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-921 $ #3=(-1207)) -2226 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-927 (-1207)) -12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) ((-929 #3#) -2226 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-1069 #0#) -12 (|has| |#2| (-1069 (-421 (-578)))) (|has| |#2| (-1131))) ((-1069 (-578)) -12 (|has| |#2| (-1069 (-578))) (|has| |#2| (-1131))) ((-1069 |#2|) |has| |#2| (-1131)) ((-1082 |#2|) -2226 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1087 |#2|) -2226 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1080) |has| |#2| (-1080)) ((-1089) |has| |#2| (-1080)) ((-1143) |has| |#2| (-1080)) ((-1131) -2226 (|has| |#2| (-1131)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1248) . T) ((-1305 |#2|) |has| |#2| (-376))) +((-3659 (((-247 |#1| |#3|) (-1 |#3| |#2| |#3|) (-247 |#1| |#2|) |#3|) 21 T ELT)) (-1483 ((|#3| (-1 |#3| |#2| |#3|) (-247 |#1| |#2|) |#3|) 23 T ELT)) (-2775 (((-247 |#1| |#3|) (-1 |#3| |#2|) (-247 |#1| |#2|)) 18 T ELT))) +(((-246 |#1| |#2| |#3|) (-10 -7 (-15 -3659 ((-247 |#1| |#3|) (-1 |#3| |#2| |#3|) (-247 |#1| |#2|) |#3|)) (-15 -1483 (|#3| (-1 |#3| |#2| |#3|) (-247 |#1| |#2|) |#3|)) (-15 -2775 ((-247 |#1| |#3|) (-1 |#3| |#2|) (-247 |#1| |#2|)))) (-793) (-1248) (-1248)) (T -246)) +((-2775 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-247 *5 *6)) (-14 *5 (-793)) (-4 *6 (-1248)) (-4 *7 (-1248)) (-5 *2 (-247 *5 *7)) (-5 *1 (-246 *5 *6 *7)))) (-1483 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-247 *5 *6)) (-14 *5 (-793)) (-4 *6 (-1248)) (-4 *2 (-1248)) (-5 *1 (-246 *5 *6 *2)))) (-3659 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-247 *6 *7)) (-14 *6 (-793)) (-4 *7 (-1248)) (-4 *5 (-1248)) (-5 *2 (-247 *6 *5)) (-5 *1 (-246 *6 *7 *5))))) +(-10 -7 (-15 -3659 ((-247 |#1| |#3|) (-1 |#3| |#2| |#3|) (-247 |#1| |#2|) |#3|)) (-15 -1483 (|#3| (-1 |#3| |#2| |#3|) (-247 |#1| |#2|) |#3|)) (-15 -2775 ((-247 |#1| |#3|) (-1 |#3| |#2|) (-247 |#1| |#2|)))) +((-4405 (((-112) $ $) NIL (|has| |#2| (-102)) ELT)) (-2972 (((-112) $) NIL (|has| |#2| (-23)) ELT)) (-4256 (($ (-950)) 62 (|has| |#2| (-1080)) ELT)) (-4430 (((-1303) $ (-578) (-578)) NIL (|has| $ (-6 -4509)) ELT)) (-3238 (($ $ $) 68 (|has| |#2| (-815)) ELT)) (-1818 (((-3 $ "failed") $ $) 53 (|has| |#2| (-133)) ELT)) (-3779 (((-112) $ (-793)) NIL T ELT)) (-1572 (((-793)) NIL (|has| |#2| (-381)) ELT)) (-4331 ((|#2| $ (-578) |#2|) NIL (|has| $ (-6 -4509)) ELT)) (-2818 (($) NIL T CONST)) (-2724 (((-3 (-578) "failed") $) NIL (-12 (|has| |#2| (-1069 (-578))) (|has| |#2| (-1131))) ELT) (((-3 (-421 (-578)) "failed") $) NIL (-12 (|has| |#2| (-1069 (-421 (-578)))) (|has| |#2| (-1131))) ELT) (((-3 |#2| "failed") $) 30 (|has| |#2| (-1131)) ELT)) (-2589 (((-578) $) NIL (-12 (|has| |#2| (-1069 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-578)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2225 (|has| |#1| (-1069 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578))))) ((-635 (-578)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-632 (-886)) . T) ((-175) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-550)) -12 (|has| |#1| (-633 (-550))) (|has| |#3| (-633 (-550)))) ((-633 (-917 (-392))) -12 (|has| |#1| (-633 (-917 (-392)))) (|has| |#3| (-633 (-917 (-392))))) ((-633 (-917 (-578))) -12 (|has| |#1| (-633 (-917 (-578)))) (|has| |#3| (-633 (-917 (-578))))) ((-236 $) -2225 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2225 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-425 |#1|) . T) ((-466) -2225 (|has| |#1| (-938)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-570) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-578)))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-578)))) ((-670 #1=(-578)) |has| |#1| (-660 (-578))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-578)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-578))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-578)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1207)) -2225 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-921 $ |#3|) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-927 |#3|) . T) ((-929 #2#) -2225 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-929 |#3|) . T) ((-911 (-392)) -12 (|has| |#1| (-911 (-392))) (|has| |#3| (-911 (-392)))) ((-911 (-578)) -12 (|has| |#1| (-911 (-578))) (|has| |#3| (-911 (-578)))) ((-978 |#1| |#4| |#3|) . T) ((-938) |has| |#1| (-938)) ((-1069 (-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) ((-1069 (-578)) |has| |#1| (-1069 (-578))) ((-1069 |#1|) . T) ((-1069 |#2|) . T) ((-1069 |#3|) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-578)))) ((-1082 |#1|) . T) ((-1082 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-578)))) ((-1087 |#1|) . T) ((-1087 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1248) . T) ((-1252) |has| |#1| (-938))) -((-4404 (((-112) $ $) 20 (|has| |#1| (-102)) ELT)) (-3718 ((|#1| $) 55 T ELT)) (-3459 ((|#1| $) 45 T ELT)) (-1933 (((-112) $ (-793)) 8 T ELT)) (-4425 (($) 7 T CONST)) (-2432 (($ $) 61 T ELT)) (-3927 (($ $) 49 T ELT)) (-2534 ((|#1| |#1| $) 47 T ELT)) (-1630 ((|#1| $) 46 T ELT)) (-3903 (((-666 |#1|) $) 31 (|has| $ (-6 -4507)) ELT)) (-2445 (((-112) $ (-793)) 9 T ELT)) (-3296 (((-666 |#1|) $) 30 (|has| $ (-6 -4507)) ELT)) (-2446 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1131)) (|has| $ (-6 -4507))) ELT)) (-2198 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4508)) ELT)) (-2774 (($ (-1 |#1| |#1|) $) 36 T ELT)) (-2629 (((-112) $ (-793)) 10 T ELT)) (-4442 (((-793) $) 62 T ELT)) (-1377 (((-1189) $) 23 (|has| |#1| (-1131)) ELT)) (-3828 ((|#1| $) 40 T ELT)) (-1999 ((|#1| |#1| $) 53 T ELT)) (-4106 ((|#1| |#1| $) 52 T ELT)) (-1470 (($ |#1| $) 41 T ELT)) (-1562 (((-793) $) 56 T ELT)) (-2363 (((-1151) $) 22 (|has| |#1| (-1131)) ELT)) (-4103 ((|#1| $) 63 T ELT)) (-1730 ((|#1| $) 51 T ELT)) (-1732 ((|#1| $) 50 T ELT)) (-3509 ((|#1| $) 42 T ELT)) (-3658 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4507)) ELT)) (-1450 (($ $ (-666 (-306 |#1|))) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ELT) (($ $ (-306 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ELT) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ELT) (($ $ (-666 |#1|) (-666 |#1|)) 24 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ELT)) (-2769 (((-112) $ $) 14 T ELT)) (-1644 ((|#1| |#1| $) 59 T ELT)) (-1839 (((-112) $) 11 T ELT)) (-2955 (($) 12 T ELT)) (-3190 ((|#1| $) 60 T ELT)) (-2047 (($) 58 T ELT) (($ (-666 |#1|)) 57 T ELT)) (-2240 (((-793) $) 44 T ELT)) (-2372 (((-793) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4507)) ELT) (((-793) |#1| $) 29 (-12 (|has| |#1| (-1131)) (|has| $ (-6 -4507))) ELT)) (-4354 (($ $) 13 T ELT)) (-2863 (((-886) $) 18 (|has| |#1| (-632 (-886))) ELT)) (-3174 ((|#1| $) 54 T ELT)) (-3793 (((-112) $ $) 21 (|has| |#1| (-102)) ELT)) (-2500 (($ (-666 |#1|)) 43 T ELT)) (-3743 ((|#1| $) 64 T ELT)) (-2840 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4507)) ELT)) (-2353 (((-112) $ $) 19 (|has| |#1| (-102)) ELT)) (-4415 (((-793) $) 6 (|has| $ (-6 -4507)) ELT))) +((-3854 (*1 *2 *3) (-12 (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *4 *3 *5 *6)))) (-2473 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-666 *4)))) (-2617 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-2617 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-793)))) (-3489 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-2773 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-666 (-793))))) (-3437 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-793)))) (-2773 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-666 (-793))))) (-3437 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-3615 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-112)))) (-2678 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-815)) (-4 *2 (-277 *4)))) (-1765 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-4149 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-3854 (*1 *2 *1) (-12 (-4 *3 (-240)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *3 *4 *5 *6))))) +(-13 (-978 |t#1| |t#4| |t#3|) (-234 |t#1|) (-1069 |t#2|) (-10 -8 (-15 -3854 ((-1 $ (-793)) |t#2|)) (-15 -2473 ((-666 |t#2|) $)) (-15 -2617 ((-793) $ |t#2|)) (-15 -2617 ((-793) $)) (-15 -3489 ((-793) $ |t#2|)) (-15 -2773 ((-666 (-793)) $)) (-15 -3437 ((-793) $)) (-15 -2773 ((-666 (-793)) $ |t#2|)) (-15 -3437 ((-793) $ |t#2|)) (-15 -3615 ((-112) $)) (-15 -2678 (|t#3| $)) (-15 -1765 ($ $)) (-15 -4149 ($ $)) (IF (|has| |t#1| (-240)) (PROGN (-6 (-528 |t#2| |t#1|)) (-6 (-528 |t#2| $)) (-6 (-321 $)) (-15 -3854 ((-1 $ (-793)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-578)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2226 (|has| |#1| (-1069 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578))))) ((-635 (-578)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-632 (-886)) . T) ((-175) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-550)) -12 (|has| |#1| (-633 (-550))) (|has| |#3| (-633 (-550)))) ((-633 (-917 (-392))) -12 (|has| |#1| (-633 (-917 (-392)))) (|has| |#3| (-633 (-917 (-392))))) ((-633 (-917 (-578))) -12 (|has| |#1| (-633 (-917 (-578)))) (|has| |#3| (-633 (-917 (-578))))) ((-236 $) -2226 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2226 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-425 |#1|) . T) ((-466) -2226 (|has| |#1| (-938)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-570) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-578)))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-578)))) ((-670 #1=(-578)) |has| |#1| (-660 (-578))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-578)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-578))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-578)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1207)) -2226 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-921 $ |#3|) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-927 |#3|) . T) ((-929 #2#) -2226 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-929 |#3|) . T) ((-911 (-392)) -12 (|has| |#1| (-911 (-392))) (|has| |#3| (-911 (-392)))) ((-911 (-578)) -12 (|has| |#1| (-911 (-578))) (|has| |#3| (-911 (-578)))) ((-978 |#1| |#4| |#3|) . T) ((-938) |has| |#1| (-938)) ((-1069 (-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) ((-1069 (-578)) |has| |#1| (-1069 (-578))) ((-1069 |#1|) . T) ((-1069 |#2|) . T) ((-1069 |#3|) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-578)))) ((-1082 |#1|) . T) ((-1082 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-578)))) ((-1087 |#1|) . T) ((-1087 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1248) . 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T) ((-570) |has| |#1| (-570)) ((-668 #0#) |has| |#1| (-570)) ((-668 (-578)) -2226 (|has| |#1| (-1080)) (|has| |#1| (-570)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-21))) ((-668 |#1|) -2226 (|has| |#1| (-1080)) (|has| |#1| (-175))) ((-668 $) -2226 (|has| |#1| (-1080)) (|has| |#1| (-570)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-670 #0#) |has| |#1| (-570)) ((-670 #5=(-578)) -12 (|has| |#1| (-660 (-578))) (|has| |#1| (-1080))) ((-670 |#1|) -2226 (|has| |#1| (-1080)) (|has| |#1| (-175))) ((-670 $) -2226 (|has| |#1| (-1080)) (|has| |#1| (-570)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-662 #0#) |has| |#1| (-570)) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) |has| |#1| (-570)) ((-660 #5#) -12 (|has| |#1| (-660 (-578))) (|has| |#1| (-1080))) ((-660 |#1|) |has| |#1| (-1080)) ((-739 #0#) |has| |#1| (-570)) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) |has| |#1| (-570)) ((-748) -2226 (|has| |#1| (-1143)) (|has| |#1| (-1080)) (|has| |#1| (-570)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-921 $ #6=(-1207)) |has| |#1| (-1080)) ((-927 #6#) |has| |#1| (-1080)) ((-929 #6#) |has| |#1| (-1080)) ((-911 (-392)) |has| |#1| (-911 (-392))) ((-911 (-578)) |has| |#1| (-911 (-578))) ((-909 |#1|) . T) ((-949) |has| |#1| (-570)) ((-1069 (-421 (-578))) -2226 (|has| |#1| (-1069 (-421 (-578)))) (-12 (|has| |#1| (-570)) (|has| |#1| (-1069 (-578))))) ((-1069 #1#) |has| |#1| (-570)) ((-1069 (-578)) |has| |#1| (-1069 (-578))) ((-1069 #2#) . T) ((-1069 #3#) |has| |#1| (-1080)) ((-1069 #4#) . T) ((-1069 |#1|) . T) ((-1082 #0#) |has| |#1| (-570)) ((-1082 |#1|) |has| |#1| (-175)) ((-1082 $) |has| |#1| (-570)) ((-1087 #0#) |has| |#1| (-570)) ((-1087 |#1|) |has| |#1| (-175)) ((-1087 $) |has| |#1| (-570)) ((-1080) -2226 (|has| |#1| (-1080)) (|has| |#1| (-570)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1089) -2226 (|has| |#1| (-1080)) (|has| |#1| (-570)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1143) -2226 (|has| |#1| (-1143)) (|has| |#1| (-1080)) (|has| |#1| (-570)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1131) . T) ((-1248) . 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|lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -1470 ($ (-2 (|:| -2338 (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) (|:| -3026 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2079 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1188 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -3026 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| 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T) ((-236 $) -2225 (|has| |#1| (-362)) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-234 |#1|) |has| |#1| (-376)) ((-240) -2225 (|has| |#1| (-362)) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-239) -2225 (|has| |#1| (-362)) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-274 |#1|) |has| |#1| (-376)) ((-250) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-302) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-319) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-376) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-416) |has| |#1| (-362)) ((-381) -2225 (|has| |#1| (-381)) (|has| |#1| (-362))) ((-362) |has| |#1| (-362)) ((-383 |#1| |#2|) . T) ((-423 |#1| |#2|) . T) ((-390 |#1|) . T) ((-425 |#1|) . T) ((-466) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-570) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-668 #0#) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-670 #1=(-578)) |has| |#1| (-660 (-578))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-662 |#1|) . T) ((-662 $) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-660 #1#) |has| |#1| (-660 (-578))) ((-660 |#1|) . T) ((-739 #0#) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-739 |#1|) . T) ((-739 $) -2225 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-748) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-578))) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-102) . T) ((-111 #0# #0#) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -2226 (|has| |#1| (-362)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -2226 (|has| |#1| (-1069 (-421 (-578)))) (|has| |#1| (-362)) (|has| |#1| (-376))) ((-635 (-578)) . T) ((-635 |#1|) . T) ((-635 $) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-632 (-886)) . T) ((-175) . T) ((-633 |#2|) . T) ((-236 $) -2226 (|has| |#1| (-362)) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-234 |#1|) |has| |#1| (-376)) ((-240) -2226 (|has| |#1| (-362)) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-239) -2226 (|has| |#1| (-362)) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-274 |#1|) |has| |#1| (-376)) ((-250) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-302) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-319) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-376) -2226 (|has| |#1| (-362)) (|has| |#1| (-376))) ((-416) |has| |#1| (-362)) ((-381) -2226 (|has| |#1| (-381)) (|has| |#1| (-362))) ((-362) |has| |#1| (-362)) ((-383 |#1| |#2|) . T) ((-423 |#1| |#2|) . T) ((-390 |#1|) . T) ((-425 |#1|) . 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-570)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-578)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2226 (|has| |#1| (-570)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) |has| |#1| (-38 (-421 (-578)))) ((-635 (-578)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-570)) ((-632 (-886)) . T) ((-175) -2226 (|has| |#1| (-570)) (|has| |#1| (-175))) ((-302) |has| |#1| (-570)) ((-570) |has| |#1| (-570)) ((-668 #0#) |has| |#1| (-38 (-421 (-578)))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-578)))) ((-670 |#1|) . T) ((-670 $) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-578))) . T) ((-38 |#1|) . T) ((-38 $) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) . T) ((-635 (-578)) . T) ((-635 #1=(-1207)) |has| |#1| (-1069 (-1207))) ((-635 |#1|) . T) ((-635 $) . T) ((-632 (-886)) . T) ((-175) . T) ((-633 (-229)) |has| |#1| (-1053)) ((-633 (-392)) |has| |#1| (-1053)) ((-633 (-550)) |has| |#1| (-633 (-550))) ((-633 (-917 (-392))) |has| |#1| (-633 (-917 (-392)))) ((-633 (-917 (-578))) |has| |#1| (-633 (-917 (-578)))) ((-236 $) -2226 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2226 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) . T) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) . T) ((-319) . T) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-414 |#1|) . T) ((-466) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-578))) |has| |#1| (-376)) ((-38 |#1|) . T) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-376)) ((-111 |#1| |#1|) . T) ((-111 $ $) -2226 (|has| |#1| (-376)) (|has| |#1| (-302))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2226 (|has| |#1| (-1069 (-421 (-578)))) (|has| |#1| (-376))) ((-635 (-578)) . T) ((-635 |#1|) . T) ((-632 (-886)) . T) ((-633 (-550)) |has| |#1| (-633 (-550))) ((-236 $) -2226 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2226 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) |has| |#1| (-376)) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) -2226 (|has| |#1| (-376)) (|has| |#1| (-302))) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-425 |#1|) . T) ((-528 (-1207) |#1|) |has| |#1| (-528 (-1207) |#1|)) ((-528 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-668 #0#) |has| |#1| (-376)) ((-668 (-578)) . 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T) ((-102) -2226 (|has| |#1| (-1131)) (|has| |#1| (-102))) ((-632 (-886)) -2226 (|has| |#1| (-1131)) (|has| |#1| (-632 (-886)))) ((-153 |#1|) . T) ((-633 (-550)) |has| |#1| (-633 (-550))) ((-298 #0=(-578) |#1|) . T) ((-298 (-1265 (-578)) $) . T) ((-300 #0# |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ((-503 |#1|) . T) ((-618 #0# |#1|) . T) ((-528 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ((-673 |#1|) . T) ((-1041 |#1|) . T) ((-1131) |has| |#1| (-1131)) ((-1248) . T) ((-1286 |#1|) . 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T) ((-662 #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-739 #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2=(-1207)) -12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) -12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207)))) ((-929 #2#) -12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207)))) ((-1004 |#1| #0# (-1113)) . T) ((-949) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-578)))) ((-1082 #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-1082 |#1|) . T) ((-1082 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-1087 |#1|) . T) ((-1087 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1233) |has| |#1| (-38 (-421 (-578)))) ((-1236) |has| |#1| (-38 (-421 (-578)))) ((-1248) . T) ((-1252) |has| |#1| (-376)) ((-1276 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-578)) . T) ((-25) . T) ((-38 #1=(-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-578)))) ((-95) |has| |#1| (-38 (-421 (-578)))) ((-102) . T) ((-111 #1# #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-635 (-578)) . T) ((-635 #2=(-1207)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-632 (-886)) . T) ((-175) -2225 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-633 (-392)) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-633 (-550)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-550)))) ((-633 (-917 (-392))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-917 (-392))))) ((-633 (-917 (-578))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-917 (-578))))) ((-236 $) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-239) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-578)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-578) (-1143)) ((-302) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-578)))) ((-528 (-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-570) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-668 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-670 #3=(-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-578)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-578)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-748) . T) ((-813) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-817) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-870) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-871) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-874) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-921 $ #4=(-1207)) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-927 (-1207)) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-929 #4#) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-911 (-392)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-392)))) ((-911 (-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-578)))) ((-909 |#2|) |has| |#1| (-376)) ((-938) -12 (|has| |#1| (-376)) (|has| |#2| (-938))) ((-1004 |#1| #0# (-1113)) . T) ((-949) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-578)))) ((-1053) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-1069 (-421 (-578))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-578)))) ((-1069 (-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-578)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-1069 |#2|) . T) ((-1082 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1183) -12 (|has| |#1| (-376)) (|has| |#2| (-1183))) ((-1233) |has| |#1| (-38 (-421 (-578)))) ((-1236) |has| |#1| (-38 (-421 (-578)))) ((-1248) . T) ((-1252) |has| |#1| (-376)) ((-1258 |#1|) . T) ((-1276 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-578)) . T) ((-25) . T) ((-38 #1=(-421 (-578))) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-578)))) ((-95) |has| |#1| (-38 (-421 (-578)))) ((-102) . T) ((-111 #1# #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2226 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2226 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2226 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-635 (-578)) . T) ((-635 #2=(-1207)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-632 (-886)) . T) ((-175) -2226 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-633 (-392)) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-633 (-550)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-550)))) ((-633 (-917 (-392))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-917 (-392))))) ((-633 (-917 (-578))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-917 (-578))))) ((-236 $) -2226 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -2226 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-239) -2226 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-578)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-578) (-1143)) ((-302) -2226 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-578)))) ((-528 (-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-570) -2226 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-668 #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-670 #3=(-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-578)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-578)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-748) . T) ((-813) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-817) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-870) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-871) -2226 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-874) -2226 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-921 $ #4=(-1207)) -2226 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-927 (-1207)) -2226 (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-929 #4#) -2226 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-911 (-392)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-392)))) ((-911 (-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-578)))) ((-909 |#2|) |has| |#1| (-376)) ((-938) -12 (|has| |#1| (-376)) (|has| |#2| (-938))) ((-1004 |#1| #0# (-1113)) . T) ((-949) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-578)))) ((-1053) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-1069 (-421 (-578))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-578)))) ((-1069 (-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-578)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-1069 |#2|) . T) ((-1082 #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2226 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2226 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1183) -12 (|has| |#1| (-376)) (|has| |#2| (-1183))) ((-1233) |has| |#1| (-38 (-421 (-578)))) ((-1236) |has| |#1| (-38 (-421 (-578)))) ((-1248) . T) ((-1252) |has| |#1| (-376)) ((-1258 |#1|) . T) ((-1276 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-578)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2225 (|has| |#1| (-1069 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578))))) ((-635 (-578)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-886)) . T) ((-175) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-550)) -12 (|has| (-1113) (-633 (-550))) (|has| |#1| (-633 (-550)))) ((-633 (-917 (-392))) -12 (|has| (-1113) (-633 (-917 (-392)))) (|has| |#1| (-633 (-917 (-392))))) ((-633 (-917 (-578))) -12 (|has| (-1113) (-633 (-917 (-578)))) (|has| |#1| (-633 (-917 (-578))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-570)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-425 |#1|) . T) ((-466) -2225 (|has| |#1| (-938)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-570) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-578)))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-578)))) ((-670 #3=(-578)) |has| |#1| (-660 (-578))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-578)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-578))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-578)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1207)) -2225 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #2#) . T) ((-929 #4#) -2225 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-392)) -12 (|has| (-1113) (-911 (-392))) (|has| |#1| (-911 (-392)))) ((-911 (-578)) -12 (|has| (-1113) (-911 (-578))) (|has| |#1| (-911 (-578)))) ((-978 |#1| #0# #2#) . T) ((-938) |has| |#1| (-938)) ((-949) |has| |#1| (-376)) ((-1069 (-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) ((-1069 (-578)) |has| |#1| (-1069 (-578))) ((-1069 #2#) . T) ((-1069 |#1|) . T) ((-1082 #1#) |has| |#1| (-38 (-421 (-578)))) ((-1082 |#1|) . T) ((-1082 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-578)))) ((-1087 |#1|) . T) ((-1087 $) -2225 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1183) |has| |#1| (-1183)) ((-1248) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-578)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2226 (|has| |#1| (-1069 (-421 (-578)))) (|has| |#1| (-38 (-421 (-578))))) ((-635 (-578)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-886)) . T) ((-175) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-550)) -12 (|has| (-1113) (-633 (-550))) (|has| |#1| (-633 (-550)))) ((-633 (-917 (-392))) -12 (|has| (-1113) (-633 (-917 (-392)))) (|has| |#1| (-633 (-917 (-392))))) ((-633 (-917 (-578))) -12 (|has| (-1113) (-633 (-917 (-578)))) (|has| |#1| (-633 (-917 (-578))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-570)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-425 |#1|) . T) ((-466) -2226 (|has| |#1| (-938)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-570) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-578)))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-578)))) ((-670 #3=(-578)) |has| |#1| (-660 (-578))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-578)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-578))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-578)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1207)) -2226 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #2#) . T) ((-929 #4#) -2226 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-392)) -12 (|has| (-1113) (-911 (-392))) (|has| |#1| (-911 (-392)))) ((-911 (-578)) -12 (|has| (-1113) (-911 (-578))) (|has| |#1| (-911 (-578)))) ((-978 |#1| #0# #2#) . T) ((-938) |has| |#1| (-938)) ((-949) |has| |#1| (-376)) ((-1069 (-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) ((-1069 (-578)) |has| |#1| (-1069 (-578))) ((-1069 #2#) . T) ((-1069 |#1|) . T) ((-1082 #1#) |has| |#1| (-38 (-421 (-578)))) ((-1082 |#1|) . T) ((-1082 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-578)))) ((-1087 |#1|) . T) ((-1087 $) -2226 (|has| |#1| (-938)) (|has| |#1| (-570)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1183) |has| |#1| (-1183)) ((-1248) . T) ((-1252) |has| |#1| (-938))) +((-1879 (((-666 (-1113)) $) 34 T ELT)) (-2044 (($ $) 31 T ELT)) (-1859 (($ |#2| |#3|) NIL T ELT) (($ $ (-1113) |#3|) 28 T ELT) (($ $ (-666 (-1113)) (-666 |#3|)) 27 T ELT)) (-2011 (($ $) 14 T ELT)) (-2022 ((|#2| $) 12 T ELT)) (-3489 ((|#3| $) 10 T ELT))) +(((-1275 |#1| |#2| |#3|) (-10 -8 (-15 -1879 ((-666 (-1113)) |#1|)) (-15 -1859 (|#1| |#1| (-666 (-1113)) (-666 |#3|))) (-15 -1859 (|#1| |#1| (-1113) |#3|)) (-15 -2044 (|#1| |#1|)) (-15 -1859 (|#1| |#2| |#3|)) (-15 -3489 (|#3| |#1|)) (-15 -2011 (|#1| |#1|)) (-15 -2022 (|#2| |#1|))) (-1276 |#2| |#3|) (-1080) (-814)) (T -1275)) +NIL +(-10 -8 (-15 -1879 ((-666 (-1113)) |#1|)) (-15 -1859 (|#1| |#1| (-666 (-1113)) (-666 |#3|))) (-15 -1859 (|#1| |#1| (-1113) |#3|)) (-15 -2044 (|#1| |#1|)) (-15 -1859 (|#1| |#2| |#3|)) (-15 -3489 (|#3| |#1|)) (-15 -2011 (|#1| |#1|)) (-15 -2022 (|#2| |#1|))) +((-4405 (((-112) $ $) 7 T ELT)) (-2972 (((-112) $) 17 T ELT)) (-1879 (((-666 (-1113)) $) 86 T ELT)) (-1518 (((-1207) $) 118 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(-814)))) (-4245 (*1 *1 *1 *2 *2) (-12 (-4 *1 (-1276 *3 *2)) (-4 *3 (-1080)) (-4 *2 (-814)))) (-1915 (*1 *2 *1 *3) (-12 (-4 *1 (-1276 *2 *3)) (-4 *3 (-814)) (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -2863 (*2 (-1207)))) (-4 *2 (-1080)))) (-1998 (*1 *1 *1 *2) (-12 (-4 *1 (-1276 *3 *2)) (-4 *3 (-1080)) (-4 *2 (-814)))) (-1450 (*1 *2 *1 *3) (-12 (-4 *1 (-1276 *3 *4)) (-4 *3 (-1080)) (-4 *4 (-814)) (|has| *3 (-15 ** (*3 *3 *4))) (-5 *2 (-1188 *3))))) -(-13 (-1004 |t#1| |t#2| (-1113)) (-298 |t#2| |t#1|) (-10 -8 (-15 -3510 ((-1188 (-2 (|:| |k| |t#2|) (|:| |c| |t#1|))) $)) (-15 -1518 ((-1207) $)) (-15 -1731 (|t#1| $)) (-15 -1625 ($ $ (-950))) (-15 -4406 (|t#2| $)) (-15 -4406 (|t#2| $ |t#2|)) (-15 -4245 ($ $ |t#2|)) (-15 -4245 ($ $ |t#2| |t#2|)) (IF (|has| |t#1| (-15 -2863 (|t#1| (-1207)))) (IF (|has| |t#1| (-15 ** (|t#1| |t#1| |t#2|))) (-15 -1915 (|t#1| $ |t#2|)) |%noBranch|) |%noBranch|) (-15 -1998 ($ $ |t#2|)) (IF (|has| |t#2| (-1143)) (-6 (-298 $ $)) |%noBranch|) (IF (|has| |t#1| (-15 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-570)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-578)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2225 (|has| |#1| (-570)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) |has| |#1| (-38 (-421 (-578)))) ((-635 (-578)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-570)) ((-632 (-886)) . T) ((-175) -2225 (|has| |#1| (-570)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-240) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-239) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-298 |#2| |#1|) . T) ((-298 $ $) |has| |#2| (-1143)) ((-302) |has| |#1| (-570)) ((-570) |has| |#1| (-570)) ((-668 #0#) |has| |#1| (-38 (-421 (-578)))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-578)))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-578)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) |has| |#1| (-570)) ((-739 #0#) |has| |#1| (-38 (-421 (-578)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) |has| |#1| (-570)) ((-748) . T) ((-921 $ #1=(-1207)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-927 (-1207)))) ((-927 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-927 (-1207)))) ((-929 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-927 (-1207)))) ((-1004 |#1| |#2| (-1113)) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-578)))) ((-1082 |#1|) . T) ((-1082 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-578)))) ((-1087 |#1|) . T) ((-1087 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-175))) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1248) . 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NIL) (-1297 3382059 3382342 3382660 "VECTOR2" 3383236 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1296 3375013 3379763 3379806 "VECTCAT" 3380801 NIL VECTCAT (NIL T) -9 NIL 3381388 NIL) (-1295 3373955 3374281 3374671 "VECTCAT-" 3374676 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3373361 3373606 3373726 "VARIABLE" 3373870 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3373294 3373299 3373329 "UTYPE" 3373334 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3372102 3372278 3372540 "UTSODETL" 3373120 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3369494 3370002 3370526 "UTSODE" 3371643 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3360804 3367255 3367735 "UTS" 3369072 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1289 3350811 3356737 3356780 "UTSCAT" 3357892 NIL UTSCAT (NIL T) -9 NIL 3358650 NIL) (-1288 3347937 3348881 3349870 "UTSCAT-" 3349875 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1287 3347558 3347607 3347740 "UTS2" 3347888 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1286 3341425 3344368 3344411 "URAGG" 3346481 NIL URAGG (NIL T) -9 NIL 3347204 NIL) (-1285 3338148 3339227 3340350 "URAGG-" 3340355 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3333517 3336783 3337248 "UPXSSING" 3337812 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3324995 3332899 3333163 "UPXS" 3333311 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1282 3317410 3324899 3324971 "UPXSCONS" 3324976 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1281 3306158 3313612 3313674 "UPXSCCA" 3314248 NIL UPXSCCA (NIL T T) -9 NIL 3314481 NIL) (-1280 3305778 3305881 3306055 "UPXSCCA-" 3306060 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1279 3294426 3301605 3301648 "UPXSCAT" 3302296 NIL UPXSCAT (NIL T) -9 NIL 3302905 NIL) (-1278 3293850 3293935 3294114 "UPXS2" 3294341 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1277 3292486 3292757 3293108 "UPSQFREE" 3293593 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3285314 3288752 3288807 "UPSCAT" 3289887 NIL UPSCAT (NIL T T) -9 NIL 3290653 NIL) (-1275 3284470 3284725 3285052 "UPSCAT-" 3285057 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3268604 3277597 3277640 "UPOLYC" 3279741 NIL UPOLYC (NIL T) -9 NIL 3280962 NIL) (-1273 3259452 3262358 3265505 "UPOLYC-" 3265510 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1272 3259073 3259122 3259255 "UPOLYC2" 3259403 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1271 3249648 3258756 3258885 "UP" 3258992 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1270 3248969 3249094 3249258 "UPMP" 3249537 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1269 3248516 3248603 3248742 "UPDIVP" 3248882 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1268 3247054 3247333 3247649 "UPDECOMP" 3248265 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1267 3246267 3246397 3246583 "UPCDEN" 3246938 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1266 3245780 3245855 3246004 "UP2" 3246192 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1265 3244133 3244984 3245261 "UNISEG" 3245538 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1264 3243338 3243475 3243680 "UNISEG2" 3243976 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1263 3242380 3242578 3242804 "UNIFACT" 3243154 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3224190 3241692 3241934 "ULS" 3242196 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3210900 3224094 3224166 "ULSCONS" 3224171 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3190700 3203980 3204042 "ULSCCAT" 3204680 NIL ULSCCAT (NIL T T) -9 NIL 3204969 NIL) (-1259 3189696 3189995 3190383 "ULSCCAT-" 3190388 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1258 3178141 3185242 3185285 "ULSCAT" 3186148 NIL ULSCAT (NIL T) -9 NIL 3186879 NIL) (-1257 3177565 3177650 3177829 "ULS2" 3178056 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3176480 3177180 3177294 "UINT8" 3177405 T UINT8 (NIL) -8 NIL NIL 3177497) (-1255 3175394 3176094 3176208 "UINT64" 3176319 T UINT64 (NIL) -8 NIL NIL 3176411) (-1254 3174308 3175008 3175122 "UINT32" 3175233 T UINT32 (NIL) -8 NIL NIL 3175325) (-1253 3173222 3173922 3174036 "UINT16" 3174147 T UINT16 (NIL) -8 NIL NIL 3174239) (-1252 3171301 3172468 3172498 "UFD" 3172710 T UFD (NIL) -9 NIL 3172824 NIL) (-1251 3171083 3171141 3171236 "UFD-" 3171241 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3170141 3170348 3170564 "UDVO" 3170889 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3167907 3168366 3168837 "UDPO" 3169705 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3167840 3167845 3167875 "TYPE" 3167880 T TYPE (NIL) -9 NIL NIL NIL) (-1247 3167552 3167795 3167826 "TYPEAST" 3167831 T TYPEAST (NIL) -8 NIL NIL NIL) (-1246 3166505 3166725 3166965 "TWOFACT" 3167346 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3165480 3165914 3166149 "TUPLE" 3166305 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3163117 3163690 3164229 "TUBETOOL" 3164963 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3161923 3162164 3162406 "TUBE" 3162910 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3156102 3160895 3161178 "TS" 3161675 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3144244 3148859 3148956 "TSETCAT" 3154225 NIL TSETCAT (NIL T T T T) -9 NIL 3155757 NIL) (-1240 3138712 3140576 3142467 "TSETCAT-" 3142472 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1239 3133185 3134198 3135127 "TRMANIP" 3137848 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3132614 3132689 3132852 "TRIMAT" 3133117 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3130426 3130717 3131074 "TRIGMNIP" 3132363 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3129910 3130059 3130089 "TRIGCAT" 3130302 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3129555 3129658 3129799 "TRIGCAT-" 3129804 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3126169 3128413 3128694 "TREE" 3129309 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3125275 3125971 3126001 "TRANFUN" 3126036 T TRANFUN (NIL) -9 NIL 3126102 NIL) (-1232 3124494 3124745 3125025 "TRANFUN-" 3125030 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3124292 3124330 3124391 "TOPSP" 3124455 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3123622 3123755 3123909 "TOOLSIGN" 3124173 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3122136 3122799 3123038 "TEXTFILE" 3123405 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3119940 3120589 3121018 "TEX" 3121729 T TEX (NIL) -8 NIL NIL NIL) (-1227 3119715 3119752 3119824 "TEX1" 3119903 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1226 3119351 3119426 3119516 "TEMUTL" 3119647 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3117445 3117785 3118110 "TBCMPPK" 3119074 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3108772 3115531 3115587 "TBAGG" 3115987 NIL TBAGG (NIL T T) -9 NIL 3116198 NIL) (-1223 3103656 3105330 3107084 "TBAGG-" 3107089 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3103022 3103147 3103292 "TANEXP" 3103545 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3102473 3102797 3102887 "TALGOP" 3102967 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3095487 3102330 3102423 "TABLE" 3102428 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1219 3094881 3094998 3095136 "TABLEAU" 3095384 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1218 3089411 3090709 3091957 "TABLBUMP" 3093667 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3088621 3088780 3088961 "SYSTEM" 3089252 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3085026 3085779 3086562 "SYSSOLP" 3087872 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3084788 3084981 3085012 "SYSPTR" 3085017 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3083623 3084315 3084441 "SYSNNI" 3084627 NIL SYSNNI (NIL NIL) -8 NIL NIL 3084719) (-1213 3082826 3083381 3083460 "SYSINT" 3083520 NIL SYSINT (NIL NIL) -8 NIL NIL 3083565) (-1212 3078924 3080104 3080814 "SYNTAX" 3082138 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3076004 3076684 3077316 "SYMTAB" 3078314 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3071103 3072155 3073138 "SYMS" 3075043 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3068002 3070554 3070787 "SYMPOLY" 3070905 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3067507 3067594 3067717 "SYMFUNC" 3067914 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3063305 3064819 3065632 "SYMBOL" 3066716 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3056778 3058533 3060253 "SWITCH" 3061607 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3049532 3055734 3056028 "SUTS" 3056542 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3041010 3048914 3049178 "SUPXS" 3049326 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3031533 3040628 3040754 "SUP" 3040919 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3030680 3030819 3031036 "SUPFRACF" 3031401 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1201 3030295 3030360 3030473 "SUP2" 3030615 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1200 3028719 3029017 3029373 "SUMRF" 3029994 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3028042 3028120 3028312 "SUMFS" 3028640 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3009887 3027354 3027596 "SULS" 3027858 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3009435 3009709 3009779 "SUCHTAST" 3009839 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3008676 3008960 3009100 "SUCH" 3009343 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3002315 3003582 3004541 "SUBSPACE" 3007764 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3001735 3001835 3001999 "SUBRESP" 3002203 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2994929 2996400 2997711 "STTF" 3000471 NIL STTF (NIL T) -7 NIL NIL NIL) (-1192 2988940 2990222 2991369 "STTFNC" 2993829 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1191 2980057 2982122 2983916 "STTAYLOR" 2987181 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2972811 2979921 2980004 "STRTBL" 2980009 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2967208 2972520 2972619 "STRING" 2972734 T STRING (NIL) -8 NIL NIL NIL) (-1188 2959318 2964827 2965438 "STREAM" 2966632 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1187 2958822 2958905 2959049 "STREAM3" 2959235 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1186 2957786 2957987 2958222 "STREAM2" 2958635 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1185 2957468 2957526 2957619 "STREAM1" 2957728 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1184 2956460 2956665 2956896 "STINPROD" 2957284 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2955956 2956208 2956238 "STEP" 2956318 T STEP (NIL) -9 NIL 2956396 NIL) (-1182 2955071 2955445 2955593 "STEPAST" 2955830 T STEPAST (NIL) -8 NIL NIL NIL) (-1181 2948127 2954970 2955047 "STBL" 2955052 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2942685 2947290 2947333 "STAGG" 2947486 NIL STAGG (NIL T) -9 NIL 2947575 NIL) (-1179 2940237 2940989 2941861 "STAGG-" 2941866 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2938209 2940007 2940099 "STACK" 2940180 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2930216 2936350 2936806 "SREGSET" 2937839 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922563 2924010 2925523 "SRDCMPK" 2928822 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2914872 2919922 2919952 "SRAGG" 2921255 T SRAGG (NIL) -9 NIL 2921863 NIL) (-1174 2913823 2914144 2914523 "SRAGG-" 2914528 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2907407 2912770 2913191 "SQMATRIX" 2913449 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2900819 2904125 2904852 "SPLTREE" 2906752 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2896644 2897475 2898121 "SPLNODE" 2900245 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895619 2895924 2895954 "SPFCAT" 2896398 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2894314 2894566 2894830 "SPECOUT" 2895377 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2884960 2887278 2887308 "SPADXPT" 2891986 T SPADXPT (NIL) -9 NIL 2894152 NIL) (-1167 2884715 2884761 2884830 "SPADPRSR" 2884913 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2882318 2884670 2884701 "SPADAST" 2884706 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2873919 2876022 2876065 "SPACEC" 2880438 NIL SPACEC (NIL T) -9 NIL 2882254 NIL) (-1164 2871719 2873851 2873900 "SPACE3" 2873905 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2870451 2870642 2870933 "SORTPAK" 2871524 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868513 2868846 2869258 "SOLVETRA" 2870115 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867551 2867785 2868046 "SOLVESER" 2868286 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2862783 2863743 2864738 "SOLVERAD" 2866603 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858508 2859207 2859936 "SOLVEFOR" 2862150 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2852119 2857856 2857953 "SNTSCAT" 2857958 NIL SNTSCAT (NIL T T T T) -9 NIL 2858028 NIL) (-1157 2845663 2850442 2850833 "SMTS" 2851809 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2839378 2845551 2845628 "SMP" 2845633 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837507 2837838 2838236 "SMITH" 2839075 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2829039 2834086 2834189 "SMATCAT" 2835540 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836090 NIL) (-1153 2825811 2826802 2827980 "SMATCAT-" 2827985 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2823280 2825019 2825062 "SKAGG" 2825323 NIL SKAGG (NIL T) -9 NIL 2825458 NIL) (-1151 2818774 2822753 2822937 "SINT" 2823089 T SINT (NIL) -8 NIL NIL 2823251) (-1150 2818540 2818584 2818650 "SIMPAN" 2818730 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817765 2818075 2818215 "SIG" 2818422 T SIG (NIL) -8 NIL NIL NIL) (-1148 2816585 2816824 2817099 "SIGNRF" 2817524 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1147 2815400 2815569 2815853 "SIGNEF" 2816414 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1146 2814640 2814983 2815107 "SIGAST" 2815298 T SIGAST (NIL) -8 NIL NIL NIL) (-1145 2812292 2812784 2813290 "SHP" 2814181 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2805665 2812193 2812269 "SHDP" 2812274 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2805176 2805416 2805446 "SGROUP" 2805539 T SGROUP (NIL) -9 NIL 2805601 NIL) (-1142 2805028 2805060 2805133 "SGROUP-" 2805138 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2801747 2802517 2803240 "SGCF" 2804327 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2795456 2801193 2801290 "SFRTCAT" 2801295 NIL SFRTCAT (NIL T T T T) -9 NIL 2801334 NIL) (-1139 2788775 2789895 2791031 "SFRGCD" 2794439 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781793 2782974 2784160 "SFQCMPK" 2787708 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2781395 2781502 2781613 "SFORT" 2781734 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2780321 2781235 2781356 "SEXOF" 2781361 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2779236 2780202 2780270 "SEX" 2780275 T SEX (NIL) -8 NIL NIL NIL) (-1134 2774825 2775732 2775827 "SEXCAT" 2778449 NIL SEXCAT (NIL T T T T T) -9 NIL 2779009 NIL) (-1133 2771634 2774759 2774807 "SET" 2774812 NIL SET (NIL T) -8 NIL NIL NIL) (-1132 2769756 2770347 2770652 "SETMN" 2771375 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1131 2769286 2769474 2769504 "SETCAT" 2769621 T SETCAT (NIL) -9 NIL 2769706 NIL) (-1130 2769054 2769118 2769217 "SETCAT-" 2769222 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1129 2765157 2767515 2767558 "SETAGG" 2768428 NIL SETAGG (NIL T) -9 NIL 2768768 NIL) (-1128 2764579 2764731 2764968 "SETAGG-" 2764973 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1127 2763962 2764275 2764376 "SEQAST" 2764500 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2763089 2763455 2763516 "SEGXCAT" 2763802 NIL SEGXCAT (NIL T T) -9 NIL 2763922 NIL) (-1125 2762005 2762755 2762937 "SEG" 2762942 NIL SEG (NIL T) -8 NIL NIL NIL) (-1124 2760930 2761198 2761241 "SEGCAT" 2761763 NIL SEGCAT (NIL T) -9 NIL 2761984 NIL) (-1123 2759820 2760293 2760501 "SEGBIND" 2760757 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2759435 2759500 2759613 "SEGBIND2" 2759755 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1121 2758954 2759236 2759313 "SEGAST" 2759380 T SEGAST (NIL) -8 NIL NIL NIL) (-1120 2758163 2758299 2758503 "SEG2" 2758798 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1119 2757396 2758098 2758145 "SDVAR" 2758150 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2748747 2757166 2757296 "SDPOL" 2757301 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2747316 2747606 2747925 "SCPKG" 2748462 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2746438 2746652 2746844 "SCOPE" 2747146 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745634 2745792 2745971 "SCACHE" 2746293 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2745218 2745452 2745482 "SASTCAT" 2745487 T SASTCAT (NIL) -9 NIL 2745500 NIL) (-1113 2744621 2745053 2745129 "SAOS" 2745164 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2744180 2744221 2744394 "SAERFFC" 2744580 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2737207 2744077 2744157 "SAE" 2744162 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2736794 2736835 2736994 "SAEFACT" 2737166 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1109 2735097 2735429 2735830 "RURPK" 2736460 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2733674 2734040 2734345 "RULESET" 2734931 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2730789 2731427 2731885 "RULE" 2733355 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2730359 2730583 2730666 "RULECOLD" 2730741 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1105 2730143 2730177 2730248 "RTVALUE" 2730310 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729554 2729860 2729954 "RSTRCAST" 2730071 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2724324 2725197 2726117 "RSETGCD" 2728753 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2712895 2718632 2718729 "RSETCAT" 2722848 NIL RSETCAT (NIL T T T T) -9 NIL 2723945 NIL) (-1101 2710714 2711361 2712185 "RSETCAT-" 2712190 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2703022 2704476 2705996 "RSDCMPK" 2709313 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2700891 2701454 2701528 "RRCC" 2702614 NIL RRCC (NIL T T) -9 NIL 2702958 NIL) (-1098 2700212 2700416 2700695 "RRCC-" 2700700 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699595 2699908 2700009 "RPTAST" 2700133 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2671981 2682707 2682774 "RPOLCAT" 2693440 NIL RPOLCAT (NIL T T T) -9 NIL 2696600 NIL) (-1095 2662951 2665819 2668941 "RPOLCAT-" 2668946 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2653404 2661162 2661644 "ROUTINE" 2662491 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649453 2653030 2653170 "ROMAN" 2653286 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647565 2648313 2648573 "ROIRC" 2649258 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2643283 2646054 2646084 "RNS" 2646388 T RNS (NIL) -9 NIL 2646662 NIL) (-1090 2641690 2642175 2642709 "RNS-" 2642784 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640983 2641487 2641517 "RNG" 2641522 T RNG (NIL) -9 NIL 2641543 NIL) (-1088 2639944 2640348 2640550 "RNGBIND" 2640834 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1087 2639239 2639717 2639760 "RMODULE" 2639765 NIL RMODULE (NIL T) -9 NIL 2639792 NIL) (-1086 2638063 2638169 2638505 "RMCAT2" 2639140 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634565 2637409 2637706 "RMATRIX" 2637825 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2627064 2629652 2629767 "RMATCAT" 2633126 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634108 NIL) (-1083 2626403 2626586 2626893 "RMATCAT-" 2626898 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2625976 2626190 2626233 "RLINSET" 2626295 NIL RLINSET (NIL T) -9 NIL 2626339 NIL) (-1081 2625537 2625618 2625746 "RINTERP" 2625895 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624461 2625135 2625165 "RING" 2625221 T RING (NIL) -9 NIL 2625313 NIL) (-1079 2624241 2624297 2624394 "RING-" 2624399 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2623052 2623319 2623577 "RIDIST" 2624005 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2613677 2622520 2622726 "RGCHAIN" 2622900 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2612935 2613419 2613460 "RGBCSPC" 2613518 NIL RGBCSPC (NIL T) -9 NIL 2613570 NIL) (-1075 2612001 2612460 2612501 "RGBCMDL" 2612733 NIL RGBCMDL (NIL T) -9 NIL 2612847 NIL) (-1074 2608941 2609609 2610279 "RF" 2611365 NIL RF (NIL T) -7 NIL NIL NIL) (-1073 2608581 2608650 2608753 "RFFACTOR" 2608872 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1072 2608300 2608341 2608438 "RFFACT" 2608540 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1071 2606351 2606781 2607163 "RFDIST" 2607940 T RFDIST (NIL) -7 NIL NIL NIL) (-1070 2605798 2605896 2606059 "RETSOL" 2606253 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2605416 2605514 2605557 "RETRACT" 2605690 NIL RETRACT (NIL T) -9 NIL 2605777 NIL) (-1068 2605259 2605290 2605377 "RETRACT-" 2605382 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2604807 2605081 2605151 "RETAST" 2605211 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2597157 2604460 2604587 "RESULT" 2604702 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595592 2596426 2596625 "RESRING" 2597060 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2595216 2595277 2595375 "RESLATC" 2595529 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2594915 2594956 2595063 "REPSQ" 2595175 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2592295 2592917 2593519 "REP" 2594335 T REP (NIL) -7 NIL NIL NIL) (-1061 2591986 2592027 2592138 "REPDB" 2592254 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1060 2585818 2587275 2588498 "REP2" 2590798 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1059 2582121 2582876 2583684 "REP1" 2585045 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1058 2574129 2580262 2580718 "REGSET" 2581751 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2572838 2573277 2573527 "REF" 2573914 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2572203 2572318 2572485 "REDORDER" 2572722 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567567 2571416 2571643 "RECLOS" 2572031 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566601 2566800 2567015 "REALSOLV" 2567374 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2566435 2566488 2566518 "REAL" 2566523 T REAL (NIL) -9 NIL 2566558 NIL) (-1052 2562882 2563720 2564604 "REAL0Q" 2565600 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1051 2558435 2559471 2560532 "REAL0" 2561863 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1050 2557846 2558152 2558246 "RDUCEAST" 2558363 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2557245 2557323 2557530 "RDIV" 2557768 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2556295 2556487 2556700 "RDIST" 2557067 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2554880 2555179 2555551 "RDETRS" 2556003 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2552674 2553146 2553684 "RDETR" 2554422 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2551293 2551577 2551974 "RDEEFS" 2552390 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2549796 2550108 2550533 "RDEEF" 2550981 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2543273 2546750 2546780 "RCFIELD" 2548075 T RCFIELD (NIL) -9 NIL 2548806 NIL) (-1042 2541229 2541841 2542537 "RCFIELD-" 2542612 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2537281 2539302 2539345 "RCAGG" 2540429 NIL RCAGG (NIL T) -9 NIL 2540894 NIL) (-1040 2536891 2537003 2537166 "RCAGG-" 2537171 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2536208 2536338 2536503 "RATRET" 2536775 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2535749 2535828 2535949 "RATFACT" 2536136 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2535027 2535177 2535329 "RANDSRC" 2535619 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2534755 2534805 2534878 "RADUTIL" 2534976 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2526879 2533586 2533897 "RADIX" 2534478 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516473 2526721 2526851 "RADFF" 2526856 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2516102 2516195 2516225 "RADCAT" 2516385 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2515872 2515932 2516032 "RADCAT-" 2516037 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2513783 2515642 2515734 "QUEUE" 2515815 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2509622 2513716 2513764 "QUAT" 2513769 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1029 2509247 2509296 2509427 "QUATCT2" 2509573 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1028 2501623 2505670 2505712 "QUATCAT" 2506503 NIL QUATCAT (NIL T) -9 NIL 2507269 NIL) (-1027 2497504 2498799 2500189 "QUATCAT-" 2500285 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1026 2494760 2496552 2496595 "QUAGG" 2496976 NIL QUAGG (NIL T) -9 NIL 2497151 NIL) (-1025 2494308 2494582 2494652 "QQUTAST" 2494712 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2493219 2493821 2493986 "QFORM" 2494189 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2482895 2489066 2489108 "QFCAT" 2489776 NIL QFCAT (NIL T) -9 NIL 2490777 NIL) (-1022 2478210 2479663 2481257 "QFCAT-" 2481353 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477835 2477884 2478015 "QFCAT2" 2478161 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1020 2477266 2477400 2477532 "QEQUAT" 2477725 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2470284 2471465 2472651 "QCMPACK" 2476199 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2467734 2468270 2468700 "QALGSET" 2469939 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2466963 2467145 2467381 "QALGSET2" 2467552 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1016 2465630 2465872 2466191 "PWFFINTB" 2466736 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2463775 2463973 2464329 "PUSHVAR" 2465444 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459502 2460718 2460761 "PTRANFN" 2462672 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2457839 2458184 2458508 "PTPACK" 2459213 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457462 2457525 2457636 "PTFUNC2" 2457776 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2451387 2456251 2456294 "PTCAT" 2456594 NIL PTCAT (NIL T) -9 NIL 2456747 NIL) (-1010 2451036 2451077 2451203 "PSQFR" 2451346 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449608 2449924 2450260 "PSEUDLIN" 2450734 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2436128 2438703 2441029 "PSETPK" 2447368 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2428836 2431864 2431962 "PSETCAT" 2435003 NIL PSETCAT (NIL T T T T) -9 NIL 2435817 NIL) (-1006 2426561 2427303 2428127 "PSETCAT-" 2428132 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2425874 2426069 2426099 "PSCURVE" 2426371 T PSCURVE (NIL) -9 NIL 2426538 NIL) (-1004 2421590 2423364 2423431 "PSCAT" 2424283 NIL PSCAT (NIL T T T) -9 NIL 2424523 NIL) (-1003 2420584 2420866 2421269 "PSCAT-" 2421274 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2418783 2419643 2419908 "PRTITION" 2420341 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2418194 2418500 2418594 "PRTDAST" 2418711 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2407038 2409460 2411650 "PRS" 2416056 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404658 2406360 2406400 "PRQAGG" 2406583 NIL PRQAGG (NIL T) -9 NIL 2406685 NIL) (-998 2403837 2404286 2404314 "PROPLOG" 2404453 T PROPLOG (NIL) -9 NIL 2404568 NIL) (-997 2403435 2403498 2403621 "PROPFUN2" 2403760 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2402732 2402871 2403043 "PROPFUN1" 2403296 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2400711 2401479 2401776 "PROPFRML" 2402468 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2400156 2400287 2400415 "PROPERTY" 2400603 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2394044 2398322 2399142 "PRODUCT" 2399382 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2391002 2393502 2393736 "PR" 2393855 NIL PR (NIL T T) -8 NIL NIL NIL) (-991 2390792 2390830 2390889 "PRINT" 2390963 T PRINT (NIL) -7 NIL NIL NIL) (-990 2390108 2390249 2390401 "PRIMES" 2390672 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-989 2388155 2388574 2389040 "PRIMELT" 2389687 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-988 2387872 2387933 2387961 "PRIMCAT" 2388085 T PRIMCAT (NIL) -9 NIL NIL NIL) (-987 2383594 2387810 2387855 "PRIMARR" 2387860 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2382583 2382779 2383007 "PRIMARR2" 2383412 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-985 2382220 2382282 2382393 "PREASSOC" 2382521 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-984 2381671 2381828 2381856 "PPCURVE" 2382061 T PPCURVE (NIL) -9 NIL 2382197 NIL) (-983 2381218 2381466 2381549 "PORTNUM" 2381608 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378555 2378976 2379568 "POLYROOT" 2380799 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2371763 2378159 2378319 "POLY" 2378428 NIL POLY (NIL T) -8 NIL NIL NIL) (-980 2371140 2371204 2371438 "POLYLIFT" 2371699 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-979 2367361 2367864 2368493 "POLYCATQ" 2370685 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-978 2353009 2359108 2359173 "POLYCAT" 2362687 NIL POLYCAT (NIL T T T) -9 NIL 2364565 NIL) (-977 2346128 2348320 2350704 "POLYCAT-" 2350709 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-976 2345709 2345783 2345903 "POLY2UP" 2346054 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-975 2345335 2345398 2345507 "POLY2" 2345646 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-974 2343996 2344259 2344535 "POLUTIL" 2345109 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2342315 2342628 2342959 "POLTOPOL" 2343718 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2337311 2342249 2342296 "POINT" 2342301 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2335444 2335855 2336230 "PNTHEORY" 2336956 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2333890 2334199 2334598 "PMTOOLS" 2335142 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2333477 2333561 2333678 "PMSYM" 2333806 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2332979 2333054 2333229 "PMQFCAT" 2333402 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2332322 2332444 2332600 "PMPRED" 2332856 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2331703 2331801 2331963 "PMPREDFS" 2332223 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-965 2330357 2330575 2330953 "PMPLCAT" 2331465 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2329883 2329968 2330120 "PMLSAGG" 2330272 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2329350 2329432 2329614 "PMKERNEL" 2329801 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2328961 2329042 2329155 "PMINS" 2329269 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328397 2328472 2328681 "PMFS" 2328886 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327613 2327743 2327948 "PMDOWN" 2328274 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2326756 2326938 2327119 "PMASS" 2327452 T PMASS (NIL) -7 NIL NIL NIL) (-958 2326005 2326139 2326302 "PMASSFS" 2326643 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-957 2325654 2325728 2325822 "PLOTTOOL" 2325931 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2320075 2321465 2322613 "PLOT" 2324526 T PLOT (NIL) -8 NIL NIL NIL) (-955 2315727 2316921 2317843 "PLOT3D" 2319173 T PLOT3D (NIL) -8 NIL NIL NIL) (-954 2314615 2314816 2315051 "PLOT1" 2315531 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-953 2289790 2294681 2299532 "PLEQN" 2309881 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289096 2289230 2289410 "PINTERP" 2289655 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2288783 2288836 2288939 "PINTERPA" 2289043 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-950 2287879 2288547 2288634 "PI" 2288674 T PI (NIL) -8 NIL NIL 2288741) (-949 2285964 2287137 2287165 "PID" 2287347 T PID (NIL) -9 NIL 2287481 NIL) (-948 2285709 2285752 2285827 "PICOERCE" 2285921 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-947 2285017 2285168 2285344 "PGROEB" 2285565 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280456 2281415 2282321 "PGE" 2284131 T PGE (NIL) -7 NIL NIL NIL) (-945 2278537 2278826 2279192 "PGCD" 2280173 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2277863 2277978 2278139 "PFRPAC" 2278421 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2274113 2276411 2276764 "PFR" 2277542 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272466 2272746 2273071 "PFOTOOLS" 2273860 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2270981 2271238 2271589 "PFOQ" 2272223 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269464 2269694 2270050 "PFO" 2270765 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2265389 2269353 2269422 "PF" 2269427 NIL PF (NIL NIL) -8 NIL NIL NIL) (-938 2262467 2263980 2264008 "PFECAT" 2264593 T PFECAT (NIL) -9 NIL 2264977 NIL) (-937 2261894 2262066 2262280 "PFECAT-" 2262285 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-936 2260467 2260749 2261050 "PFBRU" 2261643 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-935 2258297 2258685 2259117 "PFBR" 2260118 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-934 2254099 2255806 2256454 "PERM" 2257682 NIL PERM (NIL T) -8 NIL NIL NIL) (-933 2249153 2250306 2251176 "PERMGRP" 2253262 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-932 2247065 2248177 2248218 "PERMCAT" 2248618 NIL PERMCAT (NIL T) -9 NIL 2248916 NIL) (-931 2246712 2246759 2246883 "PERMAN" 2247018 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-930 2243953 2246377 2246499 "PENDTREE" 2246623 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2242834 2243097 2243138 "PDSPC" 2243671 NIL PDSPC (NIL T) -9 NIL 2243916 NIL) (-928 2241889 2242155 2242517 "PDSPC-" 2242522 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240603 2241539 2241580 "PDRING" 2241585 NIL PDRING (NIL T) -9 NIL 2241613 NIL) (-926 2239346 2240108 2240162 "PDMOD" 2240167 NIL PDMOD (NIL T T) -9 NIL 2240271 NIL) (-925 2236513 2237339 2238007 "PDEPROB" 2238698 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2234022 2234562 2235117 "PDEPACK" 2235978 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2232910 2233124 2233375 "PDECOMP" 2233821 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230427 2231318 2231346 "PDECAT" 2232133 T PDECAT (NIL) -9 NIL 2232846 NIL) (-921 2230044 2230111 2230165 "PDDOM" 2230330 NIL PDDOM (NIL T T) -9 NIL 2230410 NIL) (-920 2229857 2229893 2230000 "PDDOM-" 2230005 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229602 2229641 2229731 "PCOMP" 2229818 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2227642 2228403 2228700 "PBWLB" 2229331 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2219821 2221715 2223053 "PATTERN" 2226325 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-916 2219447 2219510 2219619 "PATTERN2" 2219758 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-915 2217156 2217592 2218049 "PATTERN1" 2219036 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-914 2214422 2215105 2215586 "PATRES" 2216721 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2213980 2214053 2214185 "PATRES2" 2214349 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-912 2211833 2212268 2212675 "PATMATCH" 2213647 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2211287 2211538 2211579 "PATMAB" 2211686 NIL PATMAB (NIL T) -9 NIL 2211769 NIL) (-910 2209733 2210141 2210399 "PATLRES" 2211092 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2209271 2209402 2209443 "PATAB" 2209448 NIL PATAB (NIL T) -9 NIL 2209620 NIL) (-908 2207411 2207848 2208271 "PARTPERM" 2208868 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2207020 2207095 2207197 "PARSURF" 2207342 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2206646 2206709 2206818 "PARSU2" 2206957 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2206404 2206450 2206517 "PARSER" 2206599 T PARSER (NIL) -7 NIL NIL NIL) (-904 2206013 2206088 2206190 "PARSCURV" 2206335 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2205639 2205702 2205811 "PARSC2" 2205950 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2205266 2205336 2205433 "PARPCURV" 2205575 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2204892 2204955 2205064 "PARPC2" 2205203 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2203881 2204265 2204447 "PARAMAST" 2204730 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2203389 2203487 2203606 "PAN2EXPR" 2203782 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2202082 2202510 2202738 "PALETTE" 2203181 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2200427 2201087 2201447 "PAIR" 2201768 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2193339 2199684 2199879 "PADICRC" 2200281 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2185575 2192683 2192868 "PADICRAT" 2193186 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2183584 2185512 2185557 "PADIC" 2185562 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2180374 2182244 2182284 "PADICCT" 2182865 NIL PADICCT (NIL NIL) -9 NIL 2183147 NIL) (-892 2179319 2179531 2179799 "PADEPAC" 2180161 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2178519 2178664 2178870 "PADE" 2179181 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2176752 2177727 2178007 "OWP" 2178323 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2176197 2176458 2176555 "OVERSET" 2176675 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2175117 2175802 2175974 "OVAR" 2176065 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2174357 2174502 2174663 "OUT" 2174976 T OUT (NIL) -7 NIL NIL NIL) (-886 2162593 2165466 2167666 "OUTFORM" 2172177 T OUTFORM (NIL) -8 NIL NIL NIL) (-885 2161875 2162190 2162317 "OUTBFILE" 2162486 T OUTBFILE (NIL) -8 NIL NIL NIL) (-884 2161152 2161347 2161375 "OUTBCON" 2161693 T OUTBCON (NIL) -9 NIL 2161859 NIL) (-883 2160735 2160865 2161022 "OUTBCON-" 2161027 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-882 2160031 2160464 2160553 "OSI" 2160666 T OSI (NIL) -8 NIL NIL NIL) (-881 2159450 2159872 2159900 "OSGROUP" 2159905 T OSGROUP (NIL) -9 NIL 2159927 NIL) (-880 2158161 2158422 2158707 "ORTHPOL" 2159197 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2155412 2157996 2158117 "OREUP" 2158122 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2152515 2155103 2155230 "ORESUP" 2155354 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2150015 2150543 2151104 "OREPCTO" 2152004 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2143393 2145888 2145929 "OREPCAT" 2148277 NIL OREPCAT (NIL T) -9 NIL 2149381 NIL) (-875 2140366 2141322 2142380 "OREPCAT-" 2142385 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2139559 2139836 2139864 "ORDTYPE" 2140173 T ORDTYPE (NIL) -9 NIL 2140336 NIL) (-873 2138860 2139076 2139331 "ORDTYPE-" 2139336 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2138216 2138599 2138757 "ORDSTRCT" 2138762 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2137714 2138084 2138112 "ORDSET" 2138117 T ORDSET (NIL) -9 NIL 2138139 NIL) (-870 2136072 2137043 2137071 "ORDRING" 2137273 T ORDRING (NIL) -9 NIL 2137398 NIL) (-869 2135693 2135811 2135955 "ORDRING-" 2135960 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2134944 2135509 2135537 "ORDMON" 2135542 T ORDMON (NIL) -9 NIL 2135563 NIL) (-867 2134088 2134253 2134448 "ORDFUNS" 2134793 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2133303 2133818 2133846 "ORDFIN" 2133911 T ORDFIN (NIL) -9 NIL 2133985 NIL) (-865 2129650 2131889 2132298 "ORDCOMP" 2132927 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-864 2128904 2129043 2129229 "ORDCOMP2" 2129510 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-863 2125425 2126395 2127209 "OPTPROB" 2128110 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2122167 2122866 2123570 "OPTPACK" 2124741 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2119780 2120606 2120634 "OPTCAT" 2121453 T OPTCAT (NIL) -9 NIL 2122103 NIL) (-860 2119098 2119457 2119562 "OPSIG" 2119695 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2118860 2118905 2118971 "OPQUERY" 2119052 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2115769 2117171 2117675 "OP" 2118389 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2115075 2115355 2115396 "OPERCAT" 2115608 NIL OPERCAT (NIL T) -9 NIL 2115705 NIL) (-856 2114818 2114886 2115003 "OPERCAT-" 2115008 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-855 2111431 2113615 2113984 "ONECOMP" 2114482 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-854 2110724 2110851 2111025 "ONECOMP2" 2111303 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-853 2110125 2110249 2110379 "OMSERVER" 2110614 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2106639 2109565 2109605 "OMSAGG" 2109666 NIL OMSAGG (NIL T) -9 NIL 2109730 NIL) (-851 2105214 2105525 2105807 "OMPKG" 2106377 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2104620 2104747 2104775 "OM" 2105074 T OM (NIL) -9 NIL NIL NIL) (-849 2102967 2104169 2104338 "OMLO" 2104501 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-848 2101903 2102074 2102294 "OMEXPR" 2102793 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-847 2101140 2101449 2101585 "OMERR" 2101787 T OMERR (NIL) -8 NIL NIL NIL) (-846 2100225 2100561 2100721 "OMERRK" 2101000 T OMERRK (NIL) -8 NIL NIL NIL) (-845 2099616 2099902 2100010 "OMENC" 2100137 T OMENC (NIL) -8 NIL NIL NIL) (-844 2093253 2094696 2095867 "OMDEV" 2098465 T OMDEV (NIL) -8 NIL NIL NIL) (-843 2092286 2092493 2092687 "OMCONN" 2093079 T OMCONN (NIL) -8 NIL NIL NIL) (-842 2090564 2091756 2091784 "OINTDOM" 2091789 T OINTDOM (NIL) -9 NIL 2091810 NIL) (-841 2087638 2089252 2089589 "OFMONOID" 2090259 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2086872 2087575 2087620 "ODVAR" 2087625 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2084009 2086617 2086772 "ODR" 2086777 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2075414 2083785 2083911 "ODPOL" 2083916 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2068757 2075286 2075391 "ODP" 2075396 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2067499 2067738 2068013 "ODETOOLS" 2068531 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2064442 2065124 2065840 "ODESYS" 2066832 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2059272 2060232 2061257 "ODERTRIC" 2063517 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2058692 2058780 2058974 "ODERED" 2059184 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2055544 2056128 2056805 "ODERAT" 2058115 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2052461 2052968 2053565 "ODEPRRIC" 2055073 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2050356 2051000 2051486 "ODEPROB" 2051995 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2046822 2047361 2048008 "ODEPRIM" 2049835 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2046065 2046173 2046433 "ODEPAL" 2046714 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2042167 2043018 2043882 "ODEPACK" 2045221 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2041210 2041335 2041557 "ODEINT" 2042056 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2035275 2036736 2038183 "ODEIFTBL" 2039783 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2030625 2031459 2032411 "ODEEF" 2034434 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2029968 2030063 2030286 "ODECONST" 2030530 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2028031 2028740 2028768 "ODECAT" 2029373 T ODECAT (NIL) -9 NIL 2029904 NIL) (-821 2024524 2027736 2027858 "OCT" 2027941 NIL OCT (NIL T) -8 NIL NIL NIL) (-820 2024156 2024205 2024332 "OCTCT2" 2024475 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-819 2018425 2021199 2021239 "OC" 2022336 NIL OC (NIL T) -9 NIL 2023194 NIL) (-818 2015460 2016400 2017390 "OC-" 2017484 NIL OC- (NIL T T) -8 NIL NIL NIL) (-817 2014683 2015253 2015281 "OCAMON" 2015286 T OCAMON (NIL) -9 NIL 2015307 NIL) (-816 2014103 2014528 2014556 "OASGP" 2014561 T OASGP (NIL) -9 NIL 2014581 NIL) (-815 2013229 2013826 2013854 "OAMONS" 2013894 T OAMONS (NIL) -9 NIL 2013937 NIL) (-814 2012520 2013049 2013077 "OAMON" 2013082 T OAMON (NIL) -9 NIL 2013102 NIL) (-813 2011631 2012269 2012297 "OAGROUP" 2012302 T OAGROUP (NIL) -9 NIL 2012322 NIL) (-812 2011313 2011369 2011458 "NUMTUBE" 2011575 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004832 2006404 2007940 "NUMQUAD" 2009797 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000552 2001576 2002601 "NUMODE" 2003827 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997833 1998773 1998801 "NUMINT" 1999724 T NUMINT (NIL) -9 NIL 2000488 NIL) (-808 1996745 1996978 1997196 "NUMFMT" 1997635 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982928 1986049 1988581 "NUMERIC" 1994252 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976639 1982376 1982471 "NTSCAT" 1982476 NIL NTSCAT (NIL T T T T) -9 NIL 1982515 NIL) (-805 1975819 1975998 1976191 "NTPOLFN" 1976478 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1962580 1972644 1973456 "NSUP" 1975040 NIL NSUP (NIL T) -8 NIL NIL NIL) (-803 1962206 1962269 1962378 "NSUP2" 1962517 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-802 1951042 1961980 1962113 "NSMP" 1962118 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949450 1949775 1950132 "NREP" 1950730 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1948029 1948293 1948651 "NPCOEF" 1949193 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1947077 1947210 1947426 "NORMRETR" 1947910 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1945088 1945408 1945817 "NORMPK" 1946785 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944767 1944801 1944925 "NORMMA" 1945054 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944531 1944724 1944753 "NONE" 1944758 T NONE (NIL) -8 NIL NIL NIL) (-795 1944314 1944349 1944418 "NONE1" 1944495 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-794 1943805 1943873 1944052 "NODE1" 1944246 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941897 1942928 1943183 "NNI" 1943530 T NNI (NIL) -8 NIL NIL 1943765) (-792 1940293 1940630 1940994 "NLINSOL" 1941565 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936474 1937529 1938428 "NIPROB" 1939414 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935213 1935465 1935767 "NFINTBAS" 1936236 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934297 1934863 1934904 "NETCLT" 1935076 NIL NETCLT (NIL T) -9 NIL 1935158 NIL) (-788 1932969 1933236 1933517 "NCODIV" 1934065 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932725 1932768 1932843 "NCNTFRAC" 1932926 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930881 1931269 1931689 "NCEP" 1932350 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929544 1930491 1930519 "NASRING" 1930629 T NASRING (NIL) -9 NIL 1930709 NIL) (-784 1929327 1929383 1929477 "NASRING-" 1929482 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928294 1928945 1928973 "NARNG" 1929090 T NARNG (NIL) -9 NIL 1929181 NIL) (-782 1927968 1928053 1928187 "NARNG-" 1928192 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926805 1927054 1927289 "NAGSP" 1927753 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917849 1919761 1921434 "NAGS" 1925152 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916373 1916705 1917036 "NAGF07" 1917538 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910845 1912202 1913509 "NAGF04" 1915086 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903717 1905427 1907060 "NAGF02" 1909232 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898881 1900041 1901158 "NAGF01" 1902620 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892461 1894075 1895660 "NAGE04" 1897316 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883522 1885751 1887881 "NAGE02" 1890351 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879415 1880422 1881386 "NAGE01" 1882578 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877192 1877744 1878302 "NAGD03" 1878877 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868888 1870870 1872824 "NAGD02" 1875258 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862627 1864124 1865564 "NAGD01" 1867468 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858764 1859658 1860495 "NAGC06" 1861810 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857211 1857561 1857917 "NAGC05" 1858428 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856575 1856706 1856850 "NAGC02" 1857087 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855376 1856103 1856143 "NAALG" 1856222 NIL NAALG (NIL T) -9 NIL 1856283 NIL) (-765 1855205 1855240 1855330 "NAALG-" 1855335 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1849077 1850263 1851450 "MULTSQFR" 1854101 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848384 1848471 1848655 "MULTFACT" 1848989 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840529 1844967 1845020 "MTSCAT" 1846090 NIL MTSCAT (NIL T T) -9 NIL 1846606 NIL) (-761 1840235 1840295 1840387 "MTHING" 1840469 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1840021 1840060 1840120 "MSYSCMD" 1840195 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1835735 1838776 1839096 "MSET" 1839734 NIL MSET (NIL T) -8 NIL NIL NIL) (-758 1832480 1835296 1835337 "MSETAGG" 1835342 NIL MSETAGG (NIL T) -9 NIL 1835376 NIL) (-757 1828072 1829859 1830604 "MRING" 1831780 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827632 1827705 1827836 "MRF2" 1827999 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827244 1827285 1827429 "MRATFAC" 1827591 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824814 1825151 1825582 "MPRFF" 1826949 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1818141 1824668 1824765 "MPOLY" 1824770 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817625 1817666 1817874 "MPCPF" 1818100 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1817133 1817182 1817366 "MPC3" 1817576 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816316 1816409 1816630 "MPC2" 1817048 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814593 1814954 1815344 "MONOTOOL" 1815976 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813738 1814121 1814149 "MONOID" 1814368 T MONOID (NIL) -9 NIL 1814515 NIL) (-747 1813254 1813403 1813584 "MONOID-" 1813589 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802208 1809074 1809133 "MONOGEN" 1809807 NIL MONOGEN (NIL T T) -9 NIL 1810263 NIL) (-745 1799258 1800161 1801161 "MONOGEN-" 1801280 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797975 1798523 1798551 "MONADWU" 1798943 T MONADWU (NIL) -9 NIL 1799181 NIL) (-743 1797305 1797506 1797754 "MONADWU-" 1797759 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796590 1796894 1796922 "MONAD" 1797129 T MONAD (NIL) -9 NIL 1797241 NIL) (-741 1796257 1796353 1796485 "MONAD-" 1796490 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794396 1795170 1795449 "MOEBIUS" 1796010 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793564 1794064 1794104 "MODULE" 1794109 NIL MODULE (NIL T) -9 NIL 1794148 NIL) (-738 1793102 1793228 1793418 "MODULE-" 1793423 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790632 1791466 1791793 "MODRING" 1792926 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787354 1788737 1789258 "MODOP" 1790161 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785840 1786421 1786698 "MODMONOM" 1787217 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774580 1784131 1784545 "MODMON" 1785477 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771406 1773424 1773700 "MODFIELD" 1774455 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770317 1770687 1770877 "MMLFORM" 1771236 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769837 1769886 1770065 "MMAP" 1770268 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767730 1768669 1768710 "MLO" 1769133 NIL MLO (NIL T) -9 NIL 1769375 NIL) (-729 1765078 1765612 1766214 "MLIFT" 1767211 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764457 1764553 1764707 "MKUCFUNC" 1764989 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1764050 1764126 1764249 "MKRECORD" 1764380 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1763073 1763259 1763487 "MKFUNC" 1763861 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762449 1762565 1762721 "MKFLCFN" 1762956 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761714 1761828 1762013 "MKBCFUNC" 1762342 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757697 1761268 1761404 "MINT" 1761598 T MINT (NIL) -8 NIL NIL NIL) (-722 1756479 1756752 1757029 "MHROWRED" 1757452 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751223 1755014 1755419 "MFLOAT" 1756094 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750568 1750656 1750827 "MFINFACT" 1751135 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746847 1747731 1748615 "MESH" 1749704 T MESH (NIL) -7 NIL NIL NIL) (-718 1745201 1745549 1745902 "MDDFACT" 1746534 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741737 1744332 1744373 "MDAGG" 1744628 NIL MDAGG (NIL T) -9 NIL 1744771 NIL) (-716 1729439 1741030 1741237 "MCMPLX" 1741550 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728558 1728722 1728923 "MCDEN" 1729288 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726406 1726718 1727098 "MCALCFN" 1728288 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725283 1725571 1725804 "MAYBE" 1726212 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722841 1723418 1723980 "MATSTOR" 1724754 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718263 1722213 1722461 "MATRIX" 1722626 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713963 1714736 1715472 "MATLIN" 1717620 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1703309 1707020 1707097 "MATCAT" 1712129 NIL MATCAT (NIL T T T) -9 NIL 1713601 NIL) (-708 1699262 1700572 1701985 "MATCAT-" 1701990 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-707 1697838 1698009 1698342 "MATCAT2" 1699097 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-706 1695914 1696274 1696658 "MAPPKG3" 1697513 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694871 1695068 1695290 "MAPPKG2" 1695738 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693328 1693654 1693981 "MAPPKG1" 1694577 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692329 1692734 1692911 "MAPPAST" 1693171 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691934 1691998 1692121 "MAPHACK3" 1692265 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691514 1691587 1691701 "MAPHACK2" 1691866 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690940 1691055 1691197 "MAPHACK1" 1691405 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688863 1689640 1689944 "MAGMA" 1690668 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688282 1688587 1688678 "MACROAST" 1688792 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684525 1686521 1686982 "M3D" 1687854 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1678005 1682836 1682877 "LZSTAGG" 1683659 NIL LZSTAGG (NIL T) -9 NIL 1683954 NIL) (-695 1673687 1675136 1676593 "LZSTAGG-" 1676598 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670600 1671578 1672065 "LWORD" 1673232 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670122 1670404 1670479 "LSTAST" 1670545 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1662050 1669893 1670027 "LSQM" 1670032 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661268 1661413 1661641 "LSPP" 1661905 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1659050 1659381 1659837 "LSMP" 1660957 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-689 1655787 1656503 1657233 "LSMP1" 1658352 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-688 1648923 1654877 1654918 "LSAGG" 1654980 NIL LSAGG (NIL T) -9 NIL 1655058 NIL) (-687 1645432 1646542 1647755 "LSAGG-" 1647760 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642727 1644576 1644825 "LPOLY" 1645227 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642303 1642394 1642517 "LPEFRAC" 1642636 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1640480 1641397 1641650 "LO" 1642135 NIL LO (NIL T T T) -8 NIL NIL NIL) (-683 1640163 1640242 1640270 "LOGIC" 1640381 T LOGIC (NIL) -9 NIL 1640463 NIL) (-682 1640019 1640048 1640119 "LOGIC-" 1640124 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-681 1639194 1639352 1639545 "LODOOPS" 1639875 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-680 1636289 1639110 1639176 "LODO" 1639181 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-679 1634813 1635062 1635415 "LODOF" 1636036 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-678 1630689 1633448 1633489 "LODOCAT" 1633927 NIL LODOCAT (NIL T) -9 NIL 1634138 NIL) (-677 1630404 1630480 1630607 "LODOCAT-" 1630612 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-676 1627390 1630245 1630363 "LODO2" 1630368 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-675 1624497 1627327 1627372 "LODO1" 1627377 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-674 1623366 1623543 1623848 "LODEEF" 1624320 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-673 1618338 1621532 1621573 "LNAGG" 1622435 NIL LNAGG (NIL T) -9 NIL 1622870 NIL) (-672 1617431 1617699 1618041 "LNAGG-" 1618046 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613411 1614356 1614995 "LMOPS" 1616846 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612710 1613188 1613229 "LMODULE" 1613234 NIL LMODULE (NIL T) -9 NIL 1613260 NIL) (-669 1609665 1612355 1612478 "LMDICT" 1612620 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1609241 1609455 1609496 "LLINSET" 1609557 NIL LLINSET (NIL T) -9 NIL 1609601 NIL) (-667 1608886 1609149 1609209 "LITERAL" 1609214 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1601340 1607820 1608124 "LIST" 1608615 NIL LIST (NIL T) -8 NIL NIL NIL) (-665 1600859 1600939 1601078 "LIST3" 1601260 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-664 1599848 1600044 1600272 "LIST2" 1600677 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597946 1598294 1598693 "LIST2MAP" 1599495 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-662 1597529 1597765 1597806 "LINSET" 1597811 NIL LINSET (NIL T) -9 NIL 1597845 NIL) (-661 1596343 1597037 1597204 "LINFORM" 1597414 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594642 1595370 1595411 "LINEXP" 1595901 NIL LINEXP (NIL T) -9 NIL 1596174 NIL) (-659 1593218 1594122 1594303 "LINELT" 1594513 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591775 1592055 1592366 "LINDEP" 1592970 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590911 1591507 1591617 "LINBASIS" 1591705 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587648 1588397 1589174 "LIMITRF" 1590166 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585933 1586247 1586656 "LIMITPS" 1587343 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1579953 1585444 1585672 "LIE" 1585754 NIL LIE (NIL T T) -8 NIL NIL NIL) (-653 1578781 1579356 1579396 "LIECAT" 1579536 NIL LIECAT (NIL T) -9 NIL 1579687 NIL) (-652 1578616 1578649 1578737 "LIECAT-" 1578742 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-651 1570803 1578156 1578312 "LIB" 1578480 T LIB (NIL) -8 NIL NIL NIL) (-650 1566372 1567321 1568256 "LGROBP" 1569920 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564310 1564644 1564994 "LF" 1566093 NIL LF (NIL T T) -7 NIL NIL NIL) (-648 1562934 1563842 1563870 "LFCAT" 1564077 T LFCAT (NIL) -9 NIL 1564216 NIL) (-647 1559794 1560466 1561154 "LEXTRIPK" 1562298 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556382 1557364 1557867 "LEXP" 1559374 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555798 1556103 1556195 "LETAST" 1556310 T LETAST (NIL) -8 NIL NIL NIL) (-644 1554184 1554509 1554910 "LEADCDET" 1555480 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553362 1553448 1553677 "LAZM3PK" 1554105 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547873 1551439 1551977 "LAUPOL" 1552874 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547446 1547496 1547657 "LAPLACE" 1547823 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545183 1546547 1546798 "LA" 1547279 NIL LA (NIL T T T) -8 NIL NIL NIL) (-639 1544031 1544747 1544788 "LALG" 1544850 NIL LALG (NIL T) -9 NIL 1544909 NIL) (-638 1543727 1543804 1543940 "LALG-" 1543945 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-637 1543556 1543586 1543627 "KVTFROM" 1543689 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542313 1542923 1543108 "KTVLOGIC" 1543391 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1542142 1542172 1542213 "KRCFROM" 1542275 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1541034 1541233 1541532 "KOVACIC" 1541942 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540863 1540893 1540934 "KONVERT" 1540996 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540692 1540722 1540763 "KOERCE" 1540825 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1538379 1539285 1539662 "KERNEL" 1540348 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-630 1537863 1537956 1538088 "KERNEL2" 1538293 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-629 1531334 1536340 1536394 "KDAGG" 1536771 NIL KDAGG (NIL T T) -9 NIL 1536977 NIL) (-628 1530845 1530987 1531192 "KDAGG-" 1531197 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523545 1530506 1530661 "KAFILE" 1530723 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1523149 1523434 1523497 "JVMOP" 1523502 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521885 1522389 1522638 "JVMMDACC" 1522920 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520821 1521275 1521480 "JVMFDACC" 1521700 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519402 1519897 1520197 "JVMCSTTG" 1520541 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518538 1518942 1519103 "JVMCFACC" 1519261 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1518216 1518455 1518504 "JVMBCODE" 1518509 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1512236 1517727 1517955 "JORDAN" 1518037 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511549 1511885 1512006 "JOINAST" 1512135 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507584 1509726 1509780 "IXAGG" 1510709 NIL IXAGG (NIL T T) -9 NIL 1511168 NIL) (-617 1506437 1506809 1507228 "IXAGG-" 1507233 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501526 1506359 1506418 "IVECTOR" 1506423 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1500250 1500529 1500795 "ITUPLE" 1501293 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498722 1498929 1499224 "ITRIGMNP" 1500072 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497449 1497671 1497954 "ITFUN3" 1498498 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1497075 1497138 1497247 "ITFUN2" 1497386 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-611 1496180 1496555 1496729 "ITFORM" 1496921 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493949 1495200 1495478 "ITAYLOR" 1495935 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482346 1488086 1489249 "ISUPS" 1492819 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481438 1481590 1481826 "ISUMP" 1482193 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476288 1481383 1481424 "ISTRING" 1481429 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475704 1476009 1476101 "ISAST" 1476216 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474901 1474995 1475211 "IRURPK" 1475618 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473813 1474038 1474278 "IRSN" 1474681 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471858 1472239 1472668 "IRRF2F" 1473451 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471599 1471643 1471719 "IRREDFFX" 1471814 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1470172 1470473 1470772 "IROOT" 1471332 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1466612 1467856 1468548 "IR" 1469512 NIL IR (NIL T) -8 NIL NIL NIL) (-599 1465751 1466105 1466256 "IRFORM" 1466481 T IRFORM (NIL) -8 NIL NIL NIL) (-598 1463340 1463859 1464425 "IR2" 1465229 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462422 1462553 1462767 "IR2F" 1463223 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-596 1462207 1462247 1462307 "IPRNTPK" 1462382 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1458160 1462096 1462165 "IPF" 1462170 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1456181 1458085 1458142 "IPADIC" 1458147 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455439 1455741 1455871 "IP4ADDR" 1456071 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454777 1455068 1455200 "IOMODE" 1455327 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453748 1454374 1454501 "IOBFILE" 1454670 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1453158 1453652 1453680 "IOBCON" 1453685 T IOBCON (NIL) -9 NIL 1453706 NIL) (-589 1452663 1452727 1452910 "INVLAPLA" 1453094 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1442233 1444665 1447051 "INTTR" 1450327 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438526 1439310 1440175 "INTTOOLS" 1441418 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1438106 1438203 1438320 "INTSLPE" 1438429 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435573 1438029 1438088 "INTRVL" 1438093 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1433151 1433687 1434262 "INTRF" 1435058 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432544 1432659 1432801 "INTRET" 1433049 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430517 1430930 1431400 "INTRAT" 1432152 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427762 1428363 1428982 "INTPM" 1430002 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424479 1425106 1425844 "INTPAF" 1427148 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419580 1420620 1421671 "INTPACK" 1423448 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1415768 1419377 1419486 "INT" 1419491 T INT (NIL) -8 NIL NIL NIL) (-577 1415014 1415172 1415380 "INTHERTR" 1415610 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-576 1414447 1414533 1414721 "INTHERAL" 1414928 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-575 1412215 1412736 1413193 "INTHEORY" 1414010 T INTHEORY (NIL) -7 NIL NIL NIL) (-574 1403547 1405242 1407014 "INTG0" 1410567 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-573 1384072 1388910 1393720 "INTFTBL" 1398757 T INTFTBL (NIL) -8 NIL NIL NIL) (-572 1383297 1383459 1383632 "INTFACT" 1383931 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-571 1380694 1381170 1381727 "INTEF" 1382851 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-570 1378891 1379786 1379814 "INTDOM" 1380115 T INTDOM (NIL) -9 NIL 1380322 NIL) (-569 1378230 1378434 1378676 "INTDOM-" 1378681 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-568 1374104 1376519 1376573 "INTCAT" 1377372 NIL INTCAT (NIL T) -9 NIL 1377693 NIL) (-567 1373558 1373679 1373807 "INTBIT" 1373996 T INTBIT (NIL) -7 NIL NIL NIL) (-566 1372239 1372411 1372718 "INTALG" 1373403 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-565 1371716 1371812 1371969 "INTAF" 1372143 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-564 1364683 1371526 1371666 "INTABL" 1371671 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-563 1363920 1364482 1364547 "INT8" 1364581 T INT8 (NIL) -8 NIL NIL 1364626) (-562 1363156 1363718 1363783 "INT64" 1363817 T INT64 (NIL) -8 NIL NIL 1363862) (-561 1362392 1362954 1363019 "INT32" 1363053 T INT32 (NIL) -8 NIL NIL 1363098) (-560 1361628 1362190 1362255 "INT16" 1362289 T INT16 (NIL) -8 NIL NIL 1362334) (-559 1355729 1359176 1359204 "INS" 1360138 T INS (NIL) -9 NIL 1360803 NIL) (-558 1352783 1353740 1354714 "INS-" 1354787 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351540 1351785 1352083 "INPSIGN" 1352536 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350634 1350775 1350972 "INPRODPF" 1351420 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349504 1349645 1349882 "INPRODFF" 1350514 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348492 1348656 1348916 "INNMFACT" 1349340 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347671 1347786 1347974 "INMODGCD" 1348391 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1346155 1346424 1346748 "INFSP" 1347416 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345315 1345456 1345639 "INFPROD0" 1346035 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1341882 1343380 1343895 "INFORM" 1344808 T INFORM (NIL) -8 NIL NIL NIL) (-549 1341480 1341552 1341650 "INFORM1" 1341817 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-548 1340985 1341092 1341206 "INFINITY" 1341386 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1340059 1340705 1340806 "INETCLTS" 1340904 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338657 1338925 1339246 "INEP" 1339807 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337718 1338554 1338619 "INDE" 1338624 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337270 1337350 1337467 "INCRMAPS" 1337645 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335992 1336539 1336745 "INBFILE" 1337084 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1331171 1332228 1333172 "INBFF" 1335080 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1330025 1330348 1330376 "INBCON" 1330889 T INBCON (NIL) -9 NIL 1331155 NIL) (-540 1329235 1329500 1329776 "INBCON-" 1329781 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328654 1328959 1329050 "INAST" 1329164 T INAST (NIL) -8 NIL NIL NIL) (-538 1328021 1328333 1328439 "IMPTAST" 1328568 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323942 1327865 1327969 "IMATRIX" 1327974 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322634 1322773 1323089 "IMATQF" 1323798 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320814 1321081 1321418 "IMATLIN" 1322390 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314729 1320738 1320796 "ILIST" 1320801 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312395 1314589 1314702 "IIARRAY2" 1314707 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1307195 1312306 1312370 "IFF" 1312375 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306476 1306812 1306928 "IFAST" 1307099 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300988 1305768 1305956 "IFARRAY" 1306333 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1300026 1300892 1300965 "IFAMON" 1300970 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299598 1299675 1299729 "IEVALAB" 1299936 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299261 1299341 1299501 "IEVALAB-" 1299506 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298642 1299176 1299238 "IDPO" 1299243 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-525 1297706 1298531 1298606 "IDPOAMS" 1298611 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-524 1296839 1297595 1297670 "IDPOAM" 1297675 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-523 1295319 1295846 1295898 "IDPC" 1296410 NIL IDPC (NIL T T) -9 NIL 1296691 NIL) (-522 1294651 1295211 1295284 "IDPAM" 1295289 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293866 1294543 1294616 "IDPAG" 1294621 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293410 1293672 1293762 "IDENT" 1293796 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289629 1290513 1291408 "IDECOMP" 1292567 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1282264 1283552 1284599 "IDEAL" 1288665 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281406 1281536 1281736 "ICDEN" 1282148 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280381 1280886 1281033 "ICARD" 1281279 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278411 1278754 1279159 "IBPTOOLS" 1280058 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273526 1278031 1278144 "IBITS" 1278330 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1270201 1270825 1271520 "IBATOOL" 1272943 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267962 1268442 1268975 "IBACHIN" 1269736 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265552 1267808 1267911 "IARRAY2" 1267916 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1261265 1265478 1265535 "IARRAY1" 1265540 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254275 1259677 1260158 "IAN" 1260804 T IAN (NIL) -8 NIL NIL NIL) (-508 1253780 1253843 1254016 "IALGFACT" 1254212 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253272 1253421 1253449 "HYPCAT" 1253656 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252774 1252927 1253113 "HYPCAT-" 1253118 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252321 1252569 1252652 "HOSTNAME" 1252711 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1252154 1252203 1252244 "HOMOTOP" 1252249 NIL HOMOTOP (NIL T) -9 NIL 1252282 NIL) (-503 1248587 1250086 1250127 "HOAGG" 1251108 NIL HOAGG (NIL T) -9 NIL 1251837 NIL) (-502 1247103 1247580 1248106 "HOAGG-" 1248111 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1240139 1246696 1246846 "HEXADEC" 1246973 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238851 1239109 1239372 "HEUGCD" 1239916 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237783 1238688 1238818 "HELLFDIV" 1238823 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235793 1237560 1237648 "HEAP" 1237727 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234990 1235345 1235479 "HEADAST" 1235679 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228377 1234905 1234967 "HDP" 1234972 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221389 1228012 1228164 "HDMP" 1228278 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220695 1220853 1221017 "HB" 1221245 T HB (NIL) -7 NIL NIL NIL) (-493 1213705 1220541 1220645 "HASHTBL" 1220650 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1213121 1213426 1213518 "HASAST" 1213633 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210527 1212743 1212925 "HACKPI" 1212959 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205699 1210380 1210493 "GTSET" 1210498 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198738 1205577 1205675 "GSTBL" 1205680 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190487 1197903 1198159 "GSERIES" 1198538 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189518 1190031 1190059 "GROUP" 1190262 T GROUP (NIL) -9 NIL 1190396 NIL) (-486 1188842 1189043 1189294 "GROUP-" 1189299 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1187191 1187530 1187917 "GROEBSOL" 1188519 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1186019 1186379 1186430 "GRMOD" 1186959 NIL GRMOD (NIL T T) -9 NIL 1187127 NIL) (-483 1185775 1185823 1185951 "GRMOD-" 1185956 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180915 1182129 1183129 "GRIMAGE" 1184795 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179309 1179642 1179966 "GRDEF" 1180611 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178741 1178869 1179010 "GRAY" 1179188 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177818 1178320 1178371 "GRALG" 1178524 NIL GRALG (NIL T T) -9 NIL 1178617 NIL) (-478 1177455 1177552 1177715 "GRALG-" 1177720 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173936 1177038 1177217 "GPOLSET" 1177361 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173284 1173347 1173605 "GOSPER" 1173873 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168854 1169722 1170248 "GMODPOL" 1172983 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167841 1168043 1168281 "GHENSEL" 1168666 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161913 1162840 1163860 "GENUPS" 1166925 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161604 1161661 1161750 "GENUFACT" 1161856 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1161004 1161093 1161258 "GENPGCD" 1161522 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160472 1160513 1160726 "GENMFACT" 1160963 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1159008 1159295 1159602 "GENEEZ" 1160215 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1152180 1158619 1158781 "GDMP" 1158931 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140919 1145951 1147057 "GCNAALG" 1151163 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1139046 1140094 1140122 "GCDDOM" 1140377 T GCDDOM (NIL) -9 NIL 1140534 NIL) (-465 1138486 1138643 1138858 "GCDDOM-" 1138863 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1137136 1137343 1137647 "GB" 1138265 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-463 1125608 1128082 1130474 "GBINTERN" 1134827 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-462 1123409 1123737 1124158 "GBF" 1125283 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-461 1122166 1122355 1122622 "GBEUCLID" 1123225 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-460 1121497 1121640 1121789 "GAUSSFAC" 1122037 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119818 1120166 1120480 "GALUTIL" 1121216 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1118078 1118400 1118724 "GALPOLYU" 1119545 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115377 1115733 1116140 "GALFACTU" 1117775 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106991 1108682 1110290 "GALFACT" 1113809 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104277 1105037 1105065 "FVFUN" 1106221 T FVFUN (NIL) -9 NIL 1106941 NIL) (-454 1103507 1103725 1103753 "FVC" 1104044 T FVC (NIL) -9 NIL 1104227 NIL) (-453 1103108 1103332 1103400 "FUNDESC" 1103459 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102681 1102905 1102986 "FUNCTION" 1103060 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1100311 1101003 1101469 "FT" 1102235 T FT (NIL) -8 NIL NIL NIL) (-450 1098988 1099612 1099815 "FTEM" 1100128 T FTEM (NIL) -8 NIL NIL NIL) (-449 1097257 1097568 1097965 "FSUPFACT" 1098679 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095576 1095943 1096275 "FST" 1096945 T FST (NIL) -8 NIL NIL NIL) (-447 1094757 1094881 1095069 "FSRED" 1095458 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093446 1093712 1094059 "FSPRMELT" 1094472 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090656 1091190 1091676 "FSPECF" 1093009 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1070883 1080430 1080471 "FS" 1084355 NIL FS (NIL T) -9 NIL 1086644 NIL) (-443 1058944 1062519 1066576 "FS-" 1066876 NIL FS- (NIL T T) -8 NIL NIL NIL) (-442 1058466 1058526 1058696 "FSINT" 1058885 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-441 1056602 1057459 1057762 "FSERIES" 1058245 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-440 1055626 1055760 1055984 "FSCINT" 1056482 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-439 1051490 1054570 1054611 "FSAGG" 1054981 NIL FSAGG (NIL T) -9 NIL 1055240 NIL) (-438 1049090 1049853 1050649 "FSAGG-" 1050744 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-437 1048114 1048275 1048502 "FSAGG2" 1048943 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-436 1045774 1046072 1046620 "FS2UPS" 1047832 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-435 1045402 1045451 1045580 "FS2" 1045725 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-434 1044268 1044451 1044753 "FS2EXPXP" 1045227 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-433 1043682 1043809 1043961 "FRUTIL" 1044148 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1034599 1039177 1040535 "FR" 1042356 NIL FR (NIL T) -8 NIL NIL NIL) (-431 1029117 1032288 1032328 "FRNAALG" 1033648 NIL FRNAALG (NIL T) -9 NIL 1034246 NIL) (-430 1024598 1025866 1027141 "FRNAALG-" 1027891 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-429 1024230 1024279 1024406 "FRNAAF2" 1024549 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-428 1022517 1023079 1023375 "FRMOD" 1024042 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-427 1020122 1020892 1021210 "FRIDEAL" 1022308 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1019307 1019400 1019691 "FRIDEAL2" 1020029 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-425 1018398 1018854 1018895 "FRETRCT" 1018900 NIL FRETRCT (NIL T) -9 NIL 1019076 NIL) (-424 1017456 1017741 1018092 "FRETRCT-" 1018097 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-423 1014270 1015740 1015799 "FRAMALG" 1016681 NIL FRAMALG (NIL T T) -9 NIL 1016973 NIL) (-422 1012308 1012859 1013489 "FRAMALG-" 1013712 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-421 1005279 1011781 1012058 "FRAC" 1012063 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1004909 1004972 1005079 "FRAC2" 1005216 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-419 1004539 1004602 1004709 "FR2" 1004846 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-418 998456 1001918 1001946 "FPS" 1003065 T FPS (NIL) -9 NIL 1003622 NIL) (-417 997881 998014 998178 "FPS-" 998324 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994833 996838 996866 "FPC" 997091 T FPC (NIL) -9 NIL 997233 NIL) (-415 994614 994666 994763 "FPC-" 994768 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993372 994102 994143 "FPATMAB" 994148 NIL FPATMAB (NIL T) -9 NIL 994300 NIL) (-413 991515 992114 992461 "FPARFRAC" 993088 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986807 987407 988089 "FORTRAN" 990947 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984493 985023 985562 "FORT" 986288 T FORT (NIL) -7 NIL NIL NIL) (-410 982067 982731 982759 "FORTFN" 983819 T FORTFN (NIL) -9 NIL 984443 NIL) (-409 981819 981881 981909 "FORTCAT" 981968 T FORTCAT (NIL) -9 NIL 982030 NIL) (-408 979823 980435 980825 "FORMULA" 981449 T FORMULA (NIL) -8 NIL NIL NIL) (-407 979605 979641 979710 "FORMULA1" 979787 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-406 979122 979180 979353 "FORDER" 979547 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 978182 978382 978575 "FOP" 978949 T FOP (NIL) -7 NIL NIL NIL) (-404 976595 977462 977636 "FNLA" 978064 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 975214 975725 975753 "FNCAT" 976213 T FNCAT (NIL) -9 NIL 976473 NIL) (-402 974657 975173 975201 "FNAME" 975206 T FNAME (NIL) -8 NIL NIL NIL) (-401 972983 974156 974184 "FMTC" 974189 T FMTC (NIL) -9 NIL 974225 NIL) (-400 971531 972919 972965 "FMONOID" 972970 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 968120 969486 969527 "FMONCAT" 970744 NIL FMONCAT (NIL T) -9 NIL 971349 NIL) (-398 967138 967862 968011 "FM" 968016 NIL FM (NIL T T) -8 NIL NIL NIL) (-397 964460 965208 965236 "FMFUN" 966380 T FMFUN (NIL) -9 NIL 967088 NIL) (-396 963693 963910 963938 "FMC" 964228 T FMC (NIL) -9 NIL 964410 NIL) (-395 960566 961618 961672 "FMCAT" 962867 NIL FMCAT (NIL T T) -9 NIL 963362 NIL) (-394 959234 960332 960432 "FM1" 960511 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-393 956972 957424 957918 "FLOATRP" 958785 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 949628 954701 955322 "FLOAT" 956371 T FLOAT (NIL) -8 NIL NIL NIL) (-391 947030 947566 948144 "FLOATCP" 949095 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-390 945548 946622 946663 "FLINEXP" 946668 NIL FLINEXP (NIL T) -9 NIL 946761 NIL) (-389 944678 944937 945265 "FLINEXP-" 945270 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943736 943898 944122 "FLASORT" 944530 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940654 941706 941758 "FLALG" 942985 NIL FLALG (NIL T T) -9 NIL 943452 NIL) (-386 933918 938063 938104 "FLAGG" 939366 NIL FLAGG (NIL T) -9 NIL 940018 NIL) (-385 932572 932983 933473 "FLAGG-" 933478 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-384 931596 931757 931984 "FLAGG2" 932425 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-383 928227 929441 929500 "FINRALG" 930628 NIL FINRALG (NIL T T) -9 NIL 931136 NIL) (-382 927351 927616 927955 "FINRALG-" 927960 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926657 926956 926984 "FINITE" 927180 T FINITE (NIL) -9 NIL 927287 NIL) (-380 918608 921187 921227 "FINAALG" 924894 NIL FINAALG (NIL T) -9 NIL 926347 NIL) (-379 913724 914990 916134 "FINAALG-" 917513 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 913002 913479 913582 "FILE" 913654 NIL FILE (NIL T) -8 NIL NIL NIL) (-377 911562 911984 912038 "FILECAT" 912722 NIL FILECAT (NIL T T) -9 NIL 912938 NIL) (-376 908958 910792 910820 "FIELD" 910860 T FIELD (NIL) -9 NIL 910940 NIL) (-375 907500 907963 908474 "FIELD-" 908479 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 905182 906135 906482 "FGROUP" 907186 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904254 904436 904656 "FGLMICPK" 905014 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899488 904179 904236 "FFX" 904241 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 899083 899150 899285 "FFSLPE" 899421 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 894959 895855 896651 "FFPOLY" 898319 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-369 894457 894499 894708 "FFPOLY2" 894917 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-368 889705 894376 894439 "FFP" 894444 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884505 889616 889680 "FF" 889685 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-366 879015 883848 884038 "FFNBX" 884359 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-365 873327 878150 878408 "FFNBP" 878869 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-364 867344 872611 872822 "FFNB" 873160 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-363 866164 866374 866689 "FFINTBAS" 867141 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-362 861740 864411 864439 "FFIELDC" 865059 T FFIELDC (NIL) -9 NIL 865435 NIL) (-361 860318 860773 861270 "FFIELDC-" 861275 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-360 859875 859933 860057 "FFHOM" 860260 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-359 857534 858057 858574 "FFF" 859390 NIL FFF (NIL T) -7 NIL NIL NIL) (-358 852548 857276 857377 "FFCGX" 857477 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-357 847566 852280 852387 "FFCGP" 852491 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-356 842145 847293 847401 "FFCG" 847502 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-355 820808 831877 831963 "FFCAT" 837128 NIL FFCAT (NIL T T T) -9 NIL 838579 NIL) (-354 815819 817053 818367 "FFCAT-" 819597 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815224 815273 815508 "FFCAT2" 815770 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-352 803877 808196 809416 "FEXPR" 814076 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802805 803274 803315 "FEVALAB" 803399 NIL FEVALAB (NIL T) -9 NIL 803660 NIL) (-350 801922 802174 802512 "FEVALAB-" 802517 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 800332 801305 801508 "FDIV" 801821 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-348 797194 798079 798194 "FDIVCAT" 799762 NIL FDIVCAT (NIL T T T T) -9 NIL 800199 NIL) (-347 796950 796983 797153 "FDIVCAT-" 797158 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-346 796164 796257 796534 "FDIV2" 796857 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-345 795072 795459 795661 "FCTRDATA" 795982 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793728 794017 794306 "FCPAK1" 794803 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792731 793228 793369 "FCOMP" 793619 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776046 779881 783419 "FC" 789213 T FC (NIL) -8 NIL NIL NIL) (-341 767741 772367 772407 "FAXF" 774209 NIL FAXF (NIL T) -9 NIL 774901 NIL) (-340 764862 765675 766500 "FAXF-" 766965 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759431 764238 764414 "FARRAY" 764719 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 753995 756378 756431 "FAMR" 757454 NIL FAMR (NIL T T) -9 NIL 757914 NIL) (-337 752819 753187 753622 "FAMR-" 753627 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751846 752741 752794 "FAMONOID" 752799 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749476 750328 750381 "FAMONC" 751322 NIL FAMONC (NIL T T) -9 NIL 751708 NIL) (-334 747950 749230 749367 "FAGROUP" 749372 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745703 746064 746467 "FACUTIL" 747631 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744790 744987 745209 "FACTFUNC" 745513 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736548 744093 744292 "EXPUPXS" 744646 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734001 734571 735157 "EXPRTUBE" 735982 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730212 730864 731594 "EXPRODE" 733340 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 714506 728861 729290 "EXPR" 729816 NIL EXPR (NIL T) -8 NIL NIL NIL) (-327 708940 709647 710453 "EXPR2UPS" 713804 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-326 708566 708629 708738 "EXPR2" 708877 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-325 698883 707717 708008 "EXPEXPAN" 708402 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698647 698840 698869 "EXIT" 698874 T EXIT (NIL) -8 NIL NIL NIL) (-323 698067 698371 698462 "EXITAST" 698576 T EXITAST (NIL) -8 NIL NIL NIL) (-322 697688 697756 697869 "EVALCYC" 697999 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697205 697347 697388 "EVALAB" 697558 NIL EVALAB (NIL T) -9 NIL 697662 NIL) (-320 696662 696808 697029 "EVALAB-" 697034 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693770 695318 695346 "EUCDOM" 695901 T EUCDOM (NIL) -9 NIL 696251 NIL) (-318 692109 692617 693207 "EUCDOM-" 693212 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 679426 682407 685157 "ESTOOLS" 689379 T ESTOOLS (NIL) -7 NIL NIL NIL) (-316 679052 679115 679224 "ESTOOLS2" 679363 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-315 678797 678845 678925 "ESTOOLS1" 679004 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-314 672498 674428 674456 "ES" 677224 T ES (NIL) -9 NIL 678634 NIL) (-313 667175 668732 670549 "ES-" 670713 NIL ES- (NIL T) -8 NIL NIL NIL) (-312 663483 664310 665090 "ESCONT" 666415 T ESCONT (NIL) -7 NIL NIL NIL) (-311 663222 663260 663342 "ESCONT1" 663445 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-310 662891 662947 663047 "ES2" 663166 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-309 662515 662579 662688 "ES1" 662827 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-308 661707 661860 662036 "ERROR" 662359 T ERROR (NIL) -7 NIL NIL NIL) (-307 654723 661566 661657 "EQTBL" 661662 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 646982 650037 651486 "EQ" 653307 NIL -1512 (NIL T) -8 NIL NIL NIL) (-305 646608 646671 646780 "EQ2" 646919 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-304 641851 642946 644039 "EP" 645547 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640391 640742 641048 "ENV" 641565 T ENV (NIL) -8 NIL NIL NIL) (-302 639351 640025 640053 "ENTIRER" 640058 T ENTIRER (NIL) -9 NIL 640104 NIL) (-301 635763 637533 637894 "EMR" 639159 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 634867 635078 635132 "ELTAGG" 635512 NIL ELTAGG (NIL T T) -9 NIL 635723 NIL) (-299 634574 634648 634789 "ELTAGG-" 634794 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634332 634367 634421 "ELTAB" 634505 NIL ELTAB (NIL T T) -9 NIL 634557 NIL) (-297 633434 633604 633803 "ELFUTS" 634183 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633158 633232 633260 "ELEMFUN" 633365 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633022 633049 633117 "ELEMFUN-" 633122 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627439 631064 631105 "ELAGG" 632045 NIL ELAGG (NIL T) -9 NIL 632508 NIL) (-293 625616 626158 626821 "ELAGG-" 626826 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 624898 625065 625221 "ELABOR" 625480 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623505 623838 624132 "ELABEXPR" 624624 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616017 618142 618971 "EFUPXS" 622780 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609143 611266 612077 "EFULS" 615292 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606580 606986 607458 "EFSTRUC" 608775 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596017 597937 599485 "EF" 605095 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 594995 595502 595651 "EAB" 595888 T EAB (NIL) -8 NIL NIL NIL) (-285 594117 594954 594982 "E04UCFA" 594987 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593239 594076 594104 "E04NAFA" 594109 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592361 593198 593226 "E04MBFA" 593231 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591483 592320 592348 "E04JAFA" 592353 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590607 591442 591470 "E04GCFA" 591475 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589731 590566 590594 "E04FDFA" 590599 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588853 589690 589718 "E04DGFA" 589723 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 582930 584378 585742 "E04AGNT" 587509 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581550 582231 582271 "DVARCAT" 582612 NIL DVARCAT (NIL T) -9 NIL 582775 NIL) (-276 580700 580966 581280 "DVARCAT-" 581285 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572661 580499 580628 "DSMP" 580633 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571012 571803 571844 "DSEXT" 572207 NIL DSEXT (NIL T) -9 NIL 572501 NIL) (-273 569201 569725 570391 "DSEXT-" 570396 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 563784 565146 566214 "DROPT" 568153 T DROPT (NIL) -8 NIL NIL NIL) (-271 563443 563508 563606 "DROPT1" 563719 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-270 558462 559684 560821 "DROPT0" 562326 T DROPT0 (NIL) -7 NIL NIL NIL) (-269 556771 557132 557518 "DRAWPT" 558096 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 551262 552281 553360 "DRAW" 555745 NIL DRAW (NIL T) -7 NIL NIL NIL) (-267 550889 550948 551066 "DRAWHACK" 551203 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-266 549590 549889 550180 "DRAWCX" 550618 T DRAWCX (NIL) -7 NIL NIL NIL) (-265 549099 549174 549325 "DRAWCURV" 549516 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-264 539417 541529 543644 "DRAWCFUN" 547004 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-263 535888 538082 538123 "DQAGG" 538752 NIL DQAGG (NIL T) -9 NIL 539026 NIL) (-262 522471 530099 530182 "DPOLCAT" 532034 NIL DPOLCAT (NIL T T T T) -9 NIL 532579 NIL) (-261 516990 518656 520614 "DPOLCAT-" 520619 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509847 516851 516949 "DPMO" 516954 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502601 509627 509794 "DPMM" 509799 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502123 502385 502474 "DOMTMPLT" 502532 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501472 501925 502005 "DOMCTOR" 502063 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500624 500952 501103 "DOMAIN" 501341 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493636 500259 500411 "DMP" 500525 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491413 492703 492744 "DMEXT" 492749 NIL DMEXT (NIL T) -9 NIL 492925 NIL) (-253 491007 491069 491213 "DLP" 491351 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484130 490334 490524 "DLIST" 490849 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480668 482955 482996 "DLAGG" 483546 NIL DLAGG (NIL T) -9 NIL 483776 NIL) (-250 479180 479994 480022 "DIVRING" 480114 T DIVRING (NIL) -9 NIL 480197 NIL) (-249 478363 478607 478907 "DIVRING-" 478912 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476405 476822 477228 "DISPLAY" 477977 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 469812 476319 476382 "DIRPROD" 476387 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-246 468642 468863 469128 "DIRPROD2" 469605 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-245 456861 463353 463406 "DIRPCAT" 463664 NIL DIRPCAT (NIL NIL T) -9 NIL 464539 NIL) (-244 454061 454829 455710 "DIRPCAT-" 456047 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453342 453508 453694 "DIOSP" 453895 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449756 452226 452267 "DIOPS" 452701 NIL DIOPS (NIL T) -9 NIL 452930 NIL) (-241 449275 449419 449610 "DIOPS-" 449615 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448182 448954 448982 "DIFRING" 448987 T DIFRING (NIL) -9 NIL 449009 NIL) (-239 447830 447928 447956 "DIFFSPC" 448075 T DIFFSPC (NIL) -9 NIL 448150 NIL) (-238 447451 447553 447705 "DIFFSPC-" 447710 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446387 446985 447026 "DIFFMOD" 447031 NIL DIFFMOD (NIL T) -9 NIL 447129 NIL) (-236 446083 446140 446181 "DIFFDOM" 446302 NIL DIFFDOM (NIL T) -9 NIL 446370 NIL) (-235 445930 445960 446044 "DIFFDOM-" 446049 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443670 445134 445175 "DIFEXT" 445180 NIL DIFEXT (NIL T) -9 NIL 445333 NIL) (-233 440704 443174 443215 "DIAGG" 443220 NIL DIAGG (NIL T) -9 NIL 443240 NIL) (-232 440052 440245 440497 "DIAGG-" 440502 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434902 439011 439288 "DHMATRIX" 439821 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430370 431423 432433 "DFSFUN" 433912 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424604 429301 429613 "DFLOAT" 430078 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422843 423148 423537 "DFINTTLS" 424312 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419662 420864 421264 "DERHAM" 422509 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417198 419437 419526 "DEQUEUE" 419606 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416440 416585 416768 "DEGRED" 417060 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412846 413615 414461 "DEFINTRF" 415668 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410383 410870 411462 "DEFINTEF" 412365 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409667 410003 410118 "DEFAST" 410288 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402703 409260 409410 "DECIMAL" 409537 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400161 400673 401179 "DDFACT" 402247 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399751 399800 399951 "DBLRESP" 400112 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398952 399521 399612 "DBASIS" 399700 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396736 397182 397543 "DBASE" 398718 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395924 396216 396362 "DATAARY" 396635 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394982 395883 395911 "D03FAFA" 395916 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394041 394941 394969 "D03EEFA" 394974 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391967 392457 392946 "D03AGNT" 393572 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391208 391926 391954 "D02EJFA" 391959 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390449 391167 391195 "D02CJFA" 391200 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389690 390408 390436 "D02BHFA" 390441 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388931 389649 389677 "D02BBFA" 389682 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382062 383717 385323 "D02AGNT" 387345 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379812 380353 380899 "D01WGTS" 381536 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378819 379771 379799 "D01TRNS" 379804 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377827 378778 378806 "D01GBFA" 378811 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376835 377786 377814 "D01FCFA" 377819 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375843 376794 376822 "D01ASFA" 376827 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374851 375802 375830 "D01AQFA" 375835 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373859 374810 374838 "D01APFA" 374843 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372867 373818 373846 "D01ANFA" 373851 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371875 372826 372854 "D01AMFA" 372859 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370883 371834 371862 "D01ALFA" 371867 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369891 370842 370870 "D01AKFA" 370875 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368899 369850 369878 "D01AJFA" 369883 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362122 363747 365308 "D01AGNT" 367358 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361441 361587 361739 "CYCLOTOM" 361990 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358096 358889 359616 "CYCLES" 360734 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357396 357542 357713 "CVMP" 357957 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355183 355495 355864 "CTRIGMNP" 357124 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354541 354977 355050 "CTOR" 355130 T CTOR (NIL) -8 NIL NIL NIL) (-189 354014 354272 354373 "CTORKIND" 354460 T CTORKIND (NIL) -8 NIL NIL NIL) (-188 353219 353607 353635 "CTORCAT" 353817 T CTORCAT (NIL) -9 NIL 353930 NIL) (-187 352793 352928 353087 "CTORCAT-" 353092 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-186 352207 352467 352575 "CTORCALL" 352717 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-185 351563 351680 351833 "CSTTOOLS" 352104 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347260 348019 348777 "CRFP" 350875 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346675 346981 347073 "CRCEAST" 347188 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345698 345907 346135 "CRAPACK" 346479 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345078 345183 345387 "CPMATCH" 345574 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344797 344831 344937 "CPIMA" 345044 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341055 341817 342536 "COORDSYS" 344132 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340443 340588 340730 "CONTOUR" 340933 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335908 338446 338938 "CONTFRAC" 339983 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335782 335809 335837 "CONDUIT" 335874 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334736 335410 335438 "COMRING" 335443 T COMRING (NIL) -9 NIL 335495 NIL) (-174 333718 334094 334278 "COMPPROP" 334572 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333373 333414 333542 "COMPLPAT" 333677 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 321756 333182 333291 "COMPLEX" 333296 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-171 321386 321449 321556 "COMPLEX2" 321693 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-170 320707 320846 321006 "COMPILER" 321246 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320419 320460 320558 "COMPFACT" 320666 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301794 314123 314163 "COMPCAT" 315167 NIL COMPCAT (NIL T) -9 NIL 316515 NIL) (-167 290682 294233 297860 "COMPCAT-" 298216 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290405 290439 290542 "COMMUPC" 290648 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290193 290233 290292 "COMMONOP" 290366 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289701 289944 290031 "COMM" 290126 T COMM (NIL) -8 NIL NIL NIL) (-163 289223 289505 289580 "COMMAAST" 289646 T COMMAAST (NIL) -8 NIL NIL NIL) (-162 288418 288666 288694 "COMBOPC" 289032 T COMBOPC (NIL) -9 NIL 289207 NIL) (-161 287272 287524 287766 "COMBINAT" 288208 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283615 284303 284930 "COMBF" 286694 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282277 282731 282966 "COLOR" 283400 T COLOR (NIL) -8 NIL NIL NIL) (-158 281693 281998 282090 "COLONAST" 282205 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281327 281380 281505 "CMPLXRT" 281640 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280715 281027 281126 "CLLCTAST" 281248 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276175 277245 278325 "CLIP" 279655 T CLIP (NIL) -7 NIL NIL NIL) (-154 274348 275276 275516 "CLIF" 276002 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270330 272466 272507 "CLAGG" 273436 NIL CLAGG (NIL T) -9 NIL 273972 NIL) (-152 268674 269209 269792 "CLAGG-" 269797 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268212 268303 268443 "CINTSLPE" 268583 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265677 266184 266732 "CHVAR" 267740 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264717 265391 265419 "CHARZ" 265424 T CHARZ (NIL) -9 NIL 265439 NIL) (-148 264465 264511 264589 "CHARPOL" 264671 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263383 264096 264124 "CHARNZ" 264171 T CHARNZ (NIL) -9 NIL 264227 NIL) (-146 260427 261512 262019 "CHAR" 262896 T CHAR (NIL) -8 NIL NIL NIL) (-145 260135 260214 260242 "CFCAT" 260353 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259358 259487 259670 "CDEN" 260019 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254955 258511 258791 "CCLASS" 259098 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254176 254363 254540 "CATEGORY" 254798 T -10 (NIL) -8 NIL NIL NIL) (-141 253671 254095 254143 "CATCTOR" 254148 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 253062 253374 253472 "CATAST" 253593 T CATAST (NIL) -8 NIL NIL NIL) (-139 252478 252783 252875 "CASEAST" 252990 T CASEAST (NIL) -8 NIL NIL NIL) (-138 247376 248635 249379 "CARTEN" 251790 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-137 246472 246632 246853 "CARTEN2" 247223 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-136 244602 245622 245879 "CARD" 246235 T CARD (NIL) -8 NIL NIL NIL) (-135 244124 244406 244481 "CAPSLAST" 244547 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243566 243822 243850 "CACHSET" 243982 T CACHSET (NIL) -9 NIL 244060 NIL) (-133 242956 243344 243372 "CABMON" 243422 T CABMON (NIL) -9 NIL 243478 NIL) (-132 242393 242660 242770 "BYTEORD" 242866 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 241151 241908 242057 "BYTE" 242220 T BYTE (NIL) -8 NIL NIL 242349) (-130 236078 240656 240828 "BYTEBUF" 240999 T BYTEBUF (NIL) -8 NIL NIL NIL) (-129 233340 235770 235877 "BTREE" 236004 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230542 232988 233110 "BTOURN" 233250 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227649 229984 230025 "BTCAT" 230093 NIL BTCAT (NIL T) -9 NIL 230170 NIL) (-126 227298 227396 227545 "BTCAT-" 227550 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222190 226544 226572 "BTAGG" 226686 T BTAGG (NIL) -9 NIL 226796 NIL) (-124 221644 221805 222011 "BTAGG-" 222016 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218380 220922 221137 "BSTREE" 221461 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217488 217644 217828 "BRILL" 218236 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213883 216186 216227 "BRAGG" 216876 NIL BRAGG (NIL T) -9 NIL 217134 NIL) (-120 212316 212818 213373 "BRAGG-" 213378 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204552 211660 211845 "BPADICRT" 212163 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202561 204489 204534 "BPADIC" 204539 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202253 202289 202403 "BOUNDZRO" 202525 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197235 198679 199591 "BOP" 201361 T BOP (NIL) -8 NIL NIL NIL) (-115 194962 195420 195895 "BOP1" 196793 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-114 194555 194712 194740 "BOOLE" 194851 T BOOLE (NIL) -9 NIL 194932 NIL) (-113 194423 194450 194516 "BOOLE-" 194521 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-112 193088 194011 194153 "BOOLEAN" 194301 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 192257 192757 192811 "BMODULE" 192816 NIL BMODULE (NIL T T) -9 NIL 192881 NIL) (-110 187578 192055 192128 "BITS" 192204 T BITS (NIL) -8 NIL NIL NIL) (-109 186975 187118 187258 "BINDING" 187458 T BINDING (NIL) -8 NIL NIL NIL) (-108 180014 186570 186719 "BINARY" 186846 T BINARY (NIL) -8 NIL NIL NIL) (-107 177621 179241 179282 "BGAGG" 179542 NIL BGAGG (NIL T) -9 NIL 179679 NIL) (-106 177446 177484 177575 "BGAGG-" 177580 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176469 176830 177035 "BFUNCT" 177261 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175139 175337 175625 "BEZOUT" 176293 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171337 173991 174321 "BBTREE" 174842 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170920 171016 171044 "BASTYPE" 171221 T BASTYPE (NIL) -9 NIL 171320 NIL) (-101 170578 170677 170812 "BASTYPE-" 170817 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 170000 170088 170240 "BALFACT" 170489 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168736 169415 169601 "AUTOMOR" 169845 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168462 168467 168493 "ATTREG" 168498 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166624 167159 167511 "ATTRBUT" 168128 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166178 166452 166518 "ATTRAST" 166576 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165678 165827 165853 "ATRIG" 166054 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165475 165528 165615 "ATRIG-" 165620 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165058 165292 165318 "ASTCAT" 165323 T ASTCAT (NIL) -9 NIL 165353 NIL) (-92 164767 164844 164963 "ASTCAT-" 164968 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162741 164543 164631 "ASTACK" 164710 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161230 161543 161908 "ASSOCEQ" 162423 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160154 160889 161013 "ASP9" 161137 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 159881 160102 160141 "ASP8" 160146 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 158641 159486 159628 "ASP80" 159770 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 157431 158276 158408 "ASP7" 158540 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 156277 157108 157226 "ASP78" 157344 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 155138 155957 156074 "ASP77" 156191 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 153942 154776 154907 "ASP74" 155038 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 152734 153577 153709 "ASP73" 153841 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 151730 152560 152660 "ASP6" 152665 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150569 151407 151525 "ASP55" 151643 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149410 150243 150362 "ASP50" 150481 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148390 149111 149221 "ASP4" 149331 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 147370 148091 148201 "ASP49" 148311 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 146046 146909 147077 "ASP42" 147259 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144715 145579 145749 "ASP41" 145933 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 143557 144392 144510 "ASP35" 144628 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143286 143505 143544 "ASP34" 143549 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143005 143090 143166 "ASP33" 143241 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141791 142640 142772 "ASP31" 142904 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141520 141739 141778 "ASP30" 141783 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141237 141324 141400 "ASP29" 141475 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140966 141185 141224 "ASP28" 141229 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140695 140914 140953 "ASP27" 140958 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139671 140393 140504 "ASP24" 140615 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138640 139473 139585 "ASP20" 139590 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137620 138341 138451 "ASP1" 138561 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 136455 137294 137413 "ASP19" 137532 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 136174 136259 136335 "ASP12" 136410 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 134918 135773 135917 "ASP10" 136061 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 132530 134762 134853 "ARRAY2" 134858 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 127890 132178 132292 "ARRAY1" 132447 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 126904 127095 127316 "ARRAY12" 127713 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 120949 123106 123181 "ARR2CAT" 125811 NIL ARR2CAT (NIL T T T) -9 NIL 126569 NIL) (-56 118239 119127 120081 "ARR2CAT-" 120086 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117490 117866 117991 "ARITY" 118132 T ARITY (NIL) -8 NIL NIL NIL) (-54 116248 116418 116717 "APPRULE" 117326 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115893 115947 116066 "APPLYORE" 116194 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115193 115486 115606 "ANY" 115791 T ANY (NIL) -8 NIL NIL NIL) (-51 114447 114594 114751 "ANY1" 115067 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 111773 112884 113211 "ANTISYM" 114171 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111217 111480 111576 "ANON" 111695 T ANON (NIL) -8 NIL NIL NIL) (-48 104373 109756 110210 "AN" 110781 T AN (NIL) -8 NIL NIL NIL) (-47 100029 101645 101696 "AMR" 102444 NIL AMR (NIL T T) -9 NIL 103044 NIL) (-46 99081 99362 99725 "AMR-" 99730 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82550 98998 99059 "ALIST" 99064 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78847 82144 82313 "ALGSC" 82468 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75297 75957 76564 "ALGPKG" 78287 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74562 74675 74859 "ALGMFACT" 75183 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70545 71176 71770 "ALGMANIP" 74146 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59884 70171 70321 "ALGFF" 70478 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59056 59211 59390 "ALGFACT" 59742 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57845 58583 58621 "ALGEBRA" 58626 NIL ALGEBRA (NIL T) -9 NIL 58667 NIL) (-37 57545 57622 57754 "ALGEBRA-" 57759 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38506 55382 55434 "ALAGG" 55570 NIL ALAGG (NIL T T) -9 NIL 55731 NIL) (-35 38006 38155 38181 "AHYP" 38382 T AHYP (NIL) -9 NIL NIL NIL) (-34 36891 37185 37211 "AGG" 37710 T AGG (NIL) -9 NIL 37989 NIL) (-33 36289 36487 36701 "AGG-" 36706 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34049 34518 34923 "AF" 35931 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33469 33774 33864 "ADDAST" 33977 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32701 32996 33152 "ACPLOT" 33331 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20258 29633 29671 "ACFS" 30278 NIL ACFS (NIL T) -9 NIL 30517 NIL) (-28 18165 18775 19537 "ACFS-" 19542 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13873 16198 16224 "ACF" 17103 T ACF (NIL) -9 NIL 17516 NIL) (-26 12505 12911 13404 "ACF-" 13409 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12015 12258 12284 "ABELSG" 12376 T ABELSG (NIL) -9 NIL 12441 NIL) (-24 11876 11907 11973 "ABELSG-" 11978 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11145 11492 11518 "ABELMON" 11688 T ABELMON (NIL) -9 NIL 11800 NIL) (-22 10785 10893 11031 "ABELMON-" 11036 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10035 10491 10517 "ABELGRP" 10589 T ABELGRP (NIL) -9 NIL 10664 NIL) (-20 9462 9627 9843 "ABELGRP-" 9848 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8724 8763 "A1AGG" 8768 NIL A1AGG (NIL T) -9 NIL 8808 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3472714 3472719 3472724 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3472699 3472704 3472709 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3472684 3472689 3472694 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472669 3472674 3472679 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1327 3471656 3472544 3472621 "ZMOD" 3472626 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1326 3470692 3470874 3471097 "ZLINDEP" 3471488 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1325 3459854 3461760 3463732 "ZDSOLVE" 3468822 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1324 3459088 3459241 3459430 "YSTREAM" 3459700 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1323 3458448 3458757 3458872 "YDIAGRAM" 3458995 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1322 3455896 3457749 3457953 "XRPOLY" 3458291 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1321 3452163 3453767 3454342 "XPR" 3455368 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1320 3449558 3451494 3451698 "XPOLY" 3451994 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1319 3446889 3448565 3448620 "XPOLYC" 3448908 NIL XPOLYC (NIL T T) -9 NIL 3449021 NIL) (-1318 3442835 3445406 3445794 "XPBWPOLY" 3446547 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1317 3438104 3440811 3440853 "XF" 3441474 NIL XF (NIL T) -9 NIL 3441874 NIL) (-1316 3437701 3437813 3437982 "XF-" 3437987 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1315 3432593 3434172 3434227 "XFALG" 3436399 NIL XFALG (NIL T T) -9 NIL 3437188 NIL) (-1314 3431708 3431830 3432035 "XEXPPKG" 3432485 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1313 3429449 3431558 3431654 "XDPOLY" 3431659 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3428104 3428842 3428885 "XALG" 3428890 NIL XALG (NIL T) -9 NIL 3429001 NIL) (-1311 3421014 3426081 3426575 "WUTSET" 3427696 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1310 3419116 3420066 3420389 "WP" 3420825 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1309 3418664 3418938 3419008 "WHILEAST" 3419068 T WHILEAST (NIL) -8 NIL NIL NIL) (-1308 3418076 3418381 3418475 "WHEREAST" 3418592 T WHEREAST (NIL) -8 NIL NIL NIL) (-1307 3416950 3417160 3417455 "WFFINTBS" 3417873 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1306 3414818 3415281 3415743 "WEIER" 3416522 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1305 3413742 3414300 3414342 "VSPACE" 3414478 NIL VSPACE (NIL T) -9 NIL 3414552 NIL) (-1304 3413574 3413607 3413698 "VSPACE-" 3413703 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1303 3413371 3413425 3413493 "VOID" 3413528 T VOID (NIL) -8 NIL NIL NIL) (-1302 3411471 3411866 3412272 "VIEW" 3412987 T VIEW (NIL) -7 NIL NIL NIL) (-1301 3407739 3408534 3409271 "VIEWDEF" 3410756 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1300 3396683 3399287 3401460 "VIEW3D" 3405588 T VIEW3D (NIL) -8 NIL NIL NIL) (-1299 3388700 3390594 3392173 "VIEW2D" 3395126 T VIEW2D (NIL) -8 NIL NIL NIL) (-1298 3383606 3388470 3388562 "VECTOR" 3388643 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1297 3382159 3382442 3382760 "VECTOR2" 3383336 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1296 3375113 3379863 3379906 "VECTCAT" 3380901 NIL VECTCAT (NIL T) -9 NIL 3381488 NIL) (-1295 3374055 3374381 3374771 "VECTCAT-" 3374776 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3373461 3373706 3373826 "VARIABLE" 3373970 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3373394 3373399 3373429 "UTYPE" 3373434 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3372202 3372378 3372640 "UTSODETL" 3373220 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3369594 3370102 3370626 "UTSODE" 3371743 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3360904 3367355 3367835 "UTS" 3369172 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1289 3350911 3356837 3356880 "UTSCAT" 3357992 NIL UTSCAT (NIL T) -9 NIL 3358750 NIL) (-1288 3348037 3348981 3349970 "UTSCAT-" 3349975 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1287 3347658 3347707 3347840 "UTS2" 3347988 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1286 3341525 3344468 3344511 "URAGG" 3346581 NIL URAGG (NIL T) -9 NIL 3347304 NIL) (-1285 3338248 3339327 3340450 "URAGG-" 3340455 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3333617 3336883 3337348 "UPXSSING" 3337912 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3325095 3332999 3333263 "UPXS" 3333411 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1282 3317510 3324999 3325071 "UPXSCONS" 3325076 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1281 3306258 3313712 3313774 "UPXSCCA" 3314348 NIL UPXSCCA (NIL T T) -9 NIL 3314581 NIL) (-1280 3305878 3305981 3306155 "UPXSCCA-" 3306160 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1279 3294526 3301705 3301748 "UPXSCAT" 3302396 NIL UPXSCAT (NIL T) -9 NIL 3303005 NIL) (-1278 3293950 3294035 3294214 "UPXS2" 3294441 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1277 3292586 3292857 3293208 "UPSQFREE" 3293693 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3285414 3288852 3288907 "UPSCAT" 3289987 NIL UPSCAT (NIL T T) -9 NIL 3290753 NIL) (-1275 3284570 3284825 3285152 "UPSCAT-" 3285157 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3268704 3277697 3277740 "UPOLYC" 3279841 NIL UPOLYC (NIL T) -9 NIL 3281062 NIL) (-1273 3259552 3262458 3265605 "UPOLYC-" 3265610 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1272 3259173 3259222 3259355 "UPOLYC2" 3259503 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1271 3249748 3258856 3258985 "UP" 3259092 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1270 3249069 3249194 3249358 "UPMP" 3249637 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1269 3248616 3248703 3248842 "UPDIVP" 3248982 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1268 3247154 3247433 3247749 "UPDECOMP" 3248365 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1267 3246367 3246497 3246683 "UPCDEN" 3247038 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1266 3245880 3245955 3246104 "UP2" 3246292 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1265 3244233 3245084 3245361 "UNISEG" 3245638 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1264 3243438 3243575 3243780 "UNISEG2" 3244076 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1263 3242480 3242678 3242904 "UNIFACT" 3243254 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3224290 3241792 3242034 "ULS" 3242296 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3211000 3224194 3224266 "ULSCONS" 3224271 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3190800 3204080 3204142 "ULSCCAT" 3204780 NIL ULSCCAT (NIL T T) -9 NIL 3205069 NIL) (-1259 3189796 3190095 3190483 "ULSCCAT-" 3190488 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1258 3178241 3185342 3185385 "ULSCAT" 3186248 NIL ULSCAT (NIL T) -9 NIL 3186979 NIL) (-1257 3177665 3177750 3177929 "ULS2" 3178156 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3176580 3177280 3177394 "UINT8" 3177505 T UINT8 (NIL) -8 NIL NIL 3177597) (-1255 3175494 3176194 3176308 "UINT64" 3176419 T UINT64 (NIL) -8 NIL NIL 3176511) (-1254 3174408 3175108 3175222 "UINT32" 3175333 T UINT32 (NIL) -8 NIL NIL 3175425) (-1253 3173322 3174022 3174136 "UINT16" 3174247 T UINT16 (NIL) -8 NIL NIL 3174339) (-1252 3171401 3172568 3172598 "UFD" 3172810 T UFD (NIL) -9 NIL 3172924 NIL) (-1251 3171183 3171241 3171336 "UFD-" 3171341 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3170241 3170448 3170664 "UDVO" 3170989 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3168007 3168466 3168937 "UDPO" 3169805 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3167940 3167945 3167975 "TYPE" 3167980 T TYPE (NIL) -9 NIL NIL NIL) (-1247 3167652 3167895 3167926 "TYPEAST" 3167931 T TYPEAST (NIL) -8 NIL NIL NIL) (-1246 3166605 3166825 3167065 "TWOFACT" 3167446 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3165580 3166014 3166249 "TUPLE" 3166405 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3163217 3163790 3164329 "TUBETOOL" 3165063 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3162023 3162264 3162506 "TUBE" 3163010 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3156202 3160995 3161278 "TS" 3161775 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3144344 3148959 3149056 "TSETCAT" 3154325 NIL TSETCAT (NIL T T T T) -9 NIL 3155857 NIL) (-1240 3138812 3140676 3142567 "TSETCAT-" 3142572 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1239 3133285 3134298 3135227 "TRMANIP" 3137948 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3132714 3132789 3132952 "TRIMAT" 3133217 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3130526 3130817 3131174 "TRIGMNIP" 3132463 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3130010 3130159 3130189 "TRIGCAT" 3130402 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3129655 3129758 3129899 "TRIGCAT-" 3129904 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3126269 3128513 3128794 "TREE" 3129409 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3125375 3126071 3126101 "TRANFUN" 3126136 T TRANFUN (NIL) -9 NIL 3126202 NIL) (-1232 3124594 3124845 3125125 "TRANFUN-" 3125130 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3124392 3124430 3124491 "TOPSP" 3124555 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3123722 3123855 3124009 "TOOLSIGN" 3124273 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3122236 3122899 3123138 "TEXTFILE" 3123505 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3120040 3120689 3121118 "TEX" 3121829 T TEX (NIL) -8 NIL NIL NIL) (-1227 3119815 3119852 3119924 "TEX1" 3120003 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1226 3119451 3119526 3119616 "TEMUTL" 3119747 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3117545 3117885 3118210 "TBCMPPK" 3119174 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3108872 3115631 3115687 "TBAGG" 3116087 NIL TBAGG (NIL T T) -9 NIL 3116298 NIL) (-1223 3103756 3105430 3107184 "TBAGG-" 3107189 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3103122 3103247 3103392 "TANEXP" 3103645 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3102573 3102897 3102987 "TALGOP" 3103067 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3095587 3102430 3102523 "TABLE" 3102528 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1219 3094981 3095098 3095236 "TABLEAU" 3095484 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1218 3089511 3090809 3092057 "TABLBUMP" 3093767 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3088721 3088880 3089061 "SYSTEM" 3089352 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3085126 3085879 3086662 "SYSSOLP" 3087972 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3084888 3085081 3085112 "SYSPTR" 3085117 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3083723 3084415 3084541 "SYSNNI" 3084727 NIL SYSNNI (NIL NIL) -8 NIL NIL 3084819) (-1213 3082926 3083481 3083560 "SYSINT" 3083620 NIL SYSINT (NIL NIL) -8 NIL NIL 3083665) (-1212 3079024 3080204 3080914 "SYNTAX" 3082238 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3076104 3076784 3077416 "SYMTAB" 3078414 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3071203 3072255 3073238 "SYMS" 3075143 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3068102 3070654 3070887 "SYMPOLY" 3071005 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3067607 3067694 3067817 "SYMFUNC" 3068014 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3063405 3064919 3065732 "SYMBOL" 3066816 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3056878 3058633 3060353 "SWITCH" 3061707 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3049632 3055834 3056128 "SUTS" 3056642 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3041110 3049014 3049278 "SUPXS" 3049426 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3031633 3040728 3040854 "SUP" 3041019 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3030780 3030919 3031136 "SUPFRACF" 3031501 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1201 3030395 3030460 3030573 "SUP2" 3030715 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1200 3028819 3029117 3029473 "SUMRF" 3030094 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3028142 3028220 3028412 "SUMFS" 3028740 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3009987 3027454 3027696 "SULS" 3027958 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3009535 3009809 3009879 "SUCHTAST" 3009939 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3008776 3009060 3009200 "SUCH" 3009443 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3002415 3003682 3004641 "SUBSPACE" 3007864 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3001835 3001935 3002099 "SUBRESP" 3002303 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2995029 2996500 2997811 "STTF" 3000571 NIL STTF (NIL T) -7 NIL NIL NIL) (-1192 2989040 2990322 2991469 "STTFNC" 2993929 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1191 2980157 2982222 2984016 "STTAYLOR" 2987281 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2972911 2980021 2980104 "STRTBL" 2980109 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2967308 2972620 2972719 "STRING" 2972834 T STRING (NIL) -8 NIL NIL NIL) (-1188 2959418 2964927 2965538 "STREAM" 2966732 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1187 2958922 2959005 2959149 "STREAM3" 2959335 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1186 2957886 2958087 2958322 "STREAM2" 2958735 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1185 2957568 2957626 2957719 "STREAM1" 2957828 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1184 2956560 2956765 2956996 "STINPROD" 2957384 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2956056 2956308 2956338 "STEP" 2956418 T STEP (NIL) -9 NIL 2956496 NIL) (-1182 2955171 2955545 2955693 "STEPAST" 2955930 T STEPAST (NIL) -8 NIL NIL NIL) (-1181 2948227 2955070 2955147 "STBL" 2955152 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2942785 2947390 2947433 "STAGG" 2947586 NIL STAGG (NIL T) -9 NIL 2947675 NIL) (-1179 2940337 2941089 2941961 "STAGG-" 2941966 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2938309 2940107 2940199 "STACK" 2940280 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2930316 2936450 2936906 "SREGSET" 2937939 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922663 2924110 2925623 "SRDCMPK" 2928922 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2914972 2920022 2920052 "SRAGG" 2921355 T SRAGG (NIL) -9 NIL 2921963 NIL) (-1174 2913923 2914244 2914623 "SRAGG-" 2914628 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2907507 2912870 2913291 "SQMATRIX" 2913549 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2900919 2904225 2904952 "SPLTREE" 2906852 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2896744 2897575 2898221 "SPLNODE" 2900345 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895719 2896024 2896054 "SPFCAT" 2896498 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2894414 2894666 2894930 "SPECOUT" 2895477 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2885060 2887378 2887408 "SPADXPT" 2892086 T SPADXPT (NIL) -9 NIL 2894252 NIL) (-1167 2884815 2884861 2884930 "SPADPRSR" 2885013 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2882418 2884770 2884801 "SPADAST" 2884806 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2874019 2876122 2876165 "SPACEC" 2880538 NIL SPACEC (NIL T) -9 NIL 2882354 NIL) (-1164 2871819 2873951 2874000 "SPACE3" 2874005 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2870551 2870742 2871033 "SORTPAK" 2871624 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868613 2868946 2869358 "SOLVETRA" 2870215 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867651 2867885 2868146 "SOLVESER" 2868386 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2862883 2863843 2864838 "SOLVERAD" 2866703 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858608 2859307 2860036 "SOLVEFOR" 2862250 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2852219 2857956 2858053 "SNTSCAT" 2858058 NIL SNTSCAT (NIL T T T T) -9 NIL 2858128 NIL) (-1157 2845763 2850542 2850933 "SMTS" 2851909 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2839478 2845651 2845728 "SMP" 2845733 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837607 2837938 2838336 "SMITH" 2839175 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2829139 2834186 2834289 "SMATCAT" 2835640 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836190 NIL) (-1153 2825911 2826902 2828080 "SMATCAT-" 2828085 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2823380 2825119 2825162 "SKAGG" 2825423 NIL SKAGG (NIL T) -9 NIL 2825558 NIL) (-1151 2818874 2822853 2823037 "SINT" 2823189 T SINT (NIL) -8 NIL NIL 2823351) (-1150 2818640 2818684 2818750 "SIMPAN" 2818830 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817865 2818175 2818315 "SIG" 2818522 T SIG (NIL) -8 NIL NIL NIL) (-1148 2816685 2816924 2817199 "SIGNRF" 2817624 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1147 2815500 2815669 2815953 "SIGNEF" 2816514 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1146 2814740 2815083 2815207 "SIGAST" 2815398 T SIGAST (NIL) -8 NIL NIL NIL) (-1145 2812392 2812884 2813390 "SHP" 2814281 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2805765 2812293 2812369 "SHDP" 2812374 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2805276 2805516 2805546 "SGROUP" 2805639 T SGROUP (NIL) -9 NIL 2805701 NIL) (-1142 2805128 2805160 2805233 "SGROUP-" 2805238 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2801847 2802617 2803340 "SGCF" 2804427 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2795556 2801293 2801390 "SFRTCAT" 2801395 NIL SFRTCAT (NIL T T T T) -9 NIL 2801434 NIL) (-1139 2788875 2789995 2791131 "SFRGCD" 2794539 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781893 2783074 2784260 "SFQCMPK" 2787808 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2781495 2781602 2781713 "SFORT" 2781834 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2780421 2781335 2781456 "SEXOF" 2781461 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2779336 2780302 2780370 "SEX" 2780375 T SEX (NIL) -8 NIL NIL NIL) (-1134 2774925 2775832 2775927 "SEXCAT" 2778549 NIL SEXCAT (NIL T T T T T) -9 NIL 2779109 NIL) (-1133 2771734 2774859 2774907 "SET" 2774912 NIL SET (NIL T) -8 NIL NIL NIL) (-1132 2769856 2770447 2770752 "SETMN" 2771475 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1131 2769386 2769574 2769604 "SETCAT" 2769721 T SETCAT (NIL) -9 NIL 2769806 NIL) (-1130 2769154 2769218 2769317 "SETCAT-" 2769322 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1129 2765257 2767615 2767658 "SETAGG" 2768528 NIL SETAGG (NIL T) -9 NIL 2768868 NIL) (-1128 2764679 2764831 2765068 "SETAGG-" 2765073 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1127 2764062 2764375 2764476 "SEQAST" 2764600 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2763189 2763555 2763616 "SEGXCAT" 2763902 NIL SEGXCAT (NIL T T) -9 NIL 2764022 NIL) (-1125 2762105 2762855 2763037 "SEG" 2763042 NIL SEG (NIL T) -8 NIL NIL NIL) (-1124 2761030 2761298 2761341 "SEGCAT" 2761863 NIL SEGCAT (NIL T) -9 NIL 2762084 NIL) (-1123 2759920 2760393 2760601 "SEGBIND" 2760857 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2759535 2759600 2759713 "SEGBIND2" 2759855 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1121 2759054 2759336 2759413 "SEGAST" 2759480 T SEGAST (NIL) -8 NIL NIL NIL) (-1120 2758263 2758399 2758603 "SEG2" 2758898 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1119 2757496 2758198 2758245 "SDVAR" 2758250 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2748847 2757266 2757396 "SDPOL" 2757401 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2747416 2747706 2748025 "SCPKG" 2748562 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2746538 2746752 2746944 "SCOPE" 2747246 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745734 2745892 2746071 "SCACHE" 2746393 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2745318 2745552 2745582 "SASTCAT" 2745587 T SASTCAT (NIL) -9 NIL 2745600 NIL) (-1113 2744721 2745153 2745229 "SAOS" 2745264 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2744280 2744321 2744494 "SAERFFC" 2744680 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2737307 2744177 2744257 "SAE" 2744262 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2736894 2736935 2737094 "SAEFACT" 2737266 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1109 2735197 2735529 2735930 "RURPK" 2736560 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2733774 2734140 2734445 "RULESET" 2735031 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2730889 2731527 2731985 "RULE" 2733455 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2730459 2730683 2730766 "RULECOLD" 2730841 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1105 2730243 2730277 2730348 "RTVALUE" 2730410 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729654 2729960 2730054 "RSTRCAST" 2730171 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2724424 2725297 2726217 "RSETGCD" 2728853 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2712995 2718732 2718829 "RSETCAT" 2722948 NIL RSETCAT (NIL T T T T) -9 NIL 2724045 NIL) (-1101 2710814 2711461 2712285 "RSETCAT-" 2712290 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2703122 2704576 2706096 "RSDCMPK" 2709413 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2700991 2701554 2701628 "RRCC" 2702714 NIL RRCC (NIL T T) -9 NIL 2703058 NIL) (-1098 2700312 2700516 2700795 "RRCC-" 2700800 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699695 2700008 2700109 "RPTAST" 2700233 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2672081 2682807 2682874 "RPOLCAT" 2693540 NIL RPOLCAT (NIL T T T) -9 NIL 2696700 NIL) (-1095 2663051 2665919 2669041 "RPOLCAT-" 2669046 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2653504 2661262 2661744 "ROUTINE" 2662591 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649553 2653130 2653270 "ROMAN" 2653386 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647665 2648413 2648673 "ROIRC" 2649358 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2643383 2646154 2646184 "RNS" 2646488 T RNS (NIL) -9 NIL 2646762 NIL) (-1090 2641790 2642275 2642809 "RNS-" 2642884 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2641083 2641587 2641617 "RNG" 2641622 T RNG (NIL) -9 NIL 2641643 NIL) (-1088 2640044 2640448 2640650 "RNGBIND" 2640934 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1087 2639339 2639817 2639860 "RMODULE" 2639865 NIL RMODULE (NIL T) -9 NIL 2639892 NIL) (-1086 2638163 2638269 2638605 "RMCAT2" 2639240 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634665 2637509 2637806 "RMATRIX" 2637925 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2627164 2629752 2629867 "RMATCAT" 2633226 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634208 NIL) (-1083 2626503 2626686 2626993 "RMATCAT-" 2626998 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2626076 2626290 2626333 "RLINSET" 2626395 NIL RLINSET (NIL T) -9 NIL 2626439 NIL) (-1081 2625637 2625718 2625846 "RINTERP" 2625995 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624561 2625235 2625265 "RING" 2625321 T RING (NIL) -9 NIL 2625413 NIL) (-1079 2624341 2624397 2624494 "RING-" 2624499 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2623152 2623419 2623677 "RIDIST" 2624105 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2613777 2622620 2622826 "RGCHAIN" 2623000 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2613035 2613519 2613560 "RGBCSPC" 2613618 NIL RGBCSPC (NIL T) -9 NIL 2613670 NIL) (-1075 2612101 2612560 2612601 "RGBCMDL" 2612833 NIL RGBCMDL (NIL T) -9 NIL 2612947 NIL) (-1074 2609041 2609709 2610379 "RF" 2611465 NIL RF (NIL T) -7 NIL NIL NIL) (-1073 2608681 2608750 2608853 "RFFACTOR" 2608972 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1072 2608400 2608441 2608538 "RFFACT" 2608640 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1071 2606451 2606881 2607263 "RFDIST" 2608040 T RFDIST (NIL) -7 NIL NIL NIL) (-1070 2605898 2605996 2606159 "RETSOL" 2606353 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2605516 2605614 2605657 "RETRACT" 2605790 NIL RETRACT (NIL T) -9 NIL 2605877 NIL) (-1068 2605359 2605390 2605477 "RETRACT-" 2605482 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2604907 2605181 2605251 "RETAST" 2605311 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2597257 2604560 2604687 "RESULT" 2604802 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595692 2596526 2596725 "RESRING" 2597160 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2595316 2595377 2595475 "RESLATC" 2595629 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2595015 2595056 2595163 "REPSQ" 2595275 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2592395 2593017 2593619 "REP" 2594435 T REP (NIL) -7 NIL NIL NIL) (-1061 2592086 2592127 2592238 "REPDB" 2592354 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1060 2585918 2587375 2588598 "REP2" 2590898 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1059 2582221 2582976 2583784 "REP1" 2585145 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1058 2574229 2580362 2580818 "REGSET" 2581851 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2572938 2573377 2573627 "REF" 2574014 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2572303 2572418 2572585 "REDORDER" 2572822 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567667 2571516 2571743 "RECLOS" 2572131 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566701 2566900 2567115 "REALSOLV" 2567474 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2566535 2566588 2566618 "REAL" 2566623 T REAL (NIL) -9 NIL 2566658 NIL) (-1052 2562982 2563820 2564704 "REAL0Q" 2565700 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1051 2558535 2559571 2560632 "REAL0" 2561963 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1050 2557946 2558252 2558346 "RDUCEAST" 2558463 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2557345 2557423 2557630 "RDIV" 2557868 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2556395 2556587 2556800 "RDIST" 2557167 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2554980 2555279 2555651 "RDETRS" 2556103 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2552774 2553246 2553784 "RDETR" 2554522 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2551393 2551677 2552074 "RDEEFS" 2552490 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2549896 2550208 2550633 "RDEEF" 2551081 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2543373 2546850 2546880 "RCFIELD" 2548175 T RCFIELD (NIL) -9 NIL 2548906 NIL) (-1042 2541329 2541941 2542637 "RCFIELD-" 2542712 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2537381 2539402 2539445 "RCAGG" 2540529 NIL RCAGG (NIL T) -9 NIL 2540994 NIL) (-1040 2536991 2537103 2537266 "RCAGG-" 2537271 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2536308 2536438 2536603 "RATRET" 2536875 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2535849 2535928 2536049 "RATFACT" 2536236 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2535127 2535277 2535429 "RANDSRC" 2535719 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2534855 2534905 2534978 "RADUTIL" 2535076 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2526979 2533686 2533997 "RADIX" 2534578 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516573 2526821 2526951 "RADFF" 2526956 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2516202 2516295 2516325 "RADCAT" 2516485 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2515972 2516032 2516132 "RADCAT-" 2516137 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2513883 2515742 2515834 "QUEUE" 2515915 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2509722 2513816 2513864 "QUAT" 2513869 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1029 2509347 2509396 2509527 "QUATCT2" 2509673 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1028 2501723 2505770 2505812 "QUATCAT" 2506603 NIL QUATCAT (NIL T) -9 NIL 2507369 NIL) (-1027 2497604 2498899 2500289 "QUATCAT-" 2500385 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1026 2494860 2496652 2496695 "QUAGG" 2497076 NIL QUAGG (NIL T) -9 NIL 2497251 NIL) (-1025 2494408 2494682 2494752 "QQUTAST" 2494812 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2493319 2493921 2494086 "QFORM" 2494289 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2482995 2489166 2489208 "QFCAT" 2489876 NIL QFCAT (NIL T) -9 NIL 2490877 NIL) (-1022 2478310 2479763 2481357 "QFCAT-" 2481453 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477935 2477984 2478115 "QFCAT2" 2478261 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1020 2477366 2477500 2477632 "QEQUAT" 2477825 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2470384 2471565 2472751 "QCMPACK" 2476299 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2467834 2468370 2468800 "QALGSET" 2470039 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2467063 2467245 2467481 "QALGSET2" 2467652 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1016 2465730 2465972 2466291 "PWFFINTB" 2466836 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2463875 2464073 2464429 "PUSHVAR" 2465544 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459602 2460818 2460861 "PTRANFN" 2462772 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2457939 2458284 2458608 "PTPACK" 2459313 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457562 2457625 2457736 "PTFUNC2" 2457876 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2451487 2456351 2456394 "PTCAT" 2456694 NIL PTCAT (NIL T) -9 NIL 2456847 NIL) (-1010 2451136 2451177 2451303 "PSQFR" 2451446 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449708 2450024 2450360 "PSEUDLIN" 2450834 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2436228 2438803 2441129 "PSETPK" 2447468 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2428936 2431964 2432062 "PSETCAT" 2435103 NIL PSETCAT (NIL T T T T) -9 NIL 2435917 NIL) (-1006 2426661 2427403 2428227 "PSETCAT-" 2428232 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2425974 2426169 2426199 "PSCURVE" 2426471 T PSCURVE (NIL) -9 NIL 2426638 NIL) (-1004 2421690 2423464 2423531 "PSCAT" 2424383 NIL PSCAT (NIL T T T) -9 NIL 2424623 NIL) (-1003 2420684 2420966 2421369 "PSCAT-" 2421374 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2418883 2419743 2420008 "PRTITION" 2420441 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2418294 2418600 2418694 "PRTDAST" 2418811 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2407138 2409560 2411750 "PRS" 2416156 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404758 2406460 2406500 "PRQAGG" 2406683 NIL PRQAGG (NIL T) -9 NIL 2406785 NIL) (-998 2403937 2404386 2404414 "PROPLOG" 2404553 T PROPLOG (NIL) -9 NIL 2404668 NIL) (-997 2403535 2403598 2403721 "PROPFUN2" 2403860 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2402832 2402971 2403143 "PROPFUN1" 2403396 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2400811 2401579 2401876 "PROPFRML" 2402568 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2400256 2400387 2400515 "PROPERTY" 2400703 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2394144 2398422 2399242 "PRODUCT" 2399482 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2391102 2393602 2393836 "PR" 2393955 NIL PR (NIL T T) -8 NIL NIL NIL) (-991 2390892 2390930 2390989 "PRINT" 2391063 T PRINT (NIL) -7 NIL NIL NIL) (-990 2390208 2390349 2390501 "PRIMES" 2390772 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-989 2388255 2388674 2389140 "PRIMELT" 2389787 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-988 2387972 2388033 2388061 "PRIMCAT" 2388185 T PRIMCAT (NIL) -9 NIL NIL NIL) (-987 2383694 2387910 2387955 "PRIMARR" 2387960 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2382683 2382879 2383107 "PRIMARR2" 2383512 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-985 2382320 2382382 2382493 "PREASSOC" 2382621 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-984 2381771 2381928 2381956 "PPCURVE" 2382161 T PPCURVE (NIL) -9 NIL 2382297 NIL) (-983 2381318 2381566 2381649 "PORTNUM" 2381708 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378655 2379076 2379668 "POLYROOT" 2380899 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2371863 2378259 2378419 "POLY" 2378528 NIL POLY (NIL T) -8 NIL NIL NIL) (-980 2371240 2371304 2371538 "POLYLIFT" 2371799 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-979 2367461 2367964 2368593 "POLYCATQ" 2370785 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-978 2353109 2359208 2359273 "POLYCAT" 2362787 NIL POLYCAT (NIL T T T) -9 NIL 2364665 NIL) (-977 2346228 2348420 2350804 "POLYCAT-" 2350809 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-976 2345809 2345883 2346003 "POLY2UP" 2346154 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-975 2345435 2345498 2345607 "POLY2" 2345746 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-974 2344096 2344359 2344635 "POLUTIL" 2345209 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2342415 2342728 2343059 "POLTOPOL" 2343818 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2337411 2342349 2342396 "POINT" 2342401 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2335544 2335955 2336330 "PNTHEORY" 2337056 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2333990 2334299 2334698 "PMTOOLS" 2335242 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2333577 2333661 2333778 "PMSYM" 2333906 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2333079 2333154 2333329 "PMQFCAT" 2333502 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2332422 2332544 2332700 "PMPRED" 2332956 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2331803 2331901 2332063 "PMPREDFS" 2332323 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-965 2330457 2330675 2331053 "PMPLCAT" 2331565 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2329983 2330068 2330220 "PMLSAGG" 2330372 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2329450 2329532 2329714 "PMKERNEL" 2329901 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2329061 2329142 2329255 "PMINS" 2329369 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328497 2328572 2328781 "PMFS" 2328986 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327713 2327843 2328048 "PMDOWN" 2328374 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2326856 2327038 2327219 "PMASS" 2327552 T PMASS (NIL) -7 NIL NIL NIL) (-958 2326105 2326239 2326402 "PMASSFS" 2326743 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-957 2325754 2325828 2325922 "PLOTTOOL" 2326031 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2320175 2321565 2322713 "PLOT" 2324626 T PLOT (NIL) -8 NIL NIL NIL) (-955 2315827 2317021 2317943 "PLOT3D" 2319273 T PLOT3D (NIL) -8 NIL NIL NIL) (-954 2314715 2314916 2315151 "PLOT1" 2315631 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-953 2289890 2294781 2299632 "PLEQN" 2309981 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289196 2289330 2289510 "PINTERP" 2289755 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2288883 2288936 2289039 "PINTERPA" 2289143 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-950 2287979 2288647 2288734 "PI" 2288774 T PI (NIL) -8 NIL NIL 2288841) (-949 2286064 2287237 2287265 "PID" 2287447 T PID (NIL) -9 NIL 2287581 NIL) (-948 2285809 2285852 2285927 "PICOERCE" 2286021 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-947 2285117 2285268 2285444 "PGROEB" 2285665 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280556 2281515 2282421 "PGE" 2284231 T PGE (NIL) -7 NIL NIL NIL) (-945 2278637 2278926 2279292 "PGCD" 2280273 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2277963 2278078 2278239 "PFRPAC" 2278521 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2274213 2276511 2276864 "PFR" 2277642 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272566 2272846 2273171 "PFOTOOLS" 2273960 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2271081 2271338 2271689 "PFOQ" 2272323 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269564 2269794 2270150 "PFO" 2270865 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2265489 2269453 2269522 "PF" 2269527 NIL PF (NIL NIL) -8 NIL NIL NIL) (-938 2262567 2264080 2264108 "PFECAT" 2264693 T PFECAT (NIL) -9 NIL 2265077 NIL) (-937 2261994 2262166 2262380 "PFECAT-" 2262385 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-936 2260567 2260849 2261150 "PFBRU" 2261743 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-935 2258397 2258785 2259217 "PFBR" 2260218 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-934 2254199 2255906 2256554 "PERM" 2257782 NIL PERM (NIL T) -8 NIL NIL NIL) (-933 2249253 2250406 2251276 "PERMGRP" 2253362 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-932 2247165 2248277 2248318 "PERMCAT" 2248718 NIL PERMCAT (NIL T) -9 NIL 2249016 NIL) (-931 2246812 2246859 2246983 "PERMAN" 2247118 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-930 2244053 2246477 2246599 "PENDTREE" 2246723 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2242934 2243197 2243238 "PDSPC" 2243771 NIL PDSPC (NIL T) -9 NIL 2244016 NIL) (-928 2241989 2242255 2242617 "PDSPC-" 2242622 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240703 2241639 2241680 "PDRING" 2241685 NIL PDRING (NIL T) -9 NIL 2241713 NIL) (-926 2239446 2240208 2240262 "PDMOD" 2240267 NIL PDMOD (NIL T T) -9 NIL 2240371 NIL) (-925 2236613 2237439 2238107 "PDEPROB" 2238798 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2234122 2234662 2235217 "PDEPACK" 2236078 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2233010 2233224 2233475 "PDECOMP" 2233921 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230527 2231418 2231446 "PDECAT" 2232233 T PDECAT (NIL) -9 NIL 2232946 NIL) (-921 2230144 2230211 2230265 "PDDOM" 2230430 NIL PDDOM (NIL T T) -9 NIL 2230510 NIL) (-920 2229957 2229993 2230100 "PDDOM-" 2230105 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229702 2229741 2229831 "PCOMP" 2229918 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2227742 2228503 2228800 "PBWLB" 2229431 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2219921 2221815 2223153 "PATTERN" 2226425 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-916 2219547 2219610 2219719 "PATTERN2" 2219858 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-915 2217256 2217692 2218149 "PATTERN1" 2219136 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-914 2214522 2215205 2215686 "PATRES" 2216821 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2214080 2214153 2214285 "PATRES2" 2214449 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-912 2211933 2212368 2212775 "PATMATCH" 2213747 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2211387 2211638 2211679 "PATMAB" 2211786 NIL PATMAB (NIL T) -9 NIL 2211869 NIL) (-910 2209833 2210241 2210499 "PATLRES" 2211192 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2209371 2209502 2209543 "PATAB" 2209548 NIL PATAB (NIL T) -9 NIL 2209720 NIL) (-908 2207511 2207948 2208371 "PARTPERM" 2208968 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2207120 2207195 2207297 "PARSURF" 2207442 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2206746 2206809 2206918 "PARSU2" 2207057 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2206504 2206550 2206617 "PARSER" 2206699 T PARSER (NIL) -7 NIL NIL NIL) (-904 2206113 2206188 2206290 "PARSCURV" 2206435 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2205739 2205802 2205911 "PARSC2" 2206050 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2205366 2205436 2205533 "PARPCURV" 2205675 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2204992 2205055 2205164 "PARPC2" 2205303 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2203981 2204365 2204547 "PARAMAST" 2204830 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2203489 2203587 2203706 "PAN2EXPR" 2203882 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2202182 2202610 2202838 "PALETTE" 2203281 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2200527 2201187 2201547 "PAIR" 2201868 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2193439 2199784 2199979 "PADICRC" 2200381 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2185675 2192783 2192968 "PADICRAT" 2193286 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2183684 2185612 2185657 "PADIC" 2185662 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2180474 2182344 2182384 "PADICCT" 2182965 NIL PADICCT (NIL NIL) -9 NIL 2183247 NIL) (-892 2179419 2179631 2179899 "PADEPAC" 2180261 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2178619 2178764 2178970 "PADE" 2179281 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2176852 2177827 2178107 "OWP" 2178423 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2176297 2176558 2176655 "OVERSET" 2176775 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2175217 2175902 2176074 "OVAR" 2176165 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2174457 2174602 2174763 "OUT" 2175076 T OUT (NIL) -7 NIL NIL NIL) (-886 2162693 2165566 2167766 "OUTFORM" 2172277 T OUTFORM (NIL) -8 NIL NIL NIL) (-885 2161975 2162290 2162417 "OUTBFILE" 2162586 T OUTBFILE (NIL) -8 NIL NIL NIL) (-884 2161252 2161447 2161475 "OUTBCON" 2161793 T OUTBCON (NIL) -9 NIL 2161959 NIL) (-883 2160835 2160965 2161122 "OUTBCON-" 2161127 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-882 2160131 2160564 2160653 "OSI" 2160766 T OSI (NIL) -8 NIL NIL NIL) (-881 2159550 2159972 2160000 "OSGROUP" 2160005 T OSGROUP (NIL) -9 NIL 2160027 NIL) (-880 2158261 2158522 2158807 "ORTHPOL" 2159297 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2155512 2158096 2158217 "OREUP" 2158222 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2152615 2155203 2155330 "ORESUP" 2155454 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2150115 2150643 2151204 "OREPCTO" 2152104 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2143493 2145988 2146029 "OREPCAT" 2148377 NIL OREPCAT (NIL T) -9 NIL 2149481 NIL) (-875 2140466 2141422 2142480 "OREPCAT-" 2142485 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2139659 2139936 2139964 "ORDTYPE" 2140273 T ORDTYPE (NIL) -9 NIL 2140436 NIL) (-873 2138960 2139176 2139431 "ORDTYPE-" 2139436 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2138316 2138699 2138857 "ORDSTRCT" 2138862 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2137814 2138184 2138212 "ORDSET" 2138217 T ORDSET (NIL) -9 NIL 2138239 NIL) (-870 2136172 2137143 2137171 "ORDRING" 2137373 T ORDRING (NIL) -9 NIL 2137498 NIL) (-869 2135793 2135911 2136055 "ORDRING-" 2136060 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2135044 2135609 2135637 "ORDMON" 2135642 T ORDMON (NIL) -9 NIL 2135663 NIL) (-867 2134188 2134353 2134548 "ORDFUNS" 2134893 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2133403 2133918 2133946 "ORDFIN" 2134011 T ORDFIN (NIL) -9 NIL 2134085 NIL) (-865 2129750 2131989 2132398 "ORDCOMP" 2133027 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-864 2129004 2129143 2129329 "ORDCOMP2" 2129610 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-863 2125525 2126495 2127309 "OPTPROB" 2128210 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2122267 2122966 2123670 "OPTPACK" 2124841 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2119880 2120706 2120734 "OPTCAT" 2121553 T OPTCAT (NIL) -9 NIL 2122203 NIL) (-860 2119198 2119557 2119662 "OPSIG" 2119795 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2118960 2119005 2119071 "OPQUERY" 2119152 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2115869 2117271 2117775 "OP" 2118489 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2115175 2115455 2115496 "OPERCAT" 2115708 NIL OPERCAT (NIL T) -9 NIL 2115805 NIL) (-856 2114918 2114986 2115103 "OPERCAT-" 2115108 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-855 2111531 2113715 2114084 "ONECOMP" 2114582 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-854 2110824 2110951 2111125 "ONECOMP2" 2111403 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-853 2110225 2110349 2110479 "OMSERVER" 2110714 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2106739 2109665 2109705 "OMSAGG" 2109766 NIL OMSAGG (NIL T) -9 NIL 2109830 NIL) (-851 2105314 2105625 2105907 "OMPKG" 2106477 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2104720 2104847 2104875 "OM" 2105174 T OM (NIL) -9 NIL NIL NIL) (-849 2103067 2104269 2104438 "OMLO" 2104601 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-848 2102003 2102174 2102394 "OMEXPR" 2102893 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-847 2101240 2101549 2101685 "OMERR" 2101887 T OMERR (NIL) -8 NIL NIL NIL) (-846 2100325 2100661 2100821 "OMERRK" 2101100 T OMERRK (NIL) -8 NIL NIL NIL) (-845 2099716 2100002 2100110 "OMENC" 2100237 T OMENC (NIL) -8 NIL NIL NIL) (-844 2093353 2094796 2095967 "OMDEV" 2098565 T OMDEV (NIL) -8 NIL NIL NIL) (-843 2092386 2092593 2092787 "OMCONN" 2093179 T OMCONN (NIL) -8 NIL NIL NIL) (-842 2090664 2091856 2091884 "OINTDOM" 2091889 T OINTDOM (NIL) -9 NIL 2091910 NIL) (-841 2087738 2089352 2089689 "OFMONOID" 2090359 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2086972 2087675 2087720 "ODVAR" 2087725 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2084109 2086717 2086872 "ODR" 2086877 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2075514 2083885 2084011 "ODPOL" 2084016 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2068857 2075386 2075491 "ODP" 2075496 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2067599 2067838 2068113 "ODETOOLS" 2068631 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2064542 2065224 2065940 "ODESYS" 2066932 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2059372 2060332 2061357 "ODERTRIC" 2063617 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2058792 2058880 2059074 "ODERED" 2059284 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2055644 2056228 2056905 "ODERAT" 2058215 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2052561 2053068 2053665 "ODEPRRIC" 2055173 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2050456 2051100 2051586 "ODEPROB" 2052095 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2046922 2047461 2048108 "ODEPRIM" 2049935 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2046165 2046273 2046533 "ODEPAL" 2046814 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2042267 2043118 2043982 "ODEPACK" 2045321 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2041310 2041435 2041657 "ODEINT" 2042156 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2035375 2036836 2038283 "ODEIFTBL" 2039883 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2030725 2031559 2032511 "ODEEF" 2034534 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2030068 2030163 2030386 "ODECONST" 2030630 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2028131 2028840 2028868 "ODECAT" 2029473 T ODECAT (NIL) -9 NIL 2030004 NIL) (-821 2024624 2027836 2027958 "OCT" 2028041 NIL OCT (NIL T) -8 NIL NIL NIL) (-820 2024256 2024305 2024432 "OCTCT2" 2024575 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-819 2018525 2021299 2021339 "OC" 2022436 NIL OC (NIL T) -9 NIL 2023294 NIL) (-818 2015560 2016500 2017490 "OC-" 2017584 NIL OC- (NIL T T) -8 NIL NIL NIL) (-817 2014783 2015353 2015381 "OCAMON" 2015386 T OCAMON (NIL) -9 NIL 2015407 NIL) (-816 2014203 2014628 2014656 "OASGP" 2014661 T OASGP (NIL) -9 NIL 2014681 NIL) (-815 2013329 2013926 2013954 "OAMONS" 2013994 T OAMONS (NIL) -9 NIL 2014037 NIL) (-814 2012620 2013149 2013177 "OAMON" 2013182 T OAMON (NIL) -9 NIL 2013202 NIL) (-813 2011731 2012369 2012397 "OAGROUP" 2012402 T OAGROUP (NIL) -9 NIL 2012422 NIL) (-812 2011413 2011469 2011558 "NUMTUBE" 2011675 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004932 2006504 2008040 "NUMQUAD" 2009897 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000652 2001676 2002701 "NUMODE" 2003927 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997933 1998873 1998901 "NUMINT" 1999824 T NUMINT (NIL) -9 NIL 2000588 NIL) (-808 1996845 1997078 1997296 "NUMFMT" 1997735 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1983028 1986149 1988681 "NUMERIC" 1994352 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976739 1982476 1982571 "NTSCAT" 1982576 NIL NTSCAT (NIL T T T T) -9 NIL 1982615 NIL) (-805 1975919 1976098 1976291 "NTPOLFN" 1976578 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1962680 1972744 1973556 "NSUP" 1975140 NIL NSUP (NIL T) -8 NIL NIL NIL) (-803 1962306 1962369 1962478 "NSUP2" 1962617 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-802 1951142 1962080 1962213 "NSMP" 1962218 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949550 1949875 1950232 "NREP" 1950830 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1948129 1948393 1948751 "NPCOEF" 1949293 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1947177 1947310 1947526 "NORMRETR" 1948010 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1945188 1945508 1945917 "NORMPK" 1946885 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944867 1944901 1945025 "NORMMA" 1945154 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944631 1944824 1944853 "NONE" 1944858 T NONE (NIL) -8 NIL NIL NIL) (-795 1944414 1944449 1944518 "NONE1" 1944595 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-794 1943905 1943973 1944152 "NODE1" 1944346 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941997 1943028 1943283 "NNI" 1943630 T NNI (NIL) -8 NIL NIL 1943865) (-792 1940393 1940730 1941094 "NLINSOL" 1941665 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936574 1937629 1938528 "NIPROB" 1939514 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935313 1935565 1935867 "NFINTBAS" 1936336 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934397 1934963 1935004 "NETCLT" 1935176 NIL NETCLT (NIL T) -9 NIL 1935258 NIL) (-788 1933069 1933336 1933617 "NCODIV" 1934165 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932825 1932868 1932943 "NCNTFRAC" 1933026 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930981 1931369 1931789 "NCEP" 1932450 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929644 1930591 1930619 "NASRING" 1930729 T NASRING (NIL) -9 NIL 1930809 NIL) (-784 1929427 1929483 1929577 "NASRING-" 1929582 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928394 1929045 1929073 "NARNG" 1929190 T NARNG (NIL) -9 NIL 1929281 NIL) (-782 1928068 1928153 1928287 "NARNG-" 1928292 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926905 1927154 1927389 "NAGSP" 1927853 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917949 1919861 1921534 "NAGS" 1925252 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916473 1916805 1917136 "NAGF07" 1917638 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910945 1912302 1913609 "NAGF04" 1915186 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903817 1905527 1907160 "NAGF02" 1909332 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898981 1900141 1901258 "NAGF01" 1902720 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892561 1894175 1895760 "NAGE04" 1897416 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883622 1885851 1887981 "NAGE02" 1890451 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879515 1880522 1881486 "NAGE01" 1882678 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877292 1877844 1878402 "NAGD03" 1878977 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868988 1870970 1872924 "NAGD02" 1875358 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862727 1864224 1865664 "NAGD01" 1867568 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858864 1859758 1860595 "NAGC06" 1861910 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857311 1857661 1858017 "NAGC05" 1858528 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856675 1856806 1856950 "NAGC02" 1857187 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855476 1856203 1856243 "NAALG" 1856322 NIL NAALG (NIL T) -9 NIL 1856383 NIL) (-765 1855305 1855340 1855430 "NAALG-" 1855435 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1849177 1850363 1851550 "MULTSQFR" 1854201 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848484 1848571 1848755 "MULTFACT" 1849089 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840629 1845067 1845120 "MTSCAT" 1846190 NIL MTSCAT (NIL T T) -9 NIL 1846706 NIL) (-761 1840335 1840395 1840487 "MTHING" 1840569 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1840121 1840160 1840220 "MSYSCMD" 1840295 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1835835 1838876 1839196 "MSET" 1839834 NIL MSET (NIL T) -8 NIL NIL NIL) (-758 1832580 1835396 1835437 "MSETAGG" 1835442 NIL MSETAGG (NIL T) -9 NIL 1835476 NIL) (-757 1828172 1829959 1830704 "MRING" 1831880 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827732 1827805 1827936 "MRF2" 1828099 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827344 1827385 1827529 "MRATFAC" 1827691 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824914 1825251 1825682 "MPRFF" 1827049 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1818241 1824768 1824865 "MPOLY" 1824870 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817725 1817766 1817974 "MPCPF" 1818200 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1817233 1817282 1817466 "MPC3" 1817676 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816416 1816509 1816730 "MPC2" 1817148 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814693 1815054 1815444 "MONOTOOL" 1816076 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813838 1814221 1814249 "MONOID" 1814468 T MONOID (NIL) -9 NIL 1814615 NIL) (-747 1813354 1813503 1813684 "MONOID-" 1813689 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802308 1809174 1809233 "MONOGEN" 1809907 NIL MONOGEN (NIL T T) -9 NIL 1810363 NIL) (-745 1799358 1800261 1801261 "MONOGEN-" 1801380 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1798075 1798623 1798651 "MONADWU" 1799043 T MONADWU (NIL) -9 NIL 1799281 NIL) (-743 1797405 1797606 1797854 "MONADWU-" 1797859 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796690 1796994 1797022 "MONAD" 1797229 T MONAD (NIL) -9 NIL 1797341 NIL) (-741 1796357 1796453 1796585 "MONAD-" 1796590 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794496 1795270 1795549 "MOEBIUS" 1796110 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793664 1794164 1794204 "MODULE" 1794209 NIL MODULE (NIL T) -9 NIL 1794248 NIL) (-738 1793202 1793328 1793518 "MODULE-" 1793523 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790732 1791566 1791893 "MODRING" 1793026 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787454 1788837 1789358 "MODOP" 1790261 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785940 1786521 1786798 "MODMONOM" 1787317 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774680 1784231 1784645 "MODMON" 1785577 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771506 1773524 1773800 "MODFIELD" 1774555 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770417 1770787 1770977 "MMLFORM" 1771336 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769937 1769986 1770165 "MMAP" 1770368 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767830 1768769 1768810 "MLO" 1769233 NIL MLO (NIL T) -9 NIL 1769475 NIL) (-729 1765178 1765712 1766314 "MLIFT" 1767311 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764557 1764653 1764807 "MKUCFUNC" 1765089 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1764150 1764226 1764349 "MKRECORD" 1764480 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1763173 1763359 1763587 "MKFUNC" 1763961 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762549 1762665 1762821 "MKFLCFN" 1763056 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761814 1761928 1762113 "MKBCFUNC" 1762442 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757797 1761368 1761504 "MINT" 1761698 T MINT (NIL) -8 NIL NIL NIL) (-722 1756579 1756852 1757129 "MHROWRED" 1757552 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751323 1755114 1755519 "MFLOAT" 1756194 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750668 1750756 1750927 "MFINFACT" 1751235 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746947 1747831 1748715 "MESH" 1749804 T MESH (NIL) -7 NIL NIL NIL) (-718 1745301 1745649 1746002 "MDDFACT" 1746634 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741837 1744432 1744473 "MDAGG" 1744728 NIL MDAGG (NIL T) -9 NIL 1744871 NIL) (-716 1729539 1741130 1741337 "MCMPLX" 1741650 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728658 1728822 1729023 "MCDEN" 1729388 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726506 1726818 1727198 "MCALCFN" 1728388 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725383 1725671 1725904 "MAYBE" 1726312 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722941 1723518 1724080 "MATSTOR" 1724854 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718363 1722313 1722561 "MATRIX" 1722726 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1714063 1714836 1715572 "MATLIN" 1717720 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1703409 1707120 1707197 "MATCAT" 1712229 NIL MATCAT (NIL T T T) -9 NIL 1713701 NIL) (-708 1699362 1700672 1702085 "MATCAT-" 1702090 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-707 1697938 1698109 1698442 "MATCAT2" 1699197 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-706 1696014 1696374 1696758 "MAPPKG3" 1697613 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694971 1695168 1695390 "MAPPKG2" 1695838 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693428 1693754 1694081 "MAPPKG1" 1694677 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692429 1692834 1693011 "MAPPAST" 1693271 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1692034 1692098 1692221 "MAPHACK3" 1692365 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691614 1691687 1691801 "MAPHACK2" 1691966 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1691040 1691155 1691297 "MAPHACK1" 1691505 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688963 1689740 1690044 "MAGMA" 1690768 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688382 1688687 1688778 "MACROAST" 1688892 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684625 1686621 1687082 "M3D" 1687954 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1678105 1682936 1682977 "LZSTAGG" 1683759 NIL LZSTAGG (NIL T) -9 NIL 1684054 NIL) (-695 1673787 1675236 1676693 "LZSTAGG-" 1676698 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670700 1671678 1672165 "LWORD" 1673332 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670222 1670504 1670579 "LSTAST" 1670645 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1662150 1669993 1670127 "LSQM" 1670132 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661368 1661513 1661741 "LSPP" 1662005 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1659150 1659481 1659937 "LSMP" 1661057 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-689 1655887 1656603 1657333 "LSMP1" 1658452 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-688 1649023 1654977 1655018 "LSAGG" 1655080 NIL LSAGG (NIL T) -9 NIL 1655158 NIL) (-687 1645532 1646642 1647855 "LSAGG-" 1647860 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642827 1644676 1644925 "LPOLY" 1645327 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642403 1642494 1642617 "LPEFRAC" 1642736 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1640580 1641497 1641750 "LO" 1642235 NIL LO (NIL T T T) -8 NIL NIL NIL) (-683 1640263 1640342 1640370 "LOGIC" 1640481 T LOGIC (NIL) -9 NIL 1640563 NIL) (-682 1640119 1640148 1640219 "LOGIC-" 1640224 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-681 1639294 1639452 1639645 "LODOOPS" 1639975 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-680 1636389 1639210 1639276 "LODO" 1639281 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-679 1634913 1635162 1635515 "LODOF" 1636136 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-678 1630789 1633548 1633589 "LODOCAT" 1634027 NIL LODOCAT (NIL T) -9 NIL 1634238 NIL) (-677 1630504 1630580 1630707 "LODOCAT-" 1630712 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-676 1627490 1630345 1630463 "LODO2" 1630468 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-675 1624597 1627427 1627472 "LODO1" 1627477 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-674 1623466 1623643 1623948 "LODEEF" 1624420 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-673 1618438 1621632 1621673 "LNAGG" 1622535 NIL LNAGG (NIL T) -9 NIL 1622970 NIL) (-672 1617531 1617799 1618141 "LNAGG-" 1618146 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613511 1614456 1615095 "LMOPS" 1616946 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612810 1613288 1613329 "LMODULE" 1613334 NIL LMODULE (NIL T) -9 NIL 1613360 NIL) (-669 1609765 1612455 1612578 "LMDICT" 1612720 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1609341 1609555 1609596 "LLINSET" 1609657 NIL LLINSET (NIL T) -9 NIL 1609701 NIL) (-667 1608986 1609249 1609309 "LITERAL" 1609314 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1601440 1607920 1608224 "LIST" 1608715 NIL LIST (NIL T) -8 NIL NIL NIL) (-665 1600959 1601039 1601178 "LIST3" 1601360 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-664 1599948 1600144 1600372 "LIST2" 1600777 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1598046 1598394 1598793 "LIST2MAP" 1599595 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-662 1597629 1597865 1597906 "LINSET" 1597911 NIL LINSET (NIL T) -9 NIL 1597945 NIL) (-661 1596443 1597137 1597304 "LINFORM" 1597514 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594742 1595470 1595511 "LINEXP" 1596001 NIL LINEXP (NIL T) -9 NIL 1596274 NIL) (-659 1593318 1594222 1594403 "LINELT" 1594613 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591875 1592155 1592466 "LINDEP" 1593070 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1591011 1591607 1591717 "LINBASIS" 1591805 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587748 1588497 1589274 "LIMITRF" 1590266 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1586033 1586347 1586756 "LIMITPS" 1587443 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1580053 1585544 1585772 "LIE" 1585854 NIL LIE (NIL T T) -8 NIL NIL NIL) (-653 1578881 1579456 1579496 "LIECAT" 1579636 NIL LIECAT (NIL T) -9 NIL 1579787 NIL) (-652 1578716 1578749 1578837 "LIECAT-" 1578842 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-651 1570903 1578256 1578412 "LIB" 1578580 T LIB (NIL) -8 NIL NIL NIL) (-650 1566472 1567421 1568356 "LGROBP" 1570020 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564410 1564744 1565094 "LF" 1566193 NIL LF (NIL T T) -7 NIL NIL NIL) (-648 1563034 1563942 1563970 "LFCAT" 1564177 T LFCAT (NIL) -9 NIL 1564316 NIL) (-647 1559894 1560566 1561254 "LEXTRIPK" 1562398 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556482 1557464 1557967 "LEXP" 1559474 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555898 1556203 1556295 "LETAST" 1556410 T LETAST (NIL) -8 NIL NIL NIL) (-644 1554284 1554609 1555010 "LEADCDET" 1555580 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553462 1553548 1553777 "LAZM3PK" 1554205 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547973 1551539 1552077 "LAUPOL" 1552974 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547546 1547596 1547757 "LAPLACE" 1547923 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545283 1546647 1546898 "LA" 1547379 NIL LA (NIL T T T) -8 NIL NIL NIL) (-639 1544131 1544847 1544888 "LALG" 1544950 NIL LALG (NIL T) -9 NIL 1545009 NIL) (-638 1543827 1543904 1544040 "LALG-" 1544045 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-637 1543656 1543686 1543727 "KVTFROM" 1543789 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542413 1543023 1543208 "KTVLOGIC" 1543491 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1542242 1542272 1542313 "KRCFROM" 1542375 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1541134 1541333 1541632 "KOVACIC" 1542042 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540963 1540993 1541034 "KONVERT" 1541096 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540792 1540822 1540863 "KOERCE" 1540925 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1538479 1539385 1539762 "KERNEL" 1540448 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-630 1537963 1538056 1538188 "KERNEL2" 1538393 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-629 1531434 1536440 1536494 "KDAGG" 1536871 NIL KDAGG (NIL T T) -9 NIL 1537077 NIL) (-628 1530945 1531087 1531292 "KDAGG-" 1531297 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523645 1530606 1530761 "KAFILE" 1530823 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1523249 1523534 1523597 "JVMOP" 1523602 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521985 1522489 1522738 "JVMMDACC" 1523020 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520921 1521375 1521580 "JVMFDACC" 1521800 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519502 1519997 1520297 "JVMCSTTG" 1520641 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518638 1519042 1519203 "JVMCFACC" 1519361 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1518316 1518555 1518604 "JVMBCODE" 1518609 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1512336 1517827 1518055 "JORDAN" 1518137 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511649 1511985 1512106 "JOINAST" 1512235 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507684 1509826 1509880 "IXAGG" 1510809 NIL IXAGG (NIL T T) -9 NIL 1511268 NIL) (-617 1506537 1506909 1507328 "IXAGG-" 1507333 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501626 1506459 1506518 "IVECTOR" 1506523 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1500350 1500629 1500895 "ITUPLE" 1501393 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498822 1499029 1499324 "ITRIGMNP" 1500172 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497549 1497771 1498054 "ITFUN3" 1498598 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1497175 1497238 1497347 "ITFUN2" 1497486 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-611 1496280 1496655 1496829 "ITFORM" 1497021 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1494049 1495300 1495578 "ITAYLOR" 1496035 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482446 1488186 1489349 "ISUPS" 1492919 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481538 1481690 1481926 "ISUMP" 1482293 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476388 1481483 1481524 "ISTRING" 1481529 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475804 1476109 1476201 "ISAST" 1476316 T ISAST (NIL) -8 NIL NIL NIL) (-605 1475001 1475095 1475311 "IRURPK" 1475718 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473913 1474138 1474378 "IRSN" 1474781 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471958 1472339 1472768 "IRRF2F" 1473551 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471699 1471743 1471819 "IRREDFFX" 1471914 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1470272 1470573 1470872 "IROOT" 1471432 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1466712 1467956 1468648 "IR" 1469612 NIL IR (NIL T) -8 NIL NIL NIL) (-599 1465851 1466205 1466356 "IRFORM" 1466581 T IRFORM (NIL) -8 NIL NIL NIL) (-598 1463440 1463959 1464525 "IR2" 1465329 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462522 1462653 1462867 "IR2F" 1463323 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-596 1462307 1462347 1462407 "IPRNTPK" 1462482 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1458260 1462196 1462265 "IPF" 1462270 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1456281 1458185 1458242 "IPADIC" 1458247 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455539 1455841 1455971 "IP4ADDR" 1456171 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454877 1455168 1455300 "IOMODE" 1455427 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453848 1454474 1454601 "IOBFILE" 1454770 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1453258 1453752 1453780 "IOBCON" 1453785 T IOBCON (NIL) -9 NIL 1453806 NIL) (-589 1452763 1452827 1453010 "INVLAPLA" 1453194 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1442333 1444765 1447151 "INTTR" 1450427 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438626 1439410 1440275 "INTTOOLS" 1441518 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1438206 1438303 1438420 "INTSLPE" 1438529 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435673 1438129 1438188 "INTRVL" 1438193 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1433251 1433787 1434362 "INTRF" 1435158 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432644 1432759 1432901 "INTRET" 1433149 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430617 1431030 1431500 "INTRAT" 1432252 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427862 1428463 1429082 "INTPM" 1430102 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424579 1425206 1425944 "INTPAF" 1427248 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419680 1420720 1421771 "INTPACK" 1423548 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1415868 1419477 1419586 "INT" 1419591 T INT (NIL) -8 NIL NIL NIL) (-577 1415114 1415272 1415480 "INTHERTR" 1415710 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-576 1414547 1414633 1414821 "INTHERAL" 1415028 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-575 1412315 1412836 1413293 "INTHEORY" 1414110 T INTHEORY (NIL) -7 NIL NIL NIL) (-574 1403647 1405342 1407114 "INTG0" 1410667 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-573 1384172 1389010 1393820 "INTFTBL" 1398857 T INTFTBL (NIL) -8 NIL NIL NIL) (-572 1383397 1383559 1383732 "INTFACT" 1384031 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-571 1380794 1381270 1381827 "INTEF" 1382951 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-570 1378991 1379886 1379914 "INTDOM" 1380215 T INTDOM (NIL) -9 NIL 1380422 NIL) (-569 1378330 1378534 1378776 "INTDOM-" 1378781 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-568 1374204 1376619 1376673 "INTCAT" 1377472 NIL INTCAT (NIL T) -9 NIL 1377793 NIL) (-567 1373658 1373779 1373907 "INTBIT" 1374096 T INTBIT (NIL) -7 NIL NIL NIL) (-566 1372339 1372511 1372818 "INTALG" 1373503 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-565 1371816 1371912 1372069 "INTAF" 1372243 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-564 1364783 1371626 1371766 "INTABL" 1371771 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-563 1364020 1364582 1364647 "INT8" 1364681 T INT8 (NIL) -8 NIL NIL 1364726) (-562 1363256 1363818 1363883 "INT64" 1363917 T INT64 (NIL) -8 NIL NIL 1363962) (-561 1362492 1363054 1363119 "INT32" 1363153 T INT32 (NIL) -8 NIL NIL 1363198) (-560 1361728 1362290 1362355 "INT16" 1362389 T INT16 (NIL) -8 NIL NIL 1362434) (-559 1355829 1359276 1359304 "INS" 1360238 T INS (NIL) -9 NIL 1360903 NIL) (-558 1352883 1353840 1354814 "INS-" 1354887 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351640 1351885 1352183 "INPSIGN" 1352636 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350734 1350875 1351072 "INPRODPF" 1351520 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349604 1349745 1349982 "INPRODFF" 1350614 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348592 1348756 1349016 "INNMFACT" 1349440 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347771 1347886 1348074 "INMODGCD" 1348491 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1346255 1346524 1346848 "INFSP" 1347516 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345415 1345556 1345739 "INFPROD0" 1346135 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1341982 1343480 1343995 "INFORM" 1344908 T INFORM (NIL) -8 NIL NIL NIL) (-549 1341580 1341652 1341750 "INFORM1" 1341917 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-548 1341085 1341192 1341306 "INFINITY" 1341486 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1340159 1340805 1340906 "INETCLTS" 1341004 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338757 1339025 1339346 "INEP" 1339907 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337818 1338654 1338719 "INDE" 1338724 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337370 1337450 1337567 "INCRMAPS" 1337745 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1336092 1336639 1336845 "INBFILE" 1337184 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1331271 1332328 1333272 "INBFF" 1335180 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1330125 1330448 1330476 "INBCON" 1330989 T INBCON (NIL) -9 NIL 1331255 NIL) (-540 1329335 1329600 1329876 "INBCON-" 1329881 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328754 1329059 1329150 "INAST" 1329264 T INAST (NIL) -8 NIL NIL NIL) (-538 1328121 1328433 1328539 "IMPTAST" 1328668 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1324042 1327965 1328069 "IMATRIX" 1328074 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322734 1322873 1323189 "IMATQF" 1323898 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320914 1321181 1321518 "IMATLIN" 1322490 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314829 1320838 1320896 "ILIST" 1320901 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312495 1314689 1314802 "IIARRAY2" 1314807 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1307295 1312406 1312470 "IFF" 1312475 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306576 1306912 1307028 "IFAST" 1307199 T IFAST (NIL) -8 NIL NIL NIL) (-530 1301088 1305868 1306056 "IFARRAY" 1306433 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1300126 1300992 1301065 "IFAMON" 1301070 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299698 1299775 1299829 "IEVALAB" 1300036 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299361 1299441 1299601 "IEVALAB-" 1299606 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298742 1299276 1299338 "IDPO" 1299343 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-525 1297806 1298631 1298706 "IDPOAMS" 1298711 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-524 1296939 1297695 1297770 "IDPOAM" 1297775 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-523 1295419 1295946 1295998 "IDPC" 1296510 NIL IDPC (NIL T T) -9 NIL 1296791 NIL) (-522 1294751 1295311 1295384 "IDPAM" 1295389 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293966 1294643 1294716 "IDPAG" 1294721 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293510 1293772 1293862 "IDENT" 1293896 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289729 1290613 1291508 "IDECOMP" 1292667 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1282364 1283652 1284699 "IDEAL" 1288765 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281506 1281636 1281836 "ICDEN" 1282248 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280481 1280986 1281133 "ICARD" 1281379 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278511 1278854 1279259 "IBPTOOLS" 1280158 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273626 1278131 1278244 "IBITS" 1278430 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1270301 1270925 1271620 "IBATOOL" 1273043 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1268062 1268542 1269075 "IBACHIN" 1269836 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265652 1267908 1268011 "IARRAY2" 1268016 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1261365 1265578 1265635 "IARRAY1" 1265640 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254375 1259777 1260258 "IAN" 1260904 T IAN (NIL) -8 NIL NIL NIL) (-508 1253880 1253943 1254116 "IALGFACT" 1254312 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253372 1253521 1253549 "HYPCAT" 1253756 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252874 1253027 1253213 "HYPCAT-" 1253218 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252421 1252669 1252752 "HOSTNAME" 1252811 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1252254 1252303 1252344 "HOMOTOP" 1252349 NIL HOMOTOP (NIL T) -9 NIL 1252382 NIL) (-503 1248687 1250186 1250227 "HOAGG" 1251208 NIL HOAGG (NIL T) -9 NIL 1251937 NIL) (-502 1247203 1247680 1248206 "HOAGG-" 1248211 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1240239 1246796 1246946 "HEXADEC" 1247073 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238951 1239209 1239472 "HEUGCD" 1240016 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237883 1238788 1238918 "HELLFDIV" 1238923 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235893 1237660 1237748 "HEAP" 1237827 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1235090 1235445 1235579 "HEADAST" 1235779 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228477 1235005 1235067 "HDP" 1235072 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221489 1228112 1228264 "HDMP" 1228378 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220795 1220953 1221117 "HB" 1221345 T HB (NIL) -7 NIL NIL NIL) (-493 1213805 1220641 1220745 "HASHTBL" 1220750 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1213221 1213526 1213618 "HASAST" 1213733 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210627 1212843 1213025 "HACKPI" 1213059 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205799 1210480 1210593 "GTSET" 1210598 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198838 1205677 1205775 "GSTBL" 1205780 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190587 1198003 1198259 "GSERIES" 1198638 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189618 1190131 1190159 "GROUP" 1190362 T GROUP (NIL) -9 NIL 1190496 NIL) (-486 1188942 1189143 1189394 "GROUP-" 1189399 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1187291 1187630 1188017 "GROEBSOL" 1188619 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1186119 1186479 1186530 "GRMOD" 1187059 NIL GRMOD (NIL T T) -9 NIL 1187227 NIL) (-483 1185875 1185923 1186051 "GRMOD-" 1186056 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1181015 1182229 1183229 "GRIMAGE" 1184895 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179409 1179742 1180066 "GRDEF" 1180711 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178841 1178969 1179110 "GRAY" 1179288 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177918 1178420 1178471 "GRALG" 1178624 NIL GRALG (NIL T T) -9 NIL 1178717 NIL) (-478 1177555 1177652 1177815 "GRALG-" 1177820 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1174036 1177138 1177317 "GPOLSET" 1177461 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173384 1173447 1173705 "GOSPER" 1173973 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168954 1169822 1170348 "GMODPOL" 1173083 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167941 1168143 1168381 "GHENSEL" 1168766 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1162013 1162940 1163960 "GENUPS" 1167025 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161704 1161761 1161850 "GENUFACT" 1161956 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1161104 1161193 1161358 "GENPGCD" 1161622 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160572 1160613 1160826 "GENMFACT" 1161063 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1159108 1159395 1159702 "GENEEZ" 1160315 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1152280 1158719 1158881 "GDMP" 1159031 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1141019 1146051 1147157 "GCNAALG" 1151263 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1139146 1140194 1140222 "GCDDOM" 1140477 T GCDDOM (NIL) -9 NIL 1140634 NIL) (-465 1138586 1138743 1138958 "GCDDOM-" 1138963 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1137236 1137443 1137747 "GB" 1138365 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-463 1125708 1128182 1130574 "GBINTERN" 1134927 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-462 1123509 1123837 1124258 "GBF" 1125383 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-461 1122266 1122455 1122722 "GBEUCLID" 1123325 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-460 1121597 1121740 1121889 "GAUSSFAC" 1122137 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119918 1120266 1120580 "GALUTIL" 1121316 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1118178 1118500 1118824 "GALPOLYU" 1119645 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115477 1115833 1116240 "GALFACTU" 1117875 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1107091 1108782 1110390 "GALFACT" 1113909 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104377 1105137 1105165 "FVFUN" 1106321 T FVFUN (NIL) -9 NIL 1107041 NIL) (-454 1103607 1103825 1103853 "FVC" 1104144 T FVC (NIL) -9 NIL 1104327 NIL) (-453 1103208 1103432 1103500 "FUNDESC" 1103559 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102781 1103005 1103086 "FUNCTION" 1103160 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1100411 1101103 1101569 "FT" 1102335 T FT (NIL) -8 NIL NIL NIL) (-450 1099088 1099712 1099915 "FTEM" 1100228 T FTEM (NIL) -8 NIL NIL NIL) (-449 1097357 1097668 1098065 "FSUPFACT" 1098779 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095676 1096043 1096375 "FST" 1097045 T FST (NIL) -8 NIL NIL NIL) (-447 1094857 1094981 1095169 "FSRED" 1095558 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093546 1093812 1094159 "FSPRMELT" 1094572 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090756 1091290 1091776 "FSPECF" 1093109 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1070983 1080530 1080571 "FS" 1084455 NIL FS (NIL T) -9 NIL 1086744 NIL) (-443 1059044 1062619 1066676 "FS-" 1066976 NIL FS- (NIL T T) -8 NIL NIL NIL) (-442 1058566 1058626 1058796 "FSINT" 1058985 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-441 1056702 1057559 1057862 "FSERIES" 1058345 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-440 1055726 1055860 1056084 "FSCINT" 1056582 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-439 1051590 1054670 1054711 "FSAGG" 1055081 NIL FSAGG (NIL T) -9 NIL 1055340 NIL) (-438 1049190 1049953 1050749 "FSAGG-" 1050844 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-437 1048214 1048375 1048602 "FSAGG2" 1049043 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-436 1045874 1046172 1046720 "FS2UPS" 1047932 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-435 1045502 1045551 1045680 "FS2" 1045825 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-434 1044368 1044551 1044853 "FS2EXPXP" 1045327 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-433 1043782 1043909 1044061 "FRUTIL" 1044248 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1034699 1039277 1040635 "FR" 1042456 NIL FR (NIL T) -8 NIL NIL NIL) (-431 1029217 1032388 1032428 "FRNAALG" 1033748 NIL FRNAALG (NIL T) -9 NIL 1034346 NIL) (-430 1024698 1025966 1027241 "FRNAALG-" 1027991 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-429 1024330 1024379 1024506 "FRNAAF2" 1024649 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-428 1022617 1023179 1023475 "FRMOD" 1024142 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-427 1020222 1020992 1021310 "FRIDEAL" 1022408 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1019407 1019500 1019791 "FRIDEAL2" 1020129 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-425 1018498 1018954 1018995 "FRETRCT" 1019000 NIL FRETRCT (NIL T) -9 NIL 1019176 NIL) (-424 1017556 1017841 1018192 "FRETRCT-" 1018197 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-423 1014370 1015840 1015899 "FRAMALG" 1016781 NIL FRAMALG (NIL T T) -9 NIL 1017073 NIL) (-422 1012408 1012959 1013589 "FRAMALG-" 1013812 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-421 1005379 1011881 1012158 "FRAC" 1012163 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1005009 1005072 1005179 "FRAC2" 1005316 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-419 1004639 1004702 1004809 "FR2" 1004946 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-418 998556 1002018 1002046 "FPS" 1003165 T FPS (NIL) -9 NIL 1003722 NIL) (-417 997981 998114 998278 "FPS-" 998424 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994933 996938 996966 "FPC" 997191 T FPC (NIL) -9 NIL 997333 NIL) (-415 994714 994766 994863 "FPC-" 994868 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993472 994202 994243 "FPATMAB" 994248 NIL FPATMAB (NIL T) -9 NIL 994400 NIL) (-413 991615 992214 992561 "FPARFRAC" 993188 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986907 987507 988189 "FORTRAN" 991047 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984593 985123 985662 "FORT" 986388 T FORT (NIL) -7 NIL NIL NIL) (-410 982167 982831 982859 "FORTFN" 983919 T FORTFN (NIL) -9 NIL 984543 NIL) (-409 981919 981981 982009 "FORTCAT" 982068 T FORTCAT (NIL) -9 NIL 982130 NIL) (-408 979923 980535 980925 "FORMULA" 981549 T FORMULA (NIL) -8 NIL NIL NIL) (-407 979705 979741 979810 "FORMULA1" 979887 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-406 979222 979280 979453 "FORDER" 979647 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 978282 978482 978675 "FOP" 979049 T FOP (NIL) -7 NIL NIL NIL) (-404 976695 977562 977736 "FNLA" 978164 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 975314 975825 975853 "FNCAT" 976313 T FNCAT (NIL) -9 NIL 976573 NIL) (-402 974757 975273 975301 "FNAME" 975306 T FNAME (NIL) -8 NIL NIL NIL) (-401 973083 974256 974284 "FMTC" 974289 T FMTC (NIL) -9 NIL 974325 NIL) (-400 971631 973019 973065 "FMONOID" 973070 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 968220 969586 969627 "FMONCAT" 970844 NIL FMONCAT (NIL T) -9 NIL 971449 NIL) (-398 967238 967962 968111 "FM" 968116 NIL FM (NIL T T) -8 NIL NIL NIL) (-397 964560 965308 965336 "FMFUN" 966480 T FMFUN (NIL) -9 NIL 967188 NIL) (-396 963793 964010 964038 "FMC" 964328 T FMC (NIL) -9 NIL 964510 NIL) (-395 960666 961718 961772 "FMCAT" 962967 NIL FMCAT (NIL T T) -9 NIL 963462 NIL) (-394 959334 960432 960532 "FM1" 960611 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-393 957072 957524 958018 "FLOATRP" 958885 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 949728 954801 955422 "FLOAT" 956471 T FLOAT (NIL) -8 NIL NIL NIL) (-391 947130 947666 948244 "FLOATCP" 949195 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-390 945648 946722 946763 "FLINEXP" 946768 NIL FLINEXP (NIL T) -9 NIL 946861 NIL) (-389 944778 945037 945365 "FLINEXP-" 945370 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943836 943998 944222 "FLASORT" 944630 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940754 941806 941858 "FLALG" 943085 NIL FLALG (NIL T T) -9 NIL 943552 NIL) (-386 934018 938163 938204 "FLAGG" 939466 NIL FLAGG (NIL T) -9 NIL 940118 NIL) (-385 932672 933083 933573 "FLAGG-" 933578 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-384 931696 931857 932084 "FLAGG2" 932525 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-383 928327 929541 929600 "FINRALG" 930728 NIL FINRALG (NIL T T) -9 NIL 931236 NIL) (-382 927451 927716 928055 "FINRALG-" 928060 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926757 927056 927084 "FINITE" 927280 T FINITE (NIL) -9 NIL 927387 NIL) (-380 918708 921287 921327 "FINAALG" 924994 NIL FINAALG (NIL T) -9 NIL 926447 NIL) (-379 913824 915090 916234 "FINAALG-" 917613 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 913102 913579 913682 "FILE" 913754 NIL FILE (NIL T) -8 NIL NIL NIL) (-377 911662 912084 912138 "FILECAT" 912822 NIL FILECAT (NIL T T) -9 NIL 913038 NIL) (-376 909058 910892 910920 "FIELD" 910960 T FIELD (NIL) -9 NIL 911040 NIL) (-375 907600 908063 908574 "FIELD-" 908579 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 905282 906235 906582 "FGROUP" 907286 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904354 904536 904756 "FGLMICPK" 905114 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899588 904279 904336 "FFX" 904341 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 899183 899250 899385 "FFSLPE" 899521 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 895059 895955 896751 "FFPOLY" 898419 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-369 894557 894599 894808 "FFPOLY2" 895017 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-368 889805 894476 894539 "FFP" 894544 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884605 889716 889780 "FF" 889785 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-366 879115 883948 884138 "FFNBX" 884459 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-365 873427 878250 878508 "FFNBP" 878969 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-364 867444 872711 872922 "FFNB" 873260 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-363 866264 866474 866789 "FFINTBAS" 867241 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-362 861840 864511 864539 "FFIELDC" 865159 T FFIELDC (NIL) -9 NIL 865535 NIL) (-361 860418 860873 861370 "FFIELDC-" 861375 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-360 859975 860033 860157 "FFHOM" 860360 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-359 857634 858157 858674 "FFF" 859490 NIL FFF (NIL T) -7 NIL NIL NIL) (-358 852648 857376 857477 "FFCGX" 857577 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-357 847666 852380 852487 "FFCGP" 852591 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-356 842245 847393 847501 "FFCG" 847602 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-355 820908 831977 832063 "FFCAT" 837228 NIL FFCAT (NIL T T T) -9 NIL 838679 NIL) (-354 815919 817153 818467 "FFCAT-" 819697 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815324 815373 815608 "FFCAT2" 815870 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-352 803977 808296 809516 "FEXPR" 814176 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802905 803374 803415 "FEVALAB" 803499 NIL FEVALAB (NIL T) -9 NIL 803760 NIL) (-350 802022 802274 802612 "FEVALAB-" 802617 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 800432 801405 801608 "FDIV" 801921 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-348 797294 798179 798294 "FDIVCAT" 799862 NIL FDIVCAT (NIL T T T T) -9 NIL 800299 NIL) (-347 797050 797083 797253 "FDIVCAT-" 797258 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-346 796264 796357 796634 "FDIV2" 796957 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-345 795172 795559 795761 "FCTRDATA" 796082 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793828 794117 794406 "FCPAK1" 794903 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792831 793328 793469 "FCOMP" 793719 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776146 779981 783519 "FC" 789313 T FC (NIL) -8 NIL NIL NIL) (-341 767841 772467 772507 "FAXF" 774309 NIL FAXF (NIL T) -9 NIL 775001 NIL) (-340 764962 765775 766600 "FAXF-" 767065 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759531 764338 764514 "FARRAY" 764819 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754095 756478 756531 "FAMR" 757554 NIL FAMR (NIL T T) -9 NIL 758014 NIL) (-337 752919 753287 753722 "FAMR-" 753727 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751946 752841 752894 "FAMONOID" 752899 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749576 750428 750481 "FAMONC" 751422 NIL FAMONC (NIL T T) -9 NIL 751808 NIL) (-334 748050 749330 749467 "FAGROUP" 749472 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745803 746164 746567 "FACUTIL" 747731 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744890 745087 745309 "FACTFUNC" 745613 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736648 744193 744392 "EXPUPXS" 744746 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734101 734671 735257 "EXPRTUBE" 736082 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730312 730964 731694 "EXPRODE" 733440 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 714606 728961 729390 "EXPR" 729916 NIL EXPR (NIL T) -8 NIL NIL NIL) (-327 709040 709747 710553 "EXPR2UPS" 713904 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-326 708666 708729 708838 "EXPR2" 708977 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-325 698983 707817 708108 "EXPEXPAN" 708502 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698747 698940 698969 "EXIT" 698974 T EXIT (NIL) -8 NIL NIL NIL) (-323 698167 698471 698562 "EXITAST" 698676 T EXITAST (NIL) -8 NIL NIL NIL) (-322 697788 697856 697969 "EVALCYC" 698099 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697305 697447 697488 "EVALAB" 697658 NIL EVALAB (NIL T) -9 NIL 697762 NIL) (-320 696762 696908 697129 "EVALAB-" 697134 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693870 695418 695446 "EUCDOM" 696001 T EUCDOM (NIL) -9 NIL 696351 NIL) (-318 692209 692717 693307 "EUCDOM-" 693312 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 679526 682507 685257 "ESTOOLS" 689479 T ESTOOLS (NIL) -7 NIL NIL NIL) (-316 679152 679215 679324 "ESTOOLS2" 679463 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-315 678897 678945 679025 "ESTOOLS1" 679104 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-314 672598 674528 674556 "ES" 677324 T ES (NIL) -9 NIL 678734 NIL) (-313 667275 668832 670649 "ES-" 670813 NIL ES- (NIL T) -8 NIL NIL NIL) (-312 663583 664410 665190 "ESCONT" 666515 T ESCONT (NIL) -7 NIL NIL NIL) (-311 663322 663360 663442 "ESCONT1" 663545 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-310 662991 663047 663147 "ES2" 663266 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-309 662615 662679 662788 "ES1" 662927 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-308 661807 661960 662136 "ERROR" 662459 T ERROR (NIL) -7 NIL NIL NIL) (-307 654823 661666 661757 "EQTBL" 661762 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 647082 650137 651586 "EQ" 653407 NIL -1512 (NIL T) -8 NIL NIL NIL) (-305 646708 646771 646880 "EQ2" 647019 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-304 641951 643046 644139 "EP" 645647 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640491 640842 641148 "ENV" 641665 T ENV (NIL) -8 NIL NIL NIL) (-302 639451 640125 640153 "ENTIRER" 640158 T ENTIRER (NIL) -9 NIL 640204 NIL) (-301 635863 637633 637994 "EMR" 639259 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 634967 635178 635232 "ELTAGG" 635612 NIL ELTAGG (NIL T T) -9 NIL 635823 NIL) (-299 634674 634748 634889 "ELTAGG-" 634894 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634432 634467 634521 "ELTAB" 634605 NIL ELTAB (NIL T T) -9 NIL 634657 NIL) (-297 633534 633704 633903 "ELFUTS" 634283 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633258 633332 633360 "ELEMFUN" 633465 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633122 633149 633217 "ELEMFUN-" 633222 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627539 631164 631205 "ELAGG" 632145 NIL ELAGG (NIL T) -9 NIL 632608 NIL) (-293 625716 626258 626921 "ELAGG-" 626926 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 624998 625165 625321 "ELABOR" 625580 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623605 623938 624232 "ELABEXPR" 624724 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616117 618242 619071 "EFUPXS" 622880 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609243 611366 612177 "EFULS" 615392 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606680 607086 607558 "EFSTRUC" 608875 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596117 598037 599585 "EF" 605195 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595095 595602 595751 "EAB" 595988 T EAB (NIL) -8 NIL NIL NIL) (-285 594217 595054 595082 "E04UCFA" 595087 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593339 594176 594204 "E04NAFA" 594209 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592461 593298 593326 "E04MBFA" 593331 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591583 592420 592448 "E04JAFA" 592453 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590707 591542 591570 "E04GCFA" 591575 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589831 590666 590694 "E04FDFA" 590699 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588953 589790 589818 "E04DGFA" 589823 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583030 584478 585842 "E04AGNT" 587609 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581650 582331 582371 "DVARCAT" 582712 NIL DVARCAT (NIL T) -9 NIL 582875 NIL) (-276 580800 581066 581380 "DVARCAT-" 581385 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572761 580599 580728 "DSMP" 580733 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571112 571903 571944 "DSEXT" 572307 NIL DSEXT (NIL T) -9 NIL 572601 NIL) (-273 569301 569825 570491 "DSEXT-" 570496 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 563884 565246 566314 "DROPT" 568253 T DROPT (NIL) -8 NIL NIL NIL) (-271 563543 563608 563706 "DROPT1" 563819 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-270 558562 559784 560921 "DROPT0" 562426 T DROPT0 (NIL) -7 NIL NIL NIL) (-269 556871 557232 557618 "DRAWPT" 558196 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 551362 552381 553460 "DRAW" 555845 NIL DRAW (NIL T) -7 NIL NIL NIL) (-267 550989 551048 551166 "DRAWHACK" 551303 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-266 549690 549989 550280 "DRAWCX" 550718 T DRAWCX (NIL) -7 NIL NIL NIL) (-265 549199 549274 549425 "DRAWCURV" 549616 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-264 539517 541629 543744 "DRAWCFUN" 547104 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-263 535988 538182 538223 "DQAGG" 538852 NIL DQAGG (NIL T) -9 NIL 539126 NIL) (-262 522571 530199 530282 "DPOLCAT" 532134 NIL DPOLCAT (NIL T T T T) -9 NIL 532679 NIL) (-261 517090 518756 520714 "DPOLCAT-" 520719 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509947 516951 517049 "DPMO" 517054 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502701 509727 509894 "DPMM" 509899 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502223 502485 502574 "DOMTMPLT" 502632 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501572 502025 502105 "DOMCTOR" 502163 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500724 501052 501203 "DOMAIN" 501441 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493736 500359 500511 "DMP" 500625 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491513 492803 492844 "DMEXT" 492849 NIL DMEXT (NIL T) -9 NIL 493025 NIL) (-253 491107 491169 491313 "DLP" 491451 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484230 490434 490624 "DLIST" 490949 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480768 483055 483096 "DLAGG" 483646 NIL DLAGG (NIL T) -9 NIL 483876 NIL) (-250 479280 480094 480122 "DIVRING" 480214 T DIVRING (NIL) -9 NIL 480297 NIL) (-249 478463 478707 479007 "DIVRING-" 479012 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476505 476922 477328 "DISPLAY" 478077 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 469912 476419 476482 "DIRPROD" 476487 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-246 468742 468963 469228 "DIRPROD2" 469705 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-245 456961 463453 463506 "DIRPCAT" 463764 NIL DIRPCAT (NIL NIL T) -9 NIL 464639 NIL) (-244 454161 454929 455810 "DIRPCAT-" 456147 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453442 453608 453794 "DIOSP" 453995 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449856 452326 452367 "DIOPS" 452801 NIL DIOPS (NIL T) -9 NIL 453030 NIL) (-241 449375 449519 449710 "DIOPS-" 449715 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448282 449054 449082 "DIFRING" 449087 T DIFRING (NIL) -9 NIL 449109 NIL) (-239 447930 448028 448056 "DIFFSPC" 448175 T DIFFSPC (NIL) -9 NIL 448250 NIL) (-238 447551 447653 447805 "DIFFSPC-" 447810 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446487 447085 447126 "DIFFMOD" 447131 NIL DIFFMOD (NIL T) -9 NIL 447229 NIL) (-236 446183 446240 446281 "DIFFDOM" 446402 NIL DIFFDOM (NIL T) -9 NIL 446470 NIL) (-235 446030 446060 446144 "DIFFDOM-" 446149 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443770 445234 445275 "DIFEXT" 445280 NIL DIFEXT (NIL T) -9 NIL 445433 NIL) (-233 440804 443274 443315 "DIAGG" 443320 NIL DIAGG (NIL T) -9 NIL 443340 NIL) (-232 440152 440345 440597 "DIAGG-" 440602 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 435002 439111 439388 "DHMATRIX" 439921 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430470 431523 432533 "DFSFUN" 434012 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424704 429401 429713 "DFLOAT" 430178 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422943 423248 423637 "DFINTTLS" 424412 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419762 420964 421364 "DERHAM" 422609 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417298 419537 419626 "DEQUEUE" 419706 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416540 416685 416868 "DEGRED" 417160 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412946 413715 414561 "DEFINTRF" 415768 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410483 410970 411562 "DEFINTEF" 412465 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409767 410103 410218 "DEFAST" 410388 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402803 409360 409510 "DECIMAL" 409637 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400261 400773 401279 "DDFACT" 402347 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399851 399900 400051 "DBLRESP" 400212 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 399052 399621 399712 "DBASIS" 399800 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396836 397282 397643 "DBASE" 398818 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 396024 396316 396462 "DATAARY" 396735 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 395082 395983 396011 "D03FAFA" 396016 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394141 395041 395069 "D03EEFA" 395074 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 392067 392557 393046 "D03AGNT" 393672 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391308 392026 392054 "D02EJFA" 392059 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390549 391267 391295 "D02CJFA" 391300 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389790 390508 390536 "D02BHFA" 390541 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 389031 389749 389777 "D02BBFA" 389782 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382162 383817 385423 "D02AGNT" 387445 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379912 380453 380999 "D01WGTS" 381636 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378919 379871 379899 "D01TRNS" 379904 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377927 378878 378906 "D01GBFA" 378911 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376935 377886 377914 "D01FCFA" 377919 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375943 376894 376922 "D01ASFA" 376927 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374951 375902 375930 "D01AQFA" 375935 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373959 374910 374938 "D01APFA" 374943 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372967 373918 373946 "D01ANFA" 373951 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371975 372926 372954 "D01AMFA" 372959 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370983 371934 371962 "D01ALFA" 371967 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369991 370942 370970 "D01AKFA" 370975 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368999 369950 369978 "D01AJFA" 369983 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362222 363847 365408 "D01AGNT" 367458 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361541 361687 361839 "CYCLOTOM" 362090 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358196 358989 359716 "CYCLES" 360834 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357496 357642 357813 "CVMP" 358057 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355283 355595 355964 "CTRIGMNP" 357224 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354641 355077 355150 "CTOR" 355230 T CTOR (NIL) -8 NIL NIL NIL) (-189 354114 354372 354473 "CTORKIND" 354560 T CTORKIND (NIL) -8 NIL NIL NIL) (-188 353319 353707 353735 "CTORCAT" 353917 T CTORCAT (NIL) -9 NIL 354030 NIL) (-187 352893 353028 353187 "CTORCAT-" 353192 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-186 352307 352567 352675 "CTORCALL" 352817 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-185 351663 351780 351933 "CSTTOOLS" 352204 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347360 348119 348877 "CRFP" 350975 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346775 347081 347173 "CRCEAST" 347288 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345798 346007 346235 "CRAPACK" 346579 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345178 345283 345487 "CPMATCH" 345674 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344897 344931 345037 "CPIMA" 345144 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341155 341917 342636 "COORDSYS" 344232 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340543 340688 340830 "CONTOUR" 341033 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 336008 338546 339038 "CONTFRAC" 340083 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335882 335909 335937 "CONDUIT" 335974 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334836 335510 335538 "COMRING" 335543 T COMRING (NIL) -9 NIL 335595 NIL) (-174 333818 334194 334378 "COMPPROP" 334672 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333473 333514 333642 "COMPLPAT" 333777 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 321856 333282 333391 "COMPLEX" 333396 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-171 321486 321549 321656 "COMPLEX2" 321793 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-170 320807 320946 321106 "COMPILER" 321346 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320519 320560 320658 "COMPFACT" 320766 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301894 314223 314263 "COMPCAT" 315267 NIL COMPCAT (NIL T) -9 NIL 316615 NIL) (-167 290782 294333 297960 "COMPCAT-" 298316 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290505 290539 290642 "COMMUPC" 290748 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290293 290333 290392 "COMMONOP" 290466 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289801 290044 290131 "COMM" 290226 T COMM (NIL) -8 NIL NIL NIL) (-163 289323 289605 289680 "COMMAAST" 289746 T COMMAAST (NIL) -8 NIL NIL NIL) (-162 288518 288766 288794 "COMBOPC" 289132 T COMBOPC (NIL) -9 NIL 289307 NIL) (-161 287372 287624 287866 "COMBINAT" 288308 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283715 284403 285030 "COMBF" 286794 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282377 282831 283066 "COLOR" 283500 T COLOR (NIL) -8 NIL NIL NIL) (-158 281793 282098 282190 "COLONAST" 282305 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281427 281480 281605 "CMPLXRT" 281740 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280815 281127 281226 "CLLCTAST" 281348 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276275 277345 278425 "CLIP" 279755 T CLIP (NIL) -7 NIL NIL NIL) (-154 274448 275376 275616 "CLIF" 276102 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270430 272566 272607 "CLAGG" 273536 NIL CLAGG (NIL T) -9 NIL 274072 NIL) (-152 268774 269309 269892 "CLAGG-" 269897 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268312 268403 268543 "CINTSLPE" 268683 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265777 266284 266832 "CHVAR" 267840 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264817 265491 265519 "CHARZ" 265524 T CHARZ (NIL) -9 NIL 265539 NIL) (-148 264565 264611 264689 "CHARPOL" 264771 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263483 264196 264224 "CHARNZ" 264271 T CHARNZ (NIL) -9 NIL 264327 NIL) (-146 260427 261537 262066 "CHAR" 262974 T CHAR (NIL) -8 NIL NIL NIL) (-145 260135 260214 260242 "CFCAT" 260353 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259358 259487 259670 "CDEN" 260019 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254955 258511 258791 "CCLASS" 259098 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254176 254363 254540 "CATEGORY" 254798 T -10 (NIL) -8 NIL NIL NIL) (-141 253671 254095 254143 "CATCTOR" 254148 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 253062 253374 253472 "CATAST" 253593 T CATAST (NIL) -8 NIL NIL NIL) (-139 252478 252783 252875 "CASEAST" 252990 T CASEAST (NIL) -8 NIL NIL NIL) (-138 247376 248635 249379 "CARTEN" 251790 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-137 246472 246632 246853 "CARTEN2" 247223 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-136 244602 245622 245879 "CARD" 246235 T CARD (NIL) -8 NIL NIL NIL) (-135 244124 244406 244481 "CAPSLAST" 244547 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243566 243822 243850 "CACHSET" 243982 T CACHSET (NIL) -9 NIL 244060 NIL) (-133 242956 243344 243372 "CABMON" 243422 T CABMON (NIL) -9 NIL 243478 NIL) (-132 242393 242660 242770 "BYTEORD" 242866 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 241151 241908 242057 "BYTE" 242220 T BYTE (NIL) -8 NIL NIL 242349) (-130 236078 240656 240828 "BYTEBUF" 240999 T BYTEBUF (NIL) -8 NIL NIL NIL) (-129 233340 235770 235877 "BTREE" 236004 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230542 232988 233110 "BTOURN" 233250 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227649 229984 230025 "BTCAT" 230093 NIL BTCAT (NIL T) -9 NIL 230170 NIL) (-126 227298 227396 227545 "BTCAT-" 227550 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222190 226544 226572 "BTAGG" 226686 T BTAGG (NIL) -9 NIL 226796 NIL) (-124 221644 221805 222011 "BTAGG-" 222016 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218380 220922 221137 "BSTREE" 221461 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217488 217644 217828 "BRILL" 218236 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213883 216186 216227 "BRAGG" 216876 NIL BRAGG (NIL T) -9 NIL 217134 NIL) (-120 212316 212818 213373 "BRAGG-" 213378 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204552 211660 211845 "BPADICRT" 212163 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202561 204489 204534 "BPADIC" 204539 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202253 202289 202403 "BOUNDZRO" 202525 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197235 198679 199591 "BOP" 201361 T BOP (NIL) -8 NIL NIL NIL) (-115 194962 195420 195895 "BOP1" 196793 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-114 194555 194712 194740 "BOOLE" 194851 T BOOLE (NIL) -9 NIL 194932 NIL) (-113 194423 194450 194516 "BOOLE-" 194521 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-112 193088 194011 194153 "BOOLEAN" 194301 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 192257 192757 192811 "BMODULE" 192816 NIL BMODULE (NIL T T) -9 NIL 192881 NIL) (-110 187578 192055 192128 "BITS" 192204 T BITS (NIL) -8 NIL NIL NIL) (-109 186975 187118 187258 "BINDING" 187458 T BINDING (NIL) -8 NIL NIL NIL) (-108 180014 186570 186719 "BINARY" 186846 T BINARY (NIL) -8 NIL NIL NIL) (-107 177621 179241 179282 "BGAGG" 179542 NIL BGAGG (NIL T) -9 NIL 179679 NIL) (-106 177446 177484 177575 "BGAGG-" 177580 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176469 176830 177035 "BFUNCT" 177261 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175139 175337 175625 "BEZOUT" 176293 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171337 173991 174321 "BBTREE" 174842 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170920 171016 171044 "BASTYPE" 171221 T BASTYPE (NIL) -9 NIL 171320 NIL) (-101 170578 170677 170812 "BASTYPE-" 170817 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 170000 170088 170240 "BALFACT" 170489 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168736 169415 169601 "AUTOMOR" 169845 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168462 168467 168493 "ATTREG" 168498 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166624 167159 167511 "ATTRBUT" 168128 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166178 166452 166518 "ATTRAST" 166576 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165678 165827 165853 "ATRIG" 166054 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165475 165528 165615 "ATRIG-" 165620 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165058 165292 165318 "ASTCAT" 165323 T ASTCAT (NIL) -9 NIL 165353 NIL) (-92 164767 164844 164963 "ASTCAT-" 164968 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162741 164543 164631 "ASTACK" 164710 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161230 161543 161908 "ASSOCEQ" 162423 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160154 160889 161013 "ASP9" 161137 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 159881 160102 160141 "ASP8" 160146 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 158641 159486 159628 "ASP80" 159770 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 157431 158276 158408 "ASP7" 158540 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 156277 157108 157226 "ASP78" 157344 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 155138 155957 156074 "ASP77" 156191 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 153942 154776 154907 "ASP74" 155038 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 152734 153577 153709 "ASP73" 153841 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 151730 152560 152660 "ASP6" 152665 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150569 151407 151525 "ASP55" 151643 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149410 150243 150362 "ASP50" 150481 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148390 149111 149221 "ASP4" 149331 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 147370 148091 148201 "ASP49" 148311 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 146046 146909 147077 "ASP42" 147259 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144715 145579 145749 "ASP41" 145933 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 143557 144392 144510 "ASP35" 144628 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143286 143505 143544 "ASP34" 143549 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143005 143090 143166 "ASP33" 143241 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141791 142640 142772 "ASP31" 142904 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141520 141739 141778 "ASP30" 141783 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141237 141324 141400 "ASP29" 141475 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140966 141185 141224 "ASP28" 141229 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140695 140914 140953 "ASP27" 140958 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139671 140393 140504 "ASP24" 140615 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138640 139473 139585 "ASP20" 139590 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137620 138341 138451 "ASP1" 138561 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 136455 137294 137413 "ASP19" 137532 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 136174 136259 136335 "ASP12" 136410 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 134918 135773 135917 "ASP10" 136061 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 132530 134762 134853 "ARRAY2" 134858 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 127890 132178 132292 "ARRAY1" 132447 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 126904 127095 127316 "ARRAY12" 127713 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 120949 123106 123181 "ARR2CAT" 125811 NIL ARR2CAT (NIL T T T) -9 NIL 126569 NIL) (-56 118239 119127 120081 "ARR2CAT-" 120086 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117490 117866 117991 "ARITY" 118132 T ARITY (NIL) -8 NIL NIL NIL) (-54 116248 116418 116717 "APPRULE" 117326 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115893 115947 116066 "APPLYORE" 116194 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115193 115486 115606 "ANY" 115791 T ANY (NIL) -8 NIL NIL NIL) (-51 114447 114594 114751 "ANY1" 115067 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 111773 112884 113211 "ANTISYM" 114171 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111217 111480 111576 "ANON" 111695 T ANON (NIL) -8 NIL NIL NIL) (-48 104373 109756 110210 "AN" 110781 T AN (NIL) -8 NIL NIL NIL) (-47 100029 101645 101696 "AMR" 102444 NIL AMR (NIL T T) -9 NIL 103044 NIL) (-46 99081 99362 99725 "AMR-" 99730 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82550 98998 99059 "ALIST" 99064 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78847 82144 82313 "ALGSC" 82468 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75297 75957 76564 "ALGPKG" 78287 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74562 74675 74859 "ALGMFACT" 75183 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70545 71176 71770 "ALGMANIP" 74146 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59884 70171 70321 "ALGFF" 70478 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59056 59211 59390 "ALGFACT" 59742 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57845 58583 58621 "ALGEBRA" 58626 NIL ALGEBRA (NIL T) -9 NIL 58667 NIL) (-37 57545 57622 57754 "ALGEBRA-" 57759 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38506 55382 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(-5 *2 + (-2 (|:| |brans| (-666 (-666 (-972 (-229))))) + (|:| |xValues| (-1125 (-229))) (|:| |yValues| (-1125 (-229))))) + (-5 *1 (-155)) (-5 *3 (-666 (-666 (-972 (-229))))))) + ((*1 *1 *2) (-12 (-5 *2 (-666 (-1125 (-392)))) (-5 *1 (-272)))) + ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-272))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1241 *3 *4 *5 *6)) (-4 *3 (-570)) (-4 *4 (-815)) + (-4 *5 (-871)) (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1241 *4 *5 *6 *3)) (-4 *4 (-570)) (-4 *5 (-815)) + (-4 *6 (-871)) (-4 *3 (-1096 *4 *5 *6)) (-5 *2 (-112))))) (((*1 *1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1080)) (-14 *4 (-666 (-1207))))) @@ -77,104 +106,99 @@ (-12 (-5 *2 (-793)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 *2) (-14 *4 *2) (-4 *5 (-175)))) ((*1 *1) (-12 (-4 *2 (-175)) (-4 *1 (-746 *2 *3)) (-4 *3 (-1274 *2))))) -(((*1 *2 *2) - (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) - (-4 *2 (-13 (-444 *3) (-1033)))))) -(((*1 *1 *1 *1) (-5 *1 (-886)))) -(((*1 *2 *3 *3 *3 *3 *4 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(-578))))) + ((*1 *2 *1) + (-12 (-4 *1 (-1317 *3)) (-4 *3 (-376)) (-5 *2 (-855 (-950))))) + ((*1 *2 *1) + (-12 (-4 *1 (-1319 *3 *4)) (-4 *3 (-871)) (-4 *4 (-1080)) + (-5 *2 (-793))))) +(((*1 *2 *1) (-12 (-4 *1 (-857 *3)) (-4 *3 (-1131)) (-5 *2 (-55))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) @@ -5191,22 +4864,32 @@ ((*1 *2 *2) (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-666 (-981 *3))) (-4 *3 (-466)) - (-5 *1 (-373 *3 *4)) (-14 *4 (-666 (-1207))))) - ((*1 *2 *2) - (|partial| -12 (-5 *2 (-666 (-802 *3 (-888 *4)))) (-4 *3 (-466)) - (-14 *4 (-666 (-1207))) (-5 *1 (-647 *3 *4))))) -(((*1 *2 *3 *4 *4 *4 *3 *4 *3) - (-12 (-5 *3 (-578)) (-5 *4 (-711 (-229))) (-5 *2 (-1066)) - (-5 *1 (-773))))) -(((*1 *2 *1) (-12 (-5 *2 (-666 (-666 (-972 (-229))))) (-5 *1 (-482))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-950)) (-5 *2 (-1303)) (-5 *1 (-1299)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-950)) (-5 *2 (-1303)) (-5 *1 (-1300))))) +(((*1 *1 *1) + (-12 (|has| *1 (-6 -4508)) (-4 *1 (-153 *2)) (-4 *2 (-1248)) + (-4 *2 (-1131))))) +(((*1 *2 *1) + (-12 (-5 *2 (-666 (-1234 *3))) (-5 *1 (-1234 *3)) (-4 *3 (-1131))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-618 *3 *4)) (-4 *3 (-1131)) (-4 *4 (-1248)) + (-5 *2 (-112))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-306 (-421 (-981 *5)))) (-5 *4 (-1207)) + (-4 *5 (-13 (-319) (-149))) + (-5 *2 (-1196 (-666 (-328 *5)) (-666 (-306 (-328 *5))))) + (-5 *1 (-1160 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-421 (-981 *5))) (-5 *4 (-1207)) + (-4 *5 (-13 (-319) (-149))) + (-5 *2 (-1196 (-666 (-328 *5)) (-666 (-306 (-328 *5))))) + (-5 *1 (-1160 *5))))) (((*1 *1 *1) (-4 *1 (-559)))) -(((*1 *2 *1) (-12 (-5 *2 (-1135)) (-5 *1 (-1211))))) +(((*1 *1 *1) (-12 (-4 *1 (-696 *2)) (-4 *2 (-1248))))) +(((*1 *2 *1 *1 *3) + (-12 (-4 *4 (-1080)) (-4 *5 (-815)) (-4 *3 (-871)) + (-5 *2 (-2 (|:| -1947 *1) (|:| -2829 *1))) (-4 *1 (-978 *4 *5 *3)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-1080)) (-5 *2 (-2 (|:| -1947 *1) (|:| -2829 *1))) + (-4 *1 (-1274 *3))))) (((*1 *1 *1) (-12 (-4 *1 (-386 *2)) (-4 *2 (-1248)) (-4 *2 (-871)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-386 *3)) (-4 *3 (-1248)))) @@ -5215,17 +4898,14 @@ ((*1 *2 *1 *3) (-12 (-4 *4 (-1080)) (-4 *5 (-815)) (-4 *3 (-871)) (-4 *6 (-1096 *4 *5 *3)) - (-5 *2 (-2 (|:| |under| *1) (|:| -3416 *1) (|:| |upper| *1))) + (-5 *2 (-2 (|:| |under| *1) (|:| -3245 *1) (|:| |upper| *1))) (-4 *1 (-1007 *4 *5 *3 *6))))) -(((*1 *2 *1) - (-12 (-5 *2 (-421 (-981 *3))) (-5 *1 (-467 *3 *4 *5 *6)) - (-4 *3 (-570)) (-4 *3 (-175)) (-14 *4 (-950)) - (-14 *5 (-666 (-1207))) (-14 *6 (-1298 (-711 *3)))))) -(((*1 *2) (-12 (-5 *2 (-1207)) (-5 *1 (-1210))))) -(((*1 *2 *3) - (-12 (-5 *3 (-666 (-578))) (-5 *2 (-933 (-578))) (-5 *1 (-946)))) - ((*1 *2) (-12 (-5 *2 (-933 (-578))) (-5 *1 (-946))))) -(((*1 *1) (-5 *1 (-159)))) +(((*1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-955))))) +(((*1 *2 *3) (-12 (-5 *3 (-950)) (-5 *2 (-933 (-578))) (-5 *1 (-946)))) + ((*1 *2 *3) + (-12 (-5 *3 (-666 (-578))) (-5 *2 (-933 (-578))) (-5 *1 (-946))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-578)) (-5 *2 (-1066)) (-5 *1 (-780))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) @@ -5242,37 +4922,35 @@ ((*1 *2 *2) (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1189)) - (-4 *4 (-13 (-466) (-1069 (-578)) (-660 (-578)))) (-5 *2 (-112)) - (-5 *1 (-228 *4 *5)) (-4 *5 (-13 (-1233) (-29 *4)))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1188 *3)) (-4 *3 (-1080)) (-5 *1 (-1191 *3))))) -(((*1 *2 *3 *3 *3 *3 *4 *3 *5 *5 *5 *3) - (-12 (-5 *3 (-578)) (-5 *5 (-711 (-229))) (-5 *4 (-229)) - (-5 *2 (-1066)) (-5 *1 (-772))))) -(((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| -2039 (-421 (-578))) (|:| -2049 (-421 (-578))))) - (-5 *2 (-421 (-578))) (-5 *1 (-1051 *4)) (-4 *4 (-1274 (-578)))))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-742)) (-5 *2 (-950)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-744)) (-5 *2 (-793))))) +(((*1 *2 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-1303)) (-5 *1 (-450))))) +(((*1 *2 *1) + (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1131)) + (-5 *2 (-2 (|:| -1635 (-578)) (|:| |var| (-631 *1)))) + (-4 *1 (-444 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-886))))) +(((*1 *2 *2 *3) + (-12 (-4 *3 (-1080)) (-5 *1 (-458 *3 *2)) (-4 *2 (-1274 *3))))) (((*1 *2 *2 *2 *3 *4) (-12 (-5 *3 (-99 *5)) (-5 *4 (-1 *5 *5)) (-4 *5 (-1080)) (-5 *1 (-877 *5 *2)) (-4 *2 (-876 *5))))) (((*1 *1 *2) (-12 (-5 *2 (-1151)) (-5 *1 (-342))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1298 (-328 (-229)))) + (-5 *2 + (-2 (|:| |additions| (-578)) (|:| |multiplications| (-578)) + (|:| |exponentiations| (-578)) (|:| |functionCalls| (-578)))) + (-5 *1 (-317))))) +(((*1 *2 *2) + (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) + (-4 *2 (-13 (-444 *3) (-1233)))))) (((*1 *1 *1) - (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) - (-4 *4 (-871)) (-4 *2 (-466))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1188 (-666 (-578)))) (-5 *3 (-666 (-578))) - (-5 *1 (-908))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-846))))) -(((*1 *1 *2) - (|partial| -12 (-5 *2 (-1313 *3 *4)) (-4 *3 (-871)) (-4 *4 (-175)) - (-5 *1 (-686 *3 *4)))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-686 *3 *4)) (-5 *1 (-1318 *3 *4)) - (-4 *3 (-871)) (-4 *4 (-175))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-543))))) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-578)))) (-4 *2 (-1080))))) +(((*1 *2 *2) (-12 (-5 *2 (-578)) (-5 *1 (-955))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-666 *2)) (-4 *2 (-978 *4 *5 *6)) (-4 *4 (-466)) + (-4 *5 (-815)) (-4 *6 (-871)) (-5 *1 (-463 *4 *5 *6 *2))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) @@ -5289,83 +4967,30 @@ ((*1 *2 *2) (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-59 *6)) (-4 *6 (-1248)) - (-4 *5 (-1248)) (-5 *2 (-59 *5)) (-5 *1 (-58 *6 *5)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *5 *7 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(-4 *6 (-1274 *4))))) + (-12 (-5 *2 (-432 (-1203 (-578)))) (-5 *1 (-194)) (-5 *3 (-578))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) @@ -5382,40 +5007,42 @@ ((*1 *2 *2) (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *1) - (-12 (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871)) (-5 *2 (-666 *1)) - (-4 *1 (-1096 *3 *4 *5))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-1203 *1)) (-4 *1 (-1043))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-355 *4 *3 *5)) (-4 *4 (-1252)) (-4 *3 (-1274 *4)) - (-4 *5 (-1274 (-421 *3))) (-5 *2 (-112)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1252)) (-4 *4 (-1274 *3)) - (-4 *5 (-1274 (-421 *4))) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1252)) (-4 *4 (-1274 *3)) - (-4 *5 (-1274 (-421 *4))) (-5 *2 (-112))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1188 *4)) (-4 *4 (-38 *3)) (-4 *4 (-1080)) + (-5 *3 (-421 (-578))) (-5 *1 (-1191 *4))))) +(((*1 *1 *2) + (-12 (-5 *2 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(-4 *2 (-1274 *4)) + (-5 *1 (-458 *4 *2)))) + ((*1 *2 *3 *2 *4) + (-12 (-5 *2 (-421 (-1203 (-328 *5)))) (-5 *3 (-1298 (-328 *5))) + (-5 *4 (-578)) (-4 *5 (-570)) (-5 *1 (-1161 *5))))) (((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-444 *3) (-1033))))) @@ -5432,24 +5059,29 @@ ((*1 *2 *2) (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) - (-12 (-5 *3 (-1189)) (-5 *4 (-578)) (-5 *5 (-711 (-172 (-229)))) - (-5 *2 (-1066)) (-5 *1 (-776))))) -(((*1 *1 *2) - (-12 (-5 *2 (-666 *1)) (-4 *3 (-1080)) (-4 *1 (-709 *3 *4 *5)) - (-4 *4 (-386 *3)) (-4 *5 (-386 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-666 *3)) (-4 *3 (-1080)) (-4 *1 (-709 *3 *4 *5)) - (-4 *4 (-386 *3)) (-4 *5 (-386 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1298 *3)) (-4 *3 (-1080)) (-5 *1 (-711 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-666 *4)) (-4 *4 (-1080)) (-4 *1 (-1154 *3 *4 *5 *6)) - (-4 *5 (-245 *3 *4)) (-4 *6 (-245 *3 *4))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-793)) (-5 *1 (-805 *2)) (-4 *2 (-38 (-421 (-578)))) + (-4 *2 (-175))))) (((*1 *1 *1) (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) (-4 *4 (-871)) (-4 *2 (-466))))) -(((*1 *2 *3) (-12 (-5 *3 (-950)) (-5 *2 (-1189)) (-5 *1 (-808))))) +(((*1 *2 *2 *3) + (-12 + (-5 *2 + (-2 (|:| |partsol| (-1298 (-421 (-981 *4)))) + (|:| -4296 (-666 (-1298 (-421 (-981 *4))))))) + (-5 *3 (-666 *7)) (-4 *4 (-13 (-319) (-149))) + (-4 *7 (-978 *4 *6 *5)) (-4 *5 (-13 (-871) (-633 (-1207)))) + (-4 *6 (-815)) (-5 *1 (-953 *4 *5 *6 *7))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-116)))) + ((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-116)))) + ((*1 *2 *1 *3) + (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) + (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) + ((*1 *2 *1) + (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) + (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-793)))) + ((*1 *2 *1) (-12 (-4 *1 (-277 *3)) (-4 *3 (-871)) (-5 *2 (-793))))) (((*1 *1 *1 *1) (-12 (-5 *1 (-671 *2 *3 *4)) (-4 *2 (-1131)) (-4 *3 (-23)) (-14 *4 *3))) @@ -5458,36 +5090,30 @@ (-14 *4 *3))) ((*1 *1 *1 *1) (-12 (-5 *1 (-697 *2)) (-4 *2 (-1080)) (-4 *2 (-1131))))) -(((*1 *2 *1) (-12 (-5 *2 (-1207)) (-5 *1 (-844))))) -(((*1 *2 *3) (-12 (-5 *3 (-950)) (-5 *2 (-933 (-578))) (-5 *1 (-946)))) - ((*1 *2 *3) - (-12 (-5 *3 (-666 (-578))) (-5 *2 (-933 (-578))) (-5 *1 (-946))))) -(((*1 *2 *3 *4 *3 *4 *4 *4) - (-12 (-5 *3 (-711 (-229))) (-5 *4 (-578)) (-5 *2 (-1066)) - (-5 *1 (-778))))) -(((*1 *2 *1) (-12 (-4 *1 (-1180 *3)) (-4 *3 (-1248)) (-5 *2 (-112))))) -(((*1 *1 *2) - (-12 (-5 *2 (-666 (-518 *3 *4 *5 *6))) (-4 *3 (-376)) (-4 *4 (-815)) - (-4 *5 (-871)) (-5 *1 (-518 *3 *4 *5 *6)) (-4 *6 (-978 *3 *4 *5)))) - ((*1 *1 *1 *1) - (-12 (-4 *2 (-376)) (-4 *3 (-815)) (-4 *4 (-871)) - (-5 *1 (-518 *2 *3 *4 *5)) (-4 *5 (-978 *2 *3 *4)))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-666 *1)) (-4 *1 (-1102 *4 *5 *6 *3)) (-4 *4 (-466)) - (-4 *5 (-815)) (-4 *6 (-871)) (-4 *3 (-1096 *4 *5 *6)))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-666 *1)) (-5 *3 (-666 *7)) (-4 *1 (-1102 *4 *5 *6 *7)) - (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) - (-4 *7 (-1096 *4 *5 *6)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-666 *7)) (-4 *7 (-1096 *4 *5 *6)) (-4 *4 (-466)) - (-4 *5 (-815)) (-4 *6 (-871)) (-5 *2 (-666 *1)) - (-4 *1 (-1102 *4 *5 *6 *7)))) - ((*1 *2 *3 *1) - (-12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) - (-4 *3 (-1096 *4 *5 *6)) (-5 *2 (-666 *1)) - (-4 *1 (-1102 *4 *5 *6 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-1129 *2)) (-4 *2 (-1131))))) +(((*1 *2 *1) (-12 (-5 *2 (-258)) (-5 *1 (-345))))) +(((*1 *2 *3 *4 *4 *3) + (-12 (-5 *3 (-578)) (-5 *4 (-711 (-229))) (-5 *2 (-1066)) + (-5 *1 (-774))))) +(((*1 *1 *1) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-578)))) (-4 *2 (-1080))))) +(((*1 *2 *2) + (-12 (-4 *3 (-1069 (-578))) (-4 *3 (-570)) (-5 *1 (-32 *3 *2)) + (-4 *2 (-444 *3)))) + ((*1 *2) + (-12 (-4 *4 (-175)) (-5 *2 (-1203 *4)) (-5 *1 (-167 *3 *4)) + (-4 *3 (-168 *4)))) + ((*1 *1 *1) (-12 (-4 *1 (-1080)) (-4 *1 (-314)))) + ((*1 *2) (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-5 *2 (-1203 *3)))) + ((*1 *2) (-12 (-4 *1 (-746 *3 *2)) (-4 *3 (-175)) (-4 *2 (-1274 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1099 *3 *2)) (-4 *3 (-13 (-870) (-376))) + (-4 *2 (-1274 *3))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) + (-4 *4 (-871)) (-4 *2 (-570)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) + (-4 *4 (-871)) (-4 *2 (-570))))) (((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-444 *3) (-1033))))) @@ -5506,39 +5132,42 @@ (-5 *1 (-1193 *3))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-1207)) (-5 *3 (-666 (-550))) (-5 *1 (-550))))) -(((*1 *2 *3 *3 *3 *3 *3 *3 *4 *4 *4 *3 *3 *5 *6 *3 *6 *6 *5 *6 *6 *6 *6 - *5 *3 *3 *3 *3 *3 *6 *6 *6 *3 *3 *3 *3 *3 *7 *4 *4 *4 *4 *3 *8 - *9) - (-12 (-5 *4 (-711 (-229))) (-5 *5 (-112)) (-5 *6 (-229)) - (-5 *7 (-711 (-578))) - (-5 *8 (-3 (|:| |fn| (-402)) (|:| |fp| (-80 CONFUN)))) - (-5 *9 (-3 (|:| |fn| (-402)) (|:| |fp| (-77 OBJFUN)))) - (-5 *3 (-578)) (-5 *2 (-1066)) (-5 *1 (-775))))) -(((*1 *1 *1 *1) (-4 *1 (-998)))) -(((*1 *2 *2) (-12 (-5 *2 (-578)) (-5 *1 (-575))))) -(((*1 *2 *3) - (-12 (-4 *4 (-570)) (-5 *2 (-112)) (-5 *1 (-287 *4 *3)) - (-4 *3 (-13 (-444 *4) (-1033)))))) +(((*1 *2 *3 *3 *3 *4 *3) + (-12 (-5 *3 (-578)) (-5 *4 (-711 (-172 (-229)))) (-5 *2 (-1066)) + (-5 *1 (-776))))) +(((*1 *2 *3) (-12 (-5 *3 (-950)) (-5 *2 (-1189)) (-5 *1 (-808))))) +(((*1 *2 *2 *3 *4 *4) + (-12 (-5 *4 (-578)) (-4 *3 (-175)) (-4 *5 (-386 *3)) + (-4 *6 (-386 *3)) (-5 *1 (-710 *3 *5 *6 *2)) + (-4 *2 (-709 *3 *5 *6))))) (((*1 *2 *3) - (-12 (-5 *3 (-1207)) (-5 *2 (-1 *6 *5)) (-5 *1 (-728 *4 *5 *6)) - (-4 *4 (-633 (-550))) (-4 *5 (-1248)) (-4 *6 (-1248))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-1298 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) - (-5 *2 (-711 *4)))) - ((*1 *2 *1) (-12 (-4 *1 (-431 *3)) (-4 *3 (-175)) (-5 *2 (-711 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-1041 *3)) (-4 *3 (-1248)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1195 *3 *4)) (-14 *3 (-950)) - (-4 *4 (-1080))))) -(((*1 *2 *1) - (-12 (-5 *2 (-666 (-666 (-793)))) (-5 *1 (-933 *3)) (-4 *3 (-1131))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-376) (-149) (-1069 (-578)))) (-4 *5 (-1274 *4)) - (-5 *2 (-2 (|:| |ans| (-421 *5)) (|:| |nosol| (-112)))) - (-5 *1 (-1046 *4 *5)) (-5 *3 (-421 *5))))) + (-12 (-5 *3 (-666 (-229))) (-5 *2 (-666 (-1189))) (-5 *1 (-195)))) + ((*1 *2 *3) + (-12 (-5 *3 (-666 (-229))) (-5 *2 (-666 (-1189))) (-5 *1 (-312)))) + ((*1 *2 *3) + (-12 (-5 *3 (-666 (-229))) (-5 *2 (-666 (-1189))) (-5 *1 (-317))))) +(((*1 *2 *1 *2) + (-12 (|has| *1 (-6 -4509)) (-4 *1 (-1286 *2)) (-4 *2 (-1248))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1298 (-666 (-2 (|:| -3529 *4) (|:| -2481 (-1151)))))) + (-4 *4 (-362)) (-5 *2 (-1303)) (-5 *1 (-542 *4))))) +(((*1 *2 *2) + (-12 (-5 *2 (-666 *7)) (-4 *7 (-1102 *3 *4 *5 *6)) (-4 *3 (-466)) + (-4 *4 (-815)) (-4 *5 (-871)) (-4 *6 (-1096 *3 *4 *5)) + (-5 *1 (-1019 *3 *4 *5 *6 *7)))) + ((*1 *2 *2) + (-12 (-5 *2 (-666 *7)) (-4 *7 (-1102 *3 *4 *5 *6)) (-4 *3 (-466)) + (-4 *4 (-815)) (-4 *5 (-871)) (-4 *6 (-1096 *3 *4 *5)) + (-5 *1 (-1138 *3 *4 *5 *6 *7))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1203 *2)) (-4 *2 (-978 (-421 (-981 *6)) *5 *4)) + (-5 *1 (-754 *5 *4 *6 *2)) (-4 *5 (-815)) + (-4 *4 (-13 (-871) (-10 -8 (-15 -1332 ((-1207) $))))) + (-4 *6 (-570))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-456 *3)) (-4 *3 (-1274 (-578)))))) (((*1 *2 *3) - (-12 (-5 *3 (-666 (-666 (-972 (-229))))) - (-5 *2 (-666 (-1125 (-229)))) (-5 *1 (-957))))) + (-12 (-5 *3 (-950)) (-5 *2 (-1209 (-421 (-578)))) (-5 *1 (-193))))) (((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-444 *3) (-1033))))) @@ -5555,40 +5184,48 @@ ((*1 *2 *2) (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-1023 *2)) (-4 *2 (-570)) (-4 *2 (-559)))) - ((*1 *1 *1) (-4 *1 (-1091)))) -(((*1 *2 *3 *4 *5 *6 *7) - (-12 (-5 *3 (-1188 (-2 (|:| |k| 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*4) (|:| |c| *3)))))) + ((*1 *2 *1) + (-12 (-5 *2 (-666 (-2 (|:| |k| (-918 *3)) (|:| |c| *4)))) + (-5 *1 (-646 *3 *4 *5)) (-4 *3 (-871)) + (-4 *4 (-13 (-175) (-739 (-421 (-578))))) (-14 *5 (-950)))) + ((*1 *2 *1) + (-12 (-5 *2 (-666 (-694 *3))) (-5 *1 (-918 *3)) (-4 *3 (-871))))) +(((*1 *2 *3 *3 *3 *4 *5 *5 *3) + (-12 (-5 *3 (-578)) (-5 *5 (-711 (-229))) (-5 *4 (-229)) + (-5 *2 (-1066)) (-5 *1 (-774))))) +(((*1 *2 *1) + (-12 (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871)) (-5 *2 (-666 *1)) + (-4 *1 (-1096 *3 *4 *5))))) (((*1 *2) - (-12 (-4 *3 (-570)) (-5 *2 (-666 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-431 *3))))) + (-12 (-4 *4 (-175)) (-5 *2 (-1203 (-981 *4))) (-5 *1 (-430 *3 *4)) + (-4 *3 (-431 *4)))) + ((*1 *2) + (-12 (-4 *1 (-431 *3)) (-4 *3 (-175)) (-4 *3 (-376)) + (-5 *2 (-1203 (-981 *3))))) + ((*1 *2) + (-12 (-5 *2 (-1203 (-421 (-981 *3)))) (-5 *1 (-467 *3 *4 *5 *6)) + (-4 *3 (-570)) (-4 *3 (-175)) (-14 *4 (-950)) + (-14 *5 (-666 (-1207))) (-14 *6 (-1298 (-711 *3)))))) (((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-444 *3) (-1033))))) @@ -5608,70 +5245,46 @@ ((*1 *2 *2) (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *1) - (|partial| -12 (-5 *2 (-1092 (-1055 *3) (-1203 (-1055 *3)))) - (-5 *1 (-1055 *3)) (-4 *3 (-13 (-870) (-376) (-1053)))))) -(((*1 *2 *3) (-12 (-5 *2 (-421 (-578))) (-5 *1 (-575)) (-5 *3 (-578)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1203 (-421 (-578)))) (-5 *1 (-971)) (-5 *3 (-578))))) -(((*1 *2) (-12 (-5 *2 (-950)) (-5 *1 (-1301)))) - ((*1 *2 *2) (-12 (-5 *2 (-950)) (-5 *1 (-1301))))) -(((*1 *1) (-4 *1 (-362))) +(((*1 *1 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) + ((*1 *1 *1 *1) (-4 *1 (-487))) + ((*1 *1 *1) (-12 (-4 *1 (-819 *2)) (-4 *2 (-175)))) + ((*1 *2 *2) (-12 (-5 *2 (-666 (-950))) (-5 *1 (-908)))) + ((*1 *1 *1) (-5 *1 (-1002))) + ((*1 *1 *1) (-12 (-4 *1 (-1028 *2)) (-4 *2 (-175))))) +(((*1 *2 *3) + (-12 (-5 *3 (-666 (-950))) (-5 *2 (-933 (-578))) (-5 *1 (-946))))) +(((*1 *2 *3) (-12 (-5 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*2 - (-666 - (-2 (|:| |eigval| (-3 (-421 (-981 *4)) (-1196 (-1207) (-981 *4)))) - (|:| |eigmult| (-793)) - (|:| |eigvec| (-666 (-711 (-421 (-981 *4)))))))) - (-5 *1 (-304 *4)) (-5 *3 (-711 (-421 (-981 *4))))))) + (-12 (-4 *4 (-570)) (-4 *5 (-815)) (-4 *6 (-871)) + (-4 *7 (-1096 *4 *5 *6)) + (-5 *2 (-2 (|:| |goodPols| (-666 *7)) (|:| |badPols| (-666 *7)))) + (-5 *1 (-1008 *4 *5 *6 *7)) (-5 *3 (-666 *7))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 (-229) (-229))) (-5 *1 (-330)) (-5 *3 (-229))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) @@ -5922,71 +5540,78 @@ ((*1 *2 *2) (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1271 *5 *4)) (-4 *4 (-466)) (-4 *4 (-842)) - (-14 *5 (-1207)) (-5 *2 (-578)) (-5 *1 (-1145 *4 *5))))) -(((*1 *2 *1) (-12 (-4 *1 (-870)) (-5 *2 (-578)))) - ((*1 *2 *1) (-12 (-5 *2 (-578)) (-5 *1 (-934 *3)) (-4 *3 (-1131)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1099 *4 *3)) (-4 *4 (-13 (-870) 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(-819 *2)) (-4 *2 (-175)))) + ((*1 *1 *2 *2) + (-12 (-5 *2 (-1030 *3)) (-4 *3 (-175)) (-5 *1 (-821 *3))))) (((*1 *2 *3) - (-12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) (-5 *2 (-1303)) - (-5 *1 (-463 *4 *5 *6 *3)) (-4 *3 (-978 *4 *5 *6))))) -(((*1 *2 *3 *3) - (-12 (-5 *2 (-1188 (-666 (-578)))) (-5 *1 (-908)) - (-5 *3 (-666 (-578)))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-559)) (-5 *2 (-112))))) -(((*1 *1) (-5 *1 (-451)))) + (-12 (-5 *3 (-950)) (-5 *2 (-1203 *4)) (-5 *1 (-370 *4)) + (-4 *4 (-362))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) @@ -6110,34 +5772,41 @@ ((*1 *2 *2) (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-793)) (-5 *2 (-1271 *5 *4)) (-5 *1 (-1205 *4 *5 *6)) - (-4 *4 (-1080)) (-14 *5 (-1207)) (-14 *6 *4))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-793)) (-5 *2 (-1271 *5 *4)) (-5 *1 (-1290 *4 *5 *6)) - (-4 *4 (-1080)) (-14 *5 (-1207)) (-14 *6 *4)))) -(((*1 *1 *2) - (|partial| -12 (-5 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*4 (-666 *9)) (-4 *8 (-1096 *5 *6 *7)) + (-4 *9 (-1102 *5 *6 *7 *8)) (-4 *5 (-466)) (-4 *6 (-815)) + (-4 *7 (-871)) (-5 *2 (-793)) (-5 *1 (-1100 *5 *6 *7 *8 *9)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-666 *8)) (-5 *4 (-666 *9)) (-4 *8 (-1096 *5 *6 *7)) + (-4 *9 (-1140 *5 *6 *7 *8)) (-4 *5 (-466)) (-4 *6 (-815)) + (-4 *7 (-871)) (-5 *2 (-793)) (-5 *1 (-1176 *5 *6 *7 *8 *9))))) +(((*1 *2 *3) + (-12 (-4 *4 (-570)) (-5 *2 (-112)) (-5 *1 (-287 *4 *3)) + (-4 *3 (-13 (-444 *4) (-1033)))))) +(((*1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-1037)))) + ((*1 *2 *2) (-12 (-5 *2 (-578)) (-5 *1 (-1037))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *5 (-631 *4)) (-5 *6 (-1207)) + (-4 *4 (-13 (-444 *7) (-27) (-1233))) + (-4 *7 (-13 (-466) (-1069 (-578)) (-149) (-660 (-578)))) + (-5 *2 + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -4296 (-666 *4)))) + (-5 *1 (-580 *7 *4 *3)) (-4 *3 (-678 *4)) (-4 *3 (-1131))))) (((*1 *2 *1) - (-12 (-4 *3 (-1080)) (-5 *2 (-1298 *3)) (-5 *1 (-734 *3 *4)) - (-4 *4 (-1274 *3))))) -(((*1 *2 *3) (-12 (-5 *3 (-793)) (-5 *2 (-392)) (-5 *1 (-1071))))) -(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1066))))) + (|partial| -12 (-4 *1 (-1260 *3 *2)) (-4 *3 (-1080)) + (-4 *2 (-1289 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-116))))) +(((*1 *1 *1 *2) + (-12 (-5 *1 (-1171 *3 *2)) (-4 *3 (-13 (-1131) (-34))) + (-4 *2 (-13 (-1131) (-34)))))) +(((*1 *2 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *4 *4 + *4 *6 *4) + (-12 (-5 *4 (-578)) (-5 *5 (-711 (-229))) (-5 *6 (-697 (-229))) + (-5 *3 (-229)) (-5 *2 (-1066)) (-5 *1 (-772))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) @@ -6157,20 +5826,12 @@ ((*1 *2 *2) (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-793)) (-4 *1 (-1315 *3 *4)) (-4 *3 (-871)) - (-4 *4 (-1080)) (-4 *4 (-175)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1315 *2 *3)) (-4 *2 (-871)) (-4 *3 (-1080)) - (-4 *3 (-175))))) -(((*1 *2 *2) - (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) - (-4 *2 (-13 (-444 *3) (-1233)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1165 *3)) (-4 *3 (-1080)) - (-5 *2 (-666 (-666 (-666 (-972 *3)))))))) -(((*1 *2) (-12 (-5 *2 (-898)) (-5 *1 (-1301)))) - ((*1 *2 *2) (-12 (-5 *2 (-898)) (-5 *1 (-1301))))) +(((*1 *2 *1) (-12 (-4 *1 (-819 *2)) (-4 *2 (-175))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-804 *2)) (-4 *2 (-1080))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1207)) (-5 *2 (-1 *6 *5)) (-5 *1 (-728 *4 *5 *6)) + (-4 *4 (-633 (-550))) (-4 *5 (-1248)) (-4 *6 (-1248))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1014 *2)) (-4 *2 (-1233))))) (((*1 *2 *3 *2) (-12 (-5 *2 (-666 (-392))) (-5 *3 (-666 (-272))) (-5 *1 (-270)))) ((*1 *2 *1 *2) (-12 (-5 *2 (-666 (-392))) (-5 *1 (-482)))) @@ -6179,24 +5840,29 @@ (-12 (-5 *3 (-950)) (-5 *4 (-898)) (-5 *2 (-1303)) (-5 *1 (-1299)))) ((*1 *2 *1 *3 *4) (-12 (-5 *3 (-950)) (-5 *4 (-1189)) (-5 *2 (-1303)) (-5 *1 (-1299))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-815)) (-4 *6 (-871)) - (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-666 (-666 *7))) - (-5 *1 (-462 *4 *5 *6 *7)) (-5 *3 (-666 *7)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-13 (-319) (-149))) (-4 *6 (-815)) - (-4 *7 (-871)) (-4 *8 (-978 *5 *6 *7)) (-5 *2 (-666 (-666 *8))) - (-5 *1 (-462 *5 *6 *7 *8)) (-5 *3 (-666 *8))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1291 *3 *2)) - (-4 *2 (-1289 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-186 (-257))) (-5 *1 (-256))))) -(((*1 *2 *2 *2 *2) - (-12 (-5 *2 (-421 (-1203 (-328 *3)))) (-4 *3 (-570)) - (-5 *1 (-1161 *3))))) -(((*1 *1 *1 *2 *2) - (|partial| -12 (-5 *2 (-950)) (-5 *1 (-1132 *3 *4)) (-14 *3 *2) - (-14 *4 *2)))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-793)) (-5 *3 (-972 *5)) (-4 *5 (-1080)) + (-5 *1 (-1195 *4 *5)) (-14 *4 (-950)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-666 (-793))) (-5 *3 (-793)) (-5 *1 (-1195 *4 *5)) + (-14 *4 (-950)) (-4 *5 (-1080)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-666 (-793))) (-5 *3 (-972 *5)) (-4 *5 (-1080)) + (-5 *1 (-1195 *4 *5)) (-14 *4 (-950))))) +(((*1 *2 *2 *3) + (-12 (-4 *3 (-319)) (-5 *1 (-469 *3 *2)) (-4 *2 (-1274 *3)))) + ((*1 *2 *2 *3) + (-12 (-4 *3 (-319)) (-5 *1 (-474 *3 *2)) (-4 *2 (-1274 *3)))) + ((*1 *2 *2 *3) + (-12 (-4 *3 (-319)) (-14 *4 *3) (-14 *5 (-1 *3 *3 (-793))) + (-5 *1 (-553 *3 *2 *4 *5)) (-4 *2 (-1274 *3))))) +(((*1 *1 *2) (-12 (-5 *2 (-666 *3)) (-4 *3 (-1131)) (-5 *1 (-91 *3))))) +(((*1 *2 *3 *3 *3 *3 *3 *4 *3 *4 *3 *5 *5 *3) + (-12 (-5 *3 (-578)) (-5 *4 (-112)) (-5 *5 (-711 (-172 (-229)))) + (-5 *2 (-1066)) (-5 *1 (-777))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-666 *5)) (-5 *4 (-950)) (-4 *5 (-871)) + (-5 *2 (-59 (-666 (-694 *5)))) (-5 *1 (-694 *5))))) (((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-444 *3) (-1033))))) @@ -6213,19 +5879,35 @@ (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3)))) ((*1 *1 *1) (-4 *1 (-1236)))) -(((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-793)) (-4 *1 (-1096 *3 *4 *5)) (-4 *3 (-1080)) - (-4 *4 (-815)) (-4 *5 (-871)) (-4 *3 (-570))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1265 *3)) (-4 *3 (-1248))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-466)) (-4 *6 (-815)) (-4 *7 (-871)) - (-4 *3 (-1096 *5 *6 *7)) (-5 *2 (-666 *4)) - (-5 *1 (-1139 *5 *6 *7 *3 *4)) (-4 *4 (-1102 *5 *6 *7 *3))))) -(((*1 *2 *1) - (-12 (|has| *1 (-6 -4507)) (-4 *1 (-503 *3)) (-4 *3 (-1248)) - (-5 *2 (-666 *3)))) - ((*1 *2 *1) (-12 (-5 *2 (-666 *3)) (-5 *1 (-759 *3)) (-4 *3 (-1131)))) - ((*1 *2 *1) (-12 (-5 *2 (-666 (-453))) (-5 *1 (-889))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1298 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) + (-5 *2 (-1298 (-711 *4))))) + ((*1 *2) + (-12 (-4 *4 (-175)) (-5 *2 (-1298 (-711 *4))) (-5 *1 (-430 *3 *4)) + (-4 *3 (-431 *4)))) + ((*1 *2) + (-12 (-4 *1 (-431 *3)) (-4 *3 (-175)) (-5 *2 (-1298 (-711 *3))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-666 (-1207))) (-4 *5 (-376)) + (-5 *2 (-1298 (-711 (-421 (-981 *5))))) (-5 *1 (-1117 *5)) + (-5 *4 (-711 (-421 (-981 *5)))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-666 (-1207))) (-4 *5 (-376)) + (-5 *2 (-1298 (-711 (-981 *5)))) (-5 *1 (-1117 *5)) + (-5 *4 (-711 (-981 *5))))) + ((*1 *2 *3) + (-12 (-5 *3 (-666 (-711 *4))) (-4 *4 (-376)) + (-5 *2 (-1298 (-711 *4))) (-5 *1 (-1117 *4))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-1207)) (-4 *4 (-466)) (-4 *4 (-1131)) + (-5 *1 (-587 *4 *2)) (-4 *2 (-296)) (-4 *2 (-444 *4))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1298 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) + (-5 *2 (-711 *4)))) + ((*1 *2 *1) (-12 (-4 *1 (-431 *3)) (-4 *3 (-175)) (-5 *2 (-711 *3))))) +(((*1 *2 *3) (-12 (-5 *3 (-886)) (-5 *2 (-1303)) (-5 *1 (-1169)))) + ((*1 *2 *3) + (-12 (-5 *3 (-666 (-886))) (-5 *2 (-1303)) (-5 *1 (-1169))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-793)) (-5 *2 (-666 (-1207))) (-5 *1 (-213)) (-5 *3 (-1207)))) @@ -6245,41 +5927,31 @@ ((*1 *2 *1) (-12 (-4 *1 (-1315 *3 *4)) (-4 *3 (-871)) (-4 *4 (-1080)) (-5 *2 (-666 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1274 *3)) (-4 *3 (-1080)) (-5 *2 (-1203 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-675 (-421 *6))) (-5 *4 (-421 *6)) (-4 *6 (-1274 *5)) - (-4 *5 (-13 (-376) (-149) (-1069 (-578)) (-1069 (-421 (-578))))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2311 (-666 *4)))) - (-5 *1 (-832 *5 *6)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-675 (-421 *6))) (-4 *6 (-1274 *5)) - (-4 *5 (-13 (-376) (-149) (-1069 (-578)) (-1069 (-421 (-578))))) - (-5 *2 (-2 (|:| -2311 (-666 (-421 *6))) (|:| -4301 (-711 *5)))) - (-5 *1 (-832 *5 *6)) (-5 *4 (-666 (-421 *6))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-676 *6 (-421 *6))) (-5 *4 (-421 *6)) (-4 *6 (-1274 *5)) - (-4 *5 (-13 (-376) (-149) (-1069 (-578)) (-1069 (-421 (-578))))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2311 (-666 *4)))) - (-5 *1 (-832 *5 *6)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-676 *6 (-421 *6))) (-4 *6 (-1274 *5)) - (-4 *5 (-13 (-376) (-149) (-1069 (-578)) (-1069 (-421 (-578))))) - (-5 *2 (-2 (|:| -2311 (-666 (-421 *6))) (|:| -4301 (-711 *5)))) - (-5 *1 (-832 *5 *6)) (-5 *4 (-666 (-421 *6)))))) -(((*1 *1 *2) - (-12 - (-5 *2 - (-2 (|:| |mval| (-711 *3)) (|:| |invmval| (-711 *3)) - (|:| |genIdeal| (-518 *3 *4 *5 *6)))) - (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-871)) - (-5 *1 (-518 *3 *4 *5 *6)) (-4 *6 (-978 *3 *4 *5))))) -(((*1 *2 *3 *1) - (|partial| -12 (-5 *3 (-917 *4)) (-4 *4 (-1131)) (-4 *2 (-1131)) - (-5 *1 (-914 *4 *2))))) -(((*1 *1 *2) (-12 (-5 *2 (-1151)) (-5 *1 (-843))))) +(((*1 *2 *2) (-12 (-5 *2 (-711 (-328 (-578)))) (-5 *1 (-1062))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-229)) (-5 *1 (-230)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-172 (-229))) (-5 *1 (-230)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-570)) (-5 *1 (-445 *3 *2)) (-4 *2 (-444 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1170)))) +(((*1 *1 *1 *1) + (|partial| -12 (-4 *2 (-175)) (-5 *1 (-301 *2 *3 *4 *5 *6 *7)) + (-4 *3 (-1274 *2)) (-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 *1) + (|partial| -12 (-5 *1 (-733 *2 *3 *4 *5 *6)) (-4 *2 (-175)) + (-4 *3 (-23)) (-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 *1 *1) + (|partial| -12 (-5 *1 (-737 *2 *3 *4 *5 *6)) (-4 *2 (-175)) + (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3)) + (-14 *5 (-1 (-3 *3 "failed") *3 *3)) + (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-578)) (-5 *1 (-943 *3)) (-4 *3 (-319))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-392)) (-5 *3 (-666 (-272))) (-5 *1 (-270)))) + ((*1 *1 *2) (-12 (-5 *2 (-392)) (-5 *1 (-272))))) (((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-444 *3) (-1033))))) @@ -6296,59 +5968,25 @@ (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3)))) ((*1 *1 *1) (-4 *1 (-1236)))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-793)) (-5 *2 (-112)) (-5 *1 (-601 *3)) (-4 *3 (-559))))) -(((*1 *2 *1 *3) - (|partial| -12 (-5 *3 (-1207)) (-4 *4 (-1080)) (-4 *4 (-1131)) - (-5 *2 (-2 (|:| |var| (-631 *1)) (|:| -2300 (-578)))) - (-4 *1 (-444 *4)))) - ((*1 *2 *1 *3) - (|partial| -12 (-5 *3 (-116)) (-4 *4 (-1080)) (-4 *4 (-1131)) - (-5 *2 (-2 (|:| |var| 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-(((*1 *2 *2) - (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) - (-4 *2 (-13 (-444 *3) (-1233)))))) -(((*1 *2 *3 *2) - (-12 (-4 *2 (-13 (-376) (-870))) (-5 *1 (-184 *2 *3)) - (-4 *3 (-1274 (-172 *2))))) - ((*1 *2 *3) - (-12 (-4 *2 (-13 (-376) (-870))) (-5 *1 (-184 *2 *3)) - (-4 *3 (-1274 (-172 *2)))))) + (-12 (-5 *2 (-112)) (-5 *1 (-1195 *3 *4)) (-14 *3 (-950)) + (-4 *4 (-1080))))) +(((*1 *2 *1) (-12 (-5 *2 (-1303)) (-5 *1 (-844))))) +(((*1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-955))))) +(((*1 *2 *1) + (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-871)) (-5 *2 (-112)) + (-5 *1 (-518 *3 *4 *5 *6)) (-4 *6 (-978 *3 *4 *5))))) (((*1 *1 *1 *1) - (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) - (-4 *4 (-871)))) - ((*1 *2 *2 *1) - (-12 (-4 *1 (-1241 *3 *4 *5 *2)) (-4 *3 (-570)) (-4 *4 (-815)) - (-4 *5 (-871)) (-4 *2 (-1096 *3 *4 *5))))) -(((*1 *2 *3) - (-12 (-5 *3 (-421 (-981 *4))) (-4 *4 (-319)) - (-5 *2 (-421 (-432 (-981 *4)))) (-5 *1 (-1073 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-981 *5)) (-4 *5 (-1080)) (-5 *2 (-495 *4 *5)) - (-5 *1 (-973 *4 *5)) (-14 *4 (-666 (-1207)))))) + (-12 (|has| *1 (-6 -4509)) (-4 *1 (-121 *2)) (-4 *2 (-1248))))) (((*1 *2 *3) - (-12 (-5 *3 (-950)) (-5 *2 (-1209 (-421 (-578)))) (-5 *1 (-193))))) + (-12 (-4 *4 (-570)) (-4 *5 (-815)) (-4 *6 (-871)) + (-4 *7 (-1096 *4 *5 *6)) + (-5 *2 (-2 (|:| |goodPols| (-666 *7)) (|:| |badPols| (-666 *7)))) + (-5 *1 (-1008 *4 *5 *6 *7)) (-5 *3 (-666 *7))))) +(((*1 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-248))))) (((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-444 *3) (-1033))))) @@ -6365,20 +6003,18 @@ (-12 (-5 *2 (-1188 *3)) (-4 *3 (-38 (-421 (-578)))) (-5 *1 (-1193 *3)))) ((*1 *1 *1) (-4 *1 (-1236)))) -(((*1 *2 *3) - (-12 (-4 *1 (-355 *4 *3 *5)) (-4 *4 (-1252)) (-4 *3 (-1274 *4)) - (-4 *5 (-1274 (-421 *3))) (-5 *2 (-112)))) - ((*1 *2 *3) - (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1252)) (-4 *4 (-1274 *3)) - (-4 *5 (-1274 (-421 *4))) (-5 *2 (-112))))) -(((*1 *2 *3 *3 *4) - (-12 (-4 *5 (-466)) (-4 *6 (-815)) (-4 *7 (-871)) - (-4 *3 (-1096 *5 *6 *7)) - (-5 *2 (-666 (-2 (|:| |val| *3) (|:| -2799 *4)))) - (-5 *1 (-1139 *5 *6 *7 *3 *4)) (-4 *4 (-1102 *5 *6 *7 *3))))) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-1281 *3 *2)) (-4 *3 (-1080)) + (-4 *2 (-1258 *3))))) (((*1 *2 *2 *2) - (|partial| -12 (-4 *3 (-376)) (-5 *1 (-923 *2 *3)) - (-4 *2 (-1274 *3))))) + (-12 (-5 *2 (-666 *6)) (-4 *6 (-1096 *3 *4 *5)) (-4 *3 (-466)) + (-4 *3 (-570)) (-4 *4 (-815)) (-4 *5 (-871)) + (-5 *1 (-1008 *3 *4 *5 *6))))) +(((*1 *2 *1) + (-12 (-5 *2 (-666 (-666 (-793)))) (-5 *1 (-933 *3)) (-4 *3 (-1131))))) +(((*1 *2 *2) + (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) + (-4 *2 (-13 (-444 *3) (-1233)))))) (((*1 *2 *1) (-12 (-4 *1 (-134)) (-5 *2 (-793)))) ((*1 *2 *3 *1 *2) (-12 (-5 *2 (-578)) (-4 *1 (-386 *3)) (-4 *3 (-1248)) @@ -6392,29 +6028,14 @@ ((*1 *2 *1) (-12 (-5 *2 (-1151)) (-5 *1 (-543)))) ((*1 *2 *3 *1 *2) (-12 (-4 *1 (-1175)) (-5 *2 (-578)) (-5 *3 (-143)))) ((*1 *2 *1 *1 *2) (-12 (-4 *1 (-1175)) (-5 *2 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(-578))))) - (-4 *4 (-13 (-319) (-149))) (-4 *5 (-13 (-871) (-633 (-1207)))) - (-4 *6 (-815)) - (-5 *2 - (-2 (|:| |partsol| (-1298 (-421 (-981 *4)))) - (|:| -2311 (-666 (-1298 (-421 (-981 *4))))))) - (-5 *1 (-953 *4 *5 *6 *7)) (-4 *7 (-978 *4 *6 *5))))) -(((*1 *2 *1) (-12 (-4 *1 (-541)) (-5 *2 (-713 (-1254)))))) -(((*1 *2 *1) - (-12 (-14 *3 (-666 (-1207))) (-4 *4 (-175)) - (-4 *5 (-245 (-4415 *3) (-793))) - (-14 *6 - (-1 (-112) (-2 (|:| -2480 *2) (|:| -2300 *5)) - (-2 (|:| -2480 *2) (|:| -2300 *5)))) - (-4 *2 (-871)) (-5 *1 (-475 *3 *4 *2 *5 *6 *7)) - (-4 *7 (-978 *4 *5 (-888 *3)))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1209 (-421 (-578)))) (-5 *1 (-193))))) -(((*1 *2 *3) (-12 (-5 *3 (-666 *2)) (-5 *1 (-1222 *2)) (-4 *2 (-376))))) -(((*1 *1 *2) - (-12 (-5 *2 (-1 *3 *3 (-578))) (-4 *3 (-1080)) (-5 *1 (-99 *3)))) - ((*1 *1 *2 *2) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1080)) (-5 *1 (-99 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1080)) (-5 *1 (-99 *3))))) + (-12 (-5 *3 (-666 *5)) (-4 *5 (-444 *4)) (-4 *4 (-570)) + (-5 *2 (-886)) (-5 *1 (-32 *4 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-666 (-666 (-229)))) (-5 *1 (-955))))) +(((*1 *2 *2) + (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) + (-4 *2 (-13 (-444 *3) (-1233)))))) +(((*1 *1 *2) (-12 (-5 *2 (-666 *1)) (-4 *1 (-314)))) + ((*1 *1 *1) (-4 *1 (-314))) + ((*1 *1 *2) (-12 (-5 *2 (-666 (-886))) (-5 *1 (-886)))) + ((*1 *1 *1) (-5 *1 (-886)))) (((*1 *2 *3) - (|partial| -12 (-5 *3 (-711 *1)) (-4 *1 (-362)) (-5 *2 (-1298 *1)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-711 *1)) (-4 *1 (-147)) (-4 *1 (-938)) - (-5 *2 (-1298 *1))))) -(((*1 *2 *1) (-12 (-4 *1 (-1026 *2)) (-4 *2 (-1248))))) -(((*1 *2 *3) (-12 (-5 *3 (-328 (-229))) (-5 *2 (-229)) (-5 *1 (-317))))) -(((*1 *1 *1 *2) - (|partial| -12 (-5 *2 (-793)) (-4 *1 (-1274 *3)) (-4 *3 (-1080))))) -(((*1 *1) (-5 *1 (-845)))) -(((*1 *2) (-12 (-5 *2 (-898)) (-5 *1 (-1301)))) - ((*1 *2 *2) (-12 (-5 *2 (-898)) (-5 *1 (-1301))))) -(((*1 *2) - (-12 (-4 *3 (-466)) (-4 *4 (-815)) (-4 *5 (-871)) - (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-1303)) - (-5 *1 (-1103 *3 *4 *5 *6 *7)) (-4 *7 (-1102 *3 *4 *5 *6)))) - ((*1 *2) - (-12 (-4 *3 (-466)) (-4 *4 (-815)) (-4 *5 (-871)) - (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-1303)) - (-5 *1 (-1139 *3 *4 *5 *6 *7)) (-4 *7 (-1102 *3 *4 *5 *6))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-1007 *4 *5 *6 *3)) (-4 *4 (-1080)) (-4 *5 (-815)) - (-4 *6 (-871)) (-4 *3 (-1096 *4 *5 *6)) (-4 *4 (-570)) - (-5 *2 (-2 (|:| |num| *3) (|:| |den| *4)))))) + (-12 (-5 *3 (-1298 *4)) (-4 *4 (-362)) (-5 *2 (-1203 *4)) + (-5 *1 (-542 *4))))) +(((*1 *2 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-1303)) (-5 *1 (-886))))) +(((*1 *2 *3 *4 *4 *3) + (-12 (-5 *3 (-578)) (-5 *4 (-711 (-229))) (-5 *2 (-1066)) + (-5 *1 (-769))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-793)) (-4 *4 (-13 (-1080) (-739 (-421 (-578))))) + (-4 *5 (-871)) (-5 *1 (-1314 *4 *5 *2)) (-4 *2 (-1319 *5 *4))))) +(((*1 *2 *3) + (-12 (-4 *4 (-570)) (-5 *2 (-793)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-431 *4))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-815)) (-4 *4 (-871)) (-4 *6 (-319)) (-5 *2 (-432 *3)) - (-5 *1 (-764 *5 *4 *6 *3)) (-4 *3 (-978 *6 *5 *4))))) + (-12 (-5 *4 (-578)) (-4 *2 (-444 *3)) (-5 *1 (-32 *3 *2)) + (-4 *3 (-1069 *4)) (-4 *3 (-570))))) +(((*1 *2 *3) + (-12 (-5 *3 (-666 (-495 *4 *5))) (-14 *4 (-666 (-1207))) + (-4 *5 (-466)) (-5 *2 (-666 (-255 *4 *5))) (-5 *1 (-650 *4 *5))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1203 (-421 (-981 *3)))) (-5 *1 (-467 *3 *4 *5 *6)) + (-4 *3 (-570)) (-4 *3 (-175)) (-14 *4 (-950)) + (-14 *5 (-666 (-1207))) (-14 *6 (-1298 (-711 *3)))))) +(((*1 *2 *3) + (-12 (-4 *4 (-1080)) + (-4 *2 (-13 (-418) (-1069 *4) (-376) (-1233) (-296))) + (-5 *1 (-457 *4 *3 *2)) (-4 *3 (-1274 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-550))))) (((*1 *2 *2 *3) (-12 (-4 *3 (-376)) (-5 *1 (-297 *3 *2)) (-4 *2 (-1289 *3))))) -(((*1 *2 *2) - (-12 (-5 *2 (-972 *3)) (-4 *3 (-13 (-376) (-1233) (-1033))) - (-5 *1 (-179 *3))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) - (|:| -3026 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) + (|:| -3789 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 @@ -6940,7 +6452,7 @@ (-3 (|:| |str| (-1188 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -3026 + (|:| -3789 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -6948,34 +6460,32 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-573))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-793)) (-5 *3 (-972 *4)) (-4 *1 (-1165 *4)) - (-4 *4 (-1080)))) - ((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-793)) (-5 *4 (-972 (-229))) (-5 *2 (-1303)) - (-5 *1 (-1300))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-1303)) (-5 *1 (-1300))))) -(((*1 *2 *1) (-12 (-5 *2 (-520)) (-5 *1 (-539)))) - ((*1 *2 *1) (-12 (-5 *2 (-520)) (-5 *1 (-1182))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-1303)) (-5 *1 (-844))))) (((*1 *2 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-1303)) (-5 *1 (-1217))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-518 (-421 (-578)) (-247 *5 (-793)) (-888 *4) - (-255 *4 (-421 (-578))))) - (-14 *4 (-666 (-1207))) (-14 *5 (-793)) (-5 *2 (-112)) - (-5 *1 (-519 *4 *5))))) -(((*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1248))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-392) (-392))) (-5 *4 (-392)) - (-5 *2 - (-2 (|:| -3528 *4) (|:| -2754 *4) (|:| |totalpts| (-578)) - (|:| |success| (-112)))) - (-5 *1 (-811)) (-5 *5 (-578))))) -(((*1 *2 *3) - (-12 (-4 *4 (-362)) (-4 *5 (-341 *4)) (-4 *6 (-1274 *5)) - (-5 *2 (-666 *3)) (-5 *1 (-799 *4 *5 *6 *3 *7)) (-4 *3 (-1274 *6)) - (-14 *7 (-950))))) + (-12 (-5 *2 (-1188 (-666 (-578)))) (-5 *1 (-908)) (-5 *3 (-578))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1131)) (-4 *5 (-1131)) + (-4 *6 (-1131)) (-5 *2 (-1 *6 *5)) (-5 *1 (-706 *4 *5 *6))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1 (-972 (-229)) (-229) (-229))) + (-5 *3 (-1 (-229) (-229) (-229) (-229))) (-5 *1 (-264))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) + (-4 *7 (-1096 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-1102 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (-12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) + (-4 *7 (-1096 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1138 *4 *5 *6 *7 *3)) (-4 *3 (-1102 *4 *5 *6 *7))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-578)) (-5 *4 (-711 (-229))) (-5 *2 (-1066)) + (-5 *1 (-769))))) +(((*1 *2 *2) + (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) + (-4 *2 (-13 (-444 *3) (-1033)))))) +(((*1 *2) (-12 (-5 *2 (-666 (-1189))) (-5 *1 (-1301)))) + ((*1 *2 *2) (-12 (-5 *2 (-666 (-1189))) (-5 *1 (-1301))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-666 *8)) (-5 *4 (-138 *5 *6 *7)) (-14 *5 (-578)) (-14 *6 (-793)) (-4 *7 (-175)) (-4 *8 (-175)) @@ -6985,81 +6495,110 @@ (-4 *8 (-1080)) (-4 *2 (-978 *9 *7 *5)) (-5 *1 (-750 *5 *6 *7 *8 *9 *4 *2)) (-4 *7 (-815)) (-4 *4 (-978 *8 *6 *5))))) -(((*1 *1 *2) 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(-1207)))) - (-4 *10 (-815)) - (-5 *2 - (-2 - (|:| |rgl| - (-666 - (-2 (|:| |eqzro| (-666 *11)) (|:| |neqzro| (-666 *11)) - (|:| |wcond| (-666 (-981 *8))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1298 (-421 (-981 *8)))) - (|:| -2311 (-666 (-1298 (-421 (-981 *8)))))))))) - (|:| |rgsz| (-578)))) - (-5 *1 (-953 *8 *9 *10 *11)) (-5 *7 (-578))))) +(((*1 *2 *2) + (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) + (-4 *2 (-13 (-444 *3) (-1033)))))) +(((*1 *2 *2) + (-12 (-4 *3 (-570)) (-5 *1 (-41 *3 *2)) + (-4 *2 + (-13 (-376) (-314) + (-10 -8 (-15 -1467 ((-1156 *3 (-631 $)) $)) + (-15 -1482 ((-1156 *3 (-631 $)) $)) + (-15 -2864 ($ (-1156 *3 (-631 $))))))))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-570)) (-5 *1 (-41 *3 *2)) + (-4 *2 + (-13 (-376) (-314) + (-10 -8 (-15 -1467 ((-1156 *3 (-631 $)) $)) + (-15 -1482 ((-1156 *3 (-631 $)) $)) + (-15 -2864 ($ (-1156 *3 (-631 $))))))))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-666 *2)) + (-4 *2 + (-13 (-376) (-314) + (-10 -8 (-15 -1467 ((-1156 *4 (-631 $)) $)) + (-15 -1482 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(-666 (-342))))) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-666 (-342))) (-4 *1 (-455)))) @@ -8817,7 +8349,7 @@ (-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 (-666 (-2 (|:| -1635 *3) (|:| -3513 *4)))) + (-12 (-5 *2 (-666 (-2 (|:| -1635 *3) (|:| -3514 *4)))) (-4 *3 (-1080)) (-4 *4 (-748)) (-5 *1 (-757 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-578)) (-4 *1 (-785)))) ((*1 *1 *2) @@ -8826,25 +8358,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) - (|:| -3026 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) + (|:| -3789 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| |mdnia| (-2 (|:| |fn| (-328 (-229))) - (|:| -3026 (-666 (-1125 (-865 (-229))))) + (|:| -3789 (-666 (-1125 (-865 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-328 (-229))) - (|:| -3026 (-666 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at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| "There are singularities at both end points") + (|:| |notEvaluated| "End point continuity not yet evaluated"))) + (-5 *1 (-195))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-578) (-578))) (-5 *1 (-374 *3)) (-4 *3 (-1131)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-793) (-793))) (-4 *1 (-399 *3)) (-4 *3 (-1131)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-23)) (-14 *5 *4) + (-5 *1 (-671 *3 *4 *5)) (-4 *3 (-1131))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-666 *7)) (-4 *7 (-871)) (-4 *5 (-938)) (-4 *6 (-815)) + (-4 *8 (-978 *5 *6 *7)) (-5 *2 (-432 (-1203 *8))) + (-5 *1 (-935 *5 *6 *7 *8)) (-5 *4 (-1203 *8)))) + ((*1 *2 *3) + (-12 (-4 *4 (-938)) (-4 *5 (-1274 *4)) (-5 *2 (-432 (-1203 *5))) + (-5 *1 (-936 *4 *5)) (-5 *3 (-1203 *5))))) +(((*1 *2 *1) + (-12 (-5 *2 (-666 (-972 *4))) (-5 *1 (-1195 *3 *4)) (-14 *3 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lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1188 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3789 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-573))))) +(((*1 *2 *1) + (-12 (-4 *3 (-466)) (-4 *4 (-871)) (-4 *5 (-815)) (-5 *2 (-666 *6)) + (-5 *1 (-1018 *3 *4 *5 *6)) (-4 *6 (-978 *3 *5 *4))))) (((*1 *2) (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1252)) (-4 *4 (-1274 *3)) (-4 *5 (-1274 (-421 *4))) (-5 *2 (-711 (-421 *4)))))) +(((*1 *2 *2) + (-12 (-5 *2 (-666 *6)) (-4 *6 (-1096 *3 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(|:| -3026 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) + (|:| -3789 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| |mdnia| (-2 (|:| |fn| (-328 (-229))) - (|:| -3026 (-666 (-1125 (-865 (-229))))) + (|:| -3789 (-666 (-1125 (-865 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) (-5 *1 (-791)))) ((*1 *2 *1) @@ -10626,26 +10366,26 @@ (-4 *4 (-815)) (-4 *5 (-871)) (-4 *1 (-1007 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1069 *2)) (-4 *2 (-1248)))) ((*1 *1 *2) - (-2225 + (-2226 (-12 (-5 *2 (-981 *3)) - (-12 (-3523 (-4 *3 (-38 (-421 (-578))))) - (-3523 (-4 *3 (-38 (-578)))) (-4 *5 (-633 (-1207)))) + (-12 (-3524 (-4 *3 (-38 (-421 (-578))))) + (-3524 (-4 *3 (-38 (-578)))) (-4 *5 (-633 (-1207)))) (-4 *3 (-1080)) (-4 *1 (-1096 *3 *4 *5)) (-4 *4 (-815)) (-4 *5 (-871))) (-12 (-5 *2 (-981 *3)) - (-12 (-3523 (-4 *3 (-559))) (-3523 (-4 *3 (-38 (-421 (-578))))) + (-12 (-3524 (-4 *3 (-559))) (-3524 (-4 *3 (-38 (-421 (-578))))) (-4 *3 (-38 (-578))) (-4 *5 (-633 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*2 *2) + (-12 (-4 *3 (-570)) (-4 *4 (-1023 *3)) (-5 *1 (-144 *3 *4 *2)) + (-4 *2 (-386 *4)))) + ((*1 *2 *3) + (-12 (-4 *4 (-570)) (-4 *5 (-1023 *4)) (-4 *2 (-386 *4)) + (-5 *1 (-517 *4 *5 *2 *3)) (-4 *3 (-386 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-711 *5)) (-4 *5 (-1023 *4)) (-4 *4 (-570)) + (-5 *2 (-711 *4)) (-5 *1 (-715 *4 *5)))) + ((*1 *2 *2) + (-12 (-4 *3 (-570)) (-4 *4 (-1023 *3)) (-5 *1 (-1267 *3 *4 *2)) + (-4 *2 (-1274 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) - (|:| -3026 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) + (|:| -3789 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 @@ -13058,7 +12929,7 @@ (-3 (|:| |str| (-1188 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -3026 + (|:| -3789 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -13066,161 +12937,154 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-573))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-578)) (-5 *2 (-1303)) (-5 *1 (-933 *4)) - (-4 *4 (-1131)))) - ((*1 *2 *1) (-12 (-5 *2 (-1303)) (-5 *1 (-933 *3)) (-4 *3 (-1131))))) -(((*1 *2 *3) +(((*1 *2 *2) + (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) + (-4 *2 (-13 (-444 *3) (-1233)))))) +(((*1 *2 *1) (-12 - (-5 *3 - (-518 (-421 (-578)) (-247 *5 (-793)) (-888 *4) - (-255 *4 (-421 (-578))))) - (-14 *4 (-666 (-1207))) (-14 *5 (-793)) (-5 *2 (-112)) - (-5 *1 (-519 *4 *5))))) -(((*1 *1 *2) (-12 (-5 *2 (-421 (-578))) (-5 *1 (-221))))) -(((*1 *1 *1) (-12 (-4 *1 (-1286 *2)) (-4 *2 (-1248))))) -(((*1 *1 *1) - (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-578)))) (-4 *2 (-1080))))) + (-5 *2 + (-666 + (-2 + (|:| -2339 + (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) + (|:| -3789 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))) + (|:| -2076 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1188 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3789 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-573)))) + ((*1 *2 *1) + (-12 (-4 *1 (-618 *3 *4)) (-4 *3 (-1131)) (-4 *4 (-1248)) + (-5 *2 (-666 *4))))) +(((*1 *2 *1) + (-12 (-4 *3 (-376)) (-4 *4 (-1274 *3)) (-4 *5 (-1274 (-421 *4))) + (-5 *2 (-1298 *6)) (-5 *1 (-349 *3 *4 *5 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(-793)) (|:| -1635 *3) (|:| |radicand| *3))) + (-5 *1 (-982 *5 *6 *7 *8 *3)) (-5 *4 (-793)) + (-4 *3 + (-13 (-376) + (-10 -8 (-15 -2864 ($ *8)) (-15 -1467 (*8 $)) (-15 -1482 (*8 $)))))))) +(((*1 *1 *2) (-12 (-5 *2 (-898)) (-5 *1 (-272)))) + ((*1 *1 *2) (-12 (-5 *2 (-392)) (-5 *1 (-272))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) + (-12 (-5 *3 (-1189)) (-5 *4 (-578)) (-5 *5 (-711 (-229))) + (-5 *2 (-1066)) (-5 *1 (-776))))) +(((*1 *2 *3 *3 *4 *4 *4 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-578)) (-5 *2 (-1066)) (-5 *1 (-770))))) +(((*1 *2 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-781))))) (((*1 *2 *3) - (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1131)) (-4 *5 (-1131)) - (-4 *6 (-1131)) (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-706 *4 *5 *6))))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-1043)) (-5 *2 (-886))))) + (-12 (-5 *3 (-666 *2)) (-4 *2 (-444 *4)) (-5 *1 (-160 *4 *2)) + (-4 *4 (-570))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-793)) (-4 *1 (-1274 *3)) (-4 *3 (-1080))))) (((*1 *2 *3) (-12 (-5 *3 (-666 (-52))) (-5 *2 (-1303)) (-5 *1 (-887))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1188 (-229))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3026 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))) - (-5 *2 (-1066)) (-5 *1 (-317))))) -(((*1 *2 *3) - (-12 (-5 *3 (-956)) - (-5 *2 - (-2 (|:| |brans| (-666 (-666 (-972 (-229))))) - (|:| |xValues| (-1125 (-229))) (|:| |yValues| (-1125 (-229))))) - (-5 *1 (-155)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-956)) (-5 *4 (-421 (-578))) - (-5 *2 - (-2 (|:| |brans| (-666 (-666 (-972 (-229))))) - (|:| |xValues| (-1125 (-229))) (|:| |yValues| (-1125 (-229))))) - (-5 *1 (-155))))) -(((*1 *2) (-12 (-5 *2 (-1303)) (-5 *1 (-450))))) +(((*1 *2 *1) + (|partial| -12 (-4 *3 (-1143)) (-4 *3 (-1131)) (-5 *2 (-666 *1)) + (-4 *1 (-444 *3)))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-666 (-917 *3))) (-5 *1 (-917 *3)) + (-4 *3 (-1131)))) + ((*1 *2 *1) + (|partial| -12 (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871)) + (-5 *2 (-666 *1)) (-4 *1 (-978 *3 *4 *5)))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-815)) (-4 *5 (-871)) (-4 *6 (-1080)) + (-4 *7 (-978 *6 *4 *5)) (-5 *2 (-666 *3)) + (-5 *1 (-979 *4 *5 *6 *7 *3)) + (-4 *3 + (-13 (-376) + (-10 -8 (-15 -2864 ($ *7)) (-15 -1467 (*7 $)) + (-15 -1482 (*7 $)))))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-578)) (-5 *2 (-1066)) (-5 *1 (-780))))) +(((*1 *1 *1) (-12 (-4 *1 (-1286 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(-4 *1 (-242 *3)) + (-4 *3 (-1131)))) + ((*1 *1 *2 *1) + (-12 (|has| *1 (-6 -4508)) (-4 *1 (-242 *2)) (-4 *2 (-1131)))) + ((*1 *1 *2 *1) + (-12 (-4 *1 (-294 *2)) (-4 *2 (-1248)) (-4 *2 (-1131)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-294 *3)) (-4 *3 (-1248)))) + ((*1 *2 *3 *1) + (|partial| -12 (-4 *1 (-629 *3 *2)) (-4 *3 (-1131)) (-4 *2 (-1131)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *2 (-1 (-112) *4)) (-5 *3 (-578)) (-4 *4 (-1131)) + (-5 *1 (-759 *4)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-578)) (-5 *1 (-759 *2)) (-4 *2 (-1131)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1171 *3 *4)) (-4 *3 (-13 (-1131) (-34))) + (-4 *4 (-13 (-1131) (-34))) (-5 *1 (-1172 *3 *4))))) +(((*1 *2 *3) (-12 (-5 *3 (-950)) (-5 *2 (-933 (-578))) (-5 *1 (-946)))) ((*1 *2 *3) - (-12 (-5 *3 (-666 (-981 *4))) - (-4 *4 (-13 (-870) (-319) (-149) (-1053))) - (-5 *2 (-666 (-666 (-1055 (-421 *4))))) (-5 *1 (-1325 *4 *5 *6)) - (-14 *5 (-666 (-1207))) (-14 *6 (-666 (-1207)))))) + (-12 (-5 *3 (-666 (-578))) (-5 *2 (-933 (-578))) (-5 *1 (-946))))) (((*1 *2 *3) - (-12 (-5 *3 (-1203 *4)) (-4 *4 (-362)) (-5 *2 (-987 (-1151))) - (-5 *1 (-359 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-666 *8)) (-5 *4 (-666 *9)) (-4 *8 (-1096 *5 *6 *7)) - (-4 *9 (-1102 *5 *6 *7 *8)) (-4 *5 (-466)) (-4 *6 (-815)) - (-4 *7 (-871)) (-5 *2 (-793)) (-5 *1 (-1100 *5 *6 *7 *8 *9)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-666 *8)) (-5 *4 (-666 *9)) (-4 *8 (-1096 *5 *6 *7)) - (-4 *9 (-1140 *5 *6 *7 *8)) (-4 *5 (-466)) (-4 *6 (-815)) - (-4 *7 (-871)) (-5 *2 (-793)) (-5 *1 (-1176 *5 *6 *7 *8 *9))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *5 *5)) - (-4 *5 (-13 (-376) (-10 -8 (-15 ** ($ $ (-421 (-578))))))) - (-5 *2 - (-2 (|:| |solns| (-666 *5)) - (|:| |maps| (-666 (-2 (|:| |arg| *5) (|:| |res| *5)))))) - (-5 *1 (-1159 *3 *5)) (-4 *3 (-1274 *5))))) + (-12 + (-5 *3 + (-2 (|:| |pde| (-666 (-328 (-229)))) + (|:| |constraints| + (-666 + (-2 (|:| |start| (-229)) (|:| |finish| (-229)) + (|:| |grid| (-793)) (|:| |boundaryType| (-578)) + (|:| |dStart| (-711 (-229))) (|:| |dFinish| (-711 (-229)))))) + (|:| |f| (-666 (-666 (-328 (-229))))) (|:| |st| (-1189)) + (|:| |tol| (-229)))) + (-5 *2 (-112)) (-5 *1 (-213))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-570) (-1069 (-578)))) (-5 *1 (-191 *3 *2)) + (-4 *2 (-13 (-27) (-1233) (-444 (-172 *3)))))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-466) (-1069 (-578)) (-660 (-578)))) + (-5 *1 (-1237 *3 *2)) (-4 *2 (-13 (-27) (-1233) (-444 *3)))))) (((*1 *1 *1) (-12 (-4 *1 (-121 *2)) (-4 *2 (-1248)))) ((*1 *1 *1) (-12 (-5 *1 (-694 *2)) (-4 *2 (-871)))) ((*1 *1 *1) (-12 (-5 *1 (-699 *2)) (-4 *2 (-871)))) @@ -13229,19 +13093,35 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-870) (-376))) (-5 *1 (-1092 *2 *3)) (-4 *3 (-1274 *2))))) -(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1249 *3)) (-4 *3 (-1131))))) -(((*1 *1 *2) (-12 (-5 *2 (-666 *3)) (-4 *3 (-1131)) (-5 *1 (-226 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-666 *3)) (-4 *3 (-1248)) (-4 *1 (-263 *3)))) - ((*1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1248))))) -(((*1 *2 *3 *4 *4 *3 *5 *3 *6 *4 *7 *8 *9) - (-12 (-5 *4 (-578)) (-5 *5 (-1189)) (-5 *6 (-711 (-229))) - (-5 *7 (-3 (|:| |fn| (-402)) (|:| |fp| (-89 G)))) - (-5 *8 (-3 (|:| |fn| (-402)) (|:| |fp| (-86 FCN)))) - (-5 *9 (-3 (|:| |fn| (-402)) (|:| |fp| (-88 OUTPUT)))) - (-5 *3 (-229)) (-5 *2 (-1066)) (-5 *1 (-771))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-709 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-386 *2)) - (-4 *4 (-386 *2))))) +(((*1 *2 *3 *3 *3 *4) + (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1274 *5)) + (-4 *5 (-13 (-376) (-149) (-1069 (-578)))) + (-5 *2 + (-2 (|:| |a| *6) (|:| |b| (-421 *6)) (|:| |h| *6) + (|:| |c1| (-421 *6)) (|:| |c2| (-421 *6)) (|:| -2291 *6))) + (-5 *1 (-1047 *5 *6)) (-5 *3 (-421 *6))))) +(((*1 *2 *2) + (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) + (-4 *2 (-13 (-444 *3) (-1233)))))) +(((*1 *1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-1093)))) + ((*1 *1 *2) (-12 (-5 *2 (-1207)) (-5 *1 (-1093))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-1203 *1)) (-5 *3 (-1207)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-1203 *1)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-981 *1)) (-4 *1 (-27)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1207)) (-4 *1 (-29 *3)) (-4 *3 (-570)))) + ((*1 *1 *1) (-12 (-4 *1 (-29 *2)) (-4 *2 (-570)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1203 *2)) (-5 *4 (-1207)) (-4 *2 (-444 *5)) + (-5 *1 (-32 *5 *2)) (-4 *5 (-570)))) + ((*1 *1 *2 *3) + (|partial| -12 (-5 *2 (-1203 *1)) (-5 *3 (-950)) (-4 *1 (-1043)))) + ((*1 *1 *2 *3 *4) + (|partial| -12 (-5 *2 (-1203 *1)) (-5 *3 (-950)) (-5 *4 (-886)) + (-4 *1 (-1043)))) + ((*1 *1 *2 *3) + (|partial| -12 (-5 *3 (-950)) (-4 *4 (-13 (-870) (-376))) + (-4 *1 (-1099 *4 *2)) (-4 *2 (-1274 *4))))) +(((*1 *1 *1 *1) (-5 *1 (-886)))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-814)))) ((*1 *1 *1) (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1080)) (-14 *3 (-666 (-1207))))) @@ -13252,10 +13132,10 @@ (-12 (-4 *1 (-395 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-1131)))) ((*1 *1 *1) (-12 (-14 *2 (-666 (-1207))) (-4 *3 (-175)) - (-4 *5 (-245 (-4415 *2) (-793))) + (-4 *5 (-245 (-4416 *2) (-793))) (-14 *6 - (-1 (-112) (-2 (|:| -2480 *4) (|:| -2300 *5)) - (-2 (|:| -2480 *4) (|:| -2300 *5)))) + (-1 (-112) (-2 (|:| -2481 *4) (|:| -4171 *5)) + (-2 (|:| -2481 *4) (|:| -4171 *5)))) (-5 *1 (-475 *2 *3 *4 *5 *6 *7)) (-4 *4 (-871)) (-4 *7 (-978 *3 *5 (-888 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-523 *2 *3)) (-4 *2 (-102)) (-4 *3 (-874)))) @@ -13271,21 +13151,29 @@ (-4 *2 (-871)))) ((*1 *1 *1) (-12 (-5 *1 (-1321 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-868))))) -(((*1 *2 *1) - (-12 (-4 *1 (-618 *2 *3)) (-4 *3 (-1248)) (-4 *2 (-1131)) - (-4 *2 (-871))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-520)) (-5 *3 (-666 (-900))) (-5 *1 (-497))))) -(((*1 *2 *3 *4 *4 *2 *2 *2 *2) - (-12 (-5 *2 (-578)) - (-5 *3 - (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-793)) (|:| |poli| *4) - (|:| |polj| *4))) - (-4 *6 (-815)) (-4 *4 (-978 *5 *6 *7)) (-4 *5 (-466)) (-4 *7 (-871)) - (-5 *1 (-463 *5 *6 *7 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *5 *4)) (-4 *4 (-1131)) (-4 *5 (-1131)) - (-5 *2 (-1 *5)) (-5 *1 (-705 *4 *5))))) +(((*1 *2 *3) + (-12 (-4 *4 (-319)) (-4 *5 (-386 *4)) (-4 *6 (-386 *4)) + (-5 *2 + (-2 (|:| |Smith| *3) (|:| |leftEqMat| *3) (|:| |rightEqMat| *3))) + (-5 *1 (-1155 *4 *5 *6 *3)) (-4 *3 (-709 *4 *5 *6))))) +(((*1 *1 *2 *1) (-12 (-5 *2 (-578)) (-5 *1 (-119 *3)) (-14 *3 *2))) + ((*1 *1 *1) (-12 (-5 *1 (-119 *2)) (-14 *2 (-578)))) + ((*1 *1 *2 *1) (-12 (-5 *2 (-578)) (-5 *1 (-895 *3)) (-14 *3 *2))) + ((*1 *1 *1) (-12 (-5 *1 (-895 *2)) (-14 *2 (-578)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-578)) (-14 *3 *2) (-5 *1 (-896 *3 *4)) + (-4 *4 (-893 *3)))) + ((*1 *1 *1) + (-12 (-14 *2 (-578)) (-5 *1 (-896 *2 *3)) (-4 *3 (-893 *2)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-578)) (-4 *1 (-1260 *3 *4)) (-4 *3 (-1080)) + (-4 *4 (-1289 *3)))) + ((*1 *1 *1) + (-12 (-4 *1 (-1260 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-1289 *2))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-578)) (-5 *2 (-1066)) (-5 *1 (-780))))) +(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-955))))) +(((*1 *1) (-5 *1 (-1113)))) (((*1 *1 *1) (-12 (-4 *1 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((*1 *2 *1) (-12 (-4 *1 (-395 *2 *3)) (-4 *3 (-1131)) (-4 *2 (-1080)))) ((*1 *2 *1) - (-12 (-14 *3 (-666 (-1207))) (-4 *5 (-245 (-4415 *3) (-793))) + (-12 (-14 *3 (-666 (-1207))) (-4 *5 (-245 (-4416 *3) (-793))) (-14 *6 - (-1 (-112) (-2 (|:| -2480 *4) (|:| -2300 *5)) - (-2 (|:| -2480 *4) (|:| -2300 *5)))) + (-1 (-112) (-2 (|:| -2481 *4) (|:| -4171 *5)) + (-2 (|:| -2481 *4) (|:| -4171 *5)))) (-4 *2 (-175)) (-5 *1 (-475 *3 *2 *4 *5 *6 *7)) (-4 *4 (-871)) (-4 *7 (-978 *2 *5 (-888 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-523 *2 *3)) (-4 *3 (-874)) (-4 *2 (-102)))) @@ -13415,39 +13253,45 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1096 *3 *4 *2)) (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *2 (-871))))) -(((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) - (-12 (-4 *1 (-819 *2)) (-4 *2 (-175)))) - ((*1 *1 *2 *2) - (-12 (-5 *2 (-1030 *3)) (-4 *3 (-175)) (-5 *1 (-821 *3))))) -(((*1 *2 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *4 *4 - *4 *6 *4) - (-12 (-5 *4 (-578)) (-5 *5 (-711 (-229))) (-5 *6 (-697 (-229))) - (-5 *3 (-229)) (-5 *2 (-1066)) (-5 *1 (-772))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-338 *3 *4)) (-4 *3 (-1080)) + (-4 *4 (-814))))) +(((*1 *2 *2) (-12 (-5 *2 (-392)) (-5 *1 (-1300)))) + ((*1 *2) (-12 (-5 *2 (-392)) (-5 *1 (-1300))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-666 *5)) (-5 *4 (-950)) (-4 *5 (-871)) - (-5 *2 (-59 (-666 (-694 *5)))) (-5 *1 (-694 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-578)) (-5 *1 (-943 *3)) (-4 *3 (-319))))) -(((*1 *2 *3) - (-12 (-4 *4 (-570)) (-4 *5 (-815)) (-4 *6 (-871)) - (-4 *7 (-1096 *4 *5 *6)) - (-5 *2 (-2 (|:| |goodPols| (-666 *7)) (|:| |badPols| (-666 *7)))) - (-5 *1 (-1008 *4 *5 *6 *7)) (-5 *3 (-666 *7))))) -(((*1 *1) (-5 *1 (-623)))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-568 *3)) (-4 *3 (-13 (-418) (-1233))) (-5 *2 (-112))))) -(((*1 *2 *1) (-12 (-4 *1 (-541)) (-5 *2 (-713 (-561)))))) -(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-956))))) + (-12 (-5 *4 (-793)) (-4 *5 (-1080)) (-5 *2 (-578)) + (-5 *1 (-457 *5 *3 *6)) (-4 *3 (-1274 *5)) + (-4 *6 (-13 (-418) (-1069 *5) (-376) (-1233) (-296))))) + ((*1 *2 *3) + (-12 (-4 *4 (-1080)) (-5 *2 (-578)) (-5 *1 (-457 *4 *3 *5)) + (-4 *3 (-1274 *4)) + (-4 *5 (-13 (-418) (-1069 *4) (-376) (-1233) (-296)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-950)) (-5 *4 (-432 *6)) (-4 *6 (-1274 *5)) + (-4 *5 (-1080)) (-5 *2 (-666 *6)) (-5 *1 (-458 *5 *6))))) (((*1 *2 *3) - (|partial| -12 (-5 *3 (-116)) (-5 *1 (-115 *2)) (-4 *2 (-1131))))) + (-12 (-5 *2 (-1 *3 *4)) (-5 *1 (-705 *4 *3)) (-4 *4 (-1131)) + (-4 *3 (-1131))))) +(((*1 *1 *2 *1) (-12 (-5 *2 (-1206)) (-5 *1 (-342))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-172 (-229))) (-5 *4 (-578)) (-5 *2 (-1066)) + (-5 *1 (-780))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-666 *5)) (-5 *4 (-950)) (-4 *5 (-871)) + (-5 *2 (-666 (-694 *5))) (-5 *1 (-694 *5))))) +(((*1 *2 *2 *3) (-12 (-5 *2 (-578)) (-5 *3 (-793)) (-5 *1 (-575))))) +(((*1 *2) + (-12 (-4 *1 (-362)) + (-5 *2 (-3 "prime" "polynomial" "normal" "cyclic"))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-814)))) ((*1 *2 *1) (-12 (-4 *1 (-395 *3 *2)) (-4 *3 (-1080)) (-4 *2 (-1131)))) ((*1 *2 *1) (-12 (-14 *3 (-666 (-1207))) (-4 *4 (-175)) - (-4 *6 (-245 (-4415 *3) (-793))) + (-4 *6 (-245 (-4416 *3) (-793))) (-14 *7 - (-1 (-112) (-2 (|:| -2480 *5) (|:| -2300 *6)) - (-2 (|:| -2480 *5) (|:| -2300 *6)))) + (-1 (-112) (-2 (|:| -2481 *5) (|:| -4171 *6)) + (-2 (|:| -2481 *5) (|:| -4171 *6)))) (-5 *2 (-735 *5 *6 *7)) (-5 *1 (-475 *3 *4 *5 *6 *7 *8)) (-4 *5 (-871)) (-4 *8 (-978 *4 *6 (-888 *3))))) ((*1 *2 *1) @@ -13456,135 +13300,111 @@ ((*1 *1 *1) (-12 (-4 *1 (-1004 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-814)) (-4 *4 (-871))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-793)) (-5 *1 (-880 *2)) (-4 *2 (-38 (-421 (-578)))) - (-4 *2 (-175))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1298 *5)) (-4 *5 (-814)) (-5 *2 (-112)) - (-5 *1 (-867 *4 *5)) (-14 *4 (-793))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-950)) (-5 *3 (-666 (-272))) (-5 *1 (-270)))) - ((*1 *1 *2) (-12 (-5 *2 (-950)) (-5 *1 (-272))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 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*2) + (-12 (-4 *4 (-175)) (-5 *2 (-112)) (-5 *1 (-379 *3 *4)) + (-4 *3 (-380 *4)))) + ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-112))))) (((*1 *2 *3) (-12 (-5 *3 (-1207)) (-4 *4 (-13 (-466) (-1069 (-578)) (-660 (-578)))) (-5 *2 (-52)) @@ -13828,48 +13680,56 @@ (-4 *3 (-1289 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1281 *3 *2)) (-4 *3 (-1080)) (-4 *2 (-1258 *3))))) -(((*1 *1 *1) (-4 *1 (-559)))) +(((*1 *2 *2) + (|partial| -12 (-5 *2 (-1203 *3)) (-4 *3 (-362)) (-5 *1 (-370 *3))))) +(((*1 *2 *3) + (-12 (-4 *1 (-861)) + (-5 *3 + (-2 (|:| |fn| (-328 (-229))) (|:| -2912 (-666 (-229))) + (|:| |lb| (-666 (-865 (-229)))) (|:| |cf| (-666 (-328 (-229)))) + (|:| |ub| (-666 (-865 (-229)))))) + (-5 *2 (-1066)))) + ((*1 *2 *3) + (-12 (-4 *1 (-861)) + (-5 *3 + (-2 (|:| |lfn| (-666 (-328 (-229)))) (|:| -2912 (-666 (-229))))) + (-5 *2 (-1066))))) +(((*1 *2 *2) + (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) + (-4 *2 (-13 (-444 *3) (-1033)))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-466)) (-4 *6 (-815)) (-4 *7 (-871)) - (-4 *3 (-1096 *5 *6 *7)) - (-5 *2 (-666 (-2 (|:| |val| *3) (|:| -2799 *4)))) - (-5 *1 (-1103 *5 *6 *7 *3 *4)) (-4 *4 (-1102 *5 *6 *7 *3))))) + (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1274 *5)) (-4 *5 (-376)) + (-5 *2 (-2 (|:| |answer| *3) (|:| |polypart| *3))) + (-5 *1 (-588 *5 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-141)) (-5 *1 (-142)))) ((*1 *2 *1) (-12 (-5 *1 (-186 *2)) (-4 *2 (-188)))) ((*1 *2 *1) (-12 (-5 *2 (-257)) (-5 *1 (-256))))) -(((*1 *2 *3) - (-12 (-5 *3 (-666 (-578))) (-5 *2 (-933 (-578))) (-5 *1 (-946)))) - ((*1 *2) (-12 (-5 *2 (-933 (-578))) (-5 *1 (-946))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1203 *3)) (-4 *3 (-1080)) (-4 *1 (-1274 *3))))) (((*1 *2 *3 *3) - (-12 (-5 *3 (-666 *2)) (-5 *1 (-182 *2)) (-4 *2 (-319)))) - ((*1 *2 *3 *2) - (-12 (-5 *3 (-666 (-666 *4))) (-5 *2 (-666 *4)) (-4 *4 (-319)) - (-5 *1 (-182 *4)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-666 *8)) - (-5 *4 - (-666 - (-2 (|:| -2311 (-711 *7)) (|:| |basisDen| *7) - (|:| |basisInv| (-711 *7))))) - (-5 *5 (-793)) (-4 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(-5 *2 (-52)) @@ -13912,57 +13772,40 @@ (-5 *1 (-473 *7 *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1260 *3 *2)) (-4 *3 (-1080)) (-4 *2 (-1289 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-570)) (-5 *2 (-112))))) -(((*1 *1 *2) (-12 (-5 *2 (-186 (-257))) (-5 *1 (-256))))) -(((*1 *2 *1 *1) - (-12 (-4 *3 (-570)) (-4 *3 (-1080)) - (-5 *2 (-2 (|:| -3855 *1) (|:| -3823 *1))) (-4 *1 (-876 *3)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-99 *5)) (-4 *5 (-570)) (-4 *5 (-1080)) - (-5 *2 (-2 (|:| -3855 *3) (|:| -3823 *3))) (-5 *1 (-877 *5 *3)) - (-4 *3 (-876 *5))))) -(((*1 *1 *2 *2) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175))))) -(((*1 *1 *2) (-12 (-5 *2 (-666 (-886))) (-5 *1 (-886))))) (((*1 *2 *3) - (-12 (-5 *3 (-666 (-666 (-972 (-229))))) (-5 *2 (-666 (-229))) - (-5 *1 (-482))))) -(((*1 *1 *1) (-4 *1 (-893 *2)))) -(((*1 *2 *2) - (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) - (-4 *2 (-13 (-444 *3) (-1033)))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-174))))) -(((*1 *2 *3 *4 *5 *6 *5 *3 *7) - (-12 (-5 *4 (-578)) - (-5 *6 - (-2 (|:| |try| (-392)) (|:| |did| (-392)) (|:| -2866 (-392)))) - (-5 *7 (-1 (-1303) (-1298 *5) (-1298 *5) (-392))) - (-5 *3 (-1298 (-392))) (-5 *5 (-392)) (-5 *2 (-1303)) - (-5 *1 (-810)))) - ((*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3) - (-12 (-5 *4 (-578)) - (-5 *6 - (-2 (|:| |try| (-392)) (|:| |did| (-392)) (|:| -2866 (-392)))) - (-5 *7 (-1 (-1303) (-1298 *5) (-1298 *5) (-392))) - (-5 *3 (-1298 (-392))) (-5 *5 (-392)) (-5 *2 (-1303)) - (-5 *1 (-810))))) -(((*1 *1 *2) - (-12 (-5 *2 (-421 (-578))) (-4 *1 (-568 *3)) - (-4 *3 (-13 (-418) (-1233))))) - ((*1 *1 *2) (-12 (-4 *1 (-568 *2)) (-4 *2 (-13 (-418) (-1233))))) - ((*1 *1 *2 *2) (-12 (-4 *1 (-568 *2)) (-4 *2 (-13 (-418) (-1233)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-570) (-1069 (-578)) (-660 (-578)))) - (-5 *1 (-288 *3 *2)) (-4 *2 (-13 (-27) (-1233) (-444 *3))))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1207)) - (-4 *4 (-13 (-570) (-1069 (-578)) (-660 (-578)))) - (-5 *1 (-288 *4 *2)) (-4 *2 (-13 (-27) (-1233) (-444 *4))))) - ((*1 *1 *1) (-5 *1 (-392))) + (-12 (-4 *4 (-38 (-421 (-578)))) + (-5 *2 (-2 (|:| -3382 (-1188 *4)) (|:| -3393 (-1188 *4)))) + (-5 *1 (-1193 *4)) (-5 *3 (-1188 *4))))) +(((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-328 (-392))) (-5 *1 (-317))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-666 (-886))) (-5 *1 (-1207))))) +(((*1 *1 *2 *2) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-711 *5)) (-5 *4 (-1298 *5)) (-4 *5 (-376)) + (-5 *2 (-112)) (-5 *1 (-689 *5)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-466)) (-4 *6 (-815)) (-4 *7 (-871)) - (-4 *3 (-1096 *5 *6 *7)) - (-5 *2 (-666 (-2 (|:| |val| *3) (|:| -2799 *4)))) - (-5 *1 (-798 *5 *6 *7 *3 *4)) (-4 *4 (-1102 *5 *6 *7 *3))))) + (-12 (-4 *5 (-376)) (-4 *6 (-13 (-386 *5) (-10 -7 (-6 -4509)))) + (-4 *4 (-13 (-386 *5) (-10 -7 (-6 -4509)))) (-5 *2 (-112)) + (-5 *1 (-690 *5 *6 *4 *3)) (-4 *3 (-709 *5 *6 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-898)) (-5 *1 (-272)))) + ((*1 *1 *2) (-12 (-5 *2 (-392)) (-5 *1 (-272))))) +(((*1 *2 *2 *2) + (|partial| -12 (-4 *3 (-13 (-570) (-149))) (-5 *1 (-1268 *3 *2)) + (-4 *2 (-1274 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-1303)) (-5 *1 (-844))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-456 *3)) (-4 *3 (-1274 (-578)))))) +(((*1 *2 *1) (-12 (-4 *1 (-1023 *2)) (-4 *2 (-570)) (-4 *2 (-559)))) + ((*1 *1 *1) (-4 *1 (-1091)))) +(((*1 *1 *1) + (-12 (-4 *2 (-376)) (-4 *3 (-815)) (-4 *4 (-871)) + (-5 *1 (-518 *2 *3 *4 *5)) (-4 *5 (-978 *2 *3 *4))))) +(((*1 *2 *3) + (|partial| -12 + (-5 *3 + (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) + (|:| -3789 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))) + (-5 *2 (-666 (-229))) (-5 *1 (-207))))) (((*1 *2 *1 *3) (-12 (-5 *2 (-421 (-578))) (-5 *1 (-119 *4)) (-14 *4 *3) (-5 *3 (-578)))) @@ -13979,29 +13822,48 @@ (-4 *3 (-1274 *2)))) ((*1 *2 *1 *3) (-12 (-4 *1 (-1276 *2 *3)) (-4 *3 (-814)) - (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -2863 (*2 (-1207)))) + (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -2864 (*2 (-1207)))) (-4 *2 (-1080))))) -(((*1 *2 *3) - (-12 (-5 *3 (-950)) (-5 *2 (-1203 *4)) (-5 *1 (-370 *4)) - (-4 *4 (-362))))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-1043)) (-5 *2 (-886))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1207)) (-5 *4 (-981 (-578))) (-5 *2 (-342)) + (-5 *1 (-344))))) +(((*1 *2 *3 *4 *5 *5) + (-12 (-5 *4 (-666 *10)) (-5 *5 (-112)) (-4 *10 (-1102 *6 *7 *8 *9)) + (-4 *6 (-466)) (-4 *7 (-815)) (-4 *8 (-871)) + (-4 *9 (-1096 *6 *7 *8)) + (-5 *2 + (-666 + (-2 (|:| -1481 (-666 *9)) (|:| -2800 *10) (|:| |ineq| (-666 *9))))) + (-5 *1 (-1019 *6 *7 *8 *9 *10)) (-5 *3 (-666 *9)))) + ((*1 *2 *3 *4 *5 *5) + (-12 (-5 *4 (-666 *10)) (-5 *5 (-112)) (-4 *10 (-1102 *6 *7 *8 *9)) + (-4 *6 (-466)) (-4 *7 (-815)) (-4 *8 (-871)) + (-4 *9 (-1096 *6 *7 *8)) + (-5 *2 + (-666 + (-2 (|:| -1481 (-666 *9)) (|:| -2800 *10) (|:| |ineq| (-666 *9))))) + (-5 *1 (-1138 *6 *7 *8 *9 *10)) (-5 *3 (-666 *9))))) (((*1 *1 *2) - (-12 (-5 *2 (-666 *5)) (-4 *5 (-175)) (-5 *1 (-138 *3 *4 *5)) - (-14 *3 (-578)) (-14 *4 (-793))))) -(((*1 *2 *3) - (-12 (-4 *4 (-815)) (-4 *5 (-871)) (-4 *6 (-319)) - (-5 *2 (-666 (-793))) (-5 *1 (-800 *3 *4 *5 *6 *7)) - (-4 *3 (-1274 *6)) (-4 *7 (-978 *6 *4 *5))))) -(((*1 *1 *1 *2 *3 *1) - (-12 (-4 *1 (-338 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-814))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-570) (-1069 (-578)))) (-4 *5 (-444 *4)) - (-5 *2 (-432 *3)) (-5 *1 (-449 *4 *5 *3)) (-4 *3 (-1274 *5))))) -(((*1 *2 *3 *4 *5 *5 *4 *6) - (-12 (-5 *4 (-578)) (-5 *6 (-1 (-1303) (-1298 *5) (-1298 *5) (-392))) - (-5 *3 (-1298 (-392))) (-5 *5 (-392)) (-5 *2 (-1303)) - (-5 *1 (-810))))) -(((*1 *2 *1) (-12 (-4 *1 (-696 *3)) (-4 *3 (-1248)) (-5 *2 (-112))))) + (-12 (-5 *2 (-694 *3)) (-4 *3 (-871)) (-4 *1 (-387 *3 *4)) + (-4 *4 (-175))))) +(((*1 *2 *2 *3 *4) + (-12 (-5 *3 (-666 (-631 *2))) (-5 *4 (-666 (-1207))) + (-4 *2 (-13 (-444 (-172 *5)) (-1033) (-1233))) (-4 *5 (-570)) + (-5 *1 (-614 *5 *6 *2)) (-4 *6 (-13 (-444 *5) (-1033) (-1233)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1207)) (-5 *4 (-981 (-578))) (-5 *2 (-342)) + (-5 *1 (-344))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1014 *2)) (-4 *2 (-1233))))) +(((*1 *1 *1 *1 *2) + (-12 (-4 *1 (-1096 *3 *4 *2)) (-4 *3 (-1080)) (-4 *4 (-815)) + (-4 *2 (-871)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) + (-4 *4 (-871))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-376)) (-4 *7 (-1274 *5)) (-4 *4 (-746 *5 *7)) + (-5 *2 (-2 (|:| -4117 (-711 *6)) (|:| |vec| (-1298 *5)))) + (-5 *1 (-833 *5 *6 *7 *4 *3)) (-4 *6 (-678 *5)) (-4 *3 (-678 *4))))) (((*1 *2 *2) (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-444 *3) (-1033))))) @@ -14034,31 +13896,44 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-1318 *3 *4)) (-4 *4 (-739 (-421 (-578)))) (-4 *3 (-871)) (-4 *4 (-175))))) -(((*1 *1) (-5 *1 (-143)))) -(((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-694 *3)) (-4 *3 (-871)))) - ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-699 *3)) (-4 *3 (-871)))) - ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-841 *3)) (-4 *3 (-871))))) -(((*1 *1) (-5 *1 (-159))) - ((*1 *2 *1) 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(-5 *4 (-421 (-578))))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-421 (-578))) + (-5 *2 (-666 (-2 (|:| -2038 *5) (|:| -2050 *5)))) (-5 *1 (-1051 *3)) + (-4 *3 (-1274 (-578))) (-5 *4 (-2 (|:| -2038 *5) (|:| -2050 *5))))) + ((*1 *2 *3) + (-12 + (-5 *2 + (-666 (-2 (|:| -2038 (-421 (-578))) (|:| -2050 (-421 (-578)))))) + (-5 *1 (-1052 *3)) (-4 *3 (-1274 (-421 (-578)))))) + ((*1 *2 *3 *4) + (-12 + (-5 *2 + (-666 (-2 (|:| -2038 (-421 (-578))) (|:| -2050 (-421 (-578)))))) + (-5 *1 (-1052 *3)) (-4 *3 (-1274 (-421 (-578)))) + (-5 *4 (-2 (|:| -2038 (-421 (-578))) (|:| -2050 (-421 (-578))))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-421 (-578))) + (-5 *2 (-666 (-2 (|:| -2038 *4) (|:| -2050 *4)))) (-5 *1 (-1052 *3)) + (-4 *3 (-1274 *4)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-421 (-578))) + (-5 *2 (-666 (-2 (|:| -2038 *5) (|:| -2050 *5)))) (-5 *1 (-1052 *3)) + (-4 *3 (-1274 *5)) (-5 *4 (-2 (|:| -2038 *5) (|:| -2050 *5)))))) +(((*1 *1 *1) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-578)))) (-4 *2 (-1080))))) +(((*1 *2 *3) + (-12 (-5 *3 (-666 *4)) (-4 *4 (-1131)) (-5 *2 (-1303)) + (-5 *1 (-1249 *4)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-666 *4)) (-4 *4 (-1131)) (-5 *2 (-1303)) + (-5 *1 (-1249 *4))))) (((*1 *2 *3) (-12 (-5 *3 @@ -14134,7 +14050,7 @@ (-5 *1 (-979 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -2863 ($ *7)) (-15 -1467 (*7 $)) (-15 -1482 (*7 $))))))) + (-10 -8 (-15 -2864 ($ *7)) (-15 -1467 (*7 $)) (-15 -1482 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-1004 *3 *4 *5)) (-4 *3 (-1080)) (-4 *4 (-814)) (-4 *5 (-871)) (-5 *2 (-666 *5)))) @@ -14144,35 +14060,37 @@ ((*1 *2 *3) (-12 (-5 *3 (-421 (-981 *4))) (-4 *4 (-570)) (-5 *2 (-666 (-1207))) (-5 *1 (-1074 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-112)) (-4 *5 (-13 (-466) (-1069 (-578)) (-660 (-578)))) + (-5 *2 + (-3 (|:| |%expansion| (-325 *5 *3 *6 *7)) + (|:| |%problem| (-2 (|:| |func| (-1189)) (|:| |prob| (-1189)))))) + (-5 *1 (-434 *5 *3 *6 *7)) (-4 *3 (-13 (-27) (-1233) (-444 *5))) + (-14 *6 (-1207)) (-14 *7 *3)))) (((*1 *2 *3) - (-12 (-5 *3 (-666 (-950))) (-5 *2 (-1209 (-421 (-578)))) - (-5 *1 (-193))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) - (-4 *4 (-871)) (-4 *2 (-466))))) + (-12 (-5 *3 (-1298 (-328 (-229)))) (-5 *2 (-1298 (-328 (-392)))) + (-5 *1 (-317))))) +(((*1 *2 *3) (-12 (-5 *3 (-793)) (-5 *2 (-1303)) (-5 *1 (-392))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-335 *2 *3)) (-4 *2 (-1131)) (-4 *3 (-133)) + (-4 *3 (-814))))) (((*1 *2 *3) - (-12 (-5 *3 (-666 *2)) (-5 *1 (-500 *2)) (-4 *2 (-1274 (-578)))))) -(((*1 *2 *1) (-12 (-4 *1 (-819 *2)) (-4 *2 (-175))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-520)) (-5 *1 (-291)))) - ((*1 *2 *1) - (-12 (-5 *2 (-3 (-578) (-229) (-520) (-1189) (-1212))) - (-5 *1 (-1212))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) - (-12 (-5 *3 (-1 (-392) (-392))) (-5 *4 (-392)) + (-12 (-4 *4 (-466)) (-5 *2 - (-2 (|:| -3528 *4) (|:| -2754 *4) (|:| |totalpts| (-578)) - (|:| |success| (-112)))) - (-5 *1 (-811)) (-5 *5 (-578))))) -(((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-1182))))) + (-666 + (-2 (|:| |eigval| (-3 (-421 (-981 *4)) (-1196 (-1207) (-981 *4)))) + (|:| |geneigvec| (-666 (-711 (-421 (-981 *4)))))))) + (-5 *1 (-304 *4)) (-5 *3 (-711 (-421 (-981 *4))))))) (((*1 *2 *2) - (-12 (-5 *2 (-666 (-666 *6))) (-4 *6 (-978 *3 *5 *4)) - (-4 *3 (-13 (-319) (-149))) (-4 *4 (-13 (-871) (-633 (-1207)))) - (-4 *5 (-815)) (-5 *1 (-953 *3 *4 *5 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-666 (-1207))) (-4 *4 (-13 (-319) (-149))) - (-4 *5 (-13 (-871) (-633 (-1207)))) (-4 *6 (-815)) - (-5 *2 (-666 (-421 (-981 *4)))) (-5 *1 (-953 *4 *5 *6 *7)) - (-4 *7 (-978 *4 *6 *5))))) + (-12 (-5 *2 (-666 *6)) (-4 *6 (-1096 *3 *4 *5)) (-4 *3 (-570)) + (-4 *4 (-815)) (-4 *5 (-871)) (-5 *1 (-1008 *3 *4 *5 *6))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1207)) + (-4 *5 (-13 (-466) (-149) (-1069 (-578)) (-660 (-578)))) + (-5 *2 (-600 *3)) (-5 *1 (-571 *5 *3)) + (-4 *3 (-13 (-27) (-1233) (-444 *5)))))) +(((*1 *2 *1) + (-12 (-4 *2 (-1131)) (-5 *1 (-993 *3 *2)) (-4 *3 (-1131))))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1203 (-421 (-1203 *2)))) (-5 *4 (-631 *2)) (-4 *2 (-13 (-444 *5) (-27) (-1233))) @@ -14189,23 +14107,23 @@ (-4 *6 (-1080)) (-4 *2 (-13 (-376) - (-10 -8 (-15 -2863 ($ *7)) (-15 -1467 (*7 $)) (-15 -1482 (*7 $))))) + (-10 -8 (-15 -2864 ($ *7)) (-15 -1467 (*7 $)) (-15 -1482 (*7 $))))) (-5 *1 (-979 *5 *4 *6 *7 *2)) (-4 *7 (-978 *6 *5 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-421 (-1203 (-421 (-981 *5))))) (-5 *4 (-1207)) (-5 *2 (-421 (-981 *5))) (-5 *1 (-1074 *5)) (-4 *5 (-570))))) -(((*1 *2) - (-12 (-4 *4 (-175)) (-5 *2 (-112)) (-5 *1 (-379 *3 *4)) - (-4 *3 (-380 *4)))) - ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-112))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-13 (-376) (-870))) - (-5 *2 (-666 (-2 (|:| -2817 (-666 *3)) (|:| -2754 *5)))) - (-5 *1 (-184 *5 *3)) (-4 *3 (-1274 (-172 *5))))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-376) (-870))) - (-5 *2 (-666 (-2 (|:| -2817 (-666 *3)) (|:| -2754 *4)))) - (-5 *1 (-184 *4 *3)) (-4 *3 (-1274 (-172 *4)))))) +(((*1 *2 *3) + (-12 (-4 *4 (-871)) (-5 *2 (-1219 (-666 *4))) (-5 *1 (-1218 *4)) + (-5 *3 (-666 *4))))) +(((*1 *2 *3 *1) + (-12 (|has| *1 (-6 -4508)) (-4 *1 (-503 *3)) (-4 *3 (-1248)) + (-4 *3 (-1131)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-934 *4)) (-4 *4 (-1131)) (-5 *2 (-112)) + (-5 *1 (-933 *4)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-950)) (-5 *2 (-112)) (-5 *1 (-1132 *4 *5)) (-14 *4 *3) + (-14 *5 *3)))) (((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-139)))) ((*1 *2 *1) (-12 (-5 *2 (-1247)) (-5 *1 (-158)))) ((*1 *2 *1) (-12 (-5 *1 (-306 *2)) (-4 *2 (-1248)))) @@ -14219,129 +14137,23 @@ (-4 *4 (-13 (-1080) (-911 *3) (-633 (-917 *3)))))) ((*1 *2 *1) (-12 (-4 *2 (-1131)) (-5 *1 (-1196 *3 *2)) (-4 *3 (-1131))))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *3 (-1207)) - (-4 *4 (-13 (-319) (-149) (-1069 (-578)) (-660 (-578)))) - (-5 *1 (-641 *4 *2)) (-4 *2 (-13 (-1233) (-988) (-29 *4)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-328 (-229))) (-5 *2 (-421 (-578))) (-5 *1 (-317))))) +(((*1 *2 *3) (-12 (-5 *3 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(((*1 *2 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-570) (-1069 (-578)))) (-5 *2 (-328 *4)) @@ -14700,39 +14546,49 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-466) (-1069 (-578)) (-660 (-578)))) (-5 *1 (-1237 *3 *2)) (-4 *2 (-13 (-27) (-1233) (-444 *3)))))) -(((*1 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-781))))) -(((*1 *2 *2) - (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) - (-4 *2 (-13 (-444 *3) (-1233)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-972 *2)) (-5 *1 (-1013 *2)) (-4 *2 (-1080))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1298 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) - (-5 *2 (-711 *4)))) - ((*1 *2) - (-12 (-4 *4 (-175)) (-5 *2 (-711 *4)) (-5 *1 (-430 *3 *4)) - (-4 *3 (-431 *4)))) - ((*1 *2) (-12 (-4 *1 (-431 *3)) (-4 *3 (-175)) (-5 *2 (-711 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-666 (-860))) (-5 *1 (-142))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-711 (-172 (-421 (-578))))) + (-5 *2 + (-666 + (-2 (|:| |outval| (-172 *4)) (|:| |outmult| (-578)) + (|:| |outvect| (-666 (-711 (-172 *4))))))) + (-5 *1 (-786 *4)) (-4 *4 (-13 (-376) (-870)))))) +(((*1 *2 *2 *2) + (-12 + (-5 *2 + (-666 + (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-793)) (|:| |poli| *6) + (|:| |polj| *6)))) + (-4 *4 (-815)) (-4 *6 (-978 *3 *4 *5)) (-4 *3 (-466)) (-4 *5 (-871)) + (-5 *1 (-463 *3 *4 *5 *6))))) +(((*1 *1) (-5 *1 (-1210)))) +(((*1 *2 *3 *4 *5 *6 *5 *3 *7) + (-12 (-5 *4 (-578)) + (-5 *6 + (-2 (|:| |try| (-392)) (|:| |did| (-392)) (|:| -2865 (-392)))) + (-5 *7 (-1 (-1303) (-1298 *5) (-1298 *5) (-392))) + (-5 *3 (-1298 (-392))) (-5 *5 (-392)) (-5 *2 (-1303)) + (-5 *1 (-810)))) + ((*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3) + (-12 (-5 *4 (-578)) + (-5 *6 + (-2 (|:| |try| (-392)) (|:| |did| (-392)) (|:| -2865 (-392)))) + (-5 *7 (-1 (-1303) (-1298 *5) (-1298 *5) (-392))) + (-5 *3 (-1298 (-392))) (-5 *5 (-392)) (-5 *2 (-1303)) + (-5 *1 (-810))))) (((*1 *1 *2) (-12 (-5 *1 (-1234 *2)) (-4 *2 (-1131)))) ((*1 *1 *2) (-12 (-5 *2 (-666 *3)) (-4 *3 (-1131)) (-5 *1 (-1234 *3)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-666 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(-344))))) (((*1 *1 *1) (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-666 (-1207))) (-14 *3 (-666 (-1207))) (-4 *4 (-401)))) @@ -14742,72 +14598,58 @@ ((*1 *1 *2) (-12 (-5 *2 (-421 (-578))) (-4 *1 (-1043)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1043)) (-5 *2 (-950)))) ((*1 *1 *1) (-4 *1 (-1043)))) -(((*1 *2 *3) (-12 (-5 *3 (-886)) (-5 *2 (-1189)) (-5 *1 (-732))))) -(((*1 *2 *3 *3) - (-12 (-5 *2 (-1188 (-666 (-578)))) (-5 *1 (-908)) - (-5 *3 (-666 (-578))))) - ((*1 *2 *3) - (-12 (-5 *2 (-1188 (-666 (-578)))) (-5 *1 (-908)) - (-5 *3 (-666 (-578)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) - (-4 *2 (-13 (-444 *3) (-1033)))))) -(((*1 *2 *3) (-12 (-5 *2 (-432 *3)) (-5 *1 (-572 *3)) (-4 *3 (-559)))) - ((*1 *2 *3) - (-12 (-4 *4 (-815)) (-4 *5 (-871)) (-4 *6 (-319)) (-5 *2 (-432 *3)) - (-5 *1 (-764 *4 *5 *6 *3)) (-4 *3 (-978 *6 *4 *5)))) - ((*1 *2 *3) - (-12 (-4 *4 (-815)) (-4 *5 (-871)) (-4 *6 (-319)) - (-4 *7 (-978 *6 *4 *5)) (-5 *2 (-432 (-1203 *7))) - (-5 *1 (-764 *4 *5 *6 *7)) (-5 *3 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*4)) (-4 *3 (-1248)) (-4 *4 (-1248))))) -(((*1 *2 *2) - (-12 (-4 *3 (-570)) (-5 *1 (-287 *3 *2)) - (-4 *2 (-13 (-444 *3) (-1033)))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-5 *1 (-902 *2)) (-4 *2 (-1248)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-5 *1 (-904 *2)) (-4 *2 (-1248)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-5 *1 (-907 *2)) (-4 *2 (-1248))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-884)) (-5 *2 (-713 (-131))) (-5 *3 (-131))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-376)) (-4 *5 (-570)) - (-5 *2 - (-2 (|:| |minor| (-666 (-950))) (|:| -1481 *3) - (|:| |minors| (-666 (-666 (-950)))) (|:| |ops| (-666 *3)))) - (-5 *1 (-90 *5 *3)) (-5 *4 (-950)) (-4 *3 (-678 *5))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 *5 *5)) (-4 *1 (-355 *4 *5 *6)) (-4 *4 (-1252)) + (-4 *5 (-1274 *4)) (-4 *6 (-1274 (-421 *5))) + (-5 *2 (-2 (|:| |num| (-711 *5)) (|:| |den| *5)))))) +(((*1 *1 *1 *1) (-4 *1 (-314))) ((*1 *1 *1) (-4 *1 (-314)))) (((*1 *2 *3 *4) (-12 (-5 *4 (-666 (-48))) (-5 *2 (-432 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1274 (-48))))) @@ -14856,7 +14698,7 @@ (-12 (-4 *4 (-13 (-871) - (-10 -8 (-15 -1335 ((-1207) $)) + (-10 -8 (-15 -1332 ((-1207) $)) (-15 -1518 ((-3 $ "failed") (-1207)))))) (-4 *5 (-815)) (-4 *7 (-570)) (-5 *2 (-432 *3)) (-5 *1 (-470 *4 *5 *6 *7 *3)) (-4 *6 (-570)) @@ -14906,13 +14748,13 @@ (-12 (-4 *4 (-815)) (-4 *5 (-13 (-871) - (-10 -8 (-15 -1335 ((-1207) $)) + (-10 -8 (-15 -1332 ((-1207) $)) (-15 -1518 ((-3 $ "failed") (-1207)))))) (-4 *6 (-319)) (-5 *2 (-432 *3)) (-5 *1 (-752 *4 *5 *6 *3)) (-4 *3 (-978 (-981 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-815)) - (-4 *5 (-13 (-871) (-10 -8 (-15 -1335 ((-1207) $))))) (-4 *6 (-570)) + (-4 *5 (-13 (-871) (-10 -8 (-15 -1332 ((-1207) $))))) (-4 *6 (-570)) (-5 *2 (-432 *3)) (-5 *1 (-754 *4 *5 *6 *3)) (-4 *3 (-978 (-421 (-981 *6)) *4 *5)))) ((*1 *2 *3) @@ -14948,130 +14790,118 @@ ((*1 *2 *1) (-12 (-5 *2 (-432 *1)) (-4 *1 (-1252)))) ((*1 *2 *3) (-12 (-5 *2 (-432 *3)) (-5 *1 (-1263 *3)) (-4 *3 (-1274 (-578)))))) -(((*1 *2 *2 *3 *4) - (-12 (-5 *3 (-666 (-631 *6))) (-5 *4 (-1207)) (-5 *2 (-631 *6)) - (-4 *6 (-444 *5)) (-4 *5 (-1131)) (-5 *1 (-587 *5 *6))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) - (|:| -3026 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) + (|:| -3789 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) - (-5 *2 - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| "There are singularities at both end points") - (|:| |notEvaluated| "End point continuity not yet evaluated"))) - (-5 *1 (-195))))) -(((*1 *2) (-12 (-5 *2 (-1303)) (-5 *1 (-97))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-666 *6)) (-4 *6 (-1096 *3 *4 *5)) (-4 *3 (-466)) - (-4 *3 (-570)) (-4 *4 (-815)) (-4 *5 (-871)) - (-5 *1 (-1008 *3 *4 *5 *6))))) -(((*1 *1) (-4 *1 (-998)))) -(((*1 *2 *3) - (-12 (-5 *3 (-950)) (-5 *2 (-1203 *4)) (-5 *1 (-602 *4)) - 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the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1188 (-229))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3026 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))))) - (-5 *1 (-573)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-793)) (-4 *1 (-717 *2)) (-4 *2 (-1131)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -2338 - (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) - (|:| |fn| (-1298 (-328 (-229)))) (|:| |yinit| (-666 (-229))) - (|:| |intvals| (-666 (-229))) (|:| |g| (-328 (-229))) - (|:| |abserr| (-229)) (|:| 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(-4315 . 36678) + (-4316 . 36471) (-4317 . 36278) (-4318 . 36225) (-4319 . 36163) + (-4320 . 36135) (-4321 . 36022) (-4322 . 35922) (-4323 . 35848) + (-4324 . 35774) (-4325 . 35690) (-4326 . 35236) (-4327 . 35153) + (-4328 . 34907) (-4329 . 34854) (-4330 . 34790) (-4331 . 33486) + (-4332 . 33454) (-4333 . 33236) (-4334 . 33141) (-4335 . 32810) + (-4336 . 32748) (-4337 . 32695) (-4338 . 32663) (-4339 . 32610) + (-4340 . 32401) (-4341 . 32328) (-4342 . 32148) (-4343 . 32051) + (-4344 . 31948) (-4345 . 31768) (-4346 . 31521) (-4347 . 31318) + (-4348 . 31199) (-4349 . 30838) (-4350 . 30359) (-4351 . 30216) + (-4352 . 30135) (-4353 . 29806) (-4354 . 29653) (-4355 . 29326) + (-4356 . 29229) (-4357 . 29098) (-4358 . 29017) (-4359 . 28964) + (-4360 . 28863) (-4361 . 28757) (-4362 . 28683) (-4363 . 28557) + (-4364 . 28435) (-4365 . 28341) (-4366 . 28264) (-4367 . 28113) + (-4368 . 26811) (-4369 . 26670) (-4370 . 26618) (-4371 . 26558) + (-4372 . 26426) (-4373 . 26282) (-4374 . 26011) (-4375 . 25090) + (-4376 . 25037) (-4377 . 24985) (-4378 . 24870) (-4379 . 24707) + (-4380 . 24539) (-4381 . 24487) (-4382 . 24407) (-4383 . 24284) + (-4384 . 23632) (-4385 . 23429) (-4386 . 23247) (-4387 . 23175) + (-4388 . 23123) (-4389 . 23052) (-4390 . 22872) (-4391 . 22691) + (-4392 . 21829) (-4393 . 21493) (-4394 . 21303) (-4395 . 21205) + (-4396 . 21149) (-4397 . 21121) (-4398 . 21047) (-4399 . 20995) + (-4400 . 20660) (-4401 . 20590) (-4402 . 20408) (-4403 . 20322) + (-4404 . 20224) (-4405 . 20137) (-4406 . 19978) (-4407 . 16679) + (-4408 . 16451) (-4409 . 15844) (-4410 . 15816) (-4411 . 15700) + (-4412 . 15602) (-4413 . 15506) (-4414 . 15347) (-4415 . 13285) + (-4416 . 12867) (-4417 . 12784) (-4418 . 12707) (-4419 . 12576) + (-4420 . 12519) (-4421 . 12431) (-4422 . 12357) (-4423 . 12202) + (-4424 . 11984) (-4425 . 11869) (-4426 . 11691) (-4427 . 11660) + (-4428 . 11492) (-4429 . 11341) (-4430 . 11217) (-4431 . 11032) + (-4432 . 10814) (-4433 . 10756) (-4434 . 10504) (-4435 . 10455) + (-4436 . 10403) (-4437 . 10275) (-4438 . 9929) (-4439 . 9836) + (-4440 . 9759) (-4441 . 9574) (-4442 . 8951) (-4443 . 8275) + (-4444 . 8180) (-4445 . 7888) (-4446 . 7804) (-4447 . 7692) + (-4448 . 7609) (-4449 . 7532) (-4450 . 7429) (-4451 . 7041) + (-4452 . 6832) (-4453 . 6674) (-4454 . 6607) (-4455 . 6471) + (-4456 . 6204) (-4457 . 6092) (-4458 . 5449) (-4459 . 5396) + (-4460 . 5269) (-4461 . 5109) (-4462 . 5058) (-4463 . 5024) + (-4464 . 4917) (-4465 . 4699) (-4466 . 4622) (-4467 . 4479) + (-4468 . 4447) (-4469 . 3836) (-4470 . 3555) (-4471 . 2639) + (-4472 . 2521) (-4473 . 2294) (-4474 . 2221) (-4475 . 2087) + (-4476 . 2053) (-4477 . 1800) (-4478 . 1615) (-4479 . 1421) + (-4480 . 1285) (-4481 . 1214) (-4482 . 1163) (-4483 . 1039) + (-4484 . 969) (-4485 . 742) (-4486 . 572) (-4487 . 197) (-4488 . 30))
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